Futures Markets (Routledge Revivals) : Their Establishment and Performance 9781135047511, 9780415835268

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Routledge Revivals

Futures Markets

First published in 1986, this book discusses many important aspects of the theory and practice of Futures Markets. It describes how Futures Markets, at the time, grew to be an increasingly important feature of the world's major financial centres. Indeed, they adopted the role of being efficient forward pricing mechanisms and this was reflected by the interest of economists in the study of risk, uncertainty and information. Here, the contributors focus on areas that were of concern in the late 1980s such as feasibility, forward pricing and returns, and the modelling of price determination in Futures Markets. Evidence is drawn from twenty-five different commodities representing all the major commodity groups; and from all the world's major centres of Futures Trading.

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Futures Markets Their Establishmentand Performance

Edited by Barry A. Goss

Routledge Taylor&FrancisGroup

First published in 1986 by Croom Helm Ltd This edition first published in 2013 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Simultaneously published in the USA and Canada by Routledge 711 Third Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 1986 Barry A. Goss All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Publisher’s Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original copies may be apparent. Disclaimer The publisher has made every effort to trace copyright holders and welcomes correspondence from those they have been unable to contact.

ISBN 13: 978-0-415-83526-8 (hbk) ISBN 13: 978-0-203-48870-6 (ebk)

FUTURES MARKETS: THEIR ESTABLISHMENT AND PERFORMANCE

Edited by Barry A. Goss

qp CROOM HELM London & Sydney

© 1986 Barry A. Goss Croom Helm Ltd, ProvidentHouse,Burrell Row Beckenham,Kent BR3 1AT Croom Helm Australia Pty Ltd, Suite 4, 6th Floor, 64-76 Kippax Street,Surry Hills, NSW 2010, Australia British Library Cataloguingin PublicationData Futuresmarkets:their establishmentand performance. 1. Commodityexchanges 2. Speculation I. Goss,Barry A. 332.64'6 HG6046 ISBN 0-7099-1181-5

Typesetin lOpt Times by Leaper& Gard Ltd, Bristol., England Printed and bound in Great Britain by Billing & Sons Limited, Worcester.

CONTENTS

Acknowledgements Introduction: Feasibility and the Consequences of Using Information in FuturesMarkets Barry A. Goss

1

1. An Institutional Analysis of FuturesContracting Cento G. Veljanovski

13

2. ExperimentalFuturesMarkets Glenn W. Harrison

43

3. Hedging,Risk and Profits: Noteson Motives for Hedgingon FuturesMarkets Basil Yamey

77

4. IntertemporalAllocation in the Australian Wool Market Barry A. Gossand David E.A. Giles

93

5. An Analysis of InvestmentHorizon and Alternative Risk-returnMeasuresfor CommodityFuturesMarkets Cheng-FewLeeand RaymondM. Leuthold

119

6. Trading Volume and Price Variability: New Evidenceon the Price Effects of Speculation David ].s. Rutledge

137

7. The Forward Pricing Functionof the London Metal Exchange Barry A. Goss

157

8. An Analysis of Gold FuturesPricesin Large and Small Markets C. RaeWestonand RossMcDonnell

175

9. The Distribution of Returnsin SydneyWool Futures KevenRainbowand PeterD. Praetz

191

10. ConjecturedModels for Trendsin FinancialPrices, Testsand Forecasts StephenJ. Taylor

209

Index

247

ACKNOWLEDGEMENTS

This volume beganwith somevery good researchpaperssubmitted by studentstaking my graduatecourse'Hedgingand Uncertainty'at MonashUniversity. At leastthat is how the papersby Veljanovski, Harrison and Rainbow began.The remainingpapersresultedfrom invitations to other researchersin the area of futures markets to contributeto this volume. While most of the papersin this book are publishedherefor the first time, acknowledgementis made to the editor of Quarterly Reviewof Economicsand Businessfor materialfrom C.F. Lee and R.M. Leuthold, 'Investmenthorizon, risk, and return in commodity futures markets: an empirical analysis with daily data', published in that journal; to the Chicago Board of Trade for permissionto reprint DJ.S. Rutledge, 'Trading volume and price variability: new evidenceon the price effectsof speculation',International ResearchSeminarProceedings,1978; to the Royal Statistical Society for permission to reprint S.l. Taylor, 'Conjectured models for trends in financial prices, tests and forecasts',Journal of the Royal Statistical Society, A, 1980; and to the editor of Chapman and Hall for permission to reprint B.A. Goss, 'The forward pricing function of the London Metal Exchange',Applied Economics,1981, a revisedversionof which appearsas Chapter7. In addition, thanks are due to Gulay A vsar for her careful assistancein compilation of the index and checkingthe proofs, to FrancaGoodwin and Philippa Geurenswho typed the manuscript so well, and to MargaretWatts and JennyFranciswho checkedit. I would like to acknowledgealso the help and co-operationI have received from the editorial and production staff of Croom Helm. This book is publishedwith the assistanceof a grant from the MonashUniversity PublicationsCommittee. B.A. Goss

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INTRODUCTION: FEASIBILITY AND THE CONSEQUENCES OF USING INFORMATION IN FUTURES MARKETS Barry A. Goss

1. Conditionsfor the Establishmentof FuturesMarkets Originally the conditions for the establishmentof futures markets were treatedas a list of commodityprerequisitesbasedon generalizations from past experience,such as price variability, ability to specify a standard grade, storability, deliverability, etc. (e.g. Houthakker,1959; seethe discussionin Section 1 of Chapter7 of this volume). Gray (1966) distinguishedbetweenthe feasibility of a futures market and its success,and referred to contractual characteristicswhich may hinder success,such as where delivery provisionsfavour one side of the market. Such a list of prerequisites,however,is not an economictheory and lacks predictive ability. In particular it was unable to predict the developmentof markets trading in commodities which are virtually non-storable(such as live beef cattle) or which are both non-storableand non-deliverable(such as trading in share price indices).! As Veljanovski points out in this volume (Chapter 1), this list of prerequisitesfocused on local examplesof economic variables such as the possibility of delivery, rather than the economic variablesthemselves,such as transactionscosts or costs of arbitrage. Telser and Higinbotham (1977) addressedthe hypothesisthat trading is most active in thosecontractswhere the net benefitsare greatest.Net benefits were related (directly) to price variability, liquidity, turnover and commitments.It was found inter alia, first, that the most actively traded commoditieshad the most variable prices; second,margin and commissioncosts vary inversely with turnover (but directly with open interest and average contract price); third, the standard deviation of market clearing prices (which varies inversely with liquidity) was found to vary inversely with turnover, as predicted. In Telser and Higinbotham the existenceof futures trading is 1

2

Introduction

predetermined,but in Veljanovski the market penetration of futures trading is an endogenousvariable as is the contractualform itself. Veljanovski brings togetheremphasison transactionscosts and the conceptof property rights to argue that futures markets develop becausethey are more efficient, in terms of transactions costs, than spot and forward markets in transferring certain bundles of property rights attachedto price. Within this framework, he usesthe property rights conceptto explain the tendency to self-regulation in futures markets, and the concentrationof trading in a few market locationsis explainedin terms of liquidity benefits. Indeed Veljanovski suggests that increasing returns favour the existenceof a few large exchanges. 2. Performanceof FuturesMarkets The literature containsno comprehensiveframework for analysing the performanceof futuresmarkets;nevertheless,thereis probably a reasonabledegree of agreement on the functions of these markets,and in the view of the presenteditor, thesemay be stated as follows: (i) Futures markets provide facilities for risk management, becausethey provide opportunitiesfor hedging. (ii) They perform a forward pricing function, and they thus facilitate the intertemporalallocation of resources. (iii) They collect and disseminateinformation. (iv) As Working (1953) showed, in the case of commodities with continuousinventories(especiallywhere thoseinventories are seasonal),they facilitate the holding of inventoriesin private hands. The real difficulty is that thereexist no clearly agreedcriteria for evaluatingthe performanceof futures marketsin thesefunctions. Still less are thesecriteria integratedinto a coherentframework. Nevertheless,somecriteria have beendevelopedfor analysingthe performance of futures markets in some of these individual functions. Over 30 yearsago severalpaperswere publishedwhich investigated the routine hedging performanceof futures markets. For example, Yamey (1951) and Graf (1953) consideredwhether

Introduction 3 profits and losses resulting from price movementswere smaller with hedging than without. This questionwas generallyanswered in the affirmative, especiallywhen spot price changeswere large. It was arguedstrongly that agentsin thesemarketspursuethe joint objectives of uncertain profit and risk reduction (Working, 1953). The important question of the ratio in which agentshold spot and futures contractswas analysedfrom a portfolio theoretic viewpoint by Stein (1961, 1964), 10hnson(1960) and Ward and Fletcher (1971). Some economistsaddressedthe difficult task of modelling and estimating the outcomesfor these portfolio type hedgers(seeRutledge,1972 and Dusak, 1973).The optimum proportion of a commitmentto be hedgedfrom a portfolio viewpoint has also been discussedby Ederington(1979), Kahl (1983) and Schneeweis(1982). This volume containsno chapterson the outcomesof hedging, although Yamey (Chapter3) offers a critique of current views of the motives for hedging,including the relative importanceof riskavoidancehedging. In particular Yamey discussesthe pecuniary and non-pecuniarybenefits of hedging, and attemptsto place in perspectivethe non-pecuniarybenefits, especially risk reduction. In this he seekssupportin the finding of Telser and Higinbotham (1977) that future marketsare more active the greaterthe degree of price volatility. Returns to traders in futures markets have received attention from time to time during the past 60 or so years. Keynes'stheory of normal backwardation(1930) (developedon the assumption that hedgersare net short and speculatorsnet long) containsthe obvious returns implication that speculatorswill receive a risk premium from hedgers. Indeed Keynes's statement in the Manchester Guardian in 1923 suggests that speculators may expect substantial returns from being persistently long (see Keynes, 1923, 1930). Houthakker (1957) and Rockwell (1967) estimatedreturnsto various groupsof tradersusing open position and price change data, and found that (individually large) professional speculatorsgained sometimesat the expenseof large hedgers,but mostly at the expenseof small traders. The questionof returns to tradershas also been addressedby analysing daily price change data, an analysis which has implicationsalso for marketefficiency (see below).Rainbowand Praetz in this volume (Chapter9) investigatewhich function best fits the distribution of returns in this sensefor Australia's longesttrading

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Introduction

contract- that for merino wool. They concludedthat the Student t distribution is the best fit, as against various rival hypotheses including the alternative that futures prices are stable Paretian (infinite variance) in distribution (as claimed by Mandelbrot, 1963). They refer to studies of share prices where the data also have favoured the Student model (e.g. Blattberg and Gonedes, 1974). Dusak (1973) examined the returns to holders of selected futures contracts (in wheat, corn and soybeans)relative to the return on 'wealth in general' (representedby the Standardand Poor index), using the Sharpe (1964)-Lintner (1965) Capital Asset Pricing Model. She found the systemic risk premium so defined, to be close to zero. In this volume Lee and Leuthold (Chapter 5) examine the returns, in the senseof proportionate price changesin futures contracts,to investmenthorizons ranging from 1 to 22 days. They also investigate the systematic risk betweenfutures contractsand shares,for a range of grains, livestock, preciousmetalsand financial futures. Their result, that there is little systematicrisk betweenfutures and shares,hasimplications for holdersof shares. Futuresmarkets,by forming prices relating to forward delivery dates,project their prices into the future. Theseprices are usedby agentsto plan future production,to price forward contractsfor the supply of commodities, and to tender for forward contracts. Agents need not transact on futures exchangesto use futures prices in this way, and the information containedin such prices is an externality to them. Agents may also use futures markets in deciding whether to store a commodity_ (using the forward premium as an indicator of whether storage is expectedto be profitable). In addition, futures marketsmay help agentsto decide the timing of input purchasesand of processingactivities according to the expectedoutcome of hedging. Agents in these latter two categoriesare of course transactorson futures markets. Thus, futures markets perform a forward pricing function, and in these ways futures prices facilitate the allocation of resourcesbetween presentand future uses(seeHicks, 1953). The process of price determination in futures markets has receivedattentionin the literature, and Pestonand Yamey (1960), Stein (1961, 1964), Telser (1958) and others have provided theoreticalmodelsof the determinationof spot and futures prices. In this volume the chapterby Gossand Giles (Chapter4) presents

Introduction 5 a model of the intertemporalallocation of supply and the determination of spot and futures prices using data from the Australian wool market. Subsequentwork by theseauthors has investigated this question using United Statescorn and soybeansdata (Giles, Gossand Chin, 1985). The formation of spot and futuresprices hasalso beenmodelled in experimental markets by Friedman, Harrison and Salmon (1983, 1984) and Plott and Sunder(1982). Friedman, Harrison and Salmon (1983) found that spot prices converged to equilibrium more rapidly with experiencedagentsand futures markets operating, than without futures markets, or with inexperienced agents.PIott and Sunder(1982) conductedexperimentsin which dividends on securitiesdependedon the state of nature drawn at randomat the start of each 'year', where sometraderswere given inside information. The authorsfound that wherethe price initially reflected the prior information of non-insiders,and the rational expectationsequilibrium (REE) differed, then agentsrevisedtheir expectationsand pricesconvergedto the REE. In the seriesof experimentsreportedin this volume, Harrison (Chapter 2) investigatesthe effects of event uncertainty on the formation of spot and futures prices, and on hedger behaviour, both with and without inside information. Economistshavediscussedfor sometime whetherfutures prices are anticipationsof delivery date spot prices, and if so whether they are unbiasedanticipations.Keynes (1930) arguedthat under 'normal' conditions the futures price would be less than the expected spot price by an amount equal to the marginal risk premium of speculators.If agents'expectationsare correct, then the futures price will be a downward biased anticipation of the subsequentspot price. Working was not fond of interpreting futures prices as predictions of later cashprices. Insteadhe favoured the view that the spread betweenvarious futures prices, and also betweenfutures and cash prices, reflected the cost of carrying the commodity betweenthe relevantdates(1942, p. 44). New information would be expectedto affect the whole spectrumof prices. Nevertheless, Working believedthat all pricesare forecastsin the sensethat they embodyinformation including expectations(1948, pp. 14-15). Many economists have addressedempirically the hypothesis that futures prices are unbiasedanticipationsof delivery date cash prices. The hypothesisis basedupon the assumptionsthat current

6

Introduction

prices reflect relevantinformation,·including agents'expectations, as fully as possible, that new information is random, and that agentsare risk neutral. It also assumes,in the view of this editor, that there are no systematicdifferencesbetweencashand futures contracts,with respectto the options of agentsunder those contracts. Empirical investigationof this hypothesismost frequently has taken the form of regressionof delivery date cash prices on laggedfutures prices, so that the unbiasedness hypothesisis tested appropriatelyby a joint test of zero interceptand unit slope.2 The unbiasednesshypothesishas been supportedfor a wide range of commoditiesincluding corn, soybeansand coffee in the USA, the pound sterling and the French franc against the US dollar, and Australianwool. On the other hand,the hypothesishas beenrejectedfor potatoesin the USA, for live catth:: in the US and Australia (with lags greaterthan three months), for US Treasury Bills, and for the DeutscheMark against the US dollar (see for example, Tomek and Gray, 1970; Kofi, 1973; Hansen and Hodrick, 1980; Leuthold, 1974; Hamburger and Platt, 1975; Giles and Goss, 1981). In the chapter by Goss in this volume (Chapter7) the unbiasedness hypothesisgenerallyis supportedfor non-ferrousmetalson the London Metal Exchange,althoughthe caseof zinc is marginal. Rejectionof this hypothesishas beenvariously accountedfor in terms of the additional valuableoptions of sellersof futures contracts, the presenceof a risk or liquidity premium, the absenceor discontinuity of inventories,and the comparativeyouthfulnessof somecontracts,etc. (seealso Breeden,1982, Gray, 1972). Whatever the economic ground sought to account for rejection, it should be stressedthat rejection of the unbiasednesshypothesis does not imply that the market under review is informationally inefficient, because of the jointly conditional nature of the hypothesis(seealso Gregoryand McCurdy, 1984; Yamey, 1984). The conditions which must be satisfied for market prices to 'fully reflect' all information are so stringentthat they are unlikely to be satisfied in the real world. Theserequirementsinclude risk neutrality of agents, zero transactionscosts, the agreementof agentson the implications of current information and also that information is costlessto acquire.Nevertheless,for the purposesof empirical study, a working definition of market efficiency may be obtainedif we interprettheseconditionsin a slightly more realistic fashion. For example, if we assumethat transactionscosts are

Introduction 7 small in relation to the value of the contract,that any disagreement among agentsabout the implications of information is not interdependent, and that costly information is utilized so as to maximize returnsfrom its acquisition, etc., then we shall have an approximation to market efficiency. Any test of the efficient marketshypothesiswith such a model, of course,is a joint test of that hypothesisand the validity of the other assumptions. If current prices in a particular market fully reflect the information in own past prices, then the expectedreturn to a trading strategybasedon that information set (only) is zero. If suchinformation is fully utilized the marketis said to be weak form efficient, and Fama (1970) has surveyed inter alia the researchon this version of the efficient markets hypothesisin securitiesmarkets. Researchon this issuein the areaof futures marketshas employed techniquessimilar to those used in the securities area, and this form of the hypothesisis usually made operationalby assuming that pricesfollow a randomwalk. This in turn has beenaddressed by runs tests, serial correlation tests, filter tests and spectral analysis. Many authorshave investigatedthe random walk hypothesis with futures market data, including Larson (1960), Stevensonand Bear (1970), Leuthold (1972), Praetz(1975) and Cargill and Rausser(1975). Generally, some evidenceof dependencein past prices has beenfound, and someauthorshave used this to reject the strict randomwalk hypothesis.Most would agree that it is unlikely that significant profits could have been madeon the basis of such information, taking into account transactions costs.Significant filter profits on somecontractsdo not imply that the whole series is non-random. In any case, rejection of the randomwalk hypothesisdoesnot necessarilymeanthat the market is weak form inefficient, becausethis hypothesis,which requires that price changesare independentlyand identically distributed,is a specialcaseof weak form efficiency. The efficiency of futures marketswith respectto publicly available information hasbeeninvestigatedby two main methods.One approachhas utilized the information in the immediately prior forecast errors3 of related commodities,thus defining theseforecast errors as the relevant set of publicly available information. Any systematicrelationshipbetweenthe current forecasterror of the commodity under review and the elementsof this information set would require rejection of the semi-strong version of the efficient marketshypothesis.On the other hand, inability to reject

8

Introduction

this hypothesis does not necessarilyimply that the market is efficient, but may simply reflect an inappropriatespecificationof the information set. This method has been used by Hansenand Hodrick (1980) for currenciesand Goss (1983) for non-ferrous metals (revised estimatesfor the latter study are included as an appendixto Chapter7 of this volume). An alternative approachhas deployed an economic model to forecast the cash price of the relevant commodity, this forecast being comparedwith that contained in the futures price. If the economic model outperforms the futures price as a predictive medium, this version of the efficient marketshypothesismust be rejected,becausethe model containsinformation not incorporated in the futures price. On the other hand, inability to reject this hypothesis(becausethe futures price outperformsthe model) does not necessarilyimply that the market is efficient but may arise from an inadequate model. This method has been used by Hamburger and Platt (1975) for Treasury Bills, Leuthold and Hartmann(1979) for hogs, Brasse(1986) for tin, and Rausserand Carter (1983) for the soybeancomplex. In this volume Taylor (Chapter 10) tests the random walk hypothesis against a rival price-trend hypothesis for a wide range of commodities, and Westonand McDonnell (Chapter8) considerthe responseof three international gold markets to external events, and also the weak form efficiency of thesemarkets. Finally, Arrow (1982) has suggestedthat futures marketsplace undueemphasison the most recentinformation, and henceexhibit excessiveprice fluctuations. In Chapter 6 of this book Rutledge examines whether incremental speculation accentuates price variation on futures markets, or respondsto that variation. He reaches the conclusion for a sample of US commodity and financial futures, that speculation essentially respondsto price variation.

Notes 1. It is the view of the presenteditor that the literatureon futures marketsis starvedof publishedfeasibility studiesfor new markets.Suchstudiesare usually preparedas consultingreports,and offer the prospectof commercialadvantageto the firm which commissionsthe report. Publicationis thereforeout of the question until suchadvantageis realized,and then the minds of the promotersare usually occupiedwith other matters.Nevertheless,studentsof this areaof economics

Introduction 9 would probably benefit if thesestudieswere published,even sometime after the establishmentof the market in question.(Sandor,1973, is a notableexception.) 2. Ordinary leastsquaresmay not be an appropriateestimator.If serial correlationis present,instrumentalvariable estimationis preferredin the interests of consistency.The use of overlappingobservationsis likely to result in serial correlationin this context. 3. A forecasterror is defined here as the differencebetweena laggedfutures price and the delivery date cash price.

References Arrow, K.J. (1982) 'Risk Perceptionin Psychologyand Economics',Economic Inquiry, 20, 1-9. Blattberg, R. and N. Gonedes(1974) 'A Comparisonof the Stableand Student Distributionsas StatisticalModels for Stock Prices',Journal of Business,47, 244-80. Brasse,V. (1986) 'Testingthe Efficiency of the Tin FuturesMarket on the LME', in K. Tucker and C. Baden Fuller (eds.), Firms and Markets: Essaysin Honour of Basil Yamey,London: Croom Helm. Breeden,D.T. (1982) 'Statement[On ResearchableIssues]',Reviewof Researchin Futures Markets, 1(2), 175-8, ChicagoBoard of Trade. Cargill, T.F. and Rausser,G.c. (1975) 'TemporalPrice Behaviourin Commodity FuturesMarkets', The Journal of Finance, 30(4), 1043-53. Dusak, K. (1973) 'FuturesTrading and Investor Returns:An Investigationof Commodity Market Risk Premium', Journal of Political Economy,81(6), 1387-406. Ederington,L.J. (1979) 'The Hedging Performanceof the New FuturesMarkets', Journal of Finance, 34(1), 157-70. Fama, E.F. (1970) 'Efficient Capital Markets: A Review of Theory and Empirical Work', Journal of Finance, 25, 383-417. Friedman,D., G.W. Harrison and J.W. Salmon(1983) 'The Informational Role of FuturesMarkets: SomeExperimentalEvidence',Chapter6 in M.E. Streit (ed.), Futures Markets: Modelling, Managingand Monitoring Futures Markets, Oxford: Blackwell. Friedman,D., G.W. Harrison and J.W. Salmon(1984) 'The Informational Efficiency of ExperimentalAsset Markets', Journal of Political Economy,92, 349-408. Giles, D.E.A. and B.A. Goss(1981) 'FuturesPricesof Forecastsof Commodity Spot Prices: Live Cattle and Wool', Australian Journal of Agricultural Economics,25,1-13. Giles, D.E.A., B.A. Gossand O.P.L. Chin (1985) 'IntertemporalAllocation in the Corn and SoybeansMarkets with Rational Expectations',AmericanJournal of Agricultural Economics,67, November(in press). Goss,B.A. (1983) 'The Semi-StrongForm Efficiency of the London Metal Exchange',AppliedEconomics,15,681-98. Graf, T.F. (1953) 'Hedging- How Effective Is It?', Journal of Farm Economics, 35,398-413. Gray, R.W. (1966) 'Why Does FuturesTrading Succeedor Fail: An Analysis of SelectedCommodities',Futures Trading Seminar,vo\. Ill, MIMIR, Madison. (1972) 'The FuturesMarket for Maine Potatoes:An Appraisal', Food ResearchInstitute Studies,11(3),313-41. Gregory, A.W. and T.H. McCurdy (1984) 'The UnbiasednessHypothesisin the

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Introduction

ForwardForeign ExchangeMarket: A CrossCountry SpecificationAnalysis', University of W. Ontario DiscussionPaperNo. 566. Hamburger,M.J. and E.N. Platt (1975) 'The ExpectationsHypothesisand the Efficiency of the TreasuryBill Market', Reviewof Economicsand Statistics, 57(2), 190-9. Hansen,L.P. and R.J. Hodrick (1980) 'Forward ExchangeRatesas Optimal Predictorsof Future Spot Rates:An EconometricAnalysis', Journal of Political Economy,88, 829-53. Hicks, J.R. (1953) Value and Capital, London: Oxford University Press. Houthakker,H.S. (1959) 'The Scopeand Limits of FuturesTrading', in M. Abramovitz et al., TheAllocation of EconomicResources,Stanford,California, StanfordUniversity Press. (1957) 'Can SpeculatorsForecastPrices', Reviewof Economicsand Statistics,39(2), 143-51. Johnson,L.L. (1960) 'The Theory of Hedgingand Speculationin Commodity Futures',Reviewof EconomicStudies,27(3), 139-51. Kahl, K.H. (1983) 'Determinationof the RecommendedHedging Ratio', AmericanJournal of Agricultural Economics,65(3), 603-5. Keynes,J.M. (1923) 'SomeAspectsof Commodity Markets', Manchester Guardian Commercial:EuropeanReconstructionSeries,Section13, 29 March. (1930) A Treatiseon Money, vol. 2, London: Macmillan. Kofi, T.A. (1973) 'A Frameworkfor Comparingthe Efficiency of Futures Markets', AmericanJournal ofAgricultural Economics,55(4), 584-94. Larson, A.B. (1960) 'Measurementof a RandomProcessin FuturesPrices', Food ResearchInstituteStudies,1,313-24. Leuthold, R.M. (1972) 'RandomWalks and Price Trends:The Live Cattle Futures Market', Journal of Finance, 27. (1974) 'The Price Performanceon the FuturesMarket of a Nonstorable Commodity: Live Beef Cattle', AmericanJournal ofAgricultural Economics, 56(2), 313-24. and P.A. Hartmann(1979) 'A Semi-strongForm Evaluationof the Efficiency of the Hog FuturesMarket', AmericanJournal ofAgricultural Economics, 61(3), 482-9. Lintner, J. (1965) 'Security Prices,Risk, and Maximal Gains from Diversification', Journal of Finance, 20, 587-615. Mandelbrot, B. (1963) 'The Variation of Certain SpeculativePrices',Journal of Business,36, 394-419. Peston,M.H. and B.S. Yamey (1960) 'Inter-temporalPrice Relationshipswith Forward Markets: A Method of Analysis', Economica,27, 355-67. Plott, CR. and S. Sunder(1982) 'Efficiency of ExperimentalSecurity Markets with Insider Information: An Application of Rational ExpectationsModels', Journal of Political Economy,90(4), 663-98. Praetz,P.D. (1975) 'Testingthe Efficient MarketsTheory on the SydneyWool FuturesExchange',Australian EconomicPapers, 14(25),240-9. Rausser,G.C. and Colin Carter(1983) 'FuturesMarket Efficiency in the Soybean Complex', Reviewof Economicsand Statistics,65, 469-78. Rockwell, CS. (1967) 'Normal Backwardation,Forecasting,and the Returnsto Commodity FuturesTraders',Food ResearchInstitute Studies,7, Supplement, 107-30. Rutledge,D.J.S. (1972) 'Hedgers'Demandfor FuturesContracts:A Theoretical Frameworkwith Applications to the.United StatesSoybeanComplex', Food ResearchInstitute Studies,11(3), 237-56. Sandor,R.L. (1973) 'Innovationby an Exchange:A CaseStudy of the Developmentof the Plywood FuturesContract',Journal of Law and

Introduction

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Economics,16, 119-36. Schneeweis,T. (1982) 'Statement[On ResearchableIssues)',Reviewof Research in Futures Markets, 1(2), 127-9. ChicagoBoard of Trade. Sharpe,W. (1964) 'Capital Asset Prices: A Theory of Market Equilibrium Under Conditionsof Risk', Journal of Finance, 19,425-42. Stein,1.L. (1961) 'The SimultaneousDeterminationof Spot and FuturesPrices', AmericanEconomicReview,51(5), 1012-25. (1964) 'The Opportunity Locus in a Hedging Decision: A Correction', AmericanEconomicReview,54(5), 762-3. Stevenson,R.A. and R.M. Bear (1970) 'Commodity Futures:Trendsor Random Walks?', Journal of Finance, 25, 65-81. Telser, L.G. (1958) 'FuturesTrading and the Storageof Cotton and Wheat', Journal of Political Economy,66(3), 233-55. and H.N. Higinbotham(1977) 'OrganizedFuturesMarkets: Costsand Benefits', Journal of Political Economy,85(5), 969-1000. Tomek, W.G. and R.W. Gray (1970) 'TemporalRelationsAmong Priceson CommodityFuturesMarkets', AmericanJournal ofAgricultural Economics, 52(3), 372-80. Ward, R.W. and L.B. Fletcher(1971) 'From Hedging to Pure Speculation', AmericanJournal of Agricultural Economics,53( 1), 71-8. Working, H. (1942) 'Quotationson Commodity Futuresas Price Forecasts', Econometrica,10(1),39-52. (1948) 'Theory of the InverseCarrying Chargein FuturesMarkets', Journal of Farm Economics,30,1-28. (1953) 'FuturesTrading and Hedging', American EconomicReview,43, 314-43. Yamey, B.S. (1951) 'Hedgingin an OrganizedProduceExchange',Manchester School, 19, 305-19. (1984) 'The EconomicPerformanceof FuturesTrading', Three BanksReview, March, 33-43.

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1

AN INSTITUTIONAL ANAL VSIS OF FUTURES CONTRACTING Cento G. Veljanovski*

This figment of delivery ... is a vestigial remnantof an age old custom,a slenderstrandof gossamerthat is easily severed,freeing the two [spot and future prices] to go where they will in fulfilling their destiny. The Gordian knot is severableonce the secretis known.1 Paradoxically,even though economicsis primarily concernedwith the study of markets,it doesnot possessa theory of markets.The entire subject of the institutions that have been developed to facilitate the trading and distribution of commodities has been eliminated from contemporary economics - markets are just assumedto exist. In the futures trading literature the issue of market developmentand innovation had been tackled in a rather crude way. Initially, a commoditiesapproachhad been adopted. The emergenceof futurestradingwasexplainedby referenceto a set of feasibility conditions relating mainly to the common physical characteristicsof commoditiesthat have been successfullytraded on organizedfutures exchanges.The inadequacyof this approach is shown by a contractionin the numberof commoncharacteristics as futures trading has expanded.In short, there does not exist a satisfactoryand comprehensivetheory of futures markets.2 In this chapterI proposeto sketchthe rudimentsof a theory of futures contractingthat has predictive power.3 The theory is based on the hypothesisthat new contracts and institutions evolve to facilitate trade in order to maximize the wealth of individuals and in particularto reducethe directcostsof transacting. 1. Brief Review of Feasibility Conditions A futures market is an organizedexchangedealing in standardized contractsfor forward delivery or settlement.Futuresmarketsare widely held to serveseveralfunctions ranging from the transferof 13

14

An InstitutionalAnalysisof Futures Contracting

the risk of price fluctuations to those better able to bear them (hedging),as guidesto future cashpricesand market expectations (thus assistinginventory control and businessplanning) and as a forum for speculation. Economists have devoted most of their attention to modelling the process and performanceof futures trading and relatively little to developinga theory of why futures markets develop in one commodity rather than another. In my view this neglect can be attributed to two principal factors - the economists'generalpreoccupationwith pricing behaviour,and the bad image acquired by institutional analysis among North American economistsdue largely to the legal economicsof John R. Commons(1934) and his followers.4 It is now firmly recognized amongmany economists,however,that the study of institutions is not only amenable toeconomicanalysisbut crucial to the understandingof economicactivity. This recognitionhasspawneda new field of study, law-and-economics,5and much work has been undertakenon the economicaspectsof contract.6 In the textbook model of perfect competition, where the same physical commoditiesare sold and consumedon different dates,it is assumedthat there exists a 'universalregime of futures markets, ... extendedto all times and all commodities'(Arrow, 1981, p. 4; Radner, 1970). The real world is a radical departurefrom this theoreticalideal - there are in fact very few commoditiestraded in organizedfutures markets. The questionnaturally arises as to what are the factors which determinethe feasibility of futures trading. In the past economists have attemptedto answerthis questionby listing a set of so-called 'feasibility conditions'.That is, a set of conditionsthat are seento be necessaryfor a commodityto be eligible for futures contracting. The list of conditions changeswith the authority consulted,but a modest list representativeof this approachis provided by Goss (1972). In additionto price volatility anda spotmarketcommitment on thepartof the potentialhedger,Goss(1972,pp. 4-6) lists five preconditions: (1) The commodity must be homogeneousor, alternatively, it must be possibleto specify a standardgradeand measuredeviations from that grade. (2) Delivery of the commoditymust be possibleunder the contract. (3) Storageof the commoditymust be possible.

An InstitutionalAnalysisof FuturesContracting 15

( 4) There must be a speculativeelement presentwhich is net short or net long respectivelyto take up the balanceof open positions. (5) There must be sufficient liquid assetsto facilitate market settlement. Conditions (1) to (3) reflect the commodity emphasis of the feasibility approach; that the feasibility of futures contracting dependson the characteristicsof the physicalcommoditytraded. The commodity approach to futures trading feasibility has proved unsatisfactory. As futures trading has expanded, the number of preconditionshas contractedin size. The extensionof trading to financial futures, which has witnessed an explosive growth in recent years, indeed seversfutures from any necessary connectionswith physical commodities. Most of the other conditions havebeenrenderedredundant.Sometime ago Houthakker (1959a, p. 158) wrote: 'The mainspringof futures trading, ... is the needto finance inventoriesin the face of fluctuating prices. A pre-requisitefor sustainedtrading, therefore, is the existenceof considerableinventories.'Yet in the US, in 1964, trading startedin live beef futures and has since been extendedto fresh eggs, live hogs and fresh broiler chickens,all of which are not stored. Gray and Rutledge(1971) note that the extensionof futures trading to thesecommoditieswas facilitated by a contractualinnovation; that of changingthe delivery instrumentfrom the conventionalwarehouse receipt to one that was 'a call on production'. Delivery of the commodityin settlementof a futures contracthas always been regardedas crucial. Goss and Yamey (1978, p. 11) provide the orthodox rationalefor this condition: 'the possibility of settlement by delivery binds together the two (spot and futures) market prices'. In February1982 this condition was also violated when the KansasCity Board of Tradebegantrading a contracton the Value Line Index of 1,700 stocks. The stock index future acceptsthe radical principle of cashsettlement,i.e. insteadof the possibility of obtaining the physical commodity, or in this case the stocks on which the index is based,in settlement,the contractcan be closed by a pure cash transfer. Five other stock index futures have also beenauthorisedin the US (Lascelles,1982). That the commodity approachto futures trading feasibility has proved to be unsatisfactoryshould not be surprising. It is after all ad hoc, proceedingon the assumptionthat the characteristicsof

16

An InstitutionalAnalysisofFutures Contracting

commoditiessuccessfullytradedon organizedfutures exchangesin the past provide a guide to the class of commodities that are susceptibleto futures trading. Clearly to the extent that the feasibility conditions do provide a guide it is becausethey are correlated with other factors that economizeon the costsof transacting. 2. Theoretical Framework

Nature of Exchange The conventional view of exchangeis trade in physical commodities.This characterizationof exchangeis acceptableso long as the analysisis limited to transactionsinvolving homogeneouscontractual obligations. Once the inquiry is extendedto considerthe choice of market, or, more correctly, the bundle of contractual obligations,the standardapproachno longer suffices. Insteadof treatingthe physicalcommodityas the primary object tradedin marketsthe transactionis substitutedas the basic unit of analysis.Every transactioninvolves a contract,whetheran explicit legally enforceableset of promisesor an implicit understanding, and a transferof contractualobligations.7 As Commons(1934, p. 58) emphasizes'[T]ransactions... are not the exchangeof commoditiesin the physical senseof "delivery", they are the alienation and acquisition of future ownership of physical things'. All exchangeapart from barterinvolves future obligations- contracts are executory,they involve promisesto do things in the future. The value of commoditiesis determinedby the bundle of rights transferred in transactions,and markets areplaceswheresuch rights are transferred. Transactionsgive rise to transactioncostswhich can be defined as the costs of defining, transferringand enforcing contracts.The central hypothesis advanced here is that the organization of exchangeis governed by transactioncosts and that institutional arrangementsare matched to activities so as to economize on transactioncosts(Williamson, 1979). The central role of transaction costs in understandinginstitutional innovation has been emphasizedby Coase(1937, 1960). In a world in which trade is costless,there would be no need for futures marketssince all tradeswould be adequatelygovernedby fully specified contingent claims contracts (Shavell, 1980). In actualmarkets,contractingand information are both costly, so that

An InstitutionalAnalysisof FuturesContracting 17 such contracts rarely exist. Instead other types of contractsand institutions will arise to economize on transaction costs. This simple proposition was suggestedby Coase (1937) many years ago, when he arguedthat the produceexchangeis 'a techniquefor minimising contractcosts'. To explain institutional innovation, the standard economic assumption of self-interestedmaximizing behaviour is adopted. Individuals or groupsof individuals are assumedto take advantage of new opportunitiesfor enhancingtheir wealth. Institutions will evolve and be fashionedto facilitate wealth maximization.That is, it is assumed that the structure of institutions in society is determinedby economicforces. In the face of positive and differential transactioncosts, the choice of contractualmode will affect the wealth of individuals, whether through its impact on expectedbenefits or on the magnitude of transactioncosts.At anyonetime an individual will hold a portfolio of contractualobligations(Crocker, 1973).The optimal portfolio will be determined by the usual maximizing rules. Supposethat different contractualarrangementsalter the variance of expected wealth and that individuals exhibit risk aversion. Following Cheung(1969a, 1969b), the choice of contract will be governed by comparing their relative benefits in terms of risk reduction with their transactioncosts. The individual will choose that contract, or, more specifically, that risk-sharingarrangement that maximizesexpectedutility. If the (expected)variance of income is used as a measureof risk, risk averse individuals will prefer a lower variance. The varianceof incomecan be loweredfor the individual by alternative contractual arrangementsdesigned to share the risk of price changes.For example,in the caseof agriculturalland leases,fixedrent leasesplace the bulk of the risk of price fluctuations on the leasee,whereasa sharecroppingcontract sharesthe risk of price changes between lessor and lessee. Forward contracts are analogous to fixed-rent leases in that if the commodity price increases,thosewho havesold forward lose; if it falls they gain. On the other hand, both futures and sharecroppingcontractssharethe risk of price fluctuations and hencetend to lower the varianceof expectedreturnsto hedgers.8 In order to determinewhethera contractualarrangementwith a low varianceis preferredto one with a higher variance,the transaction costsof using the respectivecontractsmust be considered.

18

An InstitutionalAnalysisofFuturesContracting

Supposean individual has a choice between two contractual arrangementsthat differ in terms of their expectedbenefits and that thesebenefitsdecline with the individual's usageof eachcontract. In Figure 1.1, the marginal expectedpresentvalue curvesfor two contracts,1 and 2, are drawn and labelled as MB) and MB2 respectively.The marginal transactioncostsof using eachcontract differ but are assumedto be constant. If the choice between these two contracts were mutually exclusive the individual would choose contract 2 since its net present value (NMB2) is greatest; area HP20 > IP)O. The additional gain associatedwith contract 2 can be separatedinto two effects; AFEB due to its greaterability to maximize the individual's return and CFGD attributedto its lower transactioncosts. In fact, an individual would be willing to pay a sum up to thesetwo amounts(AGDCE or HP2P)I) to usecontract2. If contract1 were a forward contract and contract 2 a futures contract, the area AGDCE can be viewed as a paymentthat hedgerswould be willFigure 1.1 f

A

b b b

b

b

b

b

b

NMB, NMB, NMB,

MB

NMB, MB

p1

p1 NMB, NMB,

Units of Participation

An InstitutionalAnalysisofFuturesContracting 19

ing to transferto brokersand speculatorsfor the superiorability of futures contractsto maximize net benefits.Thesebenefitsneednot necessarilybe limited to risk reduction but would embraceother attractive attributes of futures trading such as improved business planning. Alternatively, if both contracting modes can be used simultaneouslythe individual will use both contracts.The profit maximizing portfolio of contracts 1 and 2 will be determinedby the usual marginal equivalences. Partial hedging of stocks and inventories will be a rational strategy. Moreover transactional efficiency aloneis capableof explainingtrading in futurescontracts. Assume that the MB curves for both contracts are identical at MB 1, but that marginal transactioncosts still differ. In this case even though futures contractsdo not enhancemarginal benefits they lower transaction costs which is sufficient to encourage futures trading. An institutional equilibrium of the type depictedin Figure 1.1 can be disturbedby exogenouschangesin either benefits or costs (Davis and North, 1971). Three categoriesof factors may change the cost-benefitratio; market, institutional and transactiontechnology. First, alterations in market opportunities brought about by changesin technology,demandand other market conditions may lead to changesin the method of organizing transactions.For example,the increasingcapital intensity of productionmay lead to greateruse of forward contractsas a way of ensuringdemandand/ or supply. Second, legal and political changescan alter the cost-benefit ratio of various institutional and contractual arrangementsby prescribinglimitations, prohibitionsor expandingthe scopeof permissible arrangements.This has been an important source of changein futures market development,particularly with the early associationof futures trading with gambling.9 The breakdownof the Bretton Woods Agreement and consequentexchangerate instability, which has led to significant growth in foreign exchange futures, is anotherexampleof the way institutional factors can promote futures trading. Third, changesin the transactioncosts of organizing and operating various institutional arrangementsdue to technological innovationsmay decreasethe costsof information, e.g. telegraph, teleprinters,telephoneand computers.

20

An InstitutionalAnalysisof Futures Contracting

Sourcesof TransactionCosts Transactioncostsarise from a variety of sources.Perhapsthe most importantfactors giving rise to transactioncostsare searchactivity, boundedrationality and opportunism. In a marketwith incompleteinformation, buyersand sellerswill haveto searcheachother out. The costsof suchsearchactivity will differ and will be greater the more geographicallydispersedand heterogeneousare buyers and sellers. Searchcosts will not only raisethe costsof activities, being equivalentoften to a proportional tax, but may preclude otherwise value-maximizing transactions from taking place. Many devices have arisen to economize on costly search; brand names, advertising, centralized produce exchanges,marketingboards,etc. Bouqded rationality precludes parties from drawing up contracts that fully define the relationship betweenthem. Bounded rationality refers to the cognitive limits of individuals in formulating and solving problems and processing information (Williamson, 1979). It leads to contract incompleteness.Thus many mattersthat could alter the value of a transactionwill not be coveredby explicit terms in the contractnegotiatedby the parties. The performancedifficulties occasionedby opportunismraise the costsof transacting.1O Each party is confrontedby what can be termeda reliability risk - the risk that the other party will default either on the whole transactionor on individual termsin a way that decreasesthe expectedwealth of the non-defaultingparty. Reliability risk is an important sourceof transactioncosts becauseit will pay individuals to guard against opportunism and contract breach. Acquiring information on the reliability of those with whom one transactsyields benefits in the form of reducedlosses due to default and incompleteor inferior performance.As BenPorath(1980, p. 5) states: They [transactioncosts] arisebecausethe partiesto transactions are different individuals with asymmetricinformation, divergent motives and mutual suspicions, and becauseexpenditure of resourcescan reduce the gap in information and protect the partiesagainsteachother. Impersonaland PersonalMarkets Transactions generally take place in two types of markets: impersonaland personalmarkets.The textbookmodel of the com-

An InstitutionalAnalysisof FuturesContracting 21 petltlve market is the archetypal impersonal market where standardizedcommoditiesare tradedbetweenpartieswhoseidentities are of no economic relevance.Facelessbuyers and sellers meet to consummatebargainsin discreteperfectly replicabletransactions. Such markets can be expected to function smoothly if there are a large number of buyers and sellers and information regardingmarket opportunitiesis easily gained. Personalmarkets are those in which the identity of the trading partiesis important. As Telser and Higinbotham (1977, p. 970) note, most market transactionsdisplay the characteristicsof a barter economy where the identity of the parties - their reliability, credit-worthiness, promptness,reasonableness, etc. - is important. Personalmarkets arise becauseof transaction idiosyncracies which diminish the relevanceof market information in assisting the parties to particular transactionsand involve transaction-specificinvestments. The uniquenessof personalmarket transactionsincreasesboth the reliability risk and the costsof default. Individuals will tend to invest resourcesin establishing their own and determining the other party's reliability and reputation. The incentive for such experiencerating is enhancedby the fact that personalmarkets involve transaction-specificinvestmentsthat have low scrapvalue. The absenceof perfect replicability of personal market transactions has the effect of 'locking' the partiesinto the relationship. Moreover, investingresourcesin establishingand determiningreliability is a sunk cost. Personalmarkets arethereforecharacterized by decreasingcosts and exhibit a tendency to specializationby identity to take advantageof scaleeconomies. GovernanceStructures Governance structures are market and institutional devices designedto eliminateor reducereliability risk (Williamson, 1979). They range from market sanctionssuch as price adjustmentsand loss of customto formal legal penaltiesimposedby the courts. In impersonalcompetitive markets,price adjustmentswill be a relatively efficient meansof regulatingand compensatingfor reliability risk (Klein and Leffler, 1981). If the probability of default is perceivedas non-trivial, a seller will demanda price premium and the buyer a price discount. Governanceby price premia/discounts in impersonalmarketsis virtually self-enforcing.If the risk comes from sellers,buyerswill either turn to other sellersor reducetheir demandfor the product. The unreliable seller will then be forced

22

An InstitutionalAnalysisofFutures Contracting

to improve his servicesor go out of business.Market governance will tend to be most effective the more competitive the market, which in turn dependson the degreeof producthomogeneityand flow of information betweenbuyer and seller. In personalmarkets, governancewill generally occur through reputationand experiencerating. The desireto retain the goodwill associatedwith a reputation of being reliable and reasonablein adapting to contract difficulties may discourage opportunism. However, opportunismis not necessarilydeterredby the prospect of a bad reputationor the existenceof goodwill. As Telser(1980, p. 36) points out: The accumulationof a fund of goodwill of a buyer toward a seller that dependson pastexperiencestandsas a temptationto the seller to cheat the buyers and convert the goodwill into ready cash. It is the prospect of the loss of future gain that detersand the existenceof pastgoodwill that invites cheating. Reliability risk can be reducedby non-marketforms of governancerangingfrom vertical integrationand self-regulationto legal penaltiesundercontractlaw. Opportunism can be reduced by undertaking the production and distribution of intermediatetasks, thus subjecting all transactions to the authority relation, i.e. principal-agentrather than market relations. The firm is one such device (Alchian and Demsetz, 1972), a futures exchange another. Group selfregulation can also be used to reduceopportunismand reliability risks. Such governanceis common among the professionsand in commodityfutures exchanges.Although self-regulationmay introduce monopoly elements into the market, it can also remedy information problems by ensuring the integrity of traders and imposingminimum quality standards. 3. The Organizationof FuturesTrading Before investigatingthe transactioncost economizingfeaturesof futures contracts,it will be helpful to discussthe nature and processof futures trading.

An InstitutionalAnalysisofFuturesContracting 23 Hedging Theory The futures literature presentsthe following characterizationof futures trading. The commercialdemandfor futures contractsis seenas coming from hedgersand speculators.A potential hedger is one who is confrontedby price volatility and a 'price risk' - the chancethat the price will move in an unfavourabledirection. The hedgerentersthe futures market in order to transferthe price risk to anotherparty. In doing this the hedger replacesthe price risk with a basis risk - that spot and futures prices will not move in parallel. If the price spreadbetweenspot and futures pricesis constant at the time the contract is sold, and when it is bought the hedgeis said to be perfect, then the risk (both price and basis) is eliminated. A short hedgeris one who sells a futures contractand incurs a liability to deliver the 'commodity' during the maturity month of the contract at the price prevailing when the initial transaction took place. If the contractis settledby delivery, the net changein the value of the assetis the original futures price minus the spot price during the delivery month. Typically the seller of a futures contract will offset his obligation to deliver by the purchaseof a futures contract, thus extinguishing his net obligations to the market. If this is done, the net changein the value of the assetdue to futures trading is the differencein the two futures prices.A long hedgeror buyer of a futures contract confronts the mirror-image of thesechanges. The extentto which the price of a forward futures contractcan exceedthe spot price (called a contango)is limited by arbitrage. The maximum difference cannot exceed the marginal cost of storageuntil maturity plus delivery costs.A larger contangowould give arbitrageursa risklessprofit by buying in the spot market and simultaneouslyselling futures. The extent to which the spot price exceedsthe futures price, called a backwardation,is not necessarily constrainedby arbitrage.To take advantageof a large backwardation requiresthat the arbitrageursimultaneouslysell spot and buy futures. The ability to do this obviously dependson the volume of stock held by traderswilling to take advantageof the backwardation. If the stock is limited, a large backwardationmay result. Thus a short hedger has a limited basis risk whereasthe long hedgerhasa potentiallylargerbasisrisk, thoughnot an unbounded one because,as the futurescontractnearsmaturity, future and spot priceswill converge.

24

An InstitutionalAnalysisofFutures Contracting

The Naturesof Futures Contracts The object tradedin a futures market is not the actual commodity but a futures contract.Typically there is one standardcontractper commodity relating to a large quantity and specifiedquality of the commodity. All the terms of each contract except the price are determinedby the rules of the exchangeso that the only term that is negotiated during trading is the sale price of the contract. Trading in futures contracts is centralized on the floor of the exchange(the 'pit'), is limited to specifiedhours and to a restricted number of accredited members of the exchange.Trading is by 'open outcry' - an auction system where buyers shout out their bids and motion with their handsto sellers who do likewise. The settlementof futures contracts is handled by the exchangeor a clearing housewhich interposesitself betweenbuyers and sellers. The exchangemembers'obligations are to the clearing housenot to eachother and membersare liable to the clearinghouse. Futuresmarketshave severalother uniquecharacteristics.First, a futures contracthasa limited and short life. A buyer of a futures contract usually must liquidate his position in a relatively short time. The life of the longest futures contract is only 18 months (although quotations up to two years aheadare not unknown). Second, for every short position in the market there is a long position. So if hedgersare net short, speculatorsmust be net long and vice versa. ConsequentlYon the day of a price change50 per cent of positionslose and 50 per cent gain. Third, futures contracts are highly leveragedOne can usually trade on a margin of 10 per cent of the value of the contract.Thesemargins are in the nature of a security deposit that protects the broker and principal from losses against adverse price movements. In all US futures exchanges,daily limits are placedon the fluctuation of prices.This, plus the brokers' additional margin call, gives the buyer of a futures contract time to reassessthe situation and liquidate his position if desired. Fourth, futures markets operateon a 'no debt basis'. All trading gains and lossesare settledthrough the clearing house before the commencementof the next day's business. Finally, futures markets are highly organized self-regulated markets.The exchangeoverseesthe conduct of business,designs trading rules and contracts,either it or the clearing houseensures that all contractsare settledaccordingto their terms and it has the power to discipline membersof the exchangewho breachthe rules. Although the hectic and competitivenatureof futures trading has

An InstitutionalAnalysisof FuturesContracting 25

led many to refer to it as the 'last frontier of capitalism',it is none the less highly regulated capitalism, both in the form of selfregulation, as in the UK, or governmentregulation administered by the CommoditiesFuturesTrading Commission(CFTC) in the US (Gemmill, 1982; Rock, 1982). 4. Applications The Evolution of Contract

Risk and uncertainty in the form of price volatility and opportunism are major factors giving rise to futures trading. The economic significance of the distinguishing features of futures contractsis initially best discussedby comparingfutures with spot and forward contracts. Although the historical developmentof futures trading hasbeen well researched,few of the in sights distilled from this work have beenincorporatedinto the theory of futures markets.!! The origin of organizedfutures trading in its modemform can be tracedback to the New York produce exchangeswhich appearedin 1752. This, however, obscuresthe iterative nature of futures evolution. Futurestrading evolvedout of autonomousforward contractingby merchants,dealersand processorswhich was designedto increase businessefficiency. Irwin (1954) points out that futures trading evolved out of time contractsof the delivery type. Indeed, early futures markets were viewed as delivery markets in which transactionswere facilitatedby the provision of uniform rules on grade and delivery terms, and the security provided by the clearing housesin guaranteeingindividual contracts. This evolution from spot, to forward, to futures contracts suggestsa progressiveadaptationof institutions to more efficient methodsof dealing with price risk. For example, it is frequently arguedthat a preconditionfor futures trading is a well-developed cashmarketand the breakdownof forward contracting.The latter is too rigid a precondition.For example,in 1969 trading beganin plywood futures contracts,a commoditythat did not havea history of forward contracting(seeSandor,1973, pp. 131-2). The observation, however,that a breakdownin forward contractinghas frequently precededfutures contractingin the past indicatesthat the latter hasbecomean inefficient meansof dealingwith price risk. Futuresmarketsdevelopbecausetheyare a moreefficientmeans

26

An InstitutionalAnalysisofFutures Contracting

of transferring thosecontract rights attachedto price. For reasons that will be explored later, spot and forward contracting may becometoo costly. However, these three contracting modes are not mutually exclusive ways of transacting.Indeed the development of futures markets will improve the efficiency of spot and possibly of forward contracting.It is perhapsbest to view futures marketsas 'side' marketsdesignedto deal with price volatility that is poorly handledby spot and forward markets.The transactional superiorityof futures marketscomesmainly from their transactioncost reducingattributes. In dealing with price risk, futures contractshave severaltransactional advantages relative to spot and forward contracts. Sequentialspot contracts,that is spot contractswhere the terms of the contract are renegotiatedas events unfold, do not inject any certaintyinto the transaction.Such a methodof contractingis particularly liable to the hazards of opportunism and may deter investmentbecauseof the relatively high probability that the contract will be breached. Forward and futures contracts inject some certainty into the transaction.Both sharethe property that the partiesagreeto perform the terms of the contractat somefuture date. Arrow (1974, p. 8) has arguedthat time-datedcontractsare generallycostlier to enforcethan spot contracts.This is due to the absenceof the selfenforcing, near simultaneous exchange of value for value characteristic of spot transactions and the greater uncertainty attachedboth to the eventual outcome and each party's compliancewith the termsof forward contracts. Forward and futures contracts differ, however, in their susceptibility to opportunism, especially in their role of reducing price risk. First, forward contractsthat cover all feasible contingenciesare costly to devise.The information and transactioncosts will thus precludea fully specified forward contractand this contractualincompletenesswill give rise to enforcementand execution difficulties. Incomplete contracting has a clear economic justification. Given the cost of tailoring the contract to the particular needsof the parties,it will usually be cost-effectiveto use standard form contracts.In this regard,organizedforward and futures contracting have identical properties.Nevertheless,enforcementand execution difficulties can be expected to pose a more serious problem for forward contracts.This is so for severalreasons.First, in forward contracting,individuals will have to incur the expense

An InstitutionalAnalysisofFuturesContracting 27 of determining the reliability risk of the opposite party. To the extent that there are scale economiesin such specializationby identity, forward contracting will be more expensive than organized futures contracting where the exchange ensures the integrity of its membersand trading practices.Forward contracts also are subjectto high enforcementcosts where personalmarket sanctionsare weak. The penalty rules of contractlaw are costly to enforceand may not deal effectively with all types of breaches. A further disadvantageof forward contractsis that they are tied transactions. The forward contract transfers rights relating to quantity, quality and price. The last, however, may best be separated,especially when the parties are risk averse and their accessto insurancemarkets limited. Moreover, as Wachter and Williamson (1978, p. 55) have stressed,price changeshave an unfortunate zero-sum quality that increases the likelihood of opportunism.Thuswhile forward contractsmay inject certaintyinto the quantity and possiblyquality dimensionsof future transactions, it is not clear that they are the least-costadaptationto price risk. Dependingon the transactioncostsin alternativemarkets,and the strengthof governancein each, it may be desirablefor both riskspreadingand opportunism-reducingreasonsto separateprice risk from the other aspectsof time-datedtransactions. The view suggestedhere is that spot, forward and futures markets deal in different bundles of rights among different individuals. In particular, rights can be divided betweenthoserelating to quantity and quality, and those concerningcertainty of profits and costs. Forward contracts,especiallyin personalmarkets, are best suited to ensuringthat contract terms relating to the former are complied with, whereas futures contracts deal with price volatility. Futurescontractspermit the price risk to be separatedfrom the reliability risk by removing the former from the set of factors giving rise to opportunism.The governancestructuresupplied by the exchangeauthority effectively eliminates reliability risk from futures trading. The seller of a futures contractincurs a liability not to the buyer, but to the clearing house, and likewise the buyer acquiresan assetfrom the clearing house. The clearing house in effect guaranteesall transactions.In addition the exchangerules, especially regarding its members' conduct, severely limit their ability to behave opportunistically. Organized exchangesgreatly reduce default and reliability risk from futures contracts.This is

28

An InstitutionalAnalysisofFutures Contracting

achievedby transferringtransactionsover price risks from a personal to an impersonalmarket through standardform futures contractstradedin a self-regulatedmarket place.

ContractStandardization Futurescontractsare standardform contractswith only one negotiable term: price. The standardizationof futures contracts has significant implications for transactioncosts. This is so for several reasons.First, contractstandardizationeliminatesthe costsof bargaining over non-priceterms and of enforcingcontractprovisions. Second,it reducesmonitoring coststhat are generallyincurred in principal-agentrelationships.The principal only needsto give his broker instructions as to price and quantity which are easily observed.The monitoring costsin the futures marketare therefore significantly lower than thosein the spot market, where numerous othermattersrequireattentionandprovidethe brokerwith opportunities to takeadvantageof the principal. Third, contractstandardization makesall futurescontractsof a particularmaturitymonthperfect substitutes.The fungibility of futures contractsis not a property sharedby forward contractsand,as Houthakker(1959a)andTelser (1981a)havenoted,likensfuturescontractsto money.Providedthat the volume of trade is sufficient, therewill be a highly elasticexcess demandfor individual futures contracts,enabling transactionsto take place in a rapid and continuousmanner, thus significantly reducingthe risks to market makers. The liquidity and competitivenatureof futures trading will also reducethe waiting costsof brokersand speculatorsfor acceptable bids and offers. One componentof the transactioncostsof futures trading is the ask-bid spreadwhich, in a competitive situation, is directly correlatedwith the searchcostsof finding acceptablebids and offers. Demsetz's(1968) study of trading on the New York Stock Exchangepostulatesthat waiting costs,that is the time cost of waiting for acceptableexchangeprices, is an important determinant of the ask-bid spread. Working's (1967) study of 'thin' futures markets suggestsa similar relationship; that for inactive markets,scalpersmust take wider margins becauseof the greater time period betweentradesand the greateruncertaintyassociated with slower trading. Thus a positive relationshipexistsbetweenthe waiting cost and the ask-bid spread,and an inverse relationship betweenthe volume of transactionsand average transaction costs. As in all economic activities, specializationleads to increased

An InstitutionalAnalysisof FuturesContracting 29 efficiency and greaternet benefits.The existenceof specialistswith differential searchand information costsis an important factor in explaining both why large speculatorsconsistently make profits and why commodityexchangestend to minimize transactioncosts. Following Alchian (1970, pp. 30-2), the determinationof the ask-bid spreadcan be illustrated with the aid of Figure 1.2. In Figure 1.2 the curve PoPt representsthe expectedmaximum contract price that can be found in period t. The curve relates maximum expectedprice to the level of searcheffort. Speculators in futures marketswould be willing to offer a price greaterthan Po at to if they expect the discountedre-salevalue of a futures contract (net of search costs) will increase faster than the rate of interest.The highestbid price can be shown by constructingan isopresentvalue curve, P*P*, which showsthe grossexpectedpresent value of a futures contract. It is positively sloped due to the assumptionthat more intensivesearchgeneratesknowledgeabout higher return trading opportunities.Brokersand speculators,however, incur search and information costs that decreasetheir net return. The scheduleNo is the return net of searchcosts and the difference P*PI is the ask-bid spread, where PI is the expected Figure 1.2: Determination of Ask-bid Spread I

P*

P" Expectation of maximum price Pt

P; P,

P* p*,

No Net of search costs

Po No

L--------'------'--------------t/units of search t'

t'

t'

30

An InstitutionalAnalysisof FuturesContracting

future selling price. Obviously the greater the search costs the greaterwill be the margin required by brokers and speculatorsto engagein trading. For example, in a market with higher search costs, the next expectedpresentvalue schedulewill be depressed to No and the ask-bid spreadwill increaseto P*P;. The importanceof market liquidity arises not only becauseit reduceswaiting costs,but also becauseit ensuresthat competitive pressuresexist to keep waiting coststo a minimum for any volume of trade. Competitionamongfutures traderswill have the effect of weedingout thosewith excessivesearchcostsand poor forecasting ability. Studies(e.g. Rockwell, 1967) tend to supportthe view that large professional speculatorsmake consistent profits whereas smallertradersmake losses.Houthakker(1959b) attributesthis to superior access to information. Speculatorsdo better in near futures (those close to maturity), the prices of which dependon spot market conditions, i.e. stocks, location of deliverablegrades, etc., about which smaller traderswould find it difficult to acquire information. Moreover in 'thin' futures marketsmonopolisticelementsmay arise in speculativebehaviourthat increasethe costsof hedging. Gray's (1960) finding that thin markets display the largestbias is consistentwith this view.

Contract Design Although not emphasizedin the theoreticalliterature, in practice contractdesignis consideredto be crucial to the successof futures trading.12 A poorly designedcontract that does not reflect commercial reality or favours one group of traderswill lack the necessary appeal and will fail to attract a sufficient volume of trade. Contract design is a matter for the exchangewhich, as Silber (1981) notes, confrontsa basic marketing problem: how to translate the economic prerequisitesfor futures trading into contract specificationswith sufficient appeal to both hedgersand speculators. The design problem centres on contract specifications relating to delivery grade and locations, contract size, number of contract months, units for price quotations, daily price limits, trading hours and margin requirements. Silber's (1981) study found a surprising sensitivity of a new contract's success to apparentlyminor changesin its specifications.This is graphically illustrated by the simultaneousappearanceof four similar gold contractsin 1975. Two of thesecontractscalled for the delivery of 1000z gold bars whereasthe others called for 3 kg and 1 kg bars.

An InstitutionalAnalysisof FuturesContracting 31 The 1000z contractssucceededdespitethe fact that the 3 kg contract was offered on the more capitalized floor of the Chicago Board of Trade. The popular explanationis that the round figure of a 1000z simplified calculations, enabling arbitrageurs to respondmore rapidly to price discrepancies. Futurescontractsrelate to a specified grade of the commodity or to a prescribedlist of deliverableor substitutablegrades.Since only one gradecan govern the futures price, it is importantthat the contractspecify the gradethat will best reflect price movementsof the hedgedcommodity. The delivery options of futures contracts typically have the following features.In addition to the contract(or basis)gradeand delivery locations, a difference system is used that imposescontractual premia or discountsfor non-contractgradesor delivery at different locations. Two difference systemsare used to deal with the delivery of non-contract grades; the commercial difference systemand the fixed differencesystem.The commercialdifference systempermits non-contractgradesto be delivered at premia and discounts as determineddaily by the intergradedifferences prevailing in the spot market. The fixed difference system, which is more common, specifies the exact amounts to be paid if a noncontractgradeis delivered. Finally, the seller has the options as to grade,place and date (within the maturity month) of delivery. The seller'soption over thesematterswas originally introducedto prevent cornersand squeezesin the market. The standardizationof futures contractsmakesthem ill-suited as delivery instruments, and generally less than 1 per cent of futures contracts are settled by delivery. The usual method of 'closing-out' a futures contract is by reversing the transaction through the purchaseor sale of an offsetting contract. Seller's options and contract standardizationmake delivery of the commoditya potentially costly affair for the long hedger,althoughfor the short hedger it may reduce the number of transactionssince both spot and futures commitmentscan be closed with the one transaction. Contract standardizationmay also diminish the hedging properties of a contract if there are markeddisparitiesbetweenprice movementsin the contract grade and the actual grade traded by the hedgerin the spot market and/or anomaliesin the difference system.This problem could be avoided if severalcontractswere offered that reflected more closely the particular needsof groups

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of hedgers.All things being equal, such individualization would improve the hedging ability of futures trading for the individual hedger.This problemhasbeenaddressedby Working (1967), who puzzled over the question of why contract standardization occurredwhen somedegreeof contractheterogeneitywould seem more appealingto a market where traders'requirementsdiffered. Working's answer was in terms similar to the analysis of this chapter: that is, the trade-off betweentransactioncosts and the benefits derived from contract heterogeneity. According to Working, if two contracts,eachwith differing specifications,were traded, the less active one would require an increasedmargin by scalpers,which would raise the hedging cost, leading to further concentrationin the more active contractand an eventualdemise of the more costly contract. Contract heterogeneityraises transaction costs by reducing market liquidity. As Working concludes that many hedgersshould prefer a "poor" ' ... it is understandable hedge that is cheap to a more perfect hedge that is relatively expensive'.Working's analogy with insurance,that the choice is betweencoveragefor all risks at high cost or for only seriousloss at lower cost, is particularly apt. McManus and Acheson(1979) provide a different analysisof the impact of standardized delivery options and commodity specifications on the hedging property of futures contracts. Mc Manus and Acheson(M-A) contendthat futures contractsare inferior to spot (or forward) contracts (as delivery instruments) becausethe impersonalnatureof futures trading leadsto potential distortions in product quality that need to be deterredby a backwardationwhich, in turn, reducesthe attractivenessof futures contracts as a hedge. The M-A thesis is basedon the following reasoning.Futures contracts provide objective and incomplete descriptions of the commodity. This encouragesa potential deterioration in the quality of goods that will be supplied to settle futures contracts. The sellersof futures contractswill havean incentiveto deliver the lowest quality goods that satisfy the contract description in as much as thosequality attributesomitted from the description,but valuedin the spot market,will be lessintensivelyprovided. Incomplete objective commodity description createsincentives for the production of contract goods, i.e. goods designed for delivery against a futures contract. This distortion will not, however, be reflectedin the actualproductionof inferior quality contractgoods

An InstitutionalAnalysisof FuturesContracting 33 but in a backwardationin futures prices sufficient to deter their production. This implies that the futures price must lie below the expectedspot price by at least the difference in the price of contract and the 'spot' commodities. Contract incompletenessthus generatesa backwardationwhich increaseswith the extent to which the commodity is incompletelyspecifiedin the futures contract. The futures price will increaseas the contractnearsmaturity, reflecting the higher costsof producingcontractgoods. McManus and Acheson characterizethis as a moral hazard problem that is exacerbatedby the impersonalnature of futures trading. They suggestthat the subjective evaluation of quality in personalspot marketsis cheaperand superiorto tradeby objective commoditydescription. The following commentscan be madeon the M-A thesis.First, to the extent that commodity quality can be fully and objectively described,the M-A thesisdoes not apply. Futurestrading in gold, silver, metals,foreign exchangeand financial futures, therefore,is not subject to the problem of potential quality deterioration. Moreover, the monitoring of quality attributesthat can be objectively defined will be provided at lower cost through a centralized exchange than by individual traders in the spot and forward markets. Second,the M-A thesis assumesthat the alternative to futures trading is personalizedspot or forward markettransactions, where specializationby identity and subjectivequality evaluation are a cheaper means of monitoring and preventing quality deterioration.This assumptionis obviously inapplicablewhen the relevant forward market may also be impersonal and rely on objective or imperfect commodity description. A more serious criticism, however,is the assumptionthat subjectivequality evaluation is cheaperand as finely tuned in personalmarketsas M-A believe. Several empirical studies (e.g. Macaulay, 1964) have stressedthat in long-term personalcontracting,the partiestend to be flexible and respondto variation in the quality of performance in reasonableand accommodatingways. Wilson's (1980) study of personalcontractingin the New Englandfish marketsuggeststhat the SUbjectiveevaluationof quality is extremelycrude. The information and monitoring costs encounteredin the loose and illdefined long-term contracts characteristic of personal markets makes subjective quality evaluation extremely difficult. 'As a result', concludes Wilson (1980, pp. 503-4) 'implicit product quality standardsoften tend to approximatea simple "acceptable"

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or "unacceptable"stateand actual productfalls to the lowest level consistentwith acceptability.' Which is to say that precisely the identical difficulty is encounteredin the spot marketwhen product quality is not objectively definable.

Margins So far it has been arguedthat the organizationof futures trading eliminates reliability risk. This in fact is not entirely true. The governancesuppliedby the exchangeremovesthe risk of default in the settlementof futures transactionsby holding membersof the exchangeliable to the clearing house, and protects the clients of brokersfrom loss due to the latter's insolvencyor dishonesty.The broker, however, still faces the risk that his client will default. To the extent that the risk of client default is present,the brokerage costsof futures trading will rise to cover expectedlosses. The problem of client default has been handled by futures exchangesby requiring clients to pay their brokers a deposit margin, usually between1 per cent and 5 per cent of the value of the contract (Telser, 1981b). These margins serve to protect the broker from losses that may result from adversechangesin the customer's net balances. Margins are a security deposit that cushions the broker from losses arising from client default. Margins also economize on transaction costs by substituting a simple 'price rule' for the customer'slegal liability to the broker that would require costly legal proceedings to enforce. The practiceof additional margin calls, when there hasbeenan adverse movementin the customer'saccount,plus daily price limits, both serve to reduce the probability of loss due to customerdefault. Thus, unlike a customer'sliability rule, margins are finely tuned responsesdesignedto minimize customerdefault and hencetransactionscostsin futures markets.

Centralizationof Trading There is a strong tendencyfor futures trading to take place not only in one contract but also in one exchange.The centralization of trading in futures tends to increasemarket liquidity. As Telser (1981a) has argued, there are increasing returns to market liquidity due to the effect of increasesin the volume of tradeon the variance of market clearing prices. If the distribution of market clearing prices is asymptoticallynormal, a 1 per cent increasein the volume of trade will reduce the varianceby half a per cent.

An InstitutionalAnalysisof FuturesContracting 35 Thus a single market will be twice as liquid as two marketseach half its size. Silber's (1981) comprehensivestudy of contractinnovation by US exchangesfinds that the liquidity of the larger establishedexchangesis important for the successof new contracts. The successrate of new contracts for the largest five exchangesin the US was over two times that for the rest of the industry (30.2 per cent comparedto 13.6 per cent). He also found that the chancesof the competitivecoexistenceof two contractsin the same commodity is greater if they are traded on the same exchange. These findings indicate that there are increasing returns to futures trading and a tendencyfor natural monopoly markets to form. In the US the futures industry is highly concentrated.There are 14 exchangesand the three-firm concentrationratio is nearly 90 per cent (measuredin numberof contractstraded).Despitethis concentration,the rivalry betweenexchangesis fierce and the big three are responsiblefor most contractualinnovations. Although much more work needsto be done on this issue,there appears to be strong competition between exchanges,thus minimizing the likelihood that any exchangewill be able to exercize monopoly power.

ExchangeGovernance Futuresmarkets aregenerallyowned by their membersand operated as non-profit institutions. They, like the firm, can be viewed as private proprietary markets as opposed to a 'non-owned' market where autonomouscontractingtakesplace. Non-ownedor public marketstend to suffer from commonpropertyinefficiencies wheretransactioncostsare significant. This is becauseno one individual has an interest in the efficient operationof the market as such. If the inefficiencies of public marketsbecomelarge enough, individuals will have the incentive to privatize the market by establishingproperty rights in its operations. The membersof a futures exchangehave a property right in its activities, and the value of their property right dependson its efficiency. The governancemechanismprovidedin futures markets thus has severalcharacteristicsthat reflect this fact. First, although the interestsof exchangememberswill be diverse,it is reasonable to assumethat the rules of the exchangewill be fashionedto maximize the collective profit of its members.Thus exchangeswill act to promotefutures trading, reducereliability risk and maintain the

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generalintegrity of its operationsand members.Thus, unlike most other forms of regulation,self-regulationby the exchangewill tend to be economically motivated and wealth maximizing. It is of coursetrue that self-regulationcan promote monopolistic abuses, especially given the strong tendency for natural monopolies to arise in futures trading. However, the scope for monopolistic practices is greatly limited by potential competition from other futures exchanges.Moreover, members of the exchangehave a commoninterestin ensuringthe good nameof the exchange;their businessdependson it, as does the value of their seat on .the exchange.Thus eachhas an interestin the survival and reputation of the other, as evidenced by arrangementsdesigned to assist membersin financial difficulties. The nature of futures markets seemsto provide endogenous forces that causemarket regulation to be efficiency-based.Since the raison d'etre of futures trading is transactioncosts economies, it should not be surprising to find that most of the regulations devised by the industry reflect this fact. Regulationsthat did not reduce transaction costs and reliability risks simply would not survive. This view of exchangegovernanceand inter-exchangecompetitive pressuresgives rise to a testableprediction. It suggeststhat governmentregulationof futures exchangesmay be detrimentalto their performanceand efficiency. In the US, futures trading is subject to governmentregulation whereasin the UK the industry is largely self-regulated(Gemmill, 1982). One test of this aspectof the theory, suggesting that exchangesgovern efficiently, is to investigatewhetherregulationin the US has led to increasedtrade on UK (and other self-regulated) futures markets (Gemmill, 1982). 5. Feasibility ConditionsReconsidered Equippedwith the model developedabove,a few final comments can be made concerning the generally acceptedfeasibility conditions. First, it should now be fairly obvious that the 'commodity approach'missesthe essentialfactors that limit futurestrading. For example, homogeneityor near homogeneityof the commodity is not a condition per se, but refers to the fact that as heterogeneity

An InstitutionalAnalysisofFuturesContracting 37 increasesso too do the transactioncostsof trading in futures. As a rule of thumb this feasibility condition may be adequate,but one should not be surprisedto see it violated as the cost-benefitratio changesasa consequence of technologicaldevelopmentsor changing market structure. Another condition that can be cast in a different light is that of the necessityof possibledelivery of the commodityin settlementof the futures contract.We have seenthat the economicrationalefor this condition is to bind futures and spot prices. Yet the extension of :(uturestrading to stock marketindicesand financial instruments is assailing the logic of this argument and it could well be that delivery options are in large part a device to avoid the legal inferencethat futures contractsare gamblingcontracts. The necessity of delivery needs to be reappraised.In this chapterfutures markets have been characterizedas side markets which provide valuable services, whether it be price insurance, price determinationor an aid to businessplanning, for which the hedgeris willing to pay a price. Spot and futures marketsperform different functions. They tradein different propertyrights attached to physical commodities. The spot market is a delivery market where rights to specific lots of the commoditiesare traded. The futures market is where hedgerstake a position of temporaryzero ownership, transferring the rights to commoditiesfor a specified period to peoplewilling to trade in those rights in the expectation of gain. If this view is taken, there is no logical necessitywhy delivery is a necessary condition. The mechanism that permits futures marketsto exist is the relative efficiency with which they transfer propertyrights. If a futures marketperformsthis task at too greata cost, it fails. It is not delivery that binds the two markets,but the competitive forces in the futures market that keep the benefits of the servicesprovidedequal to their marginal costs. A similar view has been expressedby Henry Bakken, who assertsthat futures trading is not circumscribedby certain physical features of the commodity, particularly the 'figment of delivery'. According to Bakken, the primary purposeof futures trading is price determination,although the logic of his argumentdoes not dependon this view of the function of futures. Bakken (1960, p. 50) concludeson an especially prophetic note that bears repetition: 'It is even possible,in my way of thinking to conceiveof a universal contract rather than to have many commodity contracts

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tied to specific commodities.Under this conceptone would really engagein trading on the basisof index numbers.' Houthakker's(1959a) commentthat the possibility of delivery makes futures analogous to banknotes under a convertible currency regime can be turned on its head by assertingthat nondelivery makes futures analogousto banknotesby fiat. The fact that the latter haveno effective commoditybackingdoesnot imply that they are worthlessor tend to bear no relationshipto reality. To use Bakken'sterm, contractswould still create'net possession utility' in the form of wealth-increasingpotential. Notes *Wolfson College, Oxford. This chapteris a substantiallyrevisedversionof my paper'An Institutional Analysis of FuturesTrading' completedas part of Barry Goss'sgraduatecoursein hedgingand uncertaintyat MonashUniversity in 1975. I am grateful to Dr Gossfor his commentson the original paper. 1. Bakken (1960). 2. Gossand Yamey (1978, p. 45) comment:'we have not provideda systematicanalysisor analytical framework from which the necessaryconditionsfor the feasibility and successof futures trading can be derived. This lack of such a firm framework is a deficiencyin the theory of futures trading.' 3. Severalrecentarticles on futures trading havealso adoptedsuch a transactioncost approach.In particularTelserand Higinbotham(1977); Burns (1979); McManusand Acheson(1979). The earlier work of Houthakker(1959a) and Working (1953a,b)also emphasizesthe transactioncost-reducingaspectsof organizedfutures trading. 4. In Houthakker's(1959a,p. 134) openingparagraphhe states:'The economicanalysisof institutionsis not highly regardedor widely practisedamong contemporaryeconomists.The very word "institution" now carriesunfavourable associationswith the legalistic approachto economicphenomenathat was respectableduring the first three decadesof this century. Thereis little reasonto regret the triumphantreactionthat swept institutionalismfrom its dominantplace.' 5. This literature is surveyedin Veljanovski (1982). 6. See,for example,the readingscollectedin Kronman and Posner(1979). 7. This position is also taken by moderneconomicpropertyrights theorists. Furubotnand Pejovich (1972, p. 1139) stressthat '[T]hough sometimesforgotten, thereshouldbe no confusionabout the fact that both tradeand productioninvolve contractualarrangements.Theseactivities exist not so much to accomplishthe exchangeof goodsand servicesbut to permit the exchangeof "bundles" of propertyrights. Permissionto do things with goodsand servicesis at issue.. .' 8. Studiesgenerallyindicate that the risk per unit of unhedgedcommodityis greaterthan hedgedstock due to the close correlationof spot and futures prices. Gray and Rutledge's(1971, p. 80) surveyfinds that 'in virtually every study "basis risks" were found to be smallerthan price risks'. 9. According to Bakken (1960), 330 Bills were introducedin the US Congressduring the period 1884-1953designedto regulate,investigate,limit, prohibit and otherwiseobstructtrading in futures contracts. 10. The definition of (ex post) opportunismdiffers amongauthors.For

An InstitutionalAnalysisof FuturesContracting 39 exampleMuris (1981) doesnot contemplatebreachas opportunistic.According to Muris (1981, p. 521) opportunismoccurs'when a performing party behaves contrary to the other party's understandingof their contract,but not necessarily contrary to the agreement'sexplicit terms, leading to a transferof wealth from the other party to the performance'.I adopt a wider definition in the text. 11. AAAPSS (1911); Dumbell (1927); Irwin (1954); Bakken (1960,1966). 12. Thereare only a few studiesof futures contractsspecifications:Jesseand Johnson(1970), Powers(1967), Sandor(1973) and Silber (1981).

References AAAPSS (1911) 'American ProduceExchangeMarkets', A nnals of the American Academyof Political and SocialScience,38, 319-64. Alchian, A.A. (1970) 'Information Costs, Pricing and ResourceUnemployment'in E.S. Phelps(ed.), Micro-economicFoundationsof Employmentand Inflation Theory, New York: Norton & Co. Alchian, A.A. and H. Demsetz(1972) 'Production,Information Costsand EconomicOrganization',AmericanEconomicReview,62, 777-95. Arrow, K.J. (1974) 'Limited Knowledgeand Economic Analysis', American EconomicReview,64, 1-10. (1981) 'FuturesMarkets: SomeTheoreticalPerspectives',Journal of Futures Markets, 1. Baer, J.B. and O.G. Saxon(1948) CommodityExchangesand Futures Trading, Madison: Harper Bros. Bakken, H.H. (1960) 'Historical Evaluationand Legal Statusof FuturesTrading in American Agricultural Commodities',Futures Trading Seminar,vol. 1, Madison: MIMIR. (1966) 'FuturesTrading - Origin, Developmentand EconomicStatus', Futures Trading Seminar,vol. Ill, Madison: MIMIR Pub. Inc. Barzel, Y. (1979) 'MeasurementCost and the Organizationof Markets', Journal of Law and Economics,25,47-8. Beale, H. and T. Dugdale(1975) 'ContractsBetweenBusinessmen:Planningand the Use of ContractualRemedies',British Journal of Law and Society,2, 45-60. Ben-Porath,Y. (1980) 'The F-Connection:Families, Friendsand Firms and the Organizationof Exchange',Population DevelopmentReview,6,1-30. Bums, J.M. (1979) A Treatiseon Markets - Spots,Futuresand Options, Washington:American EnterpriseInstitute. Cheung,S.N.S. (1969a)'TransactionCosts,ResourceAllocation and the Choiceof ContractualArrangements',Journal of Law and Economics,12, 23-42. (1969b) Theoryof ShareTenancy,Chicago:University of ChicagoPress. Coase,R.H. (1937) 'The Nature of the Firm', Economica,4, 386-405. (1960) 'The Problemof Social Cost', Journal of Law and Economics,3, 1-44. Commons,J.R. (1934) Institutional Economics,New York: Macmillan. Crocker,T.D. (1973) 'ContractualChoice', Natural ResourcesJournal, 13, 561-77. Davis, L.E. and D.e. North (1971) Institutional Changeand AmericanEconomic Growth, New York: CambridgeUniversity Press. Demsetz,H. (1968) 'The Cost of Transacting',Quarterly Journal of Economics, 82,33-53. Dumbell, S. (1927) 'The Origin of Cotton Futures',EconomicHistory, 1,259-67. Furubotn,E.G. and S. Pejovich(1972) 'PropertyRights and EconomicTheory: A

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Surveyof the RecentLiterature', Journal of EconomicLiterature, 10, 1137-62. Gemmill, G. (1982) 'RegulatingFuturesMarkets: A Review in the Context of British and American Practice',paperpresentedat Conferenceon Futures Markets, Florence,11-13 March. Goss,B.A. (1972) The Theoryof Futures Trading, London: Routledge& Kegan Paul. Goss,B.A. and B. Yamey (eds.)(1976) The Economicsof Futures Trading, London: Macmillan. Gray, R.W. and J.S. Rutledge(1971) 'The Economicsof Commodity Futures:A Survey', Reviewof Marketing andAgricultural Economics,39, 59-108. Gray, R.W. (1959) 'The CharacteristicBias in SomeThin FuturesMarkets: Survey', Food ResearchInstitute Studies,1 (3), 298-312. Hieronymous,T.A. (1971) The Economicsof Futures Trading, Commodity ResearchBureauInc. Houthakker,H.S. (1959a) 'The Scopeand Limits of FuturesTrading', in M. Ambramovitz(ed.), A llocation of EconomicResources,California: Stanford University Press,135-59. (1959b) 'Can SpeculatorsForecastPrices?',Reviewof Economicsand Statistics,34, 143-51. lrwin, H. (1954) Evolution of Futures Trading, Madison: MIMIR. Jesse,E.V. and A.e. JohnsonJr. (1970) 'An Analysis of VegetableContracts', AmericanJournal ofAgricultural Economics,52, 545-53. Johnson,L.L. (1957) 'Price Instability, Hedgingand Trade Volume in the Coffee FuturesMarkets', Journal of Political Economy,65, 306-21. Klein, B. and K. Leffler (1981) 'Non-GovernmentalEnforcementof Contracts: The Role of Market Forcesin GuaranteeingQuality', Journal of Political Economy,89, 615-45. Kronman, A.T. and R.A. Posner(eds.)(1979) The Economicsof Contract Law, Boston: Little, Brown. Lascelles,D. (1982) 'US Stock Index Futures-A A New Hedgefor Investors', Financial Times, 23 June,p. 8. Lovell, M.C. and R.e. Vogel (1973) 'A CPI-FuturesMarket', Journal of Political Economy,81,1009-12. Macaulay,S. (1964) 'Non-contractualRelationsin Business:A PreliminaryStudy', AmericanSociologicalReview,28, 55-69. McManus, J. and K. Acheson(1979) 'The Costsof Transactingin Futures Markets', CarletonUniversity, manuscript. MacNeil, I.R. (1974) 'The Many Futuresof Contract',SouthernCalifornia Law Review,47, 691-816. Muris, T.J. (1981) 'OpportunisticBehaviorand the Law of Contracts',Minnesota Law Review,65, 521-90. Powers,M.J. (1967) 'Effects of ContractProvisionson the Successof a Futures Contract', Journal of Farm Economics,49, 833-43. Radner,R. (1970) 'Problemsin the Theory of MarketsUnder Uncertainty', AmericanEconomicReview(Papersand Proceedings),60, 454-60. Rock, C.A. (1982) 'RegulatoryControl Over the United States,Canadianand United Kingdom FuturesMarkets', BusinessLawyer, 37,613-36. Rockwell, e.S. (1967) 'Normal Backwardation,Forecastingand the Returnsto Speculators',Food ResearchInstitute Studies,7, 107-30. Sandor,R.L. (1973) 'Innovatingby an Exchange:A CaseStudy of the Developmentof the Plywood FuturesContract', Journal of Law and Economics,16, 119-36. Shavell,S. (1980) 'DamageMeasuresfor Breachof Contract',Bell Journal of Economics,11,466-90.

An InstitutionalAnalysisof FuturesContracting 41 Silber, W.L. (1981) 'Innovation, Competitionand New ContractDesign in Futures Markets', Journal of Futures Markets, 1, 117-22. Telser, L.e. (1980) 'A Theory of Self-enforcingAgreements',Journal of Business, 53,27-44. (1981a)'Why There Are OrganizedFuturesMarkets', Journal of Law and Economics,24, 1-22. (1981b) 'Margins and FuturesContracts',Journal of Futures Markets, 1, 225-54. Telser, L.G. and H.N. Higinbotham(1977) 'OrganizedFuturesMarkets: Costsand Benefits', Journal of Political Economy,85, 969-1000. Veljanovski, C.G. (1982) The New Law-and-Economics,Oxford: Centrefor Socio-Legal Studies. Wachter,M.L. and O.E. Williamson (1978) 'Obligational Markets and the Mechanicsof Inflation', Bell Journal of Economics,9,549-71. Williamson, O.E. (1979) 'TransactionCost Economics:the Governanceof ContractualRelations',Journal of Law and Economics,22, 549-71. Wilson, 1.A. (1980) 'Adaptationto Uncertaintyand Small NumbersExchange:the New EnglandFreshFish Market', Bell Journal of Economics,11,491-504. Working, H. (1953a)'FuturesTrading and Hedging', AmericanEconomicReview, 43,316-43. (1953b) 'Hedging Reconsidered',Journal of Farm Economics,35, 544-61. - (1967) 'Test of a Theory ConcerningFloor Trading on Commodity Exchanges',StanfordFood ResearchInstitute (supplement),7, 5-48.

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2

EXPERIMENTAL FUTURES MARKETS Glenn W. Harrison*

1. Introdnction This chapterstudiesin detail the behaviourof three experimental futures markets. The separateand joint effects of 'event uncertainty' and 'inside information' on the performanceof spot and futures marketsare also examined. This section discussesthe general experimentalmethodology employedhere and the relationshipof this chapterto the existing literature. Section 2 introduces the specific experimentaldesign, and Section 3 provides a series of theoretical equilibrium predictions concerning observablebehaviour in these markets. The experimentalresultsare presentedin Section4, in two stages:first there is an account of the observedperformanceof each market relative to theoretical predictions, followed by an analysis of the comparative performance of markets with certain controlled differences. Finally, Section 5 draws several general conclusions and providessuggestionsfor further research. Experimental auction markets involve recruited subjects who are induced,by meansof controlled market trading schedulesand standard incentive structures, to display real-time market behaviour. Experimentalcontrol of market conditions, the 'treatment variables', allows one to design groups of such experiments to gaugethe effects of thosevariableson observedbehaviour(e.g. the strength of equilibrium tendencies,efficiency of market outcomes and the variability of price movements). Each of the hypothesesto be studiedinvolves the specificationof well-defined, and hence replicable, sets of trading rules, informational imperfections and other institutional features. Smith (1982) and Plott (1982) provide excellent general statementsof the advantagesof an experimental methodology, several features of which are relevanthere. The first methodological point is that the experimental approachdoesprovide evidenceon 'real-world' markets.The fact that theseexperimentstypically involve small numbersof traders, 43

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ExperimentalFuturesMarkets

that they deal with homogeneouscommoditiesand that the experimentercan control the notional trading schedules,does not render these markets irrelevant. They are indeed special, but so are the institutional trappings of most organized exchanges.The main point, however, is the purposefor which such markets are conducted: to provide evidence on general theories. If a theory or economicprinciple is general, it shouldcoverspecialcases. The secondmethodologicalpoint follows from the first: if we cannot confirm or reject general theories in the context of controlled environments designed for the purpose of testing the theory, then the theory cannot be regardedas operationalin any useful respect. Moreover, it is often difficult to 'control' for all conceivablyrelevant influenceson market behaviourwith econometric methodsand actual market data; seeLeamer(1978, 1983) for a clearstatementof the methodologicalweaknesses of standard econometricpracticehere. An examplefrom the futures marketliteraturemay illustrate the significanceof this last point. Conventionalempirical tests of the hypothesis that futures markets induce 'unwarranted and undesirable'spot price fluctuations involve comparisonsof estimatesof spot price dispersionstatisticsfor time periodsassociated with, and then without, the presenceof active futures tradingin the good. The evidence for this class of tests has been noticeably mixed: see,for example,the resultsof Cox (1976) and his survey of other studiesusing this empirical approach.Aside from the frequent lack of a theoreticalmodel to specify the testsand interpret the results, the long time periods involved imply almost certain violations of the implied ceterisparibusassumption.Sincewe have the ability to specify the theoreticalmodels for our experimental markets,we know the underlying market structure.Thus the tests of the influence of futures trading on the informational efficiency of asset markets reported in Friedman, Harrison and Salmon (1983, 1984) do not involve joint hypothesesabout market structureand marketefficiency. A final methodologicalpoint relatesmore particularlyto the use of the experimentaltechniqueto analysethe role of information in futures market performance.One commondifficulty with analytic models of the informational aspectsof markets is the precise definition of 'the information set' of traders. Our experiments allow very detailed knowledgeof that set; for instance,they provide the ability to control which traders know what information.

ExperimentalFuturesMarkets 45 The relevanceof this point will be apparentin Sections3 and 4. Our experiments represent a synthesis of recent work by Forsythe, Palfrey and Plott (1982a), Friedman, Harrison and Salmon(1983) and Plott and Sunder(1982), hereafterreferredto as FPPa, FHSa and PS, respectively.! All of these studies employeda continuousdouble oral auction for multiple units of a single good (the 'asset')tradedagainstcash.They differ primarily in their treatmentof two critical elementsof assetvaluation: time and uncertainty. PS focused on uncertainty: their asset expired after a single period but had trader-specificmarginal values that dependedon an exogenous'stateof nature'.Tradetypically occurredbeforethe stateof naturewas revealed,althoughin somecasescertainagents (,insiders')had advanceinformation. They found that equilibrium prices usually revealedthe inside information after several repetitions of the market,at leastwhen that information was conclusive as to the true stateof nature. FPPafocused on time: their assetderived its value from cash dividends paid over two periods, but each trader knew his own dividend schedule with certainty. Inasmuch as traders did not know others' schedulesand thereforedid not initially know what prices would be available to them, there existed an endogenous type of uncertaintythat we may refer to as marketuncertainty,in contrastwith the exogenouseventuncertaintyof PS. FPPafound that assetprices approached'Rational Expectations'values after severalrepetitionsof the market. FHSa also focused on time: they employed a three-period design, and examined trader experience and the presenceof futures marketsas separatetreatmentvariablesin a settingwith no event uncertainty. FHSa confirmed the importance of both variables in speedingconvergencetowards more informationally efficient prices. They also found that spot prices were less volatile when futures marketsoperated.2 We discussthe precisenatureof the futures contractsin the next section. Friedman,Harrison and Salmon (1984), hereafterFHSb, conducted six experimentscombining the three-periodand futures market features of FHSa with the event uncertainty and inside information featuresof PS. The marketsexaminedin the present chapterare drawn from the three FHSb experimentswith futures markets.3 FHSa and FHSb study the role of futures markets by comparingexperimentsthat have them with experimentsthat do

46

ExperimentalFuturesMarkets

not; that is, by isolating the presenceof futures marketsas a treatment variable. FHSb concludethat: (i) assetmarketoutcomestend to evolve towards strong-forminformationally efficient equilibria, whether or not futures markets and/or event uncertainty are present;(ii) the presenceof futures marketsclearly stabilizesspot prices; (iii) the presenceof futures marketstendsto speedthe evolution of assetmarketsto more efficient equilibria when there is event uncertainty;and (iv) futures marketspromotethe 'leakage' of inside information, with strong-formpredictionsoutperforming semi-strong-formpredictions. The present study is not concernedwith the role of futures markets in the above sense. Rather, it is concernedwith the detailed performanceof assetmarketswith futures markets,relative to theoreticalequilibrium predictions,and with the effects of event uncertainty and inside information on spot -and futures market performance.The results presentedhere, therefore,complementthe analysisof theseexperimentscontainedin FHSb. 2. Experimental Design4

The participantsin the experiments,referred to as traders, were recruited primarily from MBA classesat the UCLA Graduate Schoolof Management- as likely a habitatfor homoeconomusas we could think of. After distributing and reviewing the instruction sheets(available on request), double oral auction markets were opened.Any traderwas free to announcebid and offer prices and acceptthe bids or offers of others5 providing he or shedid not violate any budget constraint,as discussedbelow. Transactedprices were publicly recorded.The assetstradedwere called certificates; they yielded returns, called dividends, to traders who possessed them at the end of eachtrading period. Each experimentconsistedof a seriesof 'Market Years', which can be thought of as Hicksian Weeks. Within each Market Year there were three trading periods, referred to as PeriodsA, Band C. Trading PeriodsA and B lastedfor five minutesand eachtrader could buy or sell one certificateat a time. Lot sales,short sales(i.e. short spot positionsand 'naked'short futures positions)and negative cash positions were prohibited.6 At the beginning of each Market Year eachtraderwas endowedwith two certificatesand an interest-freeloan of 20 dollars. The loans were sufficiently large

ExperimentalFuturesMarkets 47 that the liquidity constraintwas neveran impedimentto trade. Incentivesfor exchangeamong traderswere provided by varying the per certificatedividendsacrossindividuals as well as across periods.There were three trader types, with individuals randomly assignedto each group; Table 2.1 provides details of the parameterizationsfor eachexperiment.The underlying period-specific certificate returns were identical acrossMarket Years - identical in the aggregateand for each individual.7 Thus the markets were repetitively stationaryfrom year to year. Note that traders were not informed of this stationarity;they had to learn aboutit in 'real time'. Each individual was carefully monitored so that his/her private dividend profile was not observedby any other trader. Possibilities for explicit collusion were effectively nil. To motivate the experimental set-up one can think of the tradersas grain merchantstrading in warehousecertificateswhich have a par value of zero but provide eachtraderwith a finite time profile of convenienceyields. Of course, in these experiments tradersactually receiveda cash'dividend' for eachcertificate held at the end of eachtrading period, and the certificatesexpired after the Market Year ended. In Experiment1, trading in PeriodsA and B consistedeither of an immediateexchangeof cashfor certificatesat acceptedbid or offer prices (i.e. spot transactions)or a futures transaction.The futures contractconsistedof the delivery of a certificate in Period C. Futurescontractsas well as spot contractscould be written in both Period A and Period B. In PeriodsA and B dividends were paid as usual for each (spot) certificate held at the end of that period. No transactionswere allowed in Period C, but deliveries previously contractedfor were performed. An individual with a net long (short) futures position was required to take (make) delivery of the certificates, and then Period C dividends distributed. A natural interpretation of Period C is that it correspondsto the day after the last trading day in the delivery month of a futures contract. Note that an agenthad ample opportunity to offset futures positions during Periods A and B. However, becauseof the restriction on short sales,agents'short futures positions were limited to the quantity of inventoried spot certificatesat any point in time. For a given net short position an agent's spot saleswere also constrained. In all experiments traders were given a small trading commissionof 1 cent per transaction.Suchcommissionsare a standard

Yes

Yes

2

3

Yes

No

No

Insiders?

1,4* ,9 3,5,7* 2*,6,8

1,6,9 3,5,8 2,4,7

I 11 III I 11 III

5,7,9 1,3,6 2,4,8

ID#

I 11 III

Type

Agents

0.75 0.40 0.15

X

0.20 0.45 0.30

0.35 0.60 0.60

0.60 0.60 0.60

Y

Period B

0.20 0.80 0.80 0.60 0.60 0.30

0.75 0.10

Y

0.45 0.30 0.35 0.45 0.30 0.35 0.15 0.50 0.30 0.20 0.40 0.40 0.45 0.45 0.30 0.35

0.25 0.20 0.50 0.30

X

Period A

Dividend Profile

1.00 0.30 0.70 0.25 0.30 0.70

0.35 0.45 0.30

0.10 0.45 0.80

Y

0.50 0.30 1.00

X

Period C

(ii) In Experiment 3 an asterisk beside an Agent ID# denotes an insider.

(i) In Year 5 of Experiment 1 a random reassignment of agents to trader type occurred. Trader type I consisted of Agents 1, 3 and 5; type 11 of Agents 4, 6 and 8; and type III of Agents 2, 7 and 9. The parameters shown here pertain to all other market years.

Yes

Yes

2

Notes:

No

Yes

Experiment

Event Uncertainty?

Experienced Traders?

Table 2.1: Induced Experimental Market Parameters

ExperimentalFuturesMarkets 49 feature of most experimentalmarket studies; the usual rationale for their inclusion is to overcome subjective transaction costs which might be especiallyrelevantwhen transactedpricesare very closeto a market-clearingprice. At the end of eachexperimentwe paid our tradersin cashfor all profits accruedfrom dividendsand trading. The distinguishing feature of Experiments2 and 3 compared with Experiment 1 is that in the former each trader's dividend profile is specific to a 'stateof nature'.Two different states,called X and Y, were possible. At the beginning of the experimentall traderswere told that we would flip a fair coin at the end of each Period A trading round: if the coin came up headsthen state X occurs and if the coin showed tails then state Y occurs for that Market Year. At the beginning of Period A in Experiment2 all tradershad commonprior beliefs about the ultimate realizationof statesX or Y, basedon public knowledgethat each state had a 50 per cent probability of occurring for each Market Year. Trading during Period A occurredunder this well-defined event uncertainty.The uncertaintywas then resolved as advertised,8so Period B representeda posterior trading round in which agentshad the opportunity to revise their portfolio of certificate holdings under conditionsof no eventuncertainty,as in Experiment1. The futures marketin Experiments2 and 3 operatedin the samemanneras in Experiment 1, except that, in Period A, trading for Period C futures certificates was subject to the same event uncertaintyas spot trading. Some care was taken in selecting the dividend profiles in Experiments2 and 3. Note, however,that one statealways had a higher pay-out distribution over a completeMarket Year (in both experimentsthis statewas Y). Thus the marketfaced a situationof social risk. One can think of our events as a 'good crop' versus 'bad crop' alternative. The distinguishing feature of Experiment 3 compared with Experiment2 is that, in the former, one traderof eachtradertype was randomly selected to receive conclusive information about which state would occur before Period A trading took place for each Market Year.9 This was accomplishedby the experimenter leaving the room beforethe start of the experiment,flipping a coin and then writing down the resultson threeout of nine cards.Cards which read either 'No Information' or 'State - ' were put into

50

ExperimentalFuturesMarkets

envelopesand passedout to the traders. The six non-insiders thereforedid not have prior knowledge about the identity of the insiders. The experimentthen proceededin the samemanneras Experiment2 in termsof the resolutionof the eventuncertaintyat the end of PeriodA trading. 3. Equilibrium Conceptsand Predictions Following FHSa and FHSb, the various equilibrium concepts applied to our experimentsare defined in termsof the information set that traders are assumedto have available and to act upon. There are two fundamental'pieces'of information of relevancein our experiments:the market structureof dividendsconditional on eachstateof nature,and the actual stateof nature.By design,the latter piece of information is public knowledgein all three experimentsin Period B and (trivially) in the PeriodA of Experimentl. It is also shown, by design,to insidersin Period A in Experiment 3. At all times and/or for all other traders,the state of nature is information that must be 'discovered'during trading. The former piece of information, the market valuation of the asset in each period, must be 'discovered'by all traders. The four equilibrium conceptsdevelopedby FHSb as operational benchmarksto measureinformationalefficiency are:

(1) ExpectedPrivate Information (EPI) equilibrium. Prices and allocations reflect only the private structure of expected dividends; neither piece of information is reflected in market behaviour. (2) Private Information (PI) equilibrium. Prices and allocationsreflect the private structureof dividendsrelevantto the actualstateof nature;marketbehaviouronly reflectsthe second piece of information. (3) Uninformed Rational Expectations (URE) equilibrium. Prices and allocations reflect the expected market dividend structure; market behaviour reflects only the first piece of information. (4) Perfect Foresight (PF) equilibrium. Prices and allocations reflect the marketdividend structurerelevantto the actualstate of nature; both pieces of information are reflected in market behaviour.

ExperimentalFuturesMarkets 51 Clearly the EPI and URE equilibria do not apply to Experiment 1. Note also that we define the 'expecteddividend structure'as the 'actualdividend structure'for the actual stateof naturerevealedin Period B in Experiments2 and 3. Tables 2.2 and 2.3 list the various equilibrium predictions for prices and allocations. In Table 2.2 we employ the following notation: d~(z) denotesthe per-certificatedividend of trader type i (i = 1,2,3 referring to trader types I, 11 and III respectively) in Period k (k = 1,2,3 referring to PeriodsA, Band C respectively) when state of nature z obtains (z = X or Y; we drop the index z when discussingExperiment 1), n( z) denotesthe probability of state of nature z, and Z = (X,Y) denotesthe set of possiblestates of nature. The term 'leakage'is used to refer to the dissemination of inside information (concerningthe true state of nature) to the market. In termsof our experimentaldesign,n(z) == 0.5 for eachz and each trader in Experiment 2 and for the outsidersin Experiment 3. Referring back to Table 2.1, we seefor examplethat dr(z) = df(X) = $0.10 in Experiment 2; in words, the per-certificate dividend of trader type I in Period B is $0.10 if the stateof nature is X. The rationale behind the various equilibrium conceptscan be most easily appreciated by working through several specific numerical examples.ConsiderExperiment 1, in which there is no event uncertainty to complicate matters. Consider further the market valuation of each Period C futures certificate given the private dividends of each trader type in Table 2.1. Ignoring resale possibilities, and assumingnon-eo-operativebidding betweenthe three agentsof each trader type, it is clear that trader type III will end up paying $0.80 for each Period C futures certificate. If the three type III agents coiluded they could hold prices down to $0.30, just enough to induce trader types I and 11 to sell their supply of certificates (recall the 1 cent commission). We shall assume throughout an absenceof collusion. Thus $0.80 is the reservationprice for type III traderswith respectto futures certificates: they will profit by any purchasesat a lower price and any salesat a higher price. Similarly, $0.45 is the reservationprice for type 11 traders and $0.10 for type I traders. Thus we obtain the predictionsin Tables 2.2 and 2.3, noting that Period C is the final period of eachyear and that PI and PF predictionscoincide. Now considerthe market valuation of Period B spotcertificates in Experiment 1. We shall assumethat the (PI = PF) equilibrium

3

2

2

Experiment

i - max dl- $0.80 i

p(CiPI) 2

i

k-1

+ maxI I

I ZEZ

n(z)dr(z)] - $1.85

Stronger Efficiency

+ p(BIPF,z)l] ~

$2.30

: p(CiPI,z) - $0.45(X) or $0.70(V)

: p(CiEPI) - $0.50

No Leakage

: p(CiPF,z) - $0.45(X) or $0.70(V) : p(CiURE) - $0.575

With Leakage No Leakage

- $0.85(X) or $1.30(V)

p(BIPF,z)

- $0.75(X) or $1.15(V)

p(BIPI,z)

With Leakage

$1.30(X) or $1.80(V) No Leakage

=

: p(AIPF,z)

: p(AIURE) - $1.45

With Leakage

: p(AIPI,z) - $1.15(X) or $1.55(V)

: p(AIEPI) - $1.225

- max d~z) - $1.00 (X or V) i

ZEZ

- max dr(z) + p(CiPF,z) - $1.80 (X or V) i -I rt(z)p(CiPF,z) - $1.00

- maxI I n(z)[di(z) ii ZEZ

I max dr - $2.00 k-1 i 3 max dr- $1.25 -I k-2 i - max dl- $0.80 i

3

p(CiPF,z)

p(CiURE)

p(BIPF,z)

p(AIURE)

p(CiPF)

p(BIPF)

p(AIPF)

No Leakage

3 - max I dr(z) - $1.60 (X or V) i k-2 - maxI I - $0.85 n(z)d~z)] i ZEZ - max d~z) - $1.00 (X or V) i

- p(CiEPI)

+ max di- $1.25

$1.75

With Leakage

p(CiPI,z)

p(CiEPI)

p(BIPI,z)

p(AIEPI)

- p(CiPI)

p(BIPI)

i

- p(CiPI)

p(AIPI)

+ max (di + dn -

Weaker Efficiency

Table 2.2: Equilibrium Price Predictions

EP' P'

EP' P'

3

P'

Cancept

2

2

Experiment

"'

'ar "'

"' ar' 11 ar "'

"' ar , 11 ar "'

"'

"'ar'

"'

"'

X arY

Cancept

PF

PF

URE

PF

URE 'ar 11

"' ar'

X arY

A

"' or 11

11 ar 11

X ar Y X

B

X ar Y X ar Y X

Stranger Efficiency C

B

A

Weaker Efficiency

Table 2.3: Equilibrium Allocation Predictions

C

11 or "'

"' ar I

"'

X arY

54

ExperimentalFuturesMarkets

price of Period C futures certificateshas beenestablishedat $0.80 in Period A and Period B trading. Thus all traders know the marketvaluation of a Period C certificate in Period A and Period B, and can incorporatethat valuation in the computationof their Period B reservationprices.1O Again assumingnon-co-operative bidding behaviourbetweenagentsof eachtradertype, thesereservation prices are $1.00 (= $0.20 + $0.80), $1.25 (= $0.45 + $0.80) and $1.10 (= $0.30 + $0.80) for typesI,ll and III respectively. We thereforepredict that Period B certificateswill be held by type 11 agentsand that they will pay $1.25 for each one they buy. A similar logic implies Period A spot certificate Private Information reservationprices of $1.75 (= $0.75 + $1.00), $1.65 (= $0.40 + $1.25) and $1.25 (= $0.15 + $1.10) for types I, 11 and Ill, respectively.Thus we predict a PI equilibrium price of $1.75 basedsolely on traders'private information about Period A and B dividends and the public knowledgeof the Period C futures certificate marketvalue. Note that we recursivelyemploy the Period B reservation prices for each trader type when computing the Period A reservationprices. Note, also, the role of a Period C futures market operating during Period A and Period B in the computationof the PeriodB reservationprices. In the absenceof a futures market, traders would have to observe spot Period C market pricesover severalMarket Yearsin order to feel confident that the marketvaluationof a Period C certificateis $0.80. After severalyearstraderswill realize that PeriodB spot certificates have a market valuation of $1.25, and will adopt Perfect Foresight reservation prices of $2.00 ($0.75 + $1.25), $1.65 ($0.40 + $1.25) and $1.40 ($0.15 + $1.25), respectively.Thus we predict a PF equilibrium price of $2.00 for Period A spot certificates. Note that the PI and PF allocation predictions in Experiment 1 coincide; FHSb provide a hypotheticalnumericalexample in which both price and allocation predictionsdiffer. Essentiallythe samelogic appliesin Experiments2 and 3 except for the complication of event uncertaintyand inside information. The PI and PF equilibrium conceptsare exactly identical, and assumethat the actual stateof natureis known (either becauseit is publicly revealedbeforePeriodB trading or is 'leaked'in PeriodA trading by insiders).The EPI (URE) equilibrium conceptsassume that traders know the conditional PI (PF) equilibria and have commonprior probabilitiesover the two statesof nature.

ExperimentalFuturesMarkets 55 FHSa and FHSb provide a further discussionof these equilibrium concepts. 4. ExperimentalResults There are two aspectsto our reporting of results. The first is a comparisonof the observedbehaviourof each individual market with the theoreticalpredictionspresentedearlier. The secondis a comparisonof two or more markets that differ with respect to some 'treatment variable' of interest. These two aspects are related,since we are typically concernedwith the effect of a treatment variable on market performancerelative to sometheoretical benchmark(e.g. does a market with event uncertainty converge more slowly to a perfectforesight equilibrium than a marketwithout this feature?).Section4.1 examinesthe observedbehaviourof eachmarketrelative to our theoreticalpredictions,while in Section 4.2 some conclusionsabout the effects of even uncertainty and inside information on marketperformanceare drawn.

4.1 Individual Market Behaviour Figures2.1 through 2.3 chart the time seriesof transactedpricesin each market experiment. The various theoretical equilibria for eachmarketare also identified, and summarystatisticsof observed prices presented.An 'X' refers to spot prices and '0' to futures prices. Table 2.4 lists the observedallocationsof spot and futures certificatesat the end of eachperiod in eachexperiment.Table 2.5 lists the ratios of (net) sold futures and 'non-bought'futures to spot holdings. These ratios may be viewed as a measureof the degree of hedging by those traders who sell futures and those traderswho do not have boughtfutures positions,respectively. In the next three subsectionswe provide a detailed market commentaryfor eachexperiment,relating the observedbehaviour to our theoreticalequilibrium predictions.It is convenientto refer to PeriodsA, Band C by the notation PA, PB and PC, respectively. Similarly, we refer to Years 1, 2,3,4 and 5 as Yl, Y2, Y3, Y4 and Y5, respectively. All other abbreviationsare as defined previously(viz. PI, EPI, URE and PF). 4.1.1 Experiment1. Period C (Futures): In Yl futures prices are alreadyabovethe private PC valuationsof tradertypesI and 11

0.09

0.01 0.01

0.001

0.75 0.72 0.76

A

0.01 0.01

I

AB

1.49 1.07 1.67 0.14 0.10 0.06

AB

FHS4 Market Uncertalnity Experienced Subjects Spot and Futures TradIng

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

$2.10

PRICES

YEAR 1

I

BA

0.78 0.01

1.17 0.02

YEAR 2

I

0.75 0.001

1.85 1.24 0.08

AB

0.79 0.004

0.79 0.01 0.01

B

YEAR3

Figure 2.1: Observed Price Behaviour - Experiment 1

I

0.Q1

0.78

1.98 1.25 0.79

A B

0.80 0.003

0.001

0.79

YEAR4

0.Q1

0.80

2.02 0.Q3

A

YEAR5

0.81 0.01

1.23 0.02

B

FUTURES MEAN.STANDARD DEVIATION

SPOT MEAN. STANDARD DEVIATION

P(C)

P(B/PI)

P(B/PF)

P(A/PI)

P(A/PF)

30

10

~HS6 1.00

I

0985 0.005

0994 0013 0.994 0005

1003 0005

0.990 0008

0.999 0.003

0.940 0001

0986 0013

B

0.843 0019

:

2049 1.743 0007 0007 0007 0007

A

1726 0.005

B

2032 0016

A

1706 0010

B

1.970 0.015

A

YEAR 5 (X)

1660 0.017

B

YEAR 4 (X)

1.866 0.017

A

YEAR3 (Y)

1618 0021

A

YEAR 2 (Y)

1.710 0.089

A

Spot and Futures Trading

Event Uncerlalnlty Experienced Subjects

1.00 ~

1.00

1.00

1

1.20

1

1.40

1.50

1.60

1.70

180

1.90

2.00

210

2.20

PRICES $230

YEAR 1 (X)

Figure 2.2: Observed Price Behaviour - Experiment 2

FUTURES MEAf'fsTANDARD DEVIATION

MEAN STANDARD DEVIA'TION

S~

P(C/EPI)

P(C/URE) = P(C/PI) =P(C/PF)

P(B/PI)

P(A/EPI)

--I P(B/PF)

P(A/URE)

0.710 0.089

0.404 0.031

0.500 0.0

B

1.248 0.075

A

FHS9 InSider Uncertalnlly Experienced Subjects Spot and Futures Trading

1.20

1.20

1.20

1.20

0.70 1.20

.

080~ 1.20

0.90

1.00

1.20

1.20

1.30

:::

1.60

1.70

0.075

PRICES

YEAR 1 (X)

0.740 0.026 0.439 0.003

0439 0.007 0700 00

0.687 0.028

0.678 0.013

0.631 0.026

B

1.155 0.041

A

1.280

B

1.608 0.047

A

YEAR 4 (X)

1.223 0.019

B

YEAR3 (Y)

Experiment 3

1.498 0.057

A

YEAR2(Y)

Figure 2.3: Observed Price Behaviour -

0.688 0.005

1.686 0.030

AB

= P(C/PF,Y) P(B/PF,X) P(C/EPI) P(C/PI,X) = P(C/PF,X)

P(C/URE) X) P(B/PF,X) P(C/PI',Y) P(B/PF,X)

P(B/PF,X)

P(A/PI,X) = P(B/PI,Y)

P(A/PF,X) =P(B/PF,Y) P(A/EPI)

P(A/URE)

P(A/PI,Y)

P(A/PF,Y)

SPOT MEAN.STANDARD DEVIATION FUTURES 0.694 MEAN. STANDARD 0.005 DEVIATION

AB

YEAR 5 (Y)

X

X

Y Y

1 2 3 4 5

1

2 3 4 5

2

3

411 5 5 0 4

11

657783 10 0 0 18 13 2 18 0

6 5 7 3 14 11 525 9 0 10 0 0 8

13 13 13 18 14

1

14 1 0 16 0

14 8 0

3

0

10

9 8

14 14 2 7 1

1 14 0 7 2

1

14 14

00 0 0 0

1

III

Spot Certificates

18

-2 0 0 -5 0 14 00 00 01 03

14 17 18

4 6 13 2 12

6 -2 -2 0 0

-5 0 3 43 0 -2 -6 -13 3 -15

3 5 5 7 13

-3 -5 -5 0 -4

00 00 0 -7

-9

III

11

-7 -1 0 -16 0

70 -15 -16 17 18

-12 -12 -16 -10 -17

-13 -18 -18 -11 -15

-1 0 0 -2 0 -1 13 16 -1 0

11

1

Futures Certificate Period B Period A

1

-1 2 0 102 -1 0 -7 0 0 0 0 0 00

4 0 00 0 0

III

13 12 16 11 17

13 18 18 11 16

11

Period B

Notes: Positive futures certificate allocations imply a net bought position, and negative allocations a net sold position.

Y

X

X

Y Y

X

1 2 3 4 5

1

State

Year

Experiment

Period A

Table 2.4: Observed Spot and Futures Certificate Allocations

0 16 16 -1 18

13 -1 0 11 17

14 18 18 13 15

III

2 3 4 5

1

2 3 4 5

1

2 3 4 5

1

X Y Y X Y

X Y Y X X

Year State

II

0.33 — — 0.38 —

0.17 — 0.11 0.70 —

— — -

III

0.40 0.60 0.72 0.83

— — — -

1.00 — 1.00 0.22 — —

— 0.75 — 1.00 1.00 0.39 — 0.64 1.00

I

Period A

0.36 0.60 0.72 0.38 0.83

0.55 1.00 0.17 0.70 -

0.75 1.00 1.00 0.39 0.72

Total 1.00 1.00 1.00 1.00 0.94

II -

III

1.00 1.00 0.88 0.89 1.00 1.00 1.00 -

0.33 0.92 — 1.00 1.00 1.00 0.14 0.91 1.00 -

1.00 0.29 -

I

Period B

Ratio of Sold Futures to Spot Holdings

1.00 0.89 0.89 1.00 1.00

0.81 1.00 1.00 0.61 1.00

1.00 1.00 1.00 0.72 0.94

Total

0.33 0.38 -

0.17 0.0 0.11 0.70 0.0

0.0 0.0 0.0 0.39 0.64

I — — —

III

0.40 0.60 0.72 — 0.83

— —

1.00 — — 1.00 0.22 — 0.0

0.75 1.00 1.00 1.00

II

Period A

0.36 0.60 0.72 0.38 0.83

0.55 0.15 0.17 0.70 0.0

0.18 0.28 0.28 0.39 0.72

Total

II

1.00 1.00 0.88 0.89 1.00 — — 1.00

0.33 0.92 — 1.00 1.00 0.14 0.91 0.0 1.00

0.0 — 1.00 —

— 1.00 — — —

— — — -

III

Period B 1.00 1.00 — 1.00 1.00 0.29 1.00 0.0 0.94

I

0.70 0.89 0.89 1.00 1.00

0.81 1.00 1.00 0.61 0.94

1.00 1.00 1.00 0.72 0.83

Total

Ratio of Non-Bought Futures to Spot Holdings

Notes: A dash indicates that the trader type did not have a net sold or net 'non-bought' futures position at the end of the period. Clearly that trader type may none the less have had a spot position; see Table 2.4 for a complete listing of spot and futures allocations.

3

2

1

Experiment

T a b l e 2.5: H e d g i n g Ratios

ExperimentalFuturesMarkets 61

($0.10 and $0.45 respectively).By the end of PB in Y2 they are neartheir equilibrium value, and from PB in Y3 on they provide a persistentlyclear signal. Although tradesin futures generallyfollow spot trading in each period in Y3 and Y 4, there were numerousunacceptedbids and offers on futures at the time that spot contractswere being made. Thesebids and offers often contain useful information, despitenot resulting in trades. We shall discussthe allocationof futures contractsat the end of PA and PB when we discussthe spot certificate allocationsbelow. It is useful, however,to examinethe eventualPC holdings of spot certificates(theseare just the deliveredfutures contractspending at the end of PB). In Y1, Y2 and Y3 there were no misallocations in these holdings. In Y4 and Y5 some 13/18 and 15/18 were correctly allocatedrelative to both PI and PF concepts,which had identical predictions in this case. The misallocation in Y 4 is discussedbelow. Period B (Spot): Despitethe futures pricesobservedin PA and during PB, in Y1 we seethat PB spot pricesarejust below their PI equilibrium value. Significant learning apparentlyoccurs in Y2, and PB pricesare at their PF equilibrium value in Y3 and Y 4. In Y5 of this experiment we randomly reassignedagents to different dividend profiles without altering the aggregatemarket parameters.The issue here is the ability of agentsto distinguish market signals from their private signal (viz. their own dividend profile) - the essenceof our competing equilibrium notions. Despite a 'technical reaction' of sorts, especially in the P A spot market, the resultsessentiallyrepeatthe behaviourin Y 4. The fact that we observeconvergenceto the PF equilibrium price in Y 4 indeedtells us that agentshad madethe distinction betweenthese two signalswhen forming their trading strategies;our resultsin Y5 confirm this conclusion. The allocationsof PB spot certificatesin eachyear were 13/18, 18/18, 18/18, 11/18 and 16/18 relative to the PF prediction. All but one of the misallocationsin Yl are explainedby the alternative PI prediction. The misallocation in Y 4 is attributable entirely to one type I agent(number5). Her spot holdings at the end of PA in Y 4 were seven certificates, and she had mechanicallyhedged by selling sevenfutures: impeccablePF behaviourso far. (In Y3 her only P A

62

ExperimentalFuturesMarkets

transactionwas the purchaseof one spot certificate, and she had sold all three spot certificatesin PB as implied by PF behaviour.) From the sequenceof unacceptedbids and offers it appearsthat she was determinedto buy in her futures position in PB before selling off her spot holdings; recall that we did not allow net short positions at any stageof trading during any period, and that she had fully hedged in PA. There was a marked pattern in the sequenceof trading in this experimentonce prices were near to their PF values. The period would open with one or two errant (spot and futures) price signals away from the establishedequilibrium value, thesebids or offers would go unaccepted(and were sometimesgreeted with outward signs of amusementby other traders),and trading in spot and then futureswould settledown at the previously establishedprices. Virtually all traders chose to establishtheir spot position and then enter the futures market.11 Given this observedpatternin Y4, agentnumber5 was 'locked in' to her spot position by an inability to buy in her futures position until the latter part of the period. Shewas able to buy five futures during PB, but was not able to sell any spot. However, she made no seriouseffort to extricate herselffrom her self-imposedcorner by offering to buy futures for more than $0.80 and thenoffering to sell spot for lessthan $1.25 (the establishedPF prices). From Table 2.5 we see that, with the notable exceptionof the episode in Y 4 just described,virtually all of the 'non-bought' futures positions in PB representedroutine hedges.This is not to say that all spot positions were hedgedin this manner,or indeed that they were hedgedat all (e.g. considerthe holdingsof type I in Yl, Y2 and Y3 shown in Table 2.4). However, Table 2.5 does indicatethe extentof the hedgetakenby thosetradersholding spot certificateswho did not buy futures. Period A (Spot): Given the futures prices available, PA spot prices as early as Yl are well above their PI equilibrium value. Convergenceto the PF value is nearly completeby the closeof Y3 trading, and is complete by Y4. The 'technical reaction' in Y5, mentionedabove,involved one traderaggressivelybidding for spot certificatesin PA at $2.05,some5 centshigherthan marketsignals would justify (given risk neutrality). Assessingher situation at the close of P A trading, the market 'allowed' her to lighten her spot holdingsin PB at a discount(viz. some5 centsbelow the PF price in PB). This is the sameagent(number5), incidentally, who tried

ExperimentalFuturesMarkets 63

to 'stonewall'the market in PB in Y 4. Allocations in eachyear were 13/18, 13118, 13/18, 18/18 and 14/18 relative to the PF prediction. The alternativePI prediction accountsfor 4/S, S/S, % and 4/4 of the implied deviationsin each year. The PA hedging ratio for non-boughtfutures certificates to spot holdings in Table 2.S increasessteadily throughout the experiment.12 4.1.2 Experiment 2. This is the first market with exogenous event uncertainty. Equilibrium prices in PB and PC were independent of the state of nature, but P A equilibrium prices were contingent.The futures certificateallocation predictionswere contingent during PB trading, and PB spot allocation predictionswere also contingent for the PI eqUilibrium concept. The random realizationsof the stateof natureprovideda changeof statein the first two years. Period C (Futures): With uncertainty about the true state of nature in PA, futures prices in Y1 were at the EPI prediction. In Y2 there were several unacceptedbids at that value, and finally severaltradescloser to the URE prediction. From Y3 on, the P A futures priceswere at the URE value. Therewere no futurestrades in PA of YS, but there was no informationalneedfor any trades. That is, the non-acceptanceof several bids just below the equilibrium value was a sufficient signal that the PC market valuation had not changed.After the first three tradesin PB in Y1, virtually all PB futures pricesin eachyear were at the predictedequilibrium level. Spot allocationsresulting in PC from PB futures positionswere lS/18, 11118 and 17/18 for the three X years (Y1, Y4 and YS) relative to the equilibrium prediction, and 18/18 for each of the two Y years (Y2 and Y3). The misallocation in Y4 is discussed later. Period B (Spot): There was a steadybut slow movementof PB spot pricesfrom the PI to the PF equilibrium prediction.This sluggish convergenceoccurred despite clear futures prices in PB as early as Yl and the absenceof any eventuncertaintyin PB. Allocations showeda slow improvementto the PF prediction; they were 13/18, 11/18 and 17/18 in the X years,and 12/18 and 16/18 for the Y years.Virtually all of the misallocationsin the Y

64

ExperimentalFuturesMarkets

years are explained by the alternative PI prediction. The severe misallocation in Y 4 was due to one type I agent who failed to unload sevencertificates,losing 60 cents on eachone he failed to sell given prevailing prices(seebelow for further discussion).From Table 2.5 we note a clear tendencyin PB towardsthe use of routine hedges. Period A (Spot): Priceswere below the EPI value in Y1, at the EPI value in Y2, and very slowly moving to the URE value in later years. The PC futures price signal was quite precisefrom Y3 on, althoughthe PB spot signalswere not as clear. There were severe misallocations relative to the URE prediction, which was only correct in 6/18, 11/18,9/18,10/18 and 8/18 in each successiveyear. The alternative EPI prediction accountsfor 5/12 and 5/7 of the misallocationsin Y1 and Y2, respectively,but for none of the misallocationsin the last three years. An explanationof these deviations as the result of event uncertaintyis possible. One implication of the presenceof eventuncertaintyis the need to form some estimateof PC and PB prices for each state before forming reservationpricesfor P A trading. In the absenceof event uncertaintysuch estimatescould be possibleas early as Y2 (even with a PC futures marketin Y1, tradersneedto seePB spot prices for P A-valuation purposes).In the presenceof event uncertainty, such estimatesare only possibleafter tradershad observedan X and a Y year, which could havebeenmuch later in the experiment if at all.13 The necessarily greater amount of initial learning requiredto form URE reservationprices in P A (at leasttwo years, comparedto one year) in the presenceof event uncertaintyopened up numerousprofitable disequilibrium trading strategiesfor certain tradersthat would be non-profitableat equilibrium prices. An excellentexampleof the availability of such disequilibrium strategies is providedin this experimentand accountsfor the severemisallocations,relative to our equilibrium predictions,that were noted earlier. The main culprit in the misallocationsin Y3, Y 4 and Y5 was a particular type III agentwho went on a buying spreefor P A spot (contrary to EPI and URE predictions). In Y1 and Y2 PB spot prices averaged$1.618 and $1.660, respectively;even if a trader had not realized that PB market valuations were stateindependent,the expectedPB price in Y3 would have been 0.5

ExperimentalFuturesMarkets 65 (1.618) + 0.5 (1.660) = $1.639. Given this estimatefor PB prices and assumingrisk neutrality on our type III agent's behalf, his reservationprice in PA would have beencomposedof 0.5 (0.5) + 0.5 (0.3) = $0.40 expectedPA dividend plus a sale to market in PB for S1.639, giving a total reservationprice in P A of $2.039. In fact he purchasedat around $1.97, sorrowfully learned that this was a Y year and collected his 30 cents dividend; he was then greetedwith a PB spot market preparedto pay $1.706 insteadof the $1.639 he had bargainedfor! Thus, despiteY3 being a 'bad year' for him, this trader was able to survive with a few cents profit. The same strategy in Y4 and Y5, with some adjustment upwards in his PB estimateand hence his risk-neutral P A reservation price, earnedhim handsomeprofits (given that they were 'good years' for him in terms of PA dividends). Note that he was only able to profit from such a trading strategy because P A spot prices were so 'low'. Thus the misallocationsin questionwere not at all due to this type III agent'sirrationality or myopia, but market inefficiency in PA pricing. It was, in effect, the type I agentsthat were to 'blame',for not buying actively enoughin PA. 14 Relative to hedgingbehaviourin PB, we note from Table 2.5 a marked decline in the ratio of non-boughtfutures certificatesto spot holdings in PA. In Y5, the third X year experienced,there was in fact no use of the futures market in P A for hedging purposes.

4.1.3 Experiment3. This experimentintroducesinsidersinto an event uncertaintyenvironment.Parameterswere chosensuch that PA, PB andPC equilibrium priceswere contingent.In Experiment 2 PB and PC equilibrium priceswere not contingent,althoughthe allocationpredictionswere. Period C (Futures): Trading in PA of Y1 was at the EPI value. Surprisingly, however, it was the type III insider who bought in PA; his type is predicted to buy by the EPI rationale, but the insider knew that this was an X year. Perhapsrealizing his error, he sold futures aggressivelyearly in PB at low prices. The futures price eventuallyconvergedto the equilibrium value in PB. A changein stateoccurredin Y2. In P A futures prices opened at the URE value, with the URE-predictedtype III buying (only 2/6 to the insider) and type 11 selling (3/6 from the insider).

66

ExperimentalFuturesMarkets

Futuresprices then convergedto the equilibrium PF and PI value for a Y year, possibly receiving a signal as to the true state of nature from PA spot prices (discussedfurther below). Type III bought (6/12 by the insider), as predictedby the PF and PI equilibria. Another Y realizationoccurredin Y3 and P Afutures prices openedat the URE value. The type III outsiderwas buying from the type 11 insider at these prices. Consistent with leakage of insider information with thesetrades,futures prices in P A rapidly convergedon their PF and PI equilibrium value for a Y year. A fascinatingthing happenedin Y 4: futures priceswere at their PF and PI equilibrium value and a particulartype I outsiderbegan to mimic the trading stragegyof the type I insider. The insider sold two futures in PA, and the outsidersold three; the insider sold six futures in PB, and his 'shadow'sold five. This mimicry is also evident in the spot transactions of these two traders (discussed below). In Y5 there was a return to state of nature Y. Following some intraperiod leakageof insider information in P A spottrading there was heavy futures trading at the PF and PI equilibrium prices. Futuresprices in PB remainedat this equilibrium. Period B (Spot): Pricesopenedat a low level in Y1, generallyat the PI value. All of the buyerswere insiders and all of the sellers were outsiders.In PB spot priceswere midway betweenthe PI and PF equilibria; recall that initial PB futuresprice signalsunderstated the true marketvalue of a certificatein Pc. In Y3 an excellentfutures price signal was available but there was only one spot trade in PB. This is easily explained:type II is predicted by PF equilibrium to hold spot certificates in P A and PB, and by the end of PAin Y3 indeed held all 18 spot certificates.IS Thus there was simply no needfor any spot trade in PB. The sameresult is observedin Y 5, anotherY year. Y4 is an X year, with excellentfutures price signals.Recall that a certain outsider had identified the insider of 'his' type; this accounts for their parallel spot purchasesin PB. Despite this partial leakage of insider information to one outsider, PB spot priceswere kept quite low at their PI equilibrium value. Spot allocationsin the Y yearsY1, Y2 and Y3 were consistent PF 17/18, 18/18 and 18/18, respectively. with the predict~on: The spot allocationsin the X years Y 1 and Y 4 are severelymisallocatedrelative to the PF prediction,with a mere3/18 and 1/18

ExperimentalFuturesMarkets 67 being correctly predicted. Moreover,only 8/15 and 1/ 17 of these deviations are explained by the alternative PI prediction. The explanationis the low PB spot prices(relative to the PF value) and the ability to lock-in profits with futures trades. Given the prevailing low PB spot prices and the existenceofa liquid futures contract, the erstwhile type I 'culprits' did not lose on their spot purchases.This explanationaccountsfor 7/15 and 16/17 of the PF-deviationsin Yl and Y4. Given that type III agentswere not buying in PB there was no opportunity cost to the type I agents pursuingtheir strategy.Note also that there was only a 5 centsdifferencein the PB dividends(per certificate) of types III and I. Table 2.5 again indicatesa strongtendencyfor hedgingratios to approachunity, indicating the adoptionof routine hedgesin PB. Period A (Spot): In Yl spot prices for PA certificatesopened below the PI value, moved quickly to the EPI value, and settled around the PF value. The type I insider was an early bidder, and bought one unit at $1.10 and then another unit at $1.20; he thereby leaked this higher valuation to the market. The selling insiders generally held off until prices were above $1.25, reinforcing the leakage effect by refusing to supply at 'low' prices. Note also the tendency for spot prices to reach the PF value despitetradersnot having seenany PB spot valuations.This may have been due to two tradersbeing able to sell PC futures at the 'overvalued' PC price (two of the four futures certificates were purchasedby the type I insider), providing somejustification for 'high' PA prices. In Y2 there was a changein the state of nature. Spot prices openedbelow the URE value, passedthrouh that value, and convergedto the PI equilibrium. The final spot allocationshide heavy early buying by (non-PF-predicted)insidersat low pricesfor resale at higher prices later in the period. Spot prices in Y3, anotherY year, openedwhere they had closed in Y2 (viz. at the PI value). There was then a sustainedincreaseto the PF equilibrium value, accompaniedby a parallel increasein futures prices from their URE value to their PF equilibrium. The type 11 insider was an early buyer at the lower prices. Prices in Y4, the secondX year, openedbelow the PI equilibrium for an X year and settled just above that value. Despite good futures price signals, the type I insider and his outsider 'shadow'were able to buy spot without any apparentleakage.

68

ExperimentalFuturesMarkets

In Y5 spot prices picked up where they had closed in Y3, the most recentY year. After openingmidway betweenthe PI and PF equilibria for a Y year, they increasedsteadily towards the PF equilibrium. The type 11 insider bought six of the first sevenspot certificates traded, clearly revealing his inside information. The first five spot sales were by outsiders; again, the selling insiders held off before trading their endowments,in the knowledge that spot pricesshouldbe higher than was being initially offered. Spot allocationsin the X yearsY1 and Y 4 improve from 6/18 to 13/18 relative to the PF prediction, with the competing EPI prediction explaining 7/12 and 3/5 of the PF misallocations. Allocations in the Y years,Y2, Y3 and Y5, are consistentwith the PF prediction: 10/18, 18/18 and 18/18, respectively, are correctly predicted.Correspondingto the relative performanceof the PF spot predictionsin X and Y years is the relative tendency towards routine hedges in Y years (see Table 2.5). The PA hedging ratios are much lower than those at the end of PB, a patternalso found in Experiment2. 4.2 ComparativeMarket Behaviour Tables 2.6 and 2.7 presentdescriptivestatisticson the deviations of observed prices and allocations from predicted equilibrium values. Our measureof price convergencein Table 2.6 is the Root Mean SquaredDeviation (RMSD) of transactedfrom predicted (equilibrium) price. Our measureof allocation convergencein Table 2.7 is the numberof certificatesmisallocatedrelative to the prediction.16 Our predictions about futures certificate allocations by the end of Period A are quite weak: the futures market opens again in Period B of each year, allowing traders further opportunity to establishtheir final positions.Moreover,we expectPeriod A futures positionsto be takenby traderswith no intent of holding that position at the end of Period B, as well as by traderswho do have suchan intent. In Table 2.8 we examinethe significanceof the effects of event uncertainty (EU) and inside information (11) on market performanceas measuredby the forecasterrorsin Tables2.6 and 2.7. The significanceof theseeffectsis given by the probability that the treatmentvariable indicated increasesforecast error in prices or allocations.Theseprobabilitiesare obtainedfrom a (one-tail) nonparametric Mann-Whitney test for the 'slippage problem'; see Hoel (1971, pp. 310-18) or Conover (1980, pp. 215-23) for a

Year

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

Experiment

1

2

31

Y

X

Y Y

X

X X

Y Y

X

State

0.215 0.073 0.165 0.289 0.238

0.077 0.121 0.229 0.076 0.076 0.337 0.074 0.127 0.040 0.076 0.412 0.139

URE

0.595 0.434 0.330 0.269 0.251

0.297 0.104 0.128 0.232 0.272

PI

0.027 0.062 0.107 0.126 0.143

0.155 0.087 0.010 0.001 0.031

PI

0.019 0.090 0.140 0.144

EPI

0.050 0.044 0.050 0.019 0.007

PI

Futures Prices

0.158 0.060 0.013 0.008

URE

Period A

0.161 0.0 0.050 0.075 0.076 0.079 0.133 0.073 0.076 0.061 0.020 0.189 0.030 0.115 0.076 0.076 0.112 0.062 0.013 0.137 0.188 0.013 0.113

0.183 0.141 0.094 0.074 0.057

0.155 0.087 0.010 0.001 0.031

PF

Period B

0.076 0.089 0.089 0.076 0.307 0.076 0.197 0.130 0.151 0.024 0.118

0.532 0.342 0.164 0.022 0.032

PF

Spot Prices

0.161 0.023 0.121 0.182 0.199

EPI

Period A

Table 2.6: Root Mean Squared Deviations from Equilibrium Price Predictions

PI- PF

Period B

0.050 0.073 0.030 0.013 0.013

0.055 0.025 0.0 0.011 0.007

0.018 0.003 0.006 0.014 0.016

0.076 0.050 0.114 0.076 0.044 0.018 0.009 0.050 0.019 0.003 0.007 0.013

PF

70

ExperimentalFuturesMarkets

Table 2.7: Number of Certificates Misallocated Relative to Equilibrium Predictions Spot Certificates Period A Experiment Year State 1

21

3

EPI

1

—

—

2 3 4 5

—

—

—

— — —

X

PI 5 5 5 0 4

URE — — — — —

Futures Certificates Period B

Period A

PF

PI

PF

EPI

5 5

5 0

5 0

5 0 4

0 7 2

0 7 2

—

16 13

Period B

PI-PF

PI-PF

15 13

4 0

—

13 11 5

0 5 3

5 6

12 20

12 18

5 5

— — —

1 2 3

Y

13 13

—

12 7

—

Y

18

—

9

—

18

—

8

—

2 7

19

X

16 18

20

4

15

15

2 7

5

X

18

—

10

—

18

1

18

18

1

1

X Y

12 10

12

12

12

10

10

18

8

18

15 1

14 12

20 12

11

2 3 4 5

Y X Y

18 15 18

18 5 18

18 5 18

0 5 0

18 17 18

0 17 0

5

5

2 2

16 6

15 6

1 0

Note: Derived from Tables 2.3 and 2.4.

formal discussion.17 The weaker-form (stronger-form) Period A equilibria usedfor this test in Experiments1, 2 and 3 are, respectively, PI (PF), EPI (URE) and EPI (PF). The relevantequilibria in PeriodB are, of course,PI and PF in eachexperiment. Consider the results in Table 2.8 for the stronger-form (SF) comparisonsof price RMSD. There is some evidence that EU slightly decreasesforecasterror in P A prices, convincing evidence that 11 decreasesforecasterror, and a presumptionthat EU and 11 jointly have no effect on PA prices. The probability that EU increasesSF forecasterror in PB prices is very high, even when 11 is also present.The pooled resultsfor P A and PB prices support the conclusionthat EU and 11 havestrongand offsettingindividual effects on SF forecasterrors, and that their joint effect is about equal(with perhapsa slight dominanceof EU). The resultsfor the weaker-form(WF) comparisonsin P A prices are consistentwith theseconclusions. Now considerthe results for the SF comparisonsof certificate misallocations. They strongly support the conclusion that EU increasesmisallocations,11 decreasesmisallocations,and that they

1 and 2 2 and 3 1 and 3

Allocations

EU and 11

EU

EU and 11

EU

Treatment Variable SF

WF

1.0 0.232 0.995

1.0 0.111 0.655

SF 0.925 0.452 0.857

0.790 1.0 0.845 0.726 0.345 1.0 0.655

0.155 0.345 0.845 0.845 0.889 0.016 0.365 0.845 0.5 0.579 0.794

WF

Period B

Spot Market

1.0 0.367 0.999

0.485 0.573 0.640

WF

WF

0.993 0.218 0.685

WF

SF

Period A and Period B

0.889 0.210 0.5

0.845 0.421 0.610 0.302 0.845 0.845 0.655 0.579 0.610 0.421 0.736 0.485

WF-SF

Period B

Futures Market

0.845 0.722 0.905 0.579

SF

Period A

0.845 0.962 0.944 0.121 0.635 0.630 0.952

SF

Period A and Period B

Notes: EU - Event Uncertainty; 11 - Inside Information; WF - Weaker-form; SF - Stronger-form. The values shown are the probability that the treatment variable increases forecast error in the particular performance measure.

1 and 2 2 and 3 1 and 3

Experiments Compared

Prices

Performance Measure

Period A

Table 2.8: Effects of Event Uncertainty and Inside Information on Market Performance

72

ExperimentalFuturesMarkets

haveroughly offsetting effectswhen consideredjointly (again,with a slight EU dominance).Theseconclusionshold for the PA and PB results,as well as in spot and futures markets. Table 2.9 shows the significanceof the effect of our treatment variables on the hedging ratios listed in Table 2.5. A MannWhitney test is also used,with the samegeneralinterpretationas in Table 2.8. The results support the conclusionsdrawn in Section 4.1: EU has the effect of discouragingPeriod A routine hedges (i.e. EU lowers the hedge ratio), and II has the opposite effect. Theseresultsare particularly significant when we useour preferred measureof the hedging ratio, with 'non-bought futures' in the numerator. Using this measurewe also note that the 11 effect clearly dominates the EU effect when we consider the two measurements jointly. 5. Concluding Remarks

The three experimental markets studied support the following broad conclusions:(i) the presenceof event uncertaintytends to retard the efficiency of assetmarkets,as measuredby the extentto which prices and allocations reflect stronger-form equilibria; (ii) the presence of conclusive inside information encourages efficiency in an event uncertaintyenvironment;(iii) the presence of eventuncertaintyandinside information have roughly offsetting effects on efficiency, although the effect of event uncertainty dominates slightly; (iv) event uncertainty is associatedwith a marked tendencyto depart from routine hedging behaviour; and (v) the presenceof conclusiveinside information encouragesthe adoptionof routine hedges,even when event uncertaintyis a joint treatmentvariable. It should be emphasizedthat our conclusionsare drawn from a small sampleof observations.A major methodologicalattraction of our experimentalmethod, of course,is that our results may be confirmed or rejected by subsequentexperiments designed to replicate ours. This feature is particularly important if our results are used in any adversarialcontext (e.g. the formation of policy concerningthe treatmentof 'insiders'); see Kirkwood (1981, pp. 616-21) for a discussionof the probative value of experimentsin anti-trust cases.Moreover, although our conclusionshave been drawn from a small samplewe have relatively preciseprior know-

ExperimentalFuturesMarkets 73 Table 2.9: Effects of Event Uncertainty and Inside Information on Hedging Ratio

Ratio of Sold Futures to Spot Holdings Experiments Compared

Treatment Variable

1 and 2 2 and 3 1 and 3

EU

"

EU and"

Period A

Period B

0.206 0.421 0.548 0.6550.548 0.655 0.548 0.655 0.075 0.5

Ratio of Non-Bought Futures to Spot Holdings Period A

Period B

0.210 0.952 0.925

0.345 0.579 0.421

Note: The values shown are the probability that the treatment variable increasesthe hedging ratio.

ledge concerning market structure and parameters.Thus the inferenceswe can draw from a given sampleare relatively strong. There are many directions in which one could extend our experimentaldesign,severalof which are the subjectof continuing research.The effect of uncertainor incompleteinside information aboutthe stateof nature,suchas implementedby Plott and Sunder (1982; Experiment 1) and Plott and Sunder(1983) respectively, could be comparedto our examinationof the effect of conclusive inside information. The effect of insider anonymity could be easily studied,as could the wider issueof the privacy of individual trader positions; computermediationin experiments,such as introduced by Williams (1980), would greatly facilitate such extensions.Nonbinding and binding price controlsare a pervasivefeatureof many important agricultural spot markets which also feature heavilytradedfutures markets;the price-controlexperimentsof Isaacand Plott (1981) and Smith and Williams (1981) may be extendedto asset markets with or without futures trading. A similar methodologycould be usedto study the effectsof price limits and/ or price rangeson futures price movements.Finally, our experimental design could be extended to include deterministic or stochasticproduction activities and the effects of futures markets on them.

Notes "University of WesternOntario, Canada.I am indebtedto Daniel Friedman and Jon Salmonfor helpful discussions,the Centerfor the Study of Futures

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ExperimentalFuturesMarkets

Markets(Columbia University) and the Social Sciencesand HumanitiesResearch Council of Canadafor researchsupport,and Len-Kuo Hu for researchassistance. The usual disclaimerapplies. 1. The materialin the next few paragraphsis taken, with someslight modifications,from Friedman,Harrisonand Salmon(1984, Section 1). 2. This result apparentlyconflicts with someconclusionsdrawn by Forsythe, Palfrey and Plott (1982b), hereafterFPPb.They extendedtheir earlier study in two respects.They adopteda pay-outstructurethat was 'time-interdependent', in the sensethat agentscould not simply add their earningsfrom eachtrading period togetherto computetheir earningsfor the entire marketexperiment.Thus each agent'smonetaryreturnsfrom holding assetsin a given-yearwere a non-additive (indeed,non-linear)function of the numberof assetsheld in eachperiod. The main implication of this unusualdesignfeatureis that an agent'sreturn from holding assetsin the final period of eachmarket year dependson that agent's holdings at the end of the previousperiod of that year. The other extensionwas to study the informational role of futures marketsin sequentialassetmarketsmore systematicallythan was done in FPPa.Nine experimentswere conducted:five included a futures market and four did not. Note that FPPbare primarily concernedwith the joint treatmentvariable of 'experienceand the presenceof a futures market'.Their control experiments(1,3,6 and 8) employedinexperienced subjectsin a sequentialspot market with a futures market. Their comparison experiments(2, 4, 7 and 9) employedexperiencedsubjectsin a sequentialspot market without the presenceof a futures market. FPPbintentionally designedtheir treatmentvariablein this mannerin order to provide a strong test of the propositionthat sequentialspot marketsconvergemore rapidly to an informationally efficient equilibrium when futures marketsare present.FHSa was particularly concernedto isolate the separateroles of 'experience'and 'futures markets',therebyallowing an unambiguousconclusionwith respectto the role of futures marketsaloneon spot price volatility. 3. The experimentslisted as 1, 2 and 3 in the presentstudy are listed as 2, 4 and 6 respectively,in FHSb. Further,our Experiment 1 has also been reportedas Experiment4 in FHSa. Note that althoughthere is someoverlap with thesestudies in our discussionof experimentaldesign,the detailedresultsand market comparisonsin Section4 have not previously beenreported.This type of overlap of experimentsis commonin the literature, as a market that containsa treatment variable in one study may be usedas the control experimentin a subsequentstudy. 4. The materialin this sectionis a modification of Friedman,Harrisonand Salmon(1983, Section2.2). 5. Any trader was free to acceptthe bid or offer currently beforethe market, but could not acceptpreviousbids or offers. FPPaapparentlyallowed the latter procedure,since their raw data are recordedin order of tenderand do not necessarilyrecord acceptances in their real-timesequence.Our procedurehas the advantagesof allowing an 'ex post' check that all transactionssatisfy budgetand trading restrictions,and facilitating the type of analysisof real-time price formation processespresentedin Friedmanand Harrison (1984). 6. Plott and Sunder(1983) is the first study to allow short (spot) positions within a trading period. They employ a simple and apparentlyeffective penaltyon any tradershort at the endof any period (viz. a fixed pecuniarypenaltyplus the requirementthat the trader implicitly cover himself at the highesttransactionprice during the period). 7. A minor exceptionin Year 5 of Experiment1 is noted in Table 2.1. 8. Plott and Sunder(1983) introducethe idea of actually announcingstatesof naturefrom a predetermiDedsequence.Although there is no evidencethat this occurredin their experiments,we were concernedthat tradersnot begin to 'second-guess' the sequenceof events.

ExperimentalFuturesMarkets 75 9. Inconclusiveinsider information (a seriesof 'clues' as to the true state)has beenexaminedexperimentallyin Experiment1 of PS. They find that convergence to the rational expectationsequilibrium is much slower in this casecomparedto experimentswith conclusiveinside information. Plott and Sunder(1983) also implementinconclusiveinside information (no trader knows the true state,but their pooled information set is conclusive). 10. FHSadefine the PI equilibrium assumingthat tradersonly know their private valuation of Period C certificates.This is a weakerconceptthan employed here. The presentdefinition of PI equilibrium follows FHSb, and correspondsto the conceptof 'Market Information' equilibrium in FHSa. 11. This is definitely not the observedpatternin earlier yearsin which the transition from PI to PF prices is incomplete.In theseyearsthere is a healthy mixture of concurrentspot and futures trading. 12. The behaviourof the type I tradersin Yl, Y2 and Y3, holding 13/18 spot certificatesand not selling any futures, illustratesthe value of reporting the two different ratios in Table 2.5. 13. In fact it had occurredprior to Y3 in Experiments2 and 3. 14. A simple explanationfor their inactivity could of coursebe a severe aversionto risk. Thus we italicize the word 'blame'. 15. Note that type II is also predictedto hold spot certificatesin P A by the EPI equilibrium concept. 16. The futures certificate predictionsrefer to the trader type predictedto be long. If that trader type is actually short in futures, the misallocationlisted in Table 2.7 will exceed18 certificates. 17. We statethe test outcomesin terms of the probability of the hypothesis that slippagehas occurredin favour of higher forecasterrors in the second experimentlisted. The alternativehypothesisis that both samplesarise from the samepopUlation.

References Conover,W.J. (1980) Practical Non-ParametricStatistics,New York: Wiley, 2nd edn. Cox, c.c., (1976) 'FuturesTrading and Market Information', Journal of Political Economy,vo!. 84, 1215-37. Forsythe,R., T.R. Palfrey and C.R. Plott [FPPaj (1982a) 'AssetValuation in an ExperimentalMarket', Econometrica,vo!. 50, 537-67. [FPPbj, (1982b) 'FuturesMarkets and Informational Efficiency: A Laboratory Examination',GSIA Working Paper No. /l-8J-83, Carnegie-Mellon University. Friedman,D. and G.W. Harrison (1984) 'Price Formationin ExperimentalAsset Markets: A BayesianApproach',unpublishedmanuscript,Departmentof Economics,University of WesternOntario. Friedman,D., G.W. Harrison and J.W. Salmon [FHSaj (1983) 'The Informational Role of FuturesMarkets: Some ExperimentalEvidence',in M.E. Streit (ed.), Futures Markets - Modelling, Managingand Monitoring Futures Trading, Oxford: Basil B1ackwell. [FHSbj (1984) 'The Informational Efficiency of ExperimentalAsset Markets', Journal of Political Economy,vo!. 92, 3, June. Hoel, P.G. (1971) Introduction to MathematicalStatistics,New York: Wiley, 4th edn. Isaac,R.M. and C.R. Plott (1981) 'Price Controlsand the Behaviourof Auction

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Markets: An ExperimentalExamination',AmericanEconomicReview,vo\. 71, 448-59. Kirkwood, J.B. (1981) 'Antitrust Implicationsof the RecentExperimental Literatureon Collusion', in S.C. Salop(ed.), Strategy,Predation andAntitrust Analysis,Washington,D.e., US FederalTrade Commission. Learner,E.E. (1978) SpecificationSearches:Ad Hoc Inferencewith Non-ExperimentalData, New York: Wiley. (1983) 'Let's Take the Con Out of Econometrics',AmericanEconomic Review,vo!. 73, 31-43. Plot!, e.R. (1982) 'Industrial OrganizationTheory and ExperimentalEconomics', Journal of EconomicLiterature, vo!. 20, 1485-527. Plott, e.R. and S. Sunder[PS] (1982) 'Efficiency of ExperimentalSecurity Marketswith Insider Information: An Application of Rational-Expectations Models', Journal of Political Economy,vo!. 90, 663-98. (1983) 'Rational Expectationsand the Aggregationof DiverseInformation in LaboratorySecurityMarkets', SocialScienceWorking Paper No. 463, Division of the Humanitiesand Social Sciences,California Institute of Technology. Smith, V.L. (1982) 'MicroeconomicSystemsas an ExperimentalScience', AmericanEconomicReview,Vo!. 72, 923-55. Smith, V.L. and A.W. Williams (1981) 'On Nonbinding Price Controlsin a CompetitiveMarket', AmericanEconomicReview,vol. 71, 467-74. WilIiams, A.W. (1980) 'ComputerizedDouble-AuctionMarkets: SomeInitial ExperimentalResults',Journal of Business,vo!. 53,235-58.

3

HEDGING, RISK AND PROFITS: NOTES ON MOTIVES FOR HEDGING ON FUTURES MARKETS Basil Yamey*

1. Hedging and Price Risks Onceupon a time hedgingby meansof transactionsin futures contractswas almostuniversallyregardedas a practiceintendedby the hedgerto avoid, reduceor eliminate the risk of price changesby shifting that risk on to otherswilling to bear it. Hedgingwas almost always defined, described or discussedin these terms, both in materialsaddressedto thoseengagedin businessand also in academic publications. The analogy with insurancewas commonly drawn. Here are some quotationsfrom the work of the leading academicauthorswho had addressedthemselvesto the economics of futures trading beforethe SecondWorld War. For Alfred Marshall, the hedger 'does not speculate: he insures'.The short hedger'by buying a future ... does not speculate; he throws on the shouldersof the generalmarketthe risks and the chancesof gain that would have come to him through general movementsexternalto his own business'(Marshall, 1919, p. 260). J.G. Smith wrote that the 'essenceof the operation[of hedging]' is for the hedgerto eliminate 'speculativerisks for himself. Hedging enableshedgers'to insure against the risk of price fluctuations' (Smith, 1922, pp. 81,95). CharlesO. Hardy wrote that the hedger 'is securingprotectionagainsta definite risk in much the sameway that one secures protection against unknown hazard through Lloyd's policy' (Hardy, 1923, p. 72). As is well known, John Maynard Keynes discussedhedging in terms of risk avoidanceand insurance(Keynes, 1930, vol. 2, pp. 142-4). John Hicks explainedthat the 'ordinary businessman only enters into a forward contract if by so doing he can "hedge" that is to say, if the forward transactionlessensthe riskinessof his position' (Hicks, 1939, p. 137). And Kaldor pithily expressedthe by then familiar notion that 'it is the speculatorswho assumethe risks and the hedgerswho get rid of them' (Kaldor, 1939-40, p. 197). 77

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It follows from this line of thinking that any loss made by the hedger on the completedhedgedtransaction(i.e. in the case of short hedging,on the purchaseand subsequentsale of the actuals, and on the saleand subsequentpurchaseof the futures) represents a sort of insurancepremium paid to the risk-assumingspeculator (e.g. Keynes, 1930, pp. 142-3); someauthorsaddedthat the foregoing of the chanceof making a profit on the unhedgedactuals commitmentis also an insurancepremium paid for risk-avoidance (e.g. Smith, 1922, p. 86; Smith cautioned that the insurance analogy 'must not be pushedtoo far'). Some noted that in some marketsituationsthe premium might be too high, so that 'potential hedgerswill prefer not to hedge'(Hicks, 1939, p. 139). The most completeand elaboratediscussionof hedgingwas that of G. Wright Hoffman. He also wrote about hedging in terms similar to those usedby his contemporaries.'The entire-activityof future trading consistsin either assumingrisk as speculatorsor in shifting risk as hedgers'and: 'By hedgingtheir purchases(or forward sales) [of actuals1, they shift this price hazard to the shoulders of those assumingthe opposite end of their hedges' (Hoffman, 1932, pp.4, 379-80). But his detailed study went well beyond the rather limited treatment to be found in the sparse theoretical literature,and in a numberof directionsdrew attention to featureswhich were to be given considerablymore emphasisby others in some of the post-war contributions to the subject. For example,he carefully explainedthat for short hedging to be fully effective in eliminating risk it was undesirablethat actuals and futures prices should move togetherin perfect parallelism; and he noted that skilful hedgerscould make profits from their hedgingif 'able to foresee... relative changesin price'. He concludedthat it was 'the businessof hedgers... to foresee accurately and take advantageof gains in basis and to avoid as far as possible basis losses'(Hoffman, 1932, pp. 409, 418).1 All this is a far cry from the notion, most uncompromisingly expressedby Keynes, that hedgers regularly make 'losses' on their hedging, and do so willingly in exchangefor the avoidanceof the risk of larger losses on price movements. Hoffman, however, did not lose sight of what he and his contemporaries considered to be the central element in hedging, namelythe avoidanceor reductionof the risk of loss from adverse price changesby transfer of the risk to others called speculators. Hedging and the avoidance or reduction of the risk of price

Hedging, RiskandProfits 79 changeswent together,the former being motivatedby the demand for the latter. In this respectsomeof the post-wardevelopmentsin the specialistliterature representa significant break with tradition, as will be shown below. Some economists,in this new tradition, have taken great pains to avoid the risk of seemingto associate hedgingin futures, or the operationof futures markets,with avoidanceof the risk of price changes.The changein attitude cannotbe accountedfor as having beeninspiredby changesin the practiceof hedging.2 2. Arbitrage Hedging in Perspective It is self-evidentthat anyonehedginga commitmentin actualsby

the sale or purchaseof futures contracts(whetheror not equal in volume to the actuals commitment) places himself in a position which he regardsas betterthan any other courseof action open to him. A trader, processoror manufacturerhedges whenever he believes that hedging increaseshis income, pecuniary and nonpecuniaryincometakentogether.It is evidentthat the total income from a hedgedtransactionis not necessarilythe sameas the direct pecuniaryincomederived from the changein the 'basis' over the life of the hedge- basisbeing the differencebetweenthe price of the futures contractusedas the hedgeand the price of the actuals or physicals(the commodity) involved. Thus for a short-hedgingtrader the sourcesof income are as follows: (a) the direct pecuniary gain (loss), measuredby the changein the basis; (b) indirect pecuniary gains, which are the counterpartof the convenienceyield and stem from the trader's ability to satisfy promptly the unexpectedrequirementsof preferred customers-A aA gain which in part may take the form of profits on further transactionswith customers with whom the trader's goodwill is maintained or enhanced;3and (c) the nonpecuniaryincome enjoyedby a risk-aversetrader as a result of his 4 reducedexposureto price changes. From this subdivisionof gains from hedgingit follows that a trader may carry a stock of the commodity and hedge it (fully or partially) even when he expectsto incur a direct pecuniaryloss as the result of a confidently expected unfavourablechangein the basis. In a series of papers beginning in 1948, Holbrook Working (whose contributions to the study of the economics of futures

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trading overshadowthose of any of his predecessors,contemporariesor successors)placedheavystresson hedgingenteredinto by hedgers with the intention and expectationof making direct pecuniaryprofits. This type of hedging,which, following Working, may be termedcarrying-chargeor arbitragehedging, is said to be motivated by the prospects,indeed sometimesthe near certainty, of pecuniaryprofit resulting from changesin the basis relative to the cost of carrying inventory over time. Working has emphasized that this sort of hedging 'is not properly comparable with insurance'.It is not done 'from any special desire to minimise risks'.5 In fact, the generalconceptof hedgingas taking offsetting risks wholly, or even primarily, for the sake of reducing net risk, servesso badly as applied to most hedging on futures markets that we needanotherconceptfor that most commonsort of hedging.To put it briefly, we may say that hedging in commodity futures involves the purchaseor sale of futures in conjunction with anothercommitment,usually in the expectationof a favourable change in the relation between spot [actuals1 and futures prices.6 The generalimpressionleft on the readermay well be that it is carrying-chargehedgingthat predominatesin practice.And Anne Peck, writing in 1977, summarizesWorking's views in theseterms (Peck, 1977, p. 152): Working presentsa completelyrevisedview of hedgerbehavior. Hedgers are seen to be arbitragers,constantly evaluating the cash [actuals1 price relative to the futures price, seeking to profit from differential moves in these prices. The continuing concernwith the basisand its expectedchangesis at the center of eachform of hedgingWorking delineates. In fact, Working's position had becomerather more complexthan this.? The richnessof Working's treatmentof hedgingis apparent,for example, in an interestingshift in approachbetweentwo papers published respectively in 1953 and 1962. In the earlier paper Working writes:

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Incidentally, recognition of the fact that hedging may be done purely as a logical consequenceof the reasoningon which the hedgeracts (reasoning,for example, that the spot price is low relative to the future) rather than from any special desire to minimise risks, helps explain why many dealersand processors sometimeshedgeand sometimesdo not. Here selectivity in hedging or the exercise of discretion in the decisionwhetherto hedgeor not dependsupon expectationsabout changesin the basis. In the 1962 article, however, selective or discretionaryhedging is not discussedin the section on carryingchargehedging.Indeed,it is said that with carrying-chargehedging the potential hedger'sdecision 'is not primarily whether to hedge or not, but whetherto storeor not' (Working, 1962, p. 438). Instead,a new type of hedging,'selectivehedging',is introduced and discussedseparately.Here selectivity or discretionis exercized not accordingto the potentialhedger'sexpectationsabout changes in basis but accordingto his expectationsabout changesin price. Now this sounds uncommonly like risk-avoidanceor insurancetype hedging.However,Working wishesto avoid any suchidentification. He writes: 'Becausethe stocks are hedgedwhen a price decline is expected,the purposeof [selective1hedging is not risk avoidance,in the strict sense,but avoidanceof loss' (Working, 1962, p. 440). But there is no indication here or elsewherehow confident the hedgermust be about his price expectationfor his resulting hedgingdecisionto be classedas one stemmingfrom the desire to avoid loss rather than from the desire to avoid risk. In fact, Working clarifies his point of view when he equates'pure risk-avoidance'hedging with routine hedging, which he says is 'unimportantor virtually non-existentin modernbusinesspractice' (Working, 1962, p. 442). This equationis madeeven more explicit in a paperpublishedeight yearslater: 'if a business-man"hedges" regularly, making no effort to judge what price changeis likely to occur, I shall call that "insurance-type"hedging'(Working, 1970, p.33). Now I doubt whetherany applied economistwho has described hedging as risk-avoiding has had in mind the routine and automatic coveringof the hedger'sentire actualscommitmentpractised by an entirely passivehedgerS- one who hedgesregardlessof the 'premium' (if any) to be paid and the risk to be run unhedged. Working createda straw-man,and found him to havefew counter-

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parts in the real world. Oddly enough,it is Working who has provided examplesof just such cases;the grain and cotton trades,he writes, are 'the principal onesin which routine hedgingis accepted as a standardpractice in most parts of the country' (Working, 1962, p. 440). The view a la Working that arbitrage or carrying-charge hedging is preponderantin practice, that is to say the view that most hedging is done in the expectationof a direct pecuniary profit, has been expressedtrenchantly by Roger Gray (1960, p. 77): 'Most hedgers are arbitragers trying to get ahead in the world', not 'a queersort of conservativecommercialidiot striving alwaysand only to breakeven'. Nevertheless,as I haveshownelsewhere (Yamey, 1968, pp. 360-1), both Working and Gray have referred in various writings to hedging which evidently is not carrying-chargehedging or speculation on basis changes,but is describedin languagewhich points directly to the notion of riskavoidancehedging. Thus Working has referred to 'hedging pressure', a phenomenonwhich is incompatiblewith arbitragehedging. He has also referred to the 'price at which hedgedstocks will be carried',and to the renderingof a 'service forwhich hedgersare willing to pay'; and similarly, Gray has written: 'Coffee importers who require a short hedge have paid for it, as have short hedgersin Minneapoliswheatfutures'. The inappropriatenessfor arbitragehedgingof suchnotionsas paying a price for a service is obvious. Arbitrage hedging pertains to action based on the perception of a profitable opportunity. The arbitrage hedgeris not under any constraint toact: he operateswhen he expectsrelative prices to move in his favour, and refrains when he does not. He does not needa 'service' which has a cost and for which he is preparedto pay. Yet, to take anotherexample, both Working and Gray have written of hedging'needs'or the 'need' for hedging - expressionswhich seem to apply more aptly to the practiceof insurancehedgingby thosewho want to hold stocksbut to reducethe associatedrisk. However, perhaps the most pronounced withdrawal from Working's position on the preponderanceof carrying-charge hedgingis to be seenin a different contextfrom that just noted. In a path-breakingpaperpublishedin 1967, Working examines

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the activities of floor tradersor scalperson futures exchanges.One of his conclusionsis that 'to the extent that hedging orders affect the price, [short1hedgerstend to sell on price dips and to buy on price bulges'. They therefore 'tend to lose money on their transactions in futures'. Put differently, 'becausethe price dips and bulges occasionedby "market orders", and by bunchesof such orders, are often fairly large, hedgersmust incur a substantialcost [called the execution cost1, in the form of price concessions, through their frequent use of market orders to insure prompt execution when they place their hedges, and again when they lift them'. The recognitionof executioncostsdoesnot itself castdoubt on Working's earlier position on carrying-chargehedging;it simply meansthat the costsinvolved in hedgingare higher than otherwise, regardlessof the type of hedging involved. But Working goes much further. He assertsthat 'the income flow from hedgersto speculatorsis much larger than has previouslybeenestimated,and has been positive and substantial even in markets and during periods in which the seasonaltrend of futures prices by itself has afforded no income, or has been a sourceof loss, to speculatorsas a group' (Working, 1967, pp. 5,44). Now this passagemust mean that short hedgerstend to lose money on their completedhedged transactions(i.e. taking actualsand futures transactionstogether) in periods in which prices of the commodity have fallen or have been stable. Yet hedging is said to take place in these circumstancesand to produce an 'income flow from hedgersto speculators'.9 Neither Working nor Gray (1967, p. 181) seemsto be aware that this account of the importance of execution costs seriously underminesthe notion of the preponderanceof hedging of the arbitrage or carrying-chargetype, which should tend to produce direct pecuniaryprofits for the hedgers,subjectonly to the risk of abnormal or unexpectedbasis changes.If it is true that hedgers tend to lose money on their completed hedged transactionsin periodsof price decline or stability, and should expectto do so in those conditions,they cannotthen be arbitragehedgersstriving to 'get aheadin the world', not content merely to 'break even', let alone to lose money. In one respectthis breedof hedgersare then close relativesof Keynes'svariety of old-fashionedinsurance-type hedgersmade prominent in his theory of normal backwardation. Both are willing to 'lose money' to the accommodatingspeculators. The difference betweenthem is that the former are willing

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to pay a price, the 'execution cost', in order to have the 'convenience'of prompt executionof their orders(Gray, 1967, p. 181; and 1972, p. 336), while the latter are willing to pay a price, the 'insurancepremium', in order to be relieved of the risk of adverse price changes.What is clear is that both types are said to hedge even in market situationsin which they would not expectto break even or make pecuniary profits (although, of course, as noted above,they would not hedgeat all unlessthey consideredhedging to improve their position). In any event, the explanationthat hedgersare willing to pay a price to speculatorsfor the convenienceof prompt execution of their orders begs the question why they should want to have hedging orders executedat all. The fact that hedging in futures flourishes only in respectof commoditiesand other assetssubject to considerableprice volatility suggestsstrongly that it is the avoidance or reduction of price risk that is involved, and that hedgers are preparedto pay somethingfor its achievement. 3. Properties of Futures Markets

In three recent papers (one in collaboration with Harlow Higinbotham),ProfessorLesterTelser has arguedthat 'it is not the demandfor price insurancethat explainswhy there is an organized futures market' (Telser, 1980, p. 16). He is concernedto focus on what he calls 'the more fundamentalpropertiesof an organized exchange',and to criticize the erroneousconventionadoptedby 'most of the economistswho have written on the subject', of 'focusing their attention on hedging and speculation'(Telser and Higinbotham, 1977, p. 972). His explanationof the existenceof organizedfutures markets, 'briefly is this. An organizedfutures market facilitates trade among strangers' (Telser, 1981, p. 1). Moreover, it meets'the demandfor a fungible financial instrument tradedin a liquid market' (Telser, 1980, p. 16). The main point of attack on the traditional explanation, it seems, is that 'an organized futures market is not necessaryin order to obtain the advantages of hedging' (Telser and Higinbotham, 1977, p. 970; also Telser, 1980, p. 14 and 1981, p. 5). Now this is certainly true of insurance-typehedging,the type to which Telser addresseshis observations.Indeed, the same point that there are alternativesto hedgingin futures is madein someof

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the earlier literature,beginningwith Marshal1.1o It is true that the earlier writings do not say much, if anything at all, about the impersonalityof futures trading and the liquidity of active futures markets, characteristics on which Telser and Higinbothamproperly lay considerablestress- perhapsthe earlier authorstook thesethings for granted.1 1 But whetheror not earlier writers dealt with someof the points madeby Telser, his objectionsto the conventionalapproachleave open the question why the 'fundamental properties' of futures trading arrangementsare valued by those who use futures markets.12 The fact, borne out most tellingly in the TelserHiginbothamarticlel3 , that thesemarketsthrive only when there is considerableprice volatility points to the conclusion that their hedgerusersare largely motivatedby the desireto avoid or reduce the risk of adverseprice changes.That hedgersusually prefer to use futures markets,where these are active, rather than to make other arrangementsfor 'hedging'their price risks, reflects no more than that for them futures contracts and futures markets have advantagesof the kind emphasizedby Telser. Similar considerationsapply to speculation.Speculatorsdo not need organizedfutures marketsto exercisetheir forecastingskills or to try their luck. But futures marketsobviously facilitate speculation, just as they do hedging. It does not follow that it is analytically or descriptively more relevant or correct to concentrateon the propertiesof an institution ratherthan on the usesto which the institution is put. Moreover, although Telser claims that his explanationof the existence of futures markets'hasmore predictivepower' than two rival views he identifies (Telser, 1981, p. 1), in fact thy/analyticalmodel presentedprovidesno way for discriminatingbetweenthe existenceof an organized market without futures trading and that of an organizedmarket with futures trading.14 As regards the important question why there are futures markets for some commodities (and other assets) but not for others, the paperby Telser and Higinbotham, although it has few surprises, elaboratesand refines the discussion inaugurated by Marshall in 1919. In particulartheir contributionis evidentin their analysisof a feature which correspondsloosely to Marshall'scondition that to be 'suitableto be handledin an organisedmarket' a 'class of products' must be 'important enough to occupy large bodies of buyersand sellers' (Marshall, 1919, p. 256). Telser and

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Higinbotham show that volume is important in reducing the unit costsof trading. Moreover,their propositionthat the 'benefit of an organisedmarketis an increasingfunction of the numberof potential participants'and 'also an increasingfunction of the turnoverof the potentialparticipantsin that market' (Telserand Higinbotham, 1977, p. 997) is interesting,althoughthe propositionitself cannot be derivedfrom the formal theory they present. Telser and Higinbotham are critical of the hedging defenceof futures markets on the grounds that the total of benefits flowing from such markets exceedsthe benefit to hedgersalone, and, by implication, that the other componentsof benefit are more valuable than the benefit to hedgers.Working is mentioned as one 'who always put the emphasison the functions of a futures market aside from its advantagesto hedgers'(Telser and Higinbotham, 1977, p. 972). However, in so far as Working may have placed considerableemphasison non-hedgingbenefits,he was anticipated by Hoffman, an author neglectedby Telser and his co-author. Hoffman wrote (1932, p. 377): The feature stressedas being of greatestvalue has usually been the practiceof hedging.This hasbeendue partly to the fact that it is widely used and partly becausethe value of this function can be clearly demonstrated.The market-makingfunction is also far-reaching in its effect but its economic value is much more difficult to demonstrate. A further point is of interest. Hedgingand speculationresult in businessfrom which those who constituteand operatethe futures exchange benefit directly, for example, in the form of commissions. The wider economic benefits which flow from futures markets (e.g. improvementsin price formation and reduction in the amplitude of price fluctuations) are of a public-goods character,and thosewho organizeand operatethe market are not requitedfor helping to makethem possible.From the point of view of 'economicwelfare' theremay be too few futures marketsfor this reasonalone. It may well be, however,that social benefitsexceed appropriableprivate benefitsin the caseof all market institutions, and not only of thosewith futures trading.

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4. Conclnding Observations As early as 1953 Working offered the following definition of hedging(Working, 1953b, p. 560): 'Hedgingin futures consistsof making a contractto buy or sell on standardterms,establishedand supervisedby a commodityexchange,as a temporarysubstitutefor an intendedlater contractto buy or sell on other terms.' The comprehensiveness of the definition is evident. And this is perhapsthe reasonwhy it has attainedincreasing currency.Thus Anne Peck (1978, Introduction): 'Broadly speaking,a position in a futures market is a hedgeposition if it may be viewed as a substitute, albeit normally temporary,for an intendedcash [actuals1 transaction.The advantageof this definition is its generality.'But it is unfortunatethat this definition gives no hint of the motives or reasons forhedging, and no indication that active futures markets and hedgingin futures contractsare not to be found exceptwhere there is considerable volatility in prices. The demand for 'temporarysubstitute'contractsto stand in for intendedeventual actuals contracts is non-existentor too limited to justify futures marketsexceptwhere price changesare large and uncertain. Price volatility and its role in the history of futures markets explain the traditional and still common associationof hedgingin futures with the avoidanceor reductionof price risks. Perhapsthe emphasisin the traditional definition of hedging on price risks capturesmore of the businessreality of hedging than Working's all-embracingbut bland definition or his earlier near-identification of hedgingwith carrying-chargehedging.At any rate there are no good groundsfor de-emphasizingprice risks in the discussionand analysisof hedging.This is so even thoughit is true that Working's earlier iconoclasticpapersdid much to attract more attentionthan before to other important aspects and features of hedging practices, and so have enriched the study of the economicsof futures trading. In recent years the applicationof portfolio theory to the activities of participantsin futures trading once again sets risk in the centreof the hedgingstage.But it is more explicit than beforethat risk has to sharethe stagewith returnsor profits. The risk that is usually emphasized concerns the variability of the expected returns. This approach,whether in the theory or in the related empirical studies,hasso far addedlittle to the understandingof the actual behaviour of hedgers. In particular, aside from routine

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hedging,it is unlikely that a hedger,when making his hedgingand associateddecisionsin any particularsituation,is influencedby the variability of returnson a successionof hedgesin a past period or by the expectedvariability of returnson a successionof hedgesin the impending period. It is on this type of risk measurementthat empirical work examiningprices in past periodshas, perhapsperforce, been concentrated.Although thesestudieshave their value in throwing light on the behaviourof price and basisin the markets and periodsstudied,in my view they add nothing of interestto the explanationof (non-routine)hedgingpractice. Thesestudies,and the theoreticalapproachthey reflect, distract attention from the fact that the non-routinehedgertends to deal with each hedging decision in the light of the particular circumstancesprevailing at the time, and not in the light of his expectations about the variability and size of returnsfrom a sequenceof (hypothetical?)transactionsin the future (and which in turn can throw no light on the expectedoutcome of the particular hedge under consideration). Both traditional insurance-type hedging (allied, as it should be, with the notion of the exerciseof discretion and judgement, as in Working's 'selective' hedging) and also Working's arbitrage hedging involve the hedger'sassessmentof each situation discretelyand exclusively on its own merits. In this respect together they reflect the motivations of non-routine hedging. The portfolio-theory approachcontributesonly in that it may make more explicit the risk-return trade-off to be assessed by the hedgerin eachsituationseparately. Perhapsthe best descriptionof non-routinehedging would run along theselines: hedgingis the simultaneousmaking of offsetting, but not necessarily equal, transactions in related actuals and futures markets so as to reducethe risk of loss on adverseprice changes, and sometimes with the intention of profiting from expectedfavourablebasischanges.No doubt this descriptiondoes not comprehendhedging practice in its variety and detail.15 It does,however,highlight the two centralfeaturesof the motivation of most hedging practice; and it also nicely blendsthe traditional view and a newerview associatedwith Holbrook Working's name. Notes ·London Schoolof Economics. 1. Seealso Hoffman'searlier exposition(1925) e.g. pp. 80-1; and Smith

Hedging, RiskandProfits

89

(1922), ch. 7, passim. 2. Materialsintendedby exchangesor brokersfor potentialparticipantsin futures businesstoday still commonlydescribethe purposeof hedgingin termsof the avoidanceof price risks. A recentexampleis a pamphletissuedby the new InternationalPetroleumExchangeof London: 'Hedgingon futures marketsis a form of price insuranceagainstadverseprice movements.' 3. For a fuller considerationof convenienceyields, seeYamey (1971), pp. 418-19. 4. The tradermay also be able to finance his stock more cheaplyif banks considerhedgersto be more reliable borrowersbecausethey are lessexposedto price risks. 5. The following passagefrom Kaldor (1960, p. 25), showsclearly the distinction betweenrisk-avoidancehedgingand arbitragehedging: The possibility of arbitrage,i.e. buying spot and selling futuressimultaneously and holding the stock until the dateof delivery, ariseswhen the relationship betweenthe futures price and the currentprice ensuresa risklessprofit. An arbitrageoperationdiffers from an ordinary hedgingoperationonly in that the ordinary hedgerentersthe futures market in order to reducea risk arising out of a commitmentwhich occursindependentlyof the existenceof the forward market; whereasthe arbitrageurassumesrisk which he would not haveassumed if the facilities of the forward market did not enablehim to passthem on, on advantageous terms. Hence,any ordinary holder of stocksof a commodity becomesan 'arbitrageur'in so far as the existenceof the futures market tempts him not only to hedgethe stockshe would ordinarily hold, but to enlargehis termson which they stocksin relation to turnoverowing to the advantageous can be 'hedged'. The referenceto 'risklessprofit' is a simplication, sincethereis alwaysa risk, sometimessmall, that the expectedbasischangemay not materializefully. Hence one encountersthe fairly commonstatementthat a hedger'speculates'on basis changebut not on price change(see,for example,Paul et al., 1981, p. 27). Statementsof this kind do not deny the (price) risk-avoidanceaspectof hedging. 6. Quotationsfrom Working (1953a). 7. In his 1953 paperWorking noted that somehedgingwould take placeeven when a favourablechangein basiswas unlikely so that the completedhedged transactionwould result in a direct pecuniaryloss. The incurring of suchlosseswas warrantedin that commoditymarkets'must try to keepadequatestocks... to serve their customers'.In his 1962 paper,Working identifies and discussesseveraltypes of hedgingin a mannerwhich contradictsPeck'sstatement,viz. operational, selective,anticipatoryand risk-avoidancehedging.Operationalhedging,as explainedby Working (p. 439), is such that 'expectedchangesin the spot-future price relation ... can be largely ignored; and it is this fact which chiefly distinguishesoperationalfrom carrying-chargehedging'.Basisand basischangeare not mentionedin Working's discussionof the other three types of hedging.It may be noted that it is improbablethat much long hedgingfalls within the arbitrage category:seeYamey (1971), especiallyp. 432. Seealso Working (1962), p. 441. 8. Thus Hoffrnan (1932, p. 407): 'While certain typesof hedgingare thus difficult for certaininterestsand in certainyears,good hedgingpracticetendsto avoid thesetypesand to adopta policy which will fit into the prevailing situation as far as possible.This is but anotherway of sayingthat hedgingis somethingmore than simply settingup counterfuture transactionsand hoping for the best.'Testsof the effectivenessof hedging,the so-calledstability-of-basistests,make useof hypotheticalprogrammesof routine hedgingof a fixed actualscommitment.But thesetestsdo not purport to be descriptionsof actual hedgingpractice.Rather,

90

Hedging,RiskandProfits

they shouldbe seenas analysesof intermarketprice relationships. 9. The passagein Working implies that the short-livedprice dips and bulges are not reflectedin availableprice series,so that the latter pricesare not the transactionspricesat which short hedgersplaceor lift hedges,and thereforethose at which floor-trading speculatorsbuy and sell futures. In a period in which prices tend to decline (or to remain stable),if one looked at availableprice series, speculatorswould seemto lose money(or breakeven)on their deals. However, accordingto Working the price dips and bulgesare so large that the corresponding transactionspricesenablespeculatorsto tend to make profits despitethe downwardor stableprice tendencyin the market. By the sametoken, short hedgers tend to lose moneyon their futures transactions.Hencethey would make money directly on their completedhedgedtransactionsonly if they make more moneyin the actualsmarket, i.e. only if actualsprices tend to rise by more than the futures pricestend to fall. However, it is quite implausiblefor the actualspricesto tend to rise in the postulatedmarketconditions.Hencehedgerswould tend to lose money on their hedging.In other words, accordingto Working, in the postulatedmarket conditionsthe effectivebasistendsto widen over the life of the hedge(whatever the availableprice seriesmight suggest),and hedgerswould be awareof this tendency.Carrying-chargehedgingrequiresthe basisto narrow. 10. Marshall (1919), p. 266; Hardy (1923), pp. 72-3; Hoffman (1925), pp. 9, 18-20. 11. For somediscussionof what Telsercalls the 'fundamentalproperties'of futures exchanges,and of the choicebetweenhedgingin forward contractsin actualsand hedgingin futures, seeGossand Yamey (1976), pp. 8-9, 18. 12. Seealso Bear (1980), p. 32. 13. 'There is more price variability for thosegoodsthat havean organised futures market than for the goodsthat lack such markets'(Telserand Higinbotham,1977, p. 998). 14. The basictheory appliesequally to any organisedmarket',while the 'discussioncenterson organisedfutures markets'(Telserand Higinbotham, 1977, p.997). 15. Thus one may supposethat an insurance-typehedgerwould take account of the prevailing actuals-futuresprice relationshipsfor eachof the available contractmaturities(i.e. for eachof the various 'basis'values)and his expectations aboutchangesin them when decidingwhetherand to what extentto hedge,in which futures maturity to hedgeand, of course,how large a commitmentin actuals to incur.

References Bear, R.M. (1980) 'Commentary',in R.M. Leuthold and P. Dixon (eds.), LivestockFutures Trading Symposium,ChicagoBoard of Trade. Goss,B.A. and B.S. Yamey (1976) 'Introduction', The Economicsof Futures Trading, London and New York: Macmillan. Gray, R.W. (1960) 'The Importanceof Hedgingin FuturesTrading', in Futures Trading Seminar,vo!. I, 61-82, Madison: MIMIR. - (1967) 'PricesEffects of a Lack of Speculation',Food ResearchInstitute Studies,vo!. 7, 177-94. (1972) 'The FuturesMarket for Maine Potatoes:An Appraisal', Food ResearchInstituteStudies,vo!. 11,313-41. Hardy, C.O. (1923) Riskand Risk-Bearing,Chicago. Hicks. J.R. (1939) Value and Capital, London: Oxford University Press.

Hedging, RiskandProfits

91

Hoffman, G.W. (1925) Hedgingby Dealing in Grain Futures, Philadelphia. (1932) Future Trading upon OrganisedCommodityMarketsin the United States,Philadelphia:University of PennsylvaniaPress. Kaldor, N. (1939-40)contribution in 'A Symposiumon the Theory of the Forward Market', Reviewof EconomicStudies,vo!. 7, 1-27. (1960) Essayson EconomicStability and Growth, London: Duckworth. Keynes,J.M. (1930) A Treatiseon Money, vo!. 2, London: Macmillan. Marshall, A. (1919) Industry and Trade, London: Macmillan. Paul, A.B., K.H. Kahl and W.G. Tomek (1981) Performanceof FuturesMarkets: The Caseof Potatoes,WashingtonDC. Peck, A.E. (ed.) (1977) SelectedWritings on Futures Markets, VD!. 2, Chicago Board of Trade. (ed.) (1978) Readingsin FuturesMarkets: Viewsfrom the Trade, Chicago Board of Trade. Smith, J.G. (1922) OrganisedProduceMarkets, London: Longmans,Green. Telser, L.G. (1980) 'Reasonsfor Having an OrganizedFuturesMarket', in R.M. Leuthold and P. Dixon (eds.), LivestockFutures Trading Symposium,Chicago. (1981) 'Why there are OrganizedFuturesMarkets', Journal of Law and Economics,vo!. 24, 1-22. Telser, L.G. and H.N. Higinbotham(1977) 'OrganizedFuturesMarkets: Costsand Benefits', Journal of Political Economy,VD!. 85, 969-1000. Working, H. (1948) 'Theory of the InverseCarrying Chargein FuturesMarkets', Journal of Farm Economics,vo!. 30, 1-28. (1953a)'FuturesTrading and Hedging', AmericanEconomicReview,vo!. 43, 314-43. (1953b) 'Hedging Reconsidered',Journal of Farm Economics,vo!. 35, 544-61. (1962) 'New ConceptsconcerningFuturesMarkets', AmericanEconomic Review,vo!. 52, 431-59. (1967) 'Testsof a Theory ConcerningFloor Trading on Commodity Exchanges',Food ResearchInstitute Studies,vo!. 7, 5-48. (1970) 'EconomicFunctionsof FuturesMarkets', in H.H. Bakken(ed.), Futures Trading in Livestock,Madison. Yamey, B.S. (1968) 'Addendum',to 'An Investigationof Hedgingon an OrganizedProduceExchange',in P.T. Bauerand B.S. Yamey, Markets, Market Control and Marketing Reform,London: Macmillan. (1971), 'Short Hedgingand Long Hedgingin FuturesMarkets', Journal of Law and Economics,vo!. 14,413-34.

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4

INTERTEMPORAL ALLOCATION IN THE AUSTRALIAN WOOL MARKET Barry A. Goss and David E.A. Giles*

1. SimultaneousEquationsModel of Price Determinationand Storage Several years ago Pestonand Yamey (1960) published a paper which addressesthe problem of the allocation of the available supply of a commoditybetweencurrentconsumptionand storage, and the simultaneousdeterminationof spot and futures prices.To the bestof our knowledgethat model has not beenestimated.The model developedand estimatedin this chapteris an extensionof the Peston-Yameymodel to Australian wool spot and futures markets. The basic Peston-Yamey model distinguishesthree marketsfor presentconsumption,for storageand for futures contractsand our model employsthe samedivisions. The market for present consumptionis not identical with the spot market, the latter being a market where the commodity is currently priced for current delivery. An economicagent, however,may take current delivery for the purposeof (speculative)storage,and it will be seen that sometradersin the storagemarketare responsiveto the spot price. That part of available supply which is not currently consumedis allocatedto storage,either in anticipation of future requirements, or in anticipation of a future gain from expectedprice changes. Tradersholding such inventory mayor may not hedgetheir price risks. Where tradersdo not hedgeagainstthe risk of a changein the spot price, the stock is classifiedas 'unhedgedstorage'.Where an economic agent simultaneouslytakes a position in inventory and an oppositeposition in futures, the inventory is classified as 'hedgedstorage'.In the futures market, tradersmay buy and sell futures contractsbecausethey are hedging their commitmentsin the actual commodity against price risks, or becausethey anticipatea gain from an expectedchangein futures prices. In the model presentedhere, six types of economicagent are distinguished:short hedgers,short speculators,long hedgers,long

93

94

I ntertemporalA /location

speculators,speculatorsin spot and consumers,although PestonYamey did not distinguish long hedgersand short speculatorsin futures. Short hedgersare holdersof stockswho match their position in spot with an equivalentsold position in futures. Their supply of hedged storage is an increasing function of the price spread (futures price minus spot price), becauseof either an increasing marginal net cost of storage(in the case of routine hedgers),or becauseof their expectationsof the price spread(in the case of discretionaryhedgers)in the senseof Working (1953). The latter determinethe volume of their inventory and hedgingaccordingto their price spread expectations,although they are fully hedged (carrying-chargehedgers).1 Interviews reportedin an earlier study of the SydneyWool FuturesExchange(Goss,1972) indicatedthat only 1 in 25 floor member and associatemember-respondents hedgedin a routine manner.Thus 'short hedgers'supply hedged storageand futures contracts.Short speculatorssell futures contracts becauseof their expectationsof a fall in the futures price. Long hedgersare traderswho have sold wool or wool products forward, and who hedge their price risk by a long (bought) position in futures. While their price risk is the oppositeof that of short hedgers,their result from hedging is not the strict mirror image of that for short hedgers(Yamey, 1971). The Sydneywool futures market is unusualin that, for most of the months studied, the volume of long hedging exceedsthat of short hedging; the theoretical literature has almost invariably assumedthat hedgers are net short (seeHicks, 1939; Houthakker,1968), and empirical studiesdealing with open position data have found that hedgers are mostly net short (see, for example,Rockwell, 1967). Futures contractsare also demandedby long speculatorswho expect the futures price to rise. Peston-Yameyassumedthat the demandfor futures by long speculatorsalso constituteda demandfor storage,on the ground that thesetradersplannedto becomemomentaryholders(only) of the commodity at the end of the period. This treatmentseemsto be simply a device to close off the model, perhapsbecausethe activities of long hedgersare not explicitly included.2 We shall assumethat the demandfor storageis provided by long hedgers, who, althoughthey generallydo not intend to take delivery under the futures contract,plan to acquirethe physicalcommodityupon completionof the hedge: they are using the futures contractas a

IntertemporalAllocation 95 substitute for a merchandizing contract (Working, 1953). In periodsin which the volume of long hedgingexceedsthat of short hedging,we shall assumethat the supply of storageis provided by short hedgers and by short speculators to the extent that is necessaryto balancethe storagemarket. Similarly, in periods in which short hedging exceedslong hedging, we shall assumethat the demandfor storageis provided by long hedgersand by long speculatorsto the extent that is necessaryto balancethe storage market. A further categoryof market operatoris that of 'speculatorsin spot'. This group of traders holds unhedgedinventory because they expect a rise in the spot price, and correspondsto the 'merchant' category in the Peston-Yameymodel. Becausethere are no other economicagentsdealingin unhedgedstorage,PestonYamey treat the holdings of this group as involving them in a reciprocal demandfor and supply of unhedgedstorage,and we shall employ the sameinterpretation. We also distinguish the category'consumers',who demandthe physical commodityfor currentusage,and are assumedto hold no inventoriesof wool. The supply of spot to consumersis in effect that part of available supply which is not allocatedto storage.In addition to 'consumers', the original paper also distinguishes 'mixed traders', who are in effect discretionary hedgers, and 'mixed speculators',who are long in both spot and futures. We have treatedthesetwo categoriesof speculatorseparately. Peston and Yamey (1960) have explained the simultaneous determination of static equilibrium values for spot and futures prices, and haveshown that suchan equilibrium is stable(pp. 35960). The determinationof equilibrium and the stability properties of the model are not affectedby the addition of long hedgingand short speculatorcategoriesof operator. 2. Specification of Functional Relationships

Demand/orUnhedgedStorage Our initial experimentationwith this relationshipwas basedon an equationof the form:

U, = a1 + bjA, -I- Cjm, -I- djAj'+j + e^, + f xi t + vl t

96

IntertemporalAllocation

where:

mt

it rt A^ ,

=

marginal net cost of storage. This is the , marginal carrying charge (including interest) less marginal convenienceyield, which is the subjective gain from holding inventory and being 'open to sell' (see Kaldor, 1939, 1961; Yamey, 1971); foreign rate of interest; marginalrisk premium; expectedspot price, for period t + 1, formed in period t.

This basic demandequationis basedon the demandfunction for speculative storage in Brennan (1958), and Kaldor (1939, 1961). Holdersof unhedgedinventoriesexpectto gain from a rise in the spot price in excessof their marginalnet cost of storageand marginalrisk premium. In effect, their demandprice is A;+I - (mt + rt ): suchtraderswill adjusttheir holdingsof spot3 until A;+I = ~ + mt + rt • Hence,the coefficientsbl , Cl and el are expectedto be negative,while d l is expectedto be positive in sign, a priori. The foreign interestrate variable is includedbecauseof the dominance of unhedgedstorageby the Australian Wool Corporation(A WC) from 1975 onwards.The coefficient fl is expectedto be positive, a priori, becausesuch interest rates vary inversely with foreign inventory, and the latter varies inversely with A WC inventory. Although positive estimatesof fl were obtained,the inclusion of this interest rate variable (variously defined) adversely affected other estimatesof parametersin the model. The variablesm and r failed to perform, and so all three were subsequentlydeletedfrom the equation.In this and all other equations,exceptfor (4) below, seasonaldummy variableswere found to be (jointly) insignificant. In preliminary estimationthe adaptiveexpectationshypothesis performedbetterthan Mills (1962) implicit expectationshypothesis, and was finally adopted in the unhedgedstorage demand equation.Beginningwith the simplified relationship: U t = a1 + biA, + diA* , + vlt ,

with (AV i " A,') = a, (A, - A \ ) ; 0 < a, < 1

I ntertemporalAllocation 97 we obtain: U t = (1 - « O I V, + (1b, + a1d1)A t + b, (a, - l J A ^ + a1a1 + (vl t + (a1 -l)v l t _ 1 )

or u t - e 1 u t _ 1 + e2A t + e3A t_1 + e4 + ul t

°

°

(1)

The anticipatedsignson 0.1 , b1 and d1notedalreadyimply < 01 < 1 , 03 > 0, and either O2 > or, if it is negative,then 1021< (0/01)' The traders whose behaviour is representedby equation (1) may be seenas maximizersof expectednet revenuein the senseof Brennan(1958). Demandfor Futuresby Long Speculators Our initial specificationof this equationwas: where:

FLS, p*^

a2 + b2Pt + C2P;+1 + d2rt + U 2t expectedfutures price for period t + 1, formed in period t.

The interpretationof this equationis similar to that of the basic unhedgedstorage equation above, except that these speculators are holdersof futures ratherthan actuals.In this caseour attempts to representP;+l by an adaptive expectationshypothesis were unsuccessful,and shifts in expectationswere representedby a series of dummy variables linked to major events in the international wool diary during the sample period. Of these, the dummiesrepresentinganticipationof a recession(D2' D 4) failed to survive preliminary estimations,as did the risk premium variable. Hencethe final versionof this relationshipis: FLSt = 05Pt + 06D l t + 07D3t + 08 + u2t

wherethe expectedparametersignsare 05 Dl t = 1

°, °




0, and

January1972 - March 1974; to representworldwide commodityboom; = elsewhere.

98

IntertemporalAllocation D2t = 1

D3t = 1: D4t= 1:

July 1974 - February1976; to representgeneralized recession;= 0 elsewhere. March 1976 - December 1976; to represent textile consumptionrevival; = 0 elsewhere. January 1977 - December 1977; to represent lack of confidenceabout textile consumption;= 0 elsewhere.

Supplyof HedgedStorage Short hedging is undertakenby growers (with respectto growing crops of wool) and by brokers and merchants(with respect to inventories). Such traders may take routine hedges,or they may pursuean uncertaingain subjectto the constraintof risk reduction (seeJohnson,1960). The volume of short hedging is likely to be an increasing function of the forward premium for at least two reasons.First, traders are likely to believe that the larger the current forward premium, the more likely it is to decline in the future (it must disappearat maturity), and a forward premiumwhich declinesgives a gain to short hedgers.Second,if inventory holders are a competitive group independentlyseekingto maximize profits, they may be assumedto equatethe marginal net cost of storagewith the forward premium (which is the return per unit on a hedge held to maturity). If marginal net storagecosts increasewith inventories, as is usually assumed,then inventories will increase with the forward premium. A spot premium which narrows over time results in lossesto short hedgers.The holding of stocks at such times is explicable in terms of the convenienceyield, which can make net storage costs negative at the margin. Two possible indicators of the volume of wool eligible for hedging are the monthly output of greasy wool, and non-AWC inventories. We have chosenthe latter becauseof its better performancein experimentalwork. Our relationshipfor the supply of hedgedstorageis: Ht = e9 (Pt -A t ) + e10NK t + e n + u3t

(3)

where N~ is the non-AWC stock of wool, and both 89 and 810 are expectedto be positive in sign.

lntertemporalAllocation 99 Consumptionof Wool In specifying this relationshipwe have partly followed the lead of the Bureauof Agricultural Economics(BAE) (1967) in their estimation of the derived demand for raw wool in the United Kingdom. In their log-linear equation,consumptionwas a function of the price of raw wool; parametersof the demandcurve for wool products (including population, personal disposableincome and the demandfor stocksof wool tops); and parametersof the supply curve of 'other factors' (including the quantity of synthetics competingwith wool in production). The main differencesbetweenthe BAE model and the demand for wool by consumersin the model presentedhere are first that consumersin our model are assumedto carry no stocks (as consumers),that function being undertakenby holders of unhedged storageor by short hedgers.The secondmajor difference is that our period of study in the 1970s was assumedto be one where syntheticproductiondid not set the limit to market penetrationby synthetics,as it apparentlydid in the 1960s. Accordingly, substitution betweenwool and synthetics,in both consumptionand production, was assumedto be sensitiveto relative prices. Our attempts to include personal disposable income as an explanatoryvariable were unsuccessfulas a result of the strong collinearity with other variablesin the system.An index of textile production (M t ) was used as a proxy for the influence of changes in consumers'tastes,and also to capturepopulation effects. Only in this equationwere seasonaldummy variablesfound to be significant, and the specificationis: 24

InCt

=

812In(A/St )

+ 813lnM, + 2:

8j SEAS(j_13), where:

St SEASit

j=14

8j SEAS(j_13),

(4)

price of syntheticfibres. seasonaldummy variablefor the ith month of the calendaryear.

Demandfor Futuresby Long Hedgers The specificationof this equationis:

100

IntertemporalAllocation FLH, = 026 (P, - A , ) + e27D5t + e2g + u5,

where:

D5t

(5)

dummy variable to reflect the absence of excessstocksin Japanduring 1973-4. (D5t 1, January 1973 to December 1974; 0, elsewhere.)

Demandfor futures by long hedgersis undertakenby traders who have madeforward salesof wool or wool products.The price at which such forward contractsare written is not necessarilythe spot price of wool, becausespot and forward actualstransactions refer to different delivery dates. However, the forward actuals price is unknown, and so it is proposedto use the current spot price as a proxy for this, although we acknowledgethat the forward actuals price will also reflect some influencesbearing upon the similarly datedfutures price (Yamey, 1971). Hence,the differencebetweenthe current spot and futures prices is likely to overstate the difference between the forward actuals price and the current futures price. SUbject to this qualification, the position of the long hedgeris the negativeof the position of the short hedger. That is, the volume of long hedgingis a decreasingfunction of the spreadbetweenthe futures price and the forward actuals price, and so 826 is expectedto be negative,a priori. The dummy variable Os was introducedpartly to representthe impact of changesin Japanesetextile inventories upon Japanese textile production and Japanesewool purchasesin Australia, as emphasizedin market reports. Another reasonfor including 0 5 was the lack of successwith estimatesobtained when planned textile productionwas included in the equation.(We believedthat plannedproductionin approximatelyfour months' time would be appropriate,becauseinterviews with floor membersindicatedthat such hedgesare held for an averageof 18 weeks. Actual textile productionwith a lead of four monthswas employedas a proxy for these plans, which were in effect assumedto be realized.) The coefficient of Os in (4) is expectedto be positive.

Supplyof Futuresby ShortSpeculators Speculatorswho expect the futures price to fall will sell futures contracts,and will close their positions by buying futures at the anticipatedlower price, expectinga profit in return for their risk-

IntertemporalAllocation

101

taking. Their supply of futures contractsis assumedto vary directly with the currentfutures price, given their expectations,and to vary inverselywith their expectedprice, given the currentfutures price. Short speculatorsin futures may not be active until the current futuresprice exceedstheir expectedprice by an amountwhich is at leastequalto a requiredmarginal risk premium. The representationof short speculators'price expectationsby the adaptive expectations hypothesis failed to perform satisfactorily in preliminaryestimates,as did the marginalrisk premium variable.Accordingly, shifts in expectationsare representedby two dummy variables,eachof which representsanticipationof a slump in futures prices: 1 ; March 1974-March1975

D6t

o ;elsewhere.

1 ; May 1976-April 1977

D7t

o ;elsewhere.

The resultingspecificationis: sst = e29D6t + e30D7t + e31 + o32pt + u6t

(6)

where829, 830 and 832 are expectedto be positive in sign. Identities

In the accountingidentity: K, + Ct = K,_! + Z, — X, where:

Zt X, K,

(7a)

current production; currentexports; closing stock in period t,

we define the left side of (7a) as the disposalof availabledomestic supply of wool, and the right side to be the domesticavailability of wool (assumingimports of raw wool to be zero).4 Assumingthat demandfor and supply of hedgedstorageare equal at the equilibrium futures price, then equilibrium in the consumptionand storagemarketsrequires:

102

IntertemporalAllocation

(7b)

C, + H, + U, = Ct + FLH, + Ut

In periodsin which FLH, exceedsHI at the equilibrium futures price, we would have to include on the left side of (7b) sufficient (Y I) of SSI to balance the hedged storage market. Similarly, in periodsin which HI exceedsFLH, at the equilibrium futures price, we would have to include on the right side of (7b) sufficient (WI) of FLS, to balancethe marketfor hedgedstorage.This yields: C, + H, + U, + Y, = C, + FLH, + Ut + W,

(7c)

where: WI

0, when FLH, ~ HI (~ (H,

- FL~), FLH,) when HI

>

FLH,

and

YI

0, when H

I~

FLH I

(FLH, - Ht), when FLHt > Ht. The left side of (7c) representsquantities supplied, while the right side representsquantities demanded.Subtracting Ct from both sides gives the equilibrium condition in the storagemarket, and in equilibrium eachside after this deductionis also equalto ~, the quantity of stock in existence.As we assumethat the storage market achieves equilibrium every trading period, so that only equilibrium valuesare observed,then either side may be employed to derive the identity (7) below. We havechosenthe right side giving: K, = U, + FLH, + W,

(7d)

The expressionin (7) is not an accountingidentity in the sense that it holds even at times of disequilibrium; it is an identity of observedvalueswhich holds in every trading period. We can also write: H, + SS, = FLS, + FLH,

(8)

I ntertemporalA !location

103

which is the equilibrium condition in the futures market. Becauseit is assumedthat equilibrium is achievedin the futures marketevery period, (8) may be interpretedas an identity of observedvalues. Hence, we have eight endogenousvariables: Up Cl' HI' SSI' FLHt, FLSI' Pt and ~, togetherwith six behaviouralequationsand exogenous. exogenous. exogenous. the two identities(7) and (8). The variablesN~, Mp St' ~ and the dummy variablesare treatedas exogenous.

3. Data This sectiondiscussesthe definition, the collection and generation, and the interpretationof data employed in estimatingthe model presentedin Section 1. The data are discussedunder the headings 'Spot and FuturesPrices', which are the endogenousprices in the model, 'Other EndogenousVariables'and 'Other Variables'. Spotand FuturesPrices

The spot price of wool (~) is the monthly averageof weekly exogenous. auction quotations for 'average 64s' (21 micron in 1976, 22 micron in 1977) provided by the Australian Wool Corporationin Wool Market News. It is quotedin centsper kilogram, cleanbasis.s The futures price (Pt) is the monthly averageof daily prices for a futures contractapproximatelysix monthsfrom maturity, quoted in cents per kilogram, clean basis, and provided in the weekly StatisticalReportof the SydneyFuturesExchangeLtd. There are only five delivery monthsfor wool on the Exchange(March, May, July, Octoberand December),so that it was necessaryto employ an arbitrary definition of a 'six months' future', which is given below.6 Such a definition is necessaryto obtain a continuousseries of futures prices,becausethe maximum period for which any contract is quotedon the exchangeis 18 months.Moreover,interviews for the study reported in Goss (1972) indicated that typically hedgesare of 18 weeks' duration in a future approximatelysix monthsfrom maturity. Futuresprice quotationsrefer to 'standard wool' in the futures contractwhich is 64 type 78 (22 micron type 78 from 1976). Other EndogenousVariables

Australiancommodityfutures markets,unlike mostof their United Statescounterparts,do not publish or make availabledataon tum-

104

I ntertemporalAllocation

over or commitments,classified according to type of transaction such as hedging, speculative,etc., nor do the data exist in the recordsof the Exchangeor the Clearing House. Hence, the procedureadoptedin the presentproject was first to obtain monthly turnoversummariesfor all floor membersof the Exchange,andfor other members of the Clearing House. Information was then obtained as to. which floor memberseach of the other clearing membersdirectedtheir business.Finally, all floor membersof the Exchangewho traded during the sampleperiod were interviewed (whetherthey were still trading or not), and askedthe percentage composition of their businessin the categories'short hedging', 'long hedging' and 'speculation'during the sampleperiod, taking into accountany sub-periodswhich they wishedto distinguish. This proportionate breakdown of business for each floor member was applied to that member'sturnover for each month studied,and aggregationacrossmembersgeneratedmonthly turnover dataclassifiedinto 'shorthedging','long hedging'and 'speculation'. The speculationcategory was then divided between the long and short sidesso as to balancethe futures market.Turnover in the categoriesof short and long speculation(SSt and FLSt) refers to purely speculativetransactions,while turnover in the categoriesof short and long hedging(Ht and FLH t) refers to rou7 tine and discretionaryhedgingtransactions. Data for Ut were obtained as follows. In periods where the volume of long hedgingexceededthat of short hedging,the values of FLHI' being the total demandfor hedgedstorage,were subtracted from values of total stock, ~,K,, which is treated as exogenous.Hence, theequilibrium quantitiesof unhedgedstorage (Ut) were generatedas a residual.Similarly, in periodswhen short hedging predominated,values of Ht, K,, being the total supply of hedgedstorage,were subtractedfrom valuesof ~,K,, the eqUilibrium valuesof Ut again being generatedas a residual. Monthly values of A WC inventory were available and these were addedto the N~K,, data, obtainedas describedbelow, to form ~.K,, All variablesin identities (7) and (8) are expressed in terms of contracts(,lots') traded on the Exchange,where a contractrefers to a quantity of greasywool equalto 1,500 kilograms clean. Quarterly data on Australian consumptionof raw wool from Australian Bureauof Statisticssourceswere madeavailableby the A WC and were interpolated, using the program TRANSF (Wymer, 1977c), to provide monthly data for Cl' expressedin

I ntertemporalA /location

105

million kilograms, clean basis. Thesedata were then convertedto contractstraded. Other Variables

Non-AWC stock (N~), K,, which appears in equation (3), was obtained by interpolating the available annual data, using the TRANSF program. N~K,, is measuredin million kilograms, clean basis. The index of manufacturing activity (M,) which appearsin equation (5) is the index of manufacturingactivity in Australian wool textiles, as reportedin the ANZ Bank's Quarterly Survey. The synthetic price variable (S,) which appearsin equation(5) is the averageprice of acrylic tow in the USA, Japanand the EEC, weightedaccordingto production,and expressedin UK penceper kilogram. The data are made available in the InternationalWool Secretariatreport, CompetitionFrom SyntheticFibres. 4. Estimation and Results Estimationof the Model

The eight-equationsimultaneousmodel describedin Section1 has beenestimatedusing monthly time-seriesdata coveringthe period January 1973 to December1977. The model is linear in the 32 parameters,but non-linear in the endogenousvariable ~.K,, The latter variable appearsin level form in parts of the model, but in logarithmic form in equation(4). Although,in(C,) also appearsin this equation,C, itself doesnot appearelsewherein the system,so the model may be treatedas being linear in the logarithm of this variable. Equation (4) was linearizedwith respectto ~K,,by means of a first-order Taylor approximationabout samplemean values, and the resulting (linear) restrictions on the intercept term were retained in the subsequentestimation. Each of the six stochastic equationsin the model is overidentified. The computer packageSIMUL (Wymer, 1977b) was used to obtain Full Information Maximum Likelihood (FIML) estimatesof the structuralparameters.Both Ordinary LeastSquares(OLS) and Three StageLeast Squares(3SLS) estimateswere usedas starting values for the Newton-Raphsonalgorithm in SIMUL, and the same (local) maximum of the associatedlikelihood function was reachedin each case. This result is most encouraging,given the

106

IntertemporalAllocation

substantialdifferences between the OLS and 3SLS estimatesof someof the parametersin the system.The convergencetolerance for the FIML algorithm was set to 0.1 per cent in all cases. The principal weaknessof theseFIML resultswas the apparent lack of independenceamong the residuals of the structural equations(1), (2), (3) and (4). Temporalindependence for lags up to twelve periodswas testedby meansof the non-parametricSign ReversalTest (e.g. Griliches et al., 1962). This test has beenused in a simultaneousequationscontext by Giles (1977). Although there was evidence of higher-order temporal dependence,firstorder auto-correlationappearedto be the dominantphenomenon. To take accountof this, the model was re-estimated,allowance being madefor separatefirst-order auto-regressiveprocessesin the structural errors of those equationsnoted above. For example, equation(3) becomes: H,

=

e9 (P, - A,) + e10NK, + eu + u3t.

U3,

=

P3U3.-1 + e3t

h,

=

p3Ht_, + e9(P, - a ,) - p 3e9(Pt _, - a,_,) + e10NK, - p A . N K ^ + O ^ l - p ^ + e,,

where P3 is an auto-correlationparameterto be estimated,and e3t is a 'well-behaved'disturbanceterm. The other affectedequations are transformedin a correspondingway, so that each version of the model is now non-linearin the parameters.ConstrainedFIML estimateswere obtained with the package RESIMUL (Wymer, 1977a). Certain other error structurescould be allowed for in a similar way, althoughwe have not pursuedthis possibility further. Finally, inequality restrictions were placed on three of the parameters to ensurethat I'll > 0 and 1'l3 > 0, and to constrain the price elasticity implied by 1'l9 to a magnitudeconsistentwith the available prior information. The latter point is discussedin connection with Table 4.3 below.

Results In this section we shall first discussthe results for the model as a whole, and we shall then considerthe estimatesfor eachindividual equation.The FIML .estimatesof the structural parametersof the model are presented in Table 4.1, together with the FIML

I ntertemporalA /location

107

Table 4.1: FIML Parameter Estimates

Parameter

H, U,

Equation Dependent Variable

Variable

(1 ) U,

U'_l A,

H,

At - 1

°4

constant

H, H6 H7 H8

(2) FLS,

H9 H,o

(3) H,

P, D" D3t constant (P,-A,)

NK, constant

fI"

Estimate

Asymptotic Standard Error

0.763 -1.527 1.342 82.773

0.181 0.924 0.871 50.376

-0.005 1.005 0.075 2.225

0.002 0.222 0.184 0.597

0.067 0.887 9.713

0.023 0.375 5.613

(4) [ne,

2n(A,IS,) £nM, SEAS" SEAS" SEAS" SEAS 4, SEAS" SEAS 6, SEAS 7t SEAS" SEAS" SEAS,01 SEAS", constant

-0.662 0.039 -0.386xl0 ' -0.285xl0 4 0.196Xl0 ' 0.114xl0 0.193Xl0 2 0.248Xl0 2 0.310Xl0 2 0.343Xl0 2 0.354Xl0 ' 0.317x10 2 0.304x10 2 8.061

0.185 0.060 0.234xl0' 0.595Xl0 ' 0.773Xl0 ' 0.908Xl0 ' 0.109Xl0 2 0.124Xl0 2 0.140Xl0 2 O.152Xl0 2 0.164Xl0 2 0.179x10' 0.190x10' 0.594

H'6 H" (J'8

(5) FLH,

(P,-A,) D5, constant

-0.025 1.409 3.452

0.005 0.328 0.199

H29 830 83, 83,

(6) SS,

D6,

p, p, P3 P4

(1) (2) (3) (4)

1::)12

H13 H'4

U"

H16 0" H'8 H19

H,o H21

H22 H23

H'4 H"

D" constant P,

1.473 0.025 0.393 0.203XlO··' -0.082 0.296 0.850 0.939

0.134 0.110 0.378 0.11OX 10-' 0.075 0.109 0.051 0.026

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IntertemporalAllocation

estimatesof the auto-regressionparametersassociatedwith the equationsfor which the structural errors are assumedto follow a first-order auto-regressiveprocess.Theseresultsare basedon the non-linear (in the parameters)model arising when this allowance for auto-correlationis made.The usual likelihood ratio test for the validity of the over-identifying restrictions yields a X2 value of 613.0 (degreesof freedom = 186). The corresponding5 per cent critical value is 703.4, so the over-identifyingrestrictionscannotbe rejectedon the basisof this asymptotictest. All of the estimated parameters in Table 4.1 have the anticipatedsigns. As the standarderrors reportedin these tables are basedon the asymptoticcovariancematrix, and assumingthat the quantity (8j - 8Ya.s.e.(8j ) is approximatelystandardnormal in distribution (at least asymptotically), by far the majority of these estimatesare also significant at the 5 per cent level. Table 4.2 reports the Sign ReversalTest valuescalculatedfrom the structural residualsassociatedwith the estimatesin Table 4.1, after allowancefor auto-correlation.Thesestatisticsare basedon residualsign changesbetweenperiodst and (t - /l) in the sample, and are asymptoticallyX2(1) in distribution. Thereis little evidence of remaining auto-correlation,except in equation (1). The latter exceptionmight be explainedby the fact that U tt follows a moving average (rather than autoregressive) process if v tt is 'wellbehaved'.Unfortunately,we are unableto allow for this particular possibility in our estimationprocedure. Table 4.2: Sign Reversal Test Statistics Equation t

1 2 3 4 5 6 7 8 9 10 11 12

(1)

(2)

0.11 8.31' 1.84 0.33 0.02 4.89 0.00 0.56 4.89 0.20 0.16 1.10 0.05 7.22' 0.53 0.00 0.12 0.29 4.89 0.23 0.60 0.25 0.87 0.06 4.89 0.18 1.17 0.01 1.62

(3)

(4)

(5)

(6)

1.11 0.01 0.73 0.21 0.35 0.04 4.89 1.08 4.89 0.59 0.06 0.90

13.34' 2.58 0.18 0.09 0.51 0.47 2.81 0.40 3.54 4.73 1.74 0.01

1.38 3.42 1.38 1.24 0.01 0.73 2.27 0.32 2.37 0.08 2.46 0.34

1.36 0.07 0.43 0.26 0.54 2.87 0,01 1.26 0.16 1.21 1.54 2.29

, Significant at the 1 per cent level of significance.

IntertemporalAllocation

109

Table 4.3 containsthe estimatedprice elasticitiesfor eachof the equations. Except in equation (4), these are calculated at the sample mean values for the variables concerned,and asymptotic standard errors are reported in parentheses.These estimated elasticitiesare generallyplausible,although thosefor equation(5) are a little smaller in absolutevalue than anticipated:discussions with some major floor membersindicated that they would have expected long and short hedgers each to adjust their market positionsby at least 200 contractsin responseto a price changeof three cents,during the period studied. The within-samplepredictive performanceof the model is summarized in Table 4.4 in terms of percentageroot mean squared (forecast) error. These predictions are based on the restricted reducedform. The complete within-sample prediction paths are comparedwith the correspondingactual paths for a selection of the endogenousvariablesin Figures4.1 to 4.4. We shall now considerthe resultsfor eachequationin turn. In Table 4.3: Estimated Price Elasticities Equation Price

(1 )

(2)

A

P

-5.08 -2.30 (2.14) (0.79)

(4)

(3) PA

5.99 (4.44)

(A/S)

A

-6.04 (4.48)

(6)

(5) PA

A

P

0.32 -0.57 -1.86 1.87 (0.18) (0.40) (0.40) (0.25)

Table 4.4: Within-sample % RMSE from Restricted Reduced Form Endogenous

% RMSE

Variable A P U H FLH FLS SS

C

8.25 6.71 5.92 48.70 50.29 111.07 90.05 4.69

110

IntertemporalAllocation

Figure 4.1 : Wool Spot [Cash] Price 600 A ----ACTUAL ------ESTIMATE

400

1976 1976

1974 1975

1976

YEARS

1976

1977

1978

lntertemporalAllocation

111

Figure 4.2: Wool Futures Price 500 p

----ACTUAL ------ESTIMATE

400

I

I

, I

300

1976 1976

1974

1975 1976 1977 YEARS

1976

1978

112

I ntertemporalA !location

Figure 4.3: Wool Unhedged Storage 300

u

----ACTUAL ------ESTIMATE

250

200

150

100

100

OWU~~LU~UUiUUL~~~LUJLUUiL~iUULLU~UULU~

1973

1974 1975

1976

YEARS

1976

1977

1978

I ntertemporalA /location

113

Figure 4.4: Wool Hedged Storage 8 H

----ACTUAL - - - - - - ESTIMATE

7

6

5

4

3

2

2

2 1976

1976

1976

YEARS

1976

1976

1976 1978

114

I ntertemporalAllocation

equation (1), which representsthe holding of unhedged inventories of wool, the coefficients of all price variables have the expectedsigns,althoughonly the coefficientof U t- 1 (one minus the adaptiveexpectationscoefficient)is significant. Hence,the adaptive expectationshypothesis,although intended by Nerlove (1958) to represent'normal' or long-term expectations,has performedwell statisticallyin its short-andmedium-termapplicationsin this model. We are awareof the major theoreticallimitations of this hypothesis, in particularthe propertythat if currentexpectationsare correct,no revision will be madeto expectationsevenif new informationcomes to hand. However,if, as i's usuallyassumed,suchinformationcomes about randomly, we would not expect this to lead to bias in the estimatesof coefficientsof expectationalvariables,althoughit would affect their statisticalsignificance.In addition,althoughthe adaptive expectationshypothesiswill leadto underestimationof the true price expectationin times of persistentinflation, and overestimationin times of persistentdeflation, our sample period exhibited neither persistentinflation nor deflation. The A WC has occupieda dominantposition amongholdersof unhedgedinventories since 1975, and while the AWe does not behave as a conventionalspeculator,its market support responsibilities mean that it tends to increaseits inventory at times of recessionand to reduceit at times of expansion.Hence,the stockholding activities of the Awe are evidently well representedby the specificationof equation(1). In equation (2), which representsthe demandfor futures by long speculators,all parameterestimatesagain have the predicted signs, and the estimatesobtainedfor the coefficientsof the futures price and the expectationaldummy D1 are statistically significant. We note that long speculatorsin futures evidently respondonly to anticipatedexpansionaryconditions, and their demanddoes not exhibit a negative relationshipwith anticipatedslump conditions, perhapsbecausethey have alreadydivestedthemselvesof most of their long positionsbeforethe approachof a recession. It is convenientto discussthe results for both of the hedging equations,(3) and (5), together.In equation(3), which represents the supply of hedged storage and futures contracts by short hedgers,the results support the view that these economicagents determinetheir positionsaccordingto changesin the price spread, either for reasonsfor marginal net cost of storageor expectedbasis change,as discussedabove in Section 2. The parameterestimates

I ntertemporalA !location

115

for both non-AWe inventoriesand the price spreadhave the predicted signsand both are statisticallysignificant. Equation (5) representsthe demand for hedged storage and futures contractsby long hedgers.Although economic theory is less informative about the behaviourof long hedgersthan about that of short hedgers,we would have expectedthe positions of long hedgersto vary inversely with the price spread,as explained in Section 2. The results obtainedsupport this view, and the estimatedcoefficientsof the price spreadand the dummy variable D s, representingthe impact of the Japanesetextile industry on the Australian wool market, have the predicted signs, and both are statistically significant. Persuasiveevidence of the behaviour of long hedgers is scarce, perhapsbecauseof the belief - which economictheory has tendedto reflect - that in practice hedgers are generally net short. In any casethe results reported here for equation (5) may be one of the first empirical analysesof longhedgerbehaviour. Equation (4), the consumptionrelationship,performswell with a significant estimate of the relative price elasticity and a production elasticity of the predicted sign. In this equation the seasonaldummy variablesalso play an active role. As explainedin Section 2, the textile production index is used as a proxy for the influences of consumers'tastes and population changes,so the interpretationof the estimatedelasticity of 0.026 is not straightforward. In equation(6), which representsthe supply of futurescontracts by short speculators,all parameterestimateshave the predicted signs, although only one, the coefficient of the expectational dummy D 6 , is significant. We observe that short speculatorsin futures evidently respondonly to an anticipatedslump in futures prices and not to an anticipated boom, possibly for the same reasonsuggestedabovefor the lack of responseof long speculators to anticipatedslump conditions.

5. Conclusions This chapter presentsa simultaneousequationsmodel of commodity marketbehaviour,basedon Pestonand Yamey (1960) and modified for estimation purposes and to accommodate the characteristicsof the Australian wool market. We believe that this

116

IntertemporalAllocation

is for the first applicationof the Peston-Y amey model, which, in its reformulatedversion, has shownitself to be a potentially complete and sensitive formulation of commodity market phenomena. Further experimentation with expectations hypotheseswill be madein subsequentwork on other marketswith this model by the authors. The market studied is a useful vehicle for investigating the propertiesof the Peston-Yamey model: it is the world's largest wool futures market, and is a moderatelylarge futures market by world standards.Moreover, it is a well-informed market in which traders participate in an efficient price formation process (see Praetz,1975). A specialfeature of this market is that, for most of the sample period, hedgerswere net long, a feature not encountered in previoustheoreticaland empirical work. An importantaspectof our data-processing is the generationof data on the supply of and demandfor futures by long hedgers, short hedgersand speculators,which has hitherto beenunavailable for the Australian wool futures market. This has beenachievedby the utilization of floor memberinterview data and ClearingHouse turnoverrecords. The model presentedin this chapter contains functional relationships for long and short hedgers and for long and short speculatorsin futures, as well as holders of unhedgedinventories and consumers.The best performing relationships,with respectto intrasampleprediction,are thosefor consumersand for holdersof unhedged inventories, the latter being especially encouraging becausemost inventories of Australian wool are held unhedged. The hedging relationships,in which both groups of hedgersare found to respondinter alia to changesin the price spread,perform moderately well. The least well-performing functions are the speculativefutures relationships,an outcomewhich may be due to our unsophisticatedrepresentationof those agents'expectations. Nevertheless,both spot and futurespricesare well predictedby the model within the sampleperiod. Finally, our conclusion is that these results are sufficiently encouragingto warrant further researchon specification of the functional relationships,especially the representationof expectations,and an extensionto other commodities.

IntertemporalAllocation

117

Notes *Monash University, Australia. Earlier versionsof this chapterwere presented at Eighth Conferenceof Economists,La Trobe University, Melbourne,in August 1979, and to a Monashworkshop.The researchon which this chapteris basedis part of a continuing project supportedby the Australian ResearchGrants Committee.Thanksare due to the SydneyFuturesExchangeand Floor Members of the Exchange,InternationalCommoditiesClearingHouse,and the Australian Wool Corporationfor the provision of data. We also wish to thank Louis Phlips for his helpful advice and JennyLau for her painstakingresearchassistance.Any remainingerrorsare the responsibilityof the authors. 1. Hedgers'actualscommitmentsare representedin the long- or short-hedging categoriesonly to the extent that they are fully hedged.Unhedgedactualspositions or futures positionsnot matchedby actualscommitmentsare assumedto be includedin the appropriatespeculationcategory. 2. In law, the purchaseof a futures contractdoesnot give a title to any particularunit of the physical commodity,and in reality most such positionsare closedout by reversal(selling futures) rather than by taking delivery. 3. The modelsof Kaldor and Brennanassumeidentical expectations,so that A."+I is the meanexpectationfor all individuals, and the marketexpectation.If heterogeneous expectationsare assumed,then the marketexpectationA."+ I may be interpretedas a weightedaverageof individuals' mean expectedprices. 4. Pestonand Yamey (1960) do not preciselydefine the term 'available supply'. On page355 it is referredto as a 'given supply' to be allocated,while on page358 it is statedthat 'the total stock ... must be allocated'.An alternative ~K, interpretationto that adoptedin this paperis to re-write the left side of (7a) as ~Kt + Cl and to define Zt - X. as the 'availabledomesticsupply' of wool, and~Kt + Ct as the disposalof that supply. In somemonthsof the period studied,however, ~K, is negativeand the Peston-Yameymodel is not defined for negativechangesin ~Kt stocks,althoughconceivablyit could be reformulatedto admit suchcases. 5. The price clean varies inverselywith the yield, for a given greasyprice. Prior to 1973, A WC spot price quotationswere thOUght to be inflated becausesubjective appraisalof yield was employedfor wools sold at auction, and subjectiveappraisal evidently understatesthe yield comparedwith objective(core-testing)appraisal (seeDouglasand McIntyre, 1970, where the reportedestimatesof the subjective appraisalare on average3.61 per cent below thoseof the objectiveappraisals). Spot pricesduring our sampleperiod are to someextentaffectedby this factor becausecore-testingtechniqueshave beenintroducedprogressivelyfor wools sold at auction from 1973 onwards,the proportion of auction wool so testedranging from 17 per cent in 1973-4to 75 per cent by the end of our sampleperiod. Nevertheless,when spot prices were adjustedfor the presenceof subjective appraisalthe results,especiallyfor equations(1) and (4) were lesssatisfactory,and the adjustmentwas deleted.(Deliverablewools on the SydneyFuturesExchange are core tested.) 6. The definition of the six months futureis as follows: when the month is January,February,the future is July; when the month is March, April, the future is October; when the month is May, June,July, the future is December;when the month is August, September,the future is March; when the month is October, November,the future is May; when the month is December,the future is July. 7. To the extent that farmers' hedgingof growing wool is included in Ht' this variableoverstatesthe volume of inventory of raw wool.

118

IntertemporalAllocation

References Brennan,M.I. (1958) 'The Supply of Storage',AmericanEconomicReview,48, 50-72. Bureauof Agricultural Economics(1967) The Price Elasticity of Demandfor Wool in the United Kingdom,Wool EconomicResearchReport no. 11, Canberra. Douglas,S.A.S. and G.A. McIntyre (1970) Subjectiveand ObjectiveAppraisalof Wool, Wool EconomicResearchReport no. 20, Bureauof Agricultural Economics,Canberra. Giles, D.E.A. (1977) 'StatisticalInferenceand the RBA76 Project',in W.E. Norton (ed.), Conferencein AppliedEconomicResearch,Sydney: Reserve Bank of Australia. Goss,B.A. (1972) 'Trading on the SydneyWool FuturesMarket: a Test of a Theory of Speculationat the Level of the Individual', A ustratian Economic Papers, 11, 187-202. Griliches, Z., G.S. Maddala,R. Lucasand N. Wallace (1962) 'Noteson Estimated AggregateQuarterlyConsumptionFunctions',Econometrica,30,491-500. Hicks, I.R. (1939) Value and Capital, London: Oxford University Press. Houthakker,H.S. (1968) 'Normal Backwardation',in I.N. Wolfe (ed.), Value, Capital and Growth: Papersin Honour of Sir John Hicks, Edinburgh: EdinburghUniversity Press. lohnson,L.L. (1960) 'The Theory of Hedgingand Speculationin Commodity Futures',Reviewof EconomicStudies,27,139-51. Kaldor, N. (1939, 1961) 'Speculationand EconomicStability', Reviewof EconomicStudies,7,1-27. Reprintedin N. Kaldor (ed.), Essayson Economic Stability and Growth, London: Duckworth. Mills, E.S. (1962) Price, Outputand Inventory Policy, New York: Wiley. Nerlove, M. (1958) 'Adaptive Expectationsand CobwebPhenomena',Quarterly Journal of Economics,72, 227-40. Peston,M.H. and B.S. Yamey (1960) 'IntertemporalPrice RelationshipsWith ForwardMarkets: A Method of Analysis', Economica,27,355-67. Praetz,P.D. (1975) 'Testingthe Efficient MarketsTheory on the SydneyWool FuturesExchange',Australian EconomicPapers, 14,240-9. Rockwell, CS. (1967) 'Normal Backwardation,Forecasting,and the Returnsto Commodity FuturesTraders',Food ResearchInstitute Studies,7, Supplement, 107-30. Working, H. (1953) 'FuturesTrading and Hedging', AmericanEconomicReview, 43,314-43. Wymer, CR. (1977a)'ComputerPrograms:RESIMUL Manual', International MonetaryFund, Washington,D.C, mimeo. (1977b) 'ComputerPrograms:SIMUL Manual', InternationalMonetary Fund, Washington, D.C.,mimeo. (1977c) 'ComputerPrograms:TRANSF Manual', InternationalMonetary Fund, WashingtonD.C, mimeo. Yamey, B.S. (1971) 'Short Hedgingand Long Hedgingin FuturesMarkets: Symmetryand Asymmetry', The Journal of Law and Economics,14,413-34.

5

AN ANAL VSIS OF INVESTMENT HORIZON AND ALTERNATIVE RISK-RETURN MEASURES FOR COMMODITY FUTURES MARKETS Cheng-Few Lee and Raymond M. Leuthold*

1. Introduction

The natureof risk and returns,and how to measurethem in investment markets,hasbeendiscussedfor many years.Regardingcommodity futures markets, Keynes (1930) first proposed that speculatorsearneda risk premium as their reward for absorbing hedgers' risks. Gray (1961) could not find the suggestedprice biases required to support Keynes's underlying hypothesis. Rockwell (1967) measuredratesof return for groupsof tradersin commodity futures markets with semi-monthly data,but did not examine risks. Futures contracts have long been recognizedfor their ability to transferrisk from hedgersto speculators,but little is known about the risk and return relationshipand how it changes over investmenthorizons. Considerablemethodologicaladvancementhas been made in the last 15 years with respect to identifying, measuring and determiningrisk and returns. Best known for its developmentand empirical use are the Sharpe(1963) single index model (market model) and the capital assetpricing model (CAPM) developedby Sharpe(1964) and Lintner (1965). Thesemodelswill determineto what extent variations in individual rates of return are systematically related to variations in market rates of return, and the market model can be usedto decomposetotal risk into systematic and unsystematic risk components. These models have been applied to such securities as stocks, bonds, options and mutual funds, but to date the only known applications to commodity futures markets are Dusak (1973) and Bodie and Rosansky (1980). Dusak estimatedsystematicrisk for a sampleof semi-monthly pricesof wheat, corn and soybeanfutures contracts,1952-67,and found it to be close to zero in all cases.Average realized returns were also close to zero. Theseresults may be non-representative, 119

120 AnalysisofInvestmentHorizon however, becausemany traders in commodity futures markets have very short-run investmenthorizons. Semi-monthlydata may not capturethe true natureof the risk and return relationshipthat thesetradersface. Bodie and Rosansky(1980) also found systematic risk nearzero for 23 commoditiesover a 27-yearperiod, but holding period returns were strongly positive. Their results, however, are based on quarterly data, or three-month holding periods, which far exceed average investment horizons. When examining commissionhouserecords,Ross (1975) found that 52 per cent of the tradeswere held less than sevendays. Only 30 per cent were held 15 or more days. Since thesedata did not include floor traders who usually have investmenthorizons shorter than one day, the average length a contract is held is undoubtedly shorterthan that reportedby Ross. Trade expertssometimestalk of an averageholding period of three days. Recently, several analysts have examined the relationship between investment horizon and measuresof risk and returns. Chengand Deets (1971) discussedthe statisticalbiasesassociated with security rates of return estimates.Levhari and Levy (1977) point out the disparitieswhich arise when arbitrarily selecteddata are used for a period which is different from the 'true' horizon. Blume (1974) derived some unbiased estimators of long-run expected rates of return. These authors all demonstratethe importanceof the impact of investmenthorizon on the estimateof expected rates of return and related risk proxies. Empirical investigationsof this for commonstock have beendone by Cheng and Deets (1973), Levhari and Levy (1977), Lee and Morimune (1978), Lee (1976) and others. In addition, skewnessor kurtosis in the distribution of returns may vary with investmenthorizon. The shapeof the return distribution could be used as a criterion for determining the appropriatenessof an investment horizon. For example, Hagerman (1978) has shown that the distribution of stock market rates of return is not independentof changesin time horizon, while Folger and Radcliffe (1974) have found the degreeof skewnessfor stock market rates of return is not independentof investmenthorizon. Suchrelationshipsin commodityfutures marketsare not known. The purposeof this chapteris to estimatethe betasfrom the market model for 42 selectedcommodity futures contractsfrom 1972-7 in order to test the relationship between investment horizon and alternative risk-return measures,to describe the

AnalysisofInvestmentHorizon

121

probability distribution of price changesin futures over different interval lengths, and to explore the sensitivity of the results to alternative measuresof wealth. We do this by using daily futures prices, varying investmenthorizonsfrom 1 to 22 days, and using both a stock price index and a commodity price index as proxies for the return on wealth. Since a proxy for daily risk-free rates of return is difficult to obtain, the market model instead of the CAPM is usedin this empirical study. The data usedin this study are describedin the secondsection. The third section explores the relationship betweenhorizon and eachof the first four momentsof the ratesof return. In the fourth section, rates of return for the commodity futures contractsare regressedagainsteachof the two indices as risk is decomposedin eachcontract.The fifth sectionteststhe risk-returntrade-offs,and the results of the chapterare summarizedin the final sectionwith possiblefuture researchindicated. 2. The Data

The stock index usedin this paperis the Standardand Poor (S&P) CompositeIndex of 500 industrial commonstockscollecteddaily. The daily commodity futures index (CFI) is based on 27 commodities and is constructedby the Commodity ResearchBureau, Inc. The 42 individual contractsanalysedare the Decembercorn, wheat, hogs and cattle contracts,and the Novembersoybeancontract, all for 1972-7. Since there is no correspondingyear-ending contract for pork bellies, the following February contract was selected for analysis. Thus, in the tables presentedbelow, the resultsfor pork bellies under any given calendaryear refer to the Februarycontractmaturingthe following year (for example,under 1973 will be results for the February 1974 pork belly contract). Also analysed are the December gold (International Monetary Market), silver (Chicago Board of Trade) and Treasury Bill (International Monetary Market) contractsfor 1976-7. Since the contractsfor differing maturitiesof one commodity usually fluctuate fairly close together,using one contractper commodity within a year is sufficient for analysis. The above commodities also representthe most actively traded commodity futures contracts and provide an ample cross-sectionof alternative investment possibilities.

122 AnalysisofInvestmentHorizon Most contracts trade for about one year, although the exact dates for trading vary among commodities. Table 5.1 lists the numberof observationsfor eachof the 42 contractsanalysed. Commodityfutures contractsare highly leveraged.Typically, an investor needsto post only about 10 per cent of the value of the contract. As is becoming commonly accepted, and argued by Dusak (1973), from a generalequilibrium point of view the spot commodity is the relevantasset.Spot price data, however,are not readily accessible,and in some casesinvolve estimatingand discounting for storagecosts.Also, the degreeof leveragecannotbe measuredon an individual basis. Thus, for computationalconveniencewe utilize futures prices, and measurereturnsas percentage changesin unleveragedcontract values. Leveragedreturns would exceedthose reported here by about a factor of 10. Both logarithmic and arithmetic rates of return are calculated and analysed.The averagelogarithmic rates of return will be slightly smaller than the averagearithmetic rates of return, although the resultsare so similar that we presentonly the arithmetic results. Many professional traders do not hold positions overnight. Those data are not available to us, but the techniquesdeveloped herecould be appliedto transaction-by-transaction data.We chose a 22-day horizon as the maximum, since that is approximatelythe number of trading days in one calendarmonth. Due to limited computerfunds and similarity of results over horizons, we report individual commodityresultsonly for horizonsof 1-10, 15, 16, 21 and 22 days.

Table 5.1: Number of Observations in Each Contract Analysed Year Commodity Wheat Corn Soybeans Hogs Cattle Pork bellies Gold Silver Treasury Bills

1972

1975 1973 1974 1975

242 240 243 306 323 244 224 285 239 282 243 243 240 258 243 236 243 282

243 243 302 303 243 364 316

1975

1976

1977

301 312 289 287 246 209 287

244 303 285 276 279 287 236 358 349 244

304 304 279 329 290 301 366 373 373

AnalysisofInvestmentHorizon

123

3. Statistical Distributious of 42 Individual Futures Contracts and their Time-Moment Relationships

Ratesof return, both discreteand continuous,were computedfor eachof the 42 futures contractsfor eachof the above 14 horizons. For the ith horizon, returnsare computedfor the formulation (Pt+i - Pt)/Pt. The returnsare computedfor non-overlappinghorizons. For example,with 242 observationsfor the 1972 wheat contract, there are 241 one-day horizons and 24 ten-day horizons. These returnsare for the 'long' side of the market, that is, for thosewho buy and hold futures contracts.Since for every buyer there must also be a seller of a futures contract, an investor maintaining a 'short' position in the futures market would have the negativeof the return calculated for the 'long' position. Commissionsand other trading costsare ignoredin this analysis. For each of the 588 combinationsof contract and investment horizon, the averagerate of return, the standarddeviation, coefficient of variation, skewness and kurtosis were estimated. Individual resultswill not be presented.Rather,the relationshipof eachmomentwith respectto time will be discussed.This will give someunderstandingof the natureof the distribution. First, tests were conductedon the skewnessand kurtosis coefficients to determine whether rates of return are normally distributed. The formulas are: skewness = moment 3/(cubed standarddeviation),and kurtosis = moment4/(squaredvariance). The standarderrors usedto test the relativenessof the coefficients are (Snedecorand Cochran,1967, pp. 86-8):

S S

[6n(n-1)/(n-2)(n+1)(n+3)]112

(1)

[24n(n-l)2/(n-3)(n-2)(n+3)(n+5)]112

(2)

whereSI is the standarderror for skewness,S2 is the standarderror for kurtosis and n is samplesize. There is no apparentpattern to the percentageof skewnessand kurtosiscoefficientsby commodity and horizon which are sufficiently different from zero, exceptthat rates of return are more likely to be normally distributed at the longer horizons. Overall, 16 per cent of the skewnesscoefficients and 18 per cent of the kurtosis coefficientsare significantly different from zero. Thus, the vast majority of commodityratesof return over alternative horizons are normally distributed, indicating

124

AnalysisofInvestmentHorizon

standardstatisticaltestscan be conducted. To investigate time-moment relationships, the first four momentsand the coefficient of variation for eachof the 42 futures contractswere regressedagainstthe horizon length. Each contract was regressedindividually, using the momentsfrom eachhorizon. Both linear and non-linear relationshipswere tested, but the coefficients for the non-linear variables were for the most part not significantly different from zero. Among these contracts, linear relationshipswere by far the most prevalent. In any event, these tests are designed to summarize results, and not meant to test linearity per se. The slope coefficients for the averagerate of return are presented in Table 5.2. All of the mean rate of return slope coefficients, as well as all of the standarddeviationslope coefficients and all but five of the coefficient of variation slope coefficients, Table 5.2: Slope Coefficient from Time-Moment Relationship Mean Rate of Return (AT = a + bT) Year* * 1972

1973

1974

1975

1976

1977

Wheat

.231* (,006) a

.416* (.007)

.030* (.008)

-.123* (.003)

-.122* (.004)

-.054* (.003)

Corn

.080* (•013)

.254* (.008)

.200* (.002)

-.068* (.003)

-.048* (.002)

-.058* (.002)

Soybeans

.090* (.005)

.240* (.006)

.128* (.006)

-.160* (.002)

.072* (.008)

-.011* (.004)

.089*

.254* (.008)

.039* (.004)

.069* (.007)

-.053*

.051*

(.009)

(.005)

Commodity

Hogs

(.005) .059*

.048*

-.087*

.073*

-.018*

-.026*

(.008)

(.009)

(.004)

(.002)

(.004)

(.004)

.117*

.127*

.063*

.066*

-.064*

.026*

(.005)

(.006)

(.003)

(.002)

(.004)

(.004)

Gold

-.077* (.002)

.069* (.004)

Silver

-.085*

-.030*

(.001)

(.002)

.008* (.000)

.007* (.000)

Cattle Pork bellies

Treasury Bills

Notes: ' The standard error is in parenthesis. * Significantly different from zero at the 95 per cent level of confidence.

** All estimates in this table have been multiplied by 10'.

AnalysisofInvestmentHorizon

125

were significantly different from zero. This meansthat the change in thesedescriptivestatisticsis significantly relatedto the changein investmenthorizon. Table 5.2 indicatesthat of the 42 contracts,26 mean rates of return slopes were positively related to the change in horizon, while 16 contractswere negatively related. A positive (negative) relationship implies that the average rate of return increases (decreases)with respectto an increasein investmenthorizon. The sign reflects the trend of that particular contract from the 'long' side and demonstratesthe importanceof prior forecast analysis. All of the slopesfor 1972 and 1973 and all but cattle for 1974 had positive relationships. The signs of the slopes were mixed for 1975-7. The results of positive investment returns conform in general to those given by Bodie and Rosansky (1980), where quarterly data were examined.The reader is reminded that our ratesof return are for unleveredcontracts. All the slope coefficients for the standarddeviationsregressed against time are positive, meaning standard deviation increases with increasedinvestment horizon. The signs for the significant coefficient of variation slopes are the opposite of those in Table 5.2 for the averagerates of return. Of the five slopeswhich are insignificant, individual mean returns are near zero, sometimes alternatingsign over horizon, therebyinfluencing the magnitudeof the coefficient of variation. Further investigationof theseresultsshowedthat mean returns always increase(in absolutevalue) faster than the standarddeviation as horizon increases.Thus, an increasein the holding period can improve investment performance providing one is on the 'right' side of the market, i.e. long as prices rise and short when pricesfall. Finally, 13 of the 42 futures contracts have skewnesssignificantly related to investmenthorizon, while kurtosis and investment horizon are significantly related in 21 cases.For the most part, if skewnessof a contractis relatedto horizon, kurtosis of the contractis not relatedand vice versa.Thus, as opposedto the first two moments, the third and fourth moments are largely independentof each other. The results indicate that the shapeof the distribution of commodity future rates of return are not independentof alternativehorizonsused. However, no distinct pattern emerges.

126

AnalysisofInvestmentHorizon

4. Systematic Risk and Non-Systematic Risk Decomposition for 42 Individual Futures Contracts

Based upon the theory and concepts of the market model developedby Sharpe(1963) and Fama(1973), the ratesof return of the 42 individual commodity futures contractsare regressedon the stock market index and the commodity futures index. The regressionmodelsare defined as:1 R ~t mt R ~t mt R ~t mt

where

+ BsRmt + Ejt a' + BeRet + E'jt

(3)

a

(4)

rates of return for jth futures contractsin period t,

R mt

stock market (S&P) rates of return in period t,

RC!

futures market (CFI) rates of return in period t,

Ej,Ei,

error terms.

Since there are 588 contract-horizoncombinations,only summaries will be presented.Table 5.3 indicates the number of Bc coefficientssignificantly different from zero, while Table 5.4 indicatesthe numberof Bs coefficientssignificantly different from zero (in eachcaseout of 14). Theseresultsshow that ratesof return of individual futures contracts are strongly related to the rates of Table 5.3: Number of ~c Coefficients Significant (.05 Level) over 14 Alternative Horizons (1, 2, ... ,10,15,16,21,22) Year Commodity Wheat Corn Soy beans Hogs Cattle Pork bellies Gold Silver Treasury Bills

1974 1972 1973 13 10 14 14 14 14 14 14 14 14 14 14 14 10 14 14 14 14 7 14 14 10 14 14 14 14 14 9 11 13 4

1975 14 14 14 14 11 11 10 13

1976 14 11 14 11 14 14 14 6 11 4 12 14 0

1977 13 14 14 14 14 14 9 8

14 11 0

AnalysisofInvestmentHorizon

127

Table 5.4: Number of ~s Coefficients Significant (.05 Level) over 14 Alternative Horizons (1, 2, ... , 10, 15, 16, 21, 22) Year

Commodity Wheat Corn Soybeans Hogs Cattle Pork bellies Gold Silver Treasury Bills

1972

1973

1974

1975

1976

1977

1 1

0 0

0 0

0

0

0

0 0

10 3

1 0

2 0

0 1

0 0 1

1 0

0 0

0 1

0 0

4 0

0 0

0 0

0 0 0 1

0

4

return of the CFI; however,the ratesof return of individual futures contractsare generallynot significantly relatedto ratesof return of S&P. Table 5.3 indicatesthat ~c|3Cfor corn is always significantly different from zero, regardlessof horizon. However, gold has less than half of the ~c|3C coefficients significant, and none is significant for TreasuryBills. Theselatter results probably reflect the 'agricultural' bias to the CFI, and that thesecommoditiesare countercyclical to agricultural prices. It is interesting,however, that most of the silver |3 (3c |3CC coefficientsare significant. Finally, 1972 standsout as a year of relatively less significant ~c|3C coefficients in Table 5.3, althoughthe reasonis not clear. Table 5.4 shows that most of the ~s|3C coefficients are not significantly different from zero for both agricultural and nonagricultural commodities.The only unusualresult is for soybeans, 1972, where 10 of the 14 horizonsare significant. As a meansof further evaluation,equations(3) and (4) were combined into a multiple regressionequation where the rate of return was regressedon both indexesat the sametime. The results were virtually identical to thosein Tables5.3 and 5.4. Over 80 per cent of the ~c|3C coefficients were significant and substantiallyless ~sC coefficientswere significant. There was than 10 per cent of the |3 also a distinct trend for the R 2 to increaseas horizon increasedfor any given contract. Becauseof its relative simplicity, the singleindex model seemsappropriatefor our study. These results show that commodity futures contracts have a high degree of systematic risk relative to the CFI, but mostly

128

AnalysisofInvestmentHorizon

unsystematicrisk with respectto S&P. So for a portfolio consisting of common stocks, commodity futures contractswould provide diversification and would be attractive to the investor. On the other hand,an investorwith a portfolio of commodityfutures contracts would probably not want to add more non-diversifiable futures contracts to the portfolio, except for gold and Treasury Bills. Theselatter resultssupportin part thoseof Dusak (1973), who found little to no systematicrisk betweencommodityfutures contracts and the stock index using semi-monthlydata. Most of the ~ coefficientsin Bodie and Rosansky(1980) basedon quarterlydata were also insignificant. They confirm Holthausen and Hughes' (1978) findings that the ~ coefficients are very sensitive to the marketindex selected.Unfortunately,an overall wealth index does not exist. To show whetherthe CFI is relatedto the S&P index, the CFI is regressedon the S&P index to test for the existenceof systematic risk in the CFI, using the equation:

where

R R~ct

a+ ~R~t+|3C

Rct Rmt

ratesof return for CFI

T

Et

(5)

ratesof return to S&P 1, ...,22.

(The regressionresultsfor eachof 22 horizonsare not reproduced here for reasonsof space,but are availableupon request.) The ~ coefficient is significantly different from zero only for the twelve-dayhorizon, wherethe coefficient is negative.That is, there is little to no relationship, or systematicrisk, between the two indexes.2 Theseresults imply that commoditiesin the CFI can be included in an equity portfolio to reduce risk and improve performance of the portfolio. Futures contractsas a whole have no systematicrisk relative to stocks,and would serveto provide diversification within a portfolio composedof stocks. The orthogonal relationshipbetweenRct and Rmt can also empirically be used to demonstratewhy the empirical resultsof a single-indexmodel are almost indenticalto thoseof a multi-index model. In order to see the relative magnitudesof the various ~ coefficients, Tables 5.5 and 5.6 presentthe average~c and ~s|3C over

AnalysisofInvestmentHorizon

129

Table 5.5: Average ~c|3Cover Horizon Year

Commodity

1972

1973

1974

1975

1976

1977

Wheat

1.666 (.257)'

1.165 (.262)

1.344 (.133)

1.542 (.074)

1.465 (.135)

.926 (.111)

Corn

1.573 (.286)

1.522 (.155)

1.417 (.078)

1.259 (.071)

.900 (.127)

1.110 (.093)

Soybeans

.767 (.418)

1.888 (•237)

1.686 (.309)

1.554

1.988

(.113)

(.169)

.610 (.174)

1.007 (.223)

1.507 (.322)

.781

1.097 (.164)

Hogs Cattle Pork bellies

(.171)

1.889 (2.15) .952 (.151)

.758

.689

1.100

.648

.590

.631

(.203)

(.289)

(.290)

(.121)

(•138)

(.089)

.542 (.289)

.867

1.286

(.224)

(.180)

.954

1.474

.878

(.183)

(246)

Gold

.289 (.137)

.635 (.129)

Silver

.973 (.212)

.652 (.077)

Treasury Bills

(.163)

-.008 (.018)

-.001 (.023)

Note: ' The standard deviation is in parenthesis.

horizonsfor eachof the 42 contracts,respectively,while Table 5.7 shows both coefficients averagedacrosscommodity contractsfor eachhorizon. In Table 5.5 almost all of the ~c coefficients for the grains (wheat, corn and soybeans)are greater than 1.0, meaning those commoditieshave beenmore volatile than the futures market as a whole. Conversely, most of the meat product (cattle, hogs and pork bellies) ~c|3C coefficientsare less than 1.0, but greaterthan zero. These commoditieshave been less volatile than the market as a whole. The gold and silver coefficients are betweenzero and 1.0, but the TreasuryBill coefficientsare very small and negative. Table 5.6 shows that most of the |3 f\C coefficients are small in value, especiallyrelative to their standarderrors, with a high proportion of them negative.This again shows that there is little relationship betweenchangesin the stock index and changesin the value of individual commodityfutures contracts. Table 5.7 showsthe ~s|3C coefficientswhen measuredacrosscommodities to be very small for all horizons,and all negativebeyond

130

Analysisof InvestmentHorizon

|3C Table 5.6: Average ~s|3Cover Horizons Year

Commodity

1972

Wheat Corn Soybeans Hogs

1973

1974

1975

1976

1977

.487 (.334)»

-.199

.080

-.279

.267

(.348)

(.158)

(.142)

(.180)

.207 (.156)

.085 (.223)

-.080 (.259)

-.145 (•133)

-.150 (.270)

.106 (.131)

(.184) .148 (.362)

.064

.474

.171

(.180)

(.811)

-.027 (.244)

-.305 (.338)

-.101 (.123)

.049

-.000

-.294 (.288)

(.376) -.681 (.438)

-.092

-.297 (.675)

-.260

-.016 (162)

-.102 (.415)

-.521 (•199)

(.235)

(.160)

Cattle

-.423 (.405)

(•295)

(•179)

-.302 (.226)

Pork bellies

-.472 (•279)

-.138 (.441)

.032 (.208)

-.310 (.336)

.173

-.150

Gold Silver

.138

.061

Treasury Bills

-.158 (.236) (.078) (.252)

(.350)

.060 (.239)

.019 (.017)

.037 (.026)

Note: ' The standard deviation is in parenthesis.

the four-day horizon. The /3c coefficients are all slightly larger than 1.0 and very similar in magnitude regardless of the horizon. Thus, the /3c coefficients show no sensitivity to horizon, while the /3s coefficients, all small in magnitude, show decreasing, but probably not significantly changing, systematicrisk with respect to S&P over horizon.3 5. Risk-Return Trade-Off Test In Section 1, the importance of testing the existence of a risk premium (in a total risk sense)for the commodity futures contracts was explored. Alternative cross-sectionalmodels used to test this are:

Rj

=

a, + b ^j

(8)

Rj

=

a2 + b2ps

(9)

Analysisof InvestmentHorizon Table 5.7: Average Horizon (Days)

~

131

across Commodities for each Horizon

~

for Stocks

~

for Commodities

1

.041 (.132)'

1.028 (.476)

2

.012 (.151)

1.018 (.454)

3

.013 (.186)

1.060 (.474)

4

.017 (.240)

1.051 (.449)

5

-.033 (.203)

1.067 (.445)

6

--.046 (.267)

1.048 (.468)

7

-.037 (.306)

1.055 (.486)

8

-.067 (.362)

1.057 (.526)

9

-.124 (.307)

1.041 (.551)

10

-.137 (.312)

1.057 (.516)

15

-.152 (.514)

1.095 (.539)

16

-.157 (.590)

1.077 (.557)

21

-.101 (.604)

1.071 (.591)

22

-.260 (.619)

1.133 (.641)

Note: 'The standard deviation is in parenthesis.

~s,~c~s,~c

where

~s,~c~s,~c ~s,~c~s,~c

(10)

~s,~c~s,~c

averagerate of return for the jth contract

~s,~cOJ ~s,~c

standarddeviationfor the jth contract

~s,~c~s,~c

as previouslydefined.

The empirical resultsfor equations(8-10) using 42 contractsfor observationsare presentedfor 14 alternativehorizonsin Table 5.8. No relationshipexistsbetweenaverageratesof return and the esti-

AnalysisofInvestmentHorizon

132

Table 5.8: Results of Regressing Mean Rate of Return on Selected Variables in Analysing Risk-Return Trade-ofts Independent Variable Horizon (Days)

R'

13,

R'

13,

R'

2

.0494 (.0294)'

.07

.0000 (.0014)

.00

.0003 (.0004)

.01

2

.0964' (.0380)

.14

.0002 (.0024)

.00

.0008 (.0008)

.03

3

.1040' (.0461)

.11

.0005 (.0029)

.00

.0011 (.0011)

.02

4

.1004 (.0547)

.08

.0023 (.0029)

.02

.0009 (.0016)

.01

5

.1317* (.0578)

.11

-.0005 (.0044)

.00

.0018 (.0020)

.02

6

.1342' (.0604)

.11

-.0012 (.0040)

.00

.0014 (.0023)

.01

7

.1242 (.0651)

.08

.0024 (.0041)

.01

.0008 (.0026)

.00

8

.1814' (.0645)

.17

-.0007 (.0040)

.00

.0025 (.0027)

.02

9

.1844' (.0661)

.16

-.0007 (.0053)

.00

.0026 (.0030)

.02

10

.2088' (.0662)

.20

-.0026 (.0058)

.01

.0046 (.0035)

.04

15

.2824' (.0780)

.25

.0006 (.0054)

.00

.0013 (.0051)

.00

16

.2597' (.0737)

.24

.0076 (.0049)

.06

.0079 (.0052)

.06

21

.2292' (.0909)

.14

.0085 (.0061)

.05

.0046 (.0063)

.01

22

.3218' (.0736)

.32

-.0154' (.0063)

.13

.0096 (.0064)

.05

Note: '

0,

The standard error is in parenthesis.

, Significantly different from zero at the 95 per cent level of confidence.

mated~s and ~c exceptfor Ps at the 22-dayhorizon. Thereis, however, a significant positive relationship between ~ and Gj for all horizonsexceptone-, four- and seven-dayhorizons. Theseresults imply that there may exist a risk premium for commodity futures contractsif the total risk insteadof the systematicrisk measureis used. Nevertheless,this analysis does not shed any light on the normal backwardationhypothesis,since we did not adjust futures

Analysisof InvestmentHorizon

133

prices for the rise in cash prices (Gray, 1961). Also, this analysis identifies only ex-postrisk-return trade-offs. Most recently, Levy (1978) has shown that the CAPM is not necessarilyan applicabletool for decomposingthe total risk into systematicand non-systematicrisk unlesssomestrongassumptions are held. One of theseassumptionsis that the security should be widely held by investors. If the security is held by only a small group of investors,then the market rates of return obtainedfrom an overall index (e.g. S&P) will be subject to measurementerror and the estimatedbeta will be downward biased. As futures contracts are not widely held, the market rates of return calculated from the S&P index will probably be inappropriate.Nevertheless, results in this section have shed light on the usefulnessof the market model, or CAPM, and the importance of investment horizon in determiningthe risk-return relationshipof commodity futures contracts. .

6. Implications and Conclnsions

Futuresmarketsare widely recognizedas a meansfor transferring risks through hedging.This chapterreports the investigationof the statistical distribution and the time-moment relationshipsamong 42 futures contractsand the impact of investmenthorizon on the estimatedbeta coefficient. Daily data on contractsfrom 1972-7 are usedin the analysis.The use of daily data is importantbecause most contractsare held for only a few days. The meanratesof return dependupon the direction of the price movesduring the life of the contract,and they were positive for all but one contract during 1972-4. Results for 1975-7 were mixed with regardto sign. However, all ratesof return (in absolutevalue) and standarddeviationsbecamelarger as horizon increased,showing returns were not independentof horizon. Thus, investment performanceimprovedas horizon increased,as long as one was on the 'right' side of the market. The shapeof distributionsof ratesof return is also not independentof alternative horizons used. Few contracts,however, had significant third or fourth moments,indicating ratesof return are normally distributed. The ratesof return for the 42 contractsshow strong systematic (non-diversifiable) risk with respect to the commodity futures index, but in generalonly non-systematic(diversifiable) risk with

134 AnalysisofInvestmentHorizon respectto the stock index. Theselatter resultsapply to agricultural and non-agricultural commodities alike. Hence, commodity futures permit reductionof risk throughdiversificationfor a stockholder. For the commoditiesinvestor, such risk diversification can come only through investing in gold or Treasury Bill futures. In general, individual stock investors seeking risk reduction would have found the addition of commodity futures to their portfolio attractive. This set of results would be magnified if futures positionshad beenleveragedin the analysis.However,whetherthe investor should be on the short or long side of the market is a matter of forecast analysisand beyond the scopeof this chapter. These results are quite consistent across contracts as well as horizon. Unsystematicrisk and horizon are basically independent of eachother. Further work needs to be done analysing why the divergent results exist betweenthe two indexes.The security market index does not appearto be a good proxy for a capital market index, especiallyin the study of commodities.A compositewealth index is needed.It may also be that industry rather than generalmarket factors influence the pattern of inter-relationshipsamong commodity futures market returns. Industry factors may be highly correlated with returns ex post. It remains to be explored how futures relate to generalequilibrium pricing conditions. To investigate the appropriatenessof the CAPM in studying returns,we regressedcross-sectionalmeanreturnsagainstthe individual betas for each horizon. Expecting positive relationships betweenmeanreturnsand non-diversifiablerisks, we found only 1 of 28 relationshipssignificant. There was, however, a significant relationshipbetweenthe mean returns and standarddeviation in 11 out of 14 cases.Thus, there may be a slight risk premium in a total market sense, but not necessarily from normal backwardation. Further work is needed on the use of CAPM in commodityfutures, especiallyinvestigatingalternativehorizon and index combinations. Finally, the fact that commodityfutures contractshave limits in their daily price moves suggeststhat truncateddistribution techniques of analysis may be appropriate and sensitive. Another importantareaof researchwould be the impact of inflation on the futures contracts and risk-return relationships over alternative horizons and against alternative indexes.The existenceof a risk premium in commodity futures contracts needs more careful

AnalysisofInvestmentHorizon

135

analysisto distinguish betweendifferent measuresof risk. Besides the standarddeviations and beta coefficient, semi-varianceand mean absolutedeviation can also be used as risk proxies (Stone, 1973). Furtherinvestigationis also neededon the impact of autocorrelationon the momentsof the distribution and risk (premium) estimates. Nevertheless,the empirical work here has provided additional information concerning commodity futures contracts within the realm of asset price determination and portfolio management. Notes *Departmentof Financeand Departmentof Agricultural Economics,respectively, This researchwas partly funded by the University of Illinois at Urbana-Champaign. ChicagoMercantileExchange. 1. The derivation of this equationin essencecomesfrom the conceptof portfolio theory. A portfolio consistsof severalindividual assets,and to regressthe returnsof an individual securityon the returnsof the portfolio (or market returns) measuresthe sensitivity or responsiveness of the securityto that of the market. This market model can be usedeither for forecastingor risk decomposition.Our concernis for the latter. The total risk for the jth futures contract,Var can ~t' can be be decomposedas follows: Var R,, Var~t

=

Pf Var Rm, + Var Ej t

where f3l Var Rmt is systematic(non-diversifiable)risk, and Var Ejt is non-systematic(diversifiable) risk. SinceVar Rmt is commonto every futures contract,f3j can be usedas a relative measureof systematicfluctuation betweenthe jth contractand all other contractsin the market which are representedby a market index. 2. An updateof this analysisthrough 1981 showsno changein the lack of relationshipbetweenthe two indexes(seeLee, Leuthold and Cordier, 1985). 3. To investigatethe time-variancerelationshipsfor [3, and [3" 42 regressions were run in accordancewith the following two equations: pcT

=

a, + b,T

(6)

Pst

=

a, + b2T.

(7)

The resultsdemonstratethat thereexistssomerelationshipbetweenthe magnitude of [3, and 13, and investmenthorizon, althoughless than half of the coefficientsare significant and the significant onesare scatteredacrosscommoditiesand years.As expectedfrom the previousset of tables,most of the slopecoefficientsfor the [3'T regression(equation(7» are negative.Thus, there is not a strongrelationship betweenthe size of the 13 coefficient, indicating systematicrisk, and investment horizon.

136 AnalysisofInvestmentHorizon References Blume, M.E. (1974) 'UnbiasedEstimatorsof Long-run ExpectedRatesof Return', Journal of the AmericanStatisticalAssociation,69, 634-8. Bodie, Z. and V. Rosansky(1980) 'Risk and Return in Commodity Futures', Financial AnalystJournal, 36 (May-June),27-39. Cheng,P.L. and M.K. Deets(1971) 'StatisticalBiasesand SecurityRatesof Return', Journal of Financial and QuantitativeAnalysis,6, 977-94. (1973) 'SystematicRisk and the Horizon Problem', Journal of Financial and QuantitativeAnalysis,8, 299-316. Dusak,K. (1973) 'FuturesTrading and Investors'Returns:An Investigationof CommodityMarket Risk Premiums',Journal of Political Economy,81, 1387-406. Fama,E.F. (1973) 'A Note on the Market Model and the Two-ParameterModel', Journal of Finance, 28,1181-5, Fogler, H.K. and R.C Radcliffe (1974) 'A Note on Measurementof Skewness', Journal of Financial and QuantitativeAnalysis,9, 485-9. Gray, R.W. (1961) 'Searchfor a Risk Premium',Journal of Political Economy,69, 250-60. Hagerman,R.L. (1978) 'More Evidenceon the Distribution of Security Returns', Journal of Finance, 33, 1213-21. Holthausen,D.M. and J.S. Hughes(1978) 'CommodityReturnsand Capital Asset Pricing', Financial Management(Summer),37-44. Keynes,J.M. (1930) A Treatiseon Money, l/, London: Macmillan, 142-7. Lee, CF. (1976) 'InvestmentHorizon and the FunctionalForm of the Capital Asset Pricing Model', Reviewof EconomicsandStatistics,58, 356-63. Lee, CF., R.M. Leuthold and J.E. Cordier (1985) 'The Stock Market and the CommodityFuturesMarket: Diversification and Arbitrage Potential',Financial AnalystJournal, 91, (July-August),53-60. Lee, CF. and K. Morimune (1978) 'Time Aggregation,Coefficient of Determinationand SystematicRisk of the Market Model', The Financial Review,36-47. Levhari, D. and H. Levy (1977) 'The Capital Asset Pricing Model and the InvestmentHorizon', Reviewof Economicsand Statistics,59, 92-104. Levy, H. (1978) 'Equilibrium in an Imperfect Market: A Constrainton the Numberof Securitiesin a Portfolio', AmericanEconomicReview,68, 643-58. Lintner, J. (1965) 'Security Prices,Risk and Maximal Gainsfrom Diversification', Journal of Finance, 20, 587-615. Rockwell, CS. (1967) 'Normal Backwardation,Forecasting,and the Returnsto CommodityFuturesTraders',Food ResearchInstituteStudies,8 (Supplement), 107-30. Ross,R.L. (1975) 'Financial Consequences of Trading CommodityFutures Contracts',Illinois Agricultural Economics,15 (July), 27-32. Sharpe,W. (1963) 'A Simplified Model for Portfolio Analysis', Management Science,277-93. (1964) 'Capital Asset Prices: A Theory of Market Equilibrium Under Conditionsof Risk', Journal of Finance, 19,524-42. Snedecor,G.W. and W.G. Cochran(1967) StatisticalMethods,6th edn, Ames: Iowa StateUniversity Press. Stone,B. (1973) 'A GeneralClassof Three ParameterRisk Measures',Journal of Finance, 28, 675-85.

6

TRADING VOLUME AND PRICE VARIABILITY: NEW EVIDENCE: ON THE PRICE EFFECTS OF SPECULATION David J.S. Rutledge*

I had always looked on 'futures' as the creaturesof wild speculation and eminently uncertain,and I could not avoid a feeling of wonder that such operationscould be reduced within the dominion of scientific investigation,which alone is a great step in advance.(Remarksof Sir FrancisS. Powell, MP, Chairmanat a Meeting of the Royal Statistical Society, London, 24 April 1906) 1. Introduction

This chapter is concerned with the relationship between the volume of trading and the extentof price variability on commodity futures markets. The existenceof such a relationship has been documented in several places (Kent, 1973; Powers, 1970), althoughthere is less than unanimousagreementas to the underlying mechanismby which it is generated.A comparablerelationship has been found on security markets (Crouch, 1970; Epps, 1974; Epps and Epps, 1976; Osborne, 1967), and theoretical models have been proposedthere to explain it. However, these models do not appear to be readily adaptable to commodity marketsas they do not incorporateany explicit discussionof the behaviourof floor traders. The topic has receivedremarkablylittle attentionin the context of commoditymarkets,usually arising incidentally in studiesof the statistical distribution of price changes. However, as we shall attempt to show here, it deservesstudy in its own right since it bearsdirectly on the question of the price effects of speculation and, hence,on certainaspectsof marketregulation. As a point of departure,we may first note that in discussing day-to-dayvariationsin trading volume we are in fact considering day-to-dayvariations in speculation.This is becausetransactions 137

138

Trading VolumeandPrice Variability

involving hedgerson either side compriseonly a small proportion of daily trading volume. Currentstatisticsto supportthis claim are not available, but a review of the fragmentary historical data, summarizedin Table 6.1, provides an indication of the orders of magnitudeinvolved. For the purposeof this chapter,the relevant figures are those relating to trading on the Chicago Board of Trade, since the empirical analysis to be reported below is concerned only with 'central' markets. On the smaller exchanges,a very high proportion of non-hedgedtrading involves spreadingto the ChicagoBoard of Trade with the result that trading volume on thesemarketsshows a considerablyhigher componentof hedging activity (Gray, 1961, 1967).The time periodscoveredin Table 6.1 are somewhat atypical, being periods of unusually wide price movement. Even if the figures in the table considerablyunderestimate the usual volume of hedging transactions,however, it Table 6.1: Percentage of Trading Volume Involving Hedgers Hedging Transactions as Percentage of Total Volume

Period

Exchanges

Commodity

2 January 1925 18 April 1925'

Chicago Board of Trade

Wheat Corn

3

Chicago Board 3 January 1927 31 October 1927b of Trade

Wheat

5

Chicago Board of Trade

Corn

4

Minneapolis Grain Exchange

Wheat

23

Kansas City Board of Trade

Wheat

26

Duluth Grain Exchange

Wheat

45

Kansas City Board of Trade

Corn

15

Wheat

15

18 September 1947' Chicago Board of Trade

Notes: ' See US 69th Congress (1926), p. 29. These figures refer to trading in the May future only. b See US 71st Congress (1930), p. 15. , See Withrow (1960, p. 182).

Trading VolumeandPrice Variability

139

remains clear that movementsin daily trading volume primarily reflect movementsin speculativeactivity. In the subsequentsections of this chapter, we shall discuss alternativeinterpretationsof the price effects of speculation,paying specialattentionto the possibleeffects of speculationon price variability. We shall then describea methodologyfor testing for the direction of causality between two variables and apply this methodologyto the relationship betweentrading volume (speculation) and price variability. Finally, we shall considerthe implicationsof the resultsfor marketregulation. 2. Price Effects of FuturesTrading Widespreadagreementcan be found among even the most casual students of futures markets that these markets facilitate speculation. There is considerabledisagreement,however, as to the effects of such speculation. One school of thought holds that speculation performs a welfare-increasingfunction which is effected in a variety of interdependentways. First, speculationis required for a futures market to grow to sufficient maturity to facilitate hedging operations.Thus, in so far as futures trading itself producesbenefits, these may, at least in part, be attributed to speculation. Benefits of this kind include generationof increasedtraders'information about supply and demand influences (Crouch, 1970), facilitation of transactions among strangers (Telser and Higinbotham, 1977) and facilitation of risk-managementby handlersof commodities(Working, 1970). A further strand of the argumentis that speculationpromotes price stability. By providing an intertemporalarray of price information, a futures market (and, hence,speculation)enablesstockholding, production, consumptionand processingactivities to be allocated over time in an efficient fashion, thereby reducing the amplitudeof seasonalfluctuationsin cashprices. At the sametime, according to this view, speculation has the effect of mitigating short-run fluctuations in futures prices. The notion is that speculators buy futures when pricesdrift 'too low' and sell when they go 'too high'. In each case, the extent of futures price variability is reduced.This latter view, statedin the form that profitable speculation necessarilyexertsa stabilizing influence on price, has been

140

Trading VolumeandPrice Variability

associatedwith Friedman(1953), althoughit can be tracedback at least as far as Irving Fisher (1930, p. 218). As we shall seebelow, it has given rise to a protracted theoretical debate among economists. On the other hand is the view, sometimesexpressedbeforecongressionalhearings,that speculationhas a destabilizinginfluence on price and, in particular, that 'waves' of speculative activity motivated by factors unrelatedto fundamentalmarket influences may distort prices and causethem to fluctuate to an unwarranted degree.This view prevailedin 1958 when trading in onion futures was prohibitedin the United States,and it lay behindat leastsome of the criticism of futures trading which led to extensiveamendmentsto the CommodityExchangeAct in 1974. The gist of this view was expressedclearly enoughby Congressman Conte:! Both producersand consumershavesufferedas a result of huge price fluctuation. I am convincedthat someone,somewhereis profiting from all of this. And I suspectthat in some casesat least, the people responsible for the price fluctuations are amongthosebenefittingfrom them. [emphasisadded] (US 93rd Congress,1973) Furthermore, the view that speculation may exacerbatefutures price movementshasbeenacceptedby somecloseobserversof the marketplace.The then administratorof the CommodityExchange Authority, R.R. Kauffman, commentedin 1957 on speculationin the onion marketas follows: Wide and rapid price swings attract speculationwhich at times further widensthe swings,thus attractingmore speculation.This speculativefever continuesuntil the individual speculatorshave either lost their money or made enoughto satisfy them for the time being. (US 85th Congress,1957) Congresshas seensomemerit in this argumentas the Commodity FuturesTrading CommissionAct of 1974 states,in part: Excessivespeculationin any commodity undercontractsof sale of suchcommodityfor future delivery madeon or subjectto the rule of contractmarketscausingsuddenor unreasonablefluctu-

Trading VolumeandPrice Variability

141

ations or unwarrantedchangesin the price of such commodity, is an undue or unnecessaryburden on interstatecommercein such commodity. For the purposeof diminishing, eliminating, or preventingsuch burden, the Commissionshall, from time to time, after due notice and opportunity for hearing, by order, proclaim and fix such limits on the amount of trading which may be done on positions which may be held by any person undercontractsof saleof suchcommodityfor future delivery on or subjectto the rules of any contractmarketas the Commission finds are necessaryto diminish, eliminate or prevent such burden.(VS 93rd Congress,1974, pp. 54-5) At present,speculativeposition limits and daily trading limits have been fixed by the Commission for cotton, rye, soybeans,eggs, potatoes,corn and wheat. As noted above,it is possibleto constructtheoreticalmodelsof speculativebehaviourin which speculationtends to diminish the magnitudeof price fluctuations. Why then has the contrary view receivedwidespreadsupportand legislative approval?The answer lies not only in populist prejudice against speculation and the 'middleman',but also in the fact that economictheory providesno unequivocalconclusionas to the price effectsof speculation. Baumol (1957), Stein (1961) and Kemp (1973) have shown that it is possibleto constructmodelsin which speculationis profitable yet destabilizing. Baumol's illustrations of this proposition have been criticized by Telser (1959) as being unrealistic, while Stein'sexamplerests on institutional characteristicsof the foreign exchangemarket which may not be relevantfor the presentcase. Nevertheless,more recentwork by Farrell (1966) and Schimmler (1973) suggestthat the formal conditions under which the proposition that 'profitable speculationis price stabilizing' is valid are quite restrictive. It is difficult not to agree with Baumol that 'the effect of ... speculationon stability is in part an empirical question and that attempts to settle it by a priori commentsmust somewhere resort to fallacy' (Baumol, 1959, p. 302). Empirical resolutionof this questionis no easymatter,however. The courseof action usually adoptedis to examinethe variability of cash prices of a given commodity for two time periods, one in which an active futures market for the commodityexistedand one in which there was no such market. In order to attribute any observeddifferencesin price variability to the influence of futures

142

Trading VolumeandPrice Variability

trading or speculation,one must resort to a post hoc ergo propter hoc argumentand consequentlythe resultsof suchstudiesmust be interpreted with caution. Analysis along these lines has been undertaken for wheat (Hooker, 1901; Tomek, 1971), onions (Gray, 1963; Johnson,1973; Working, 1960), cotton (Chapman and Knoop, 1906; Emery, 1896), pork bellies and live cattle (Powers,1970; Taylor and Leuthold, 1974). Thesestudiesgenerally show a reductionin price variability concomitantwith futures trading. The presentchapter examinesthe question from a somewhat different viewpoint. The correlation, noted at the start of the chapter, between trading volume and price variability might be construedas evidencein supportof the hypothesisthat speculation destabilizesprice. On the other hand, it is not difficult to envisage models of speculative behaviour in which an increase in the volume of trading can be consideredas a responseto, ratherthan a causeof, increasedprice variability. This view is consistentwith the activities of scalpers and day traders as described by Working (1977, 1967). Consider, for example, the activities of scalpers who can be characterizedas 'always standingready to either buy at 1/8 cents below the last price or sell at '/8 cents above the last price'.Z If prices are regardedas promptly and appropriatelyreflecting new information which flows to the market place at an uneven rate, then the trading activities of scalperswill clearly be greateron days when prices fluctuate more. The sameconclusioncan be seen to apply to 'day traders', whose activities have been described in more detail by Working (1977, pp. 188-90). Another important classof speculativetrading is 'price-level trading'.3 Here again the greater the degree of price fluctation the more likely it is that potentially profitable short-run trends may emerge,giving rise to increasedtrading activity. Someideas havebeenexpressedin anotherway by an officer of a large trading firm: the averagespeculatoris interestedin trading in a commodity that moves. If oats are fluctuating within a range of '/4 to Ijz cent and soybeanshave a rangeof 2 to 3 centsa day, the speculator is going to be attractedto the soybeanmarket. (Withrow, 1960,p.168)

Trading VolumeandPrice Variability

143

Much importance,therefore,attachesto the direction of causality underlying the correlationbetweentrading volume and price variability. Evidencethat causalityruns from trading volume to price variability would strongly supportthe critics of futures marketsand would provide a more satisfactorybase on which regulation of speculative positions and daily trading activity could be based. Evidence in the other direction, when combined with that describedaboveon cashprice variability, would provide empirical support for thosewho arguefor somemodification of theseregulations. It shouldbe rememberedin the following sectionsthat when we speak of trading volume 'causing' price instability, or price variability 'causing'trading volume we are in fact glossingover a very complex mechanism.In fact, of course,the observedrelationship between these variables is a reflection of the extent to which traders react differently to perceivednew information. The truly 'causal'variablescannot be observedand henceour portrayal of the relationshipbetweentrading volume and price variability as a causalone is a very crudecharacterizationof the microstructureof futures markets. 3. Testing for Causality: Methodology That correlationimplies nothing aboutcauseand effect is a proposition firmly impressedupon all studentsof statistics. There are many examplesof 'nonsensecorrelations';evenwhen a correlation is symptomaticof a causalmechanism,it is generallyacceptedthat there are no empirical means of identifying the direction of causality.4 In part the difficulty is one of actually defining what the term causality means,a questionwhich has fascinatedphilosophersat least sincethe time of Hume (1888). More recently,attemptshave beenmadeto developmore explicit (and, hence,more restrictive) definitions of causalitywhich may, in some instances,allow us to identify the direction of causalitybetweentwo variables.The concept of causalityto be employedhere is essentiallythat definedby Suppes: one event is the causeof anotherif the appearanceof the first event is followed with a high probability by the appearanceof

144

Trading VolumeandPrice Variability

the second,and there is no third event we can use to factor out the probability relationshipbetweenthe first and secondevents. (Suppes,1970,p. 10) This definition restson two intuitive notions. First, that the future cannot causethe past and, second,that causality must essentially be a probabilistic concept(Grangerand Newbold, 1977, pp. 2245). Theseideashave been more rigorously developedby Granger (1969) and Sims (1972), and operationalprocedureswhich permit testing for the direction of causality have been devised by Sims (1972). To illustrate, supposethat we want to test for causalitybetween two time series(Yt ) and (Xt }.5 Employing the idea that the future cannotcausethe past,we estimatean equationin the form: m

Yt+i

a

+ L ~i i=1

n

~+i Yt+i

+ L Yi Xt-i + Ut i=O

(1)

If we reject the joint hypothesis(~i = 0; i = 1, ... m) it follows that future valuesof X help us to 'predict' the current value of Y, and we conclude that X cannot cause Y. Suppose,for purposesof illustration, that this indeedoccurs.The next step is to reversethe roles of X and Y, and estimatean equationof the form:

mn

Yt+i

a

+ L

i=1

~i Yt+i

+L

i=O

Yi Y t- i +

Ut

(2)

Suppose,in equation(2) the joint hypothesis(~i = 0; i = 1, 2, ... m) is not rejected. The possibility that Y causesX thus remains open. Finally we estimatean equationof the form: n

Yt+i

a

+ L

i=O

Yi Y t- i

+ Ut

(3)

If the hypothesis(Yi = 0; i = 0, 1, 2, ... n) is not rejected,and if the

estimatedcoefficients(Yi) are plausible,we concludethat the data supportthe hypothesisthat Y causesX ratherthan the converse. When this procedureis applied to data on two variables,Y and

Trading VolumeandPrice Variability

145

X, between which a significant correlation has been observed, there are severalpossibleoutcomes. (a) We may concludethat Y causesX. (b) We may concludethat X causesY. (c) The proceduremay prove to be inconclusive.This could occur becausewe do not reject the hypothesisYt+i (~i = 0, i = 1, ... m) in either equation(2) or equation(3). Alternatively, it may occur because ~i = 0, i = 1, 2, ... n is rejectedin equation(1) but (Yi Yt+i = 0; 1, 2, ... m) is not rejectedin equation(3). (d) We may concludethat there is no causalitybetweenX and Y. This may occur if the hypothesis(Pi = 0; i = 1, 2, ... n) is rejectedin both equations(2) and (3). It should be emphasizedthat this procedure cannot prove that

causalityruns in a particulardirection. Furthermore,the possibility remainsthat causalitymay spuriouslybe identified as flowing from one variable to another.This may occur becausewe can examine variables only in a pairwise fashion. However, Sims has argued (1972, pp. 541-3) that, with this qualification, the test will fail only in a few specific circumstancesunlikely to apply in the present study. The Granger-Simsprocedureoutlined above clearly relies on the existenceof time lags in the causal mechanismwhich are at least as long as the period betweenobservations.The importance of this for the presentstudy will be further discussedbelow. 4. Results

In this section, we describethe results of applying the procedure outlined above to daily data on trading volume and price variability for a numberof commodityfutures contracts.In the results reportedhere, the measureof price variability to be employedis the absolutevalue of the percentagechangein daily closing price. This is not the only available measureof price variability and it may not be the most appropriate- daily rangesuggestsitself as a promising alternative. Preliminary analysis indicatesthat the conclusions of the study would not be significantly altered if range were used and, as most previous studies of the relationship betweentrading volume and price variability have used measures

146

Trading VolumeandPrice Variability

basedon daily closing prices, this has been regardedas a convenient point of departure. It is intended that this question be pursuedfurther in extensionsof this study. The data base initially constructedconsisted of daily closing prices and daily trading volume for 15 commodities. For each commodity, three time periods of approximately four months' length were selected.Thesesampleperiodswere selectedto enable comparisonsto be madebetweenseveraldelivery months.Data for two of the commoditiesoriginally selected(live hogs and frozen pork bellies) were not fully analysedbecauseof the very high proportion of limit price movementsin the sampleperiods.Limit price movementsdo not necessarilypresenta problem for the type of analysis conductedhere, but if, as sometimesoccurs, there are several successivedays of limit movements,the underlying relationship betweentrading volume and price variability is distorted. On some days, limit movementsare accompaniedby very low trading volume and on others by very high trading volume. The numberof observationsin eachsampleperiod (generallyabout80) is large enoughto facilitate statisticalanalysisbut not so greatas to give rise to concernover instability in the underlying model. Full details as to the commodities,contractsand time periodsusedcan be found in the Appendix to this chapter.For the time being, however, it is worth noting that the range of commoditiesand time periodsselectedfor study representsa very greatdiversity of price behaviour,trading activity and commoditycharacteristics. In each estimatedequation,a time trend has been included to allow for any long-run influencesnot directly accountedfor in the relationshipbetweentrading volume and price variability, and all equations have been estimated, using the Cochrane-Orcutt iterative procedureto take accountof first-order serial dependence in the errors.The valuesof m and n (the lead and lag lengths)were set at three and five respectivelyin equations(1) and (2). These valueswere selectedarbitrarily but seemedsufficiently generouson a priori grounds. A further matter for considerationis the specification of the trading volume variable. It may well be preferable to express volume as a proportion of the open interest rather than to work with volume itself. This is likely to be especiallyso in analysing data from very long sample periods, but is less likely to be a problem in the presentcase. Furthermore,inclusion of the timetrend variable, at least in equationswith trading volume as the

Trading VolumeandPrice Variability

147

dependentvariable, appearsto do a satisfactoryjob of accounting for the effects of open interest movements.Nevertheless,extensions of the study will include explicit incorporation of open interestdata. Severaladditional technicalpoints must be mentioned.Testsof the joint hypothesis~i = 0; i = 1, 2, ... m and Yi = 0; i=O, 1, 2, ... n were carried out using the usual F-tests for sets of linear restrictions.In all cases,5 per cent levels of significancewere used. Becausethe dependentvariable is always constrainedto be nonnegative, the error term in equations(1), (2) and (3) cannot be normally distributed. Although extensivetesting has not yet been undertaken,preliminary indicationsusing the Shapiro-Wilk test on the Cochrane-Orcuttresiduals(Huang and Bolch, 1974) suggest that non-normalityis not a seriousproblem in the presentcase. In all, 136 contracts in 13 commodities were retained for analysis. Table 6.2 summarizes the results of applying the Granger-Simsprocedureto thesecontracts.fi Illustrative resultsfor three contractsare shown in Tables 6.3, 6.4 and 6.5. As can be seen,the results provide remarkablystrong supportfor the hypothesisthat movementsin trading volume representsa responseto, rather than a causeof, movementsin price variability. Of the 136 contractsexamined,23 exhibit so weak a relationship betweentrading volume and price variability that the question of causality does not arise. Sixteen of these (in the soybean complex, silver and IMM contracts) are commodities where spreadingactivities are particularly importantand where, as a consequence,one would expecta simple relationshipbetweentrading volume and price variability to be less prevalent.Most of the other contracts falling into this category are in commodities where futures trading is a relatively recentphenomenon. In 80 of the remaining 113 cases,the procedurewas unable to identify the direction of causality between trading volume and price variability. This is almost certainly a reflection, not of the lack of a causal relationship, but rather of the period between observationsbeing too great relative to the time lags involved. A very great proportion of variation in trading volume is a reflection of the activities of day traderswho hold zero positions overnight. Even if the trading of this group is significantly influencedby price variability, as has been suggestedin Section 2, we should not expect to find many lagged responsesgreater than one day in length. However, as we have seen in the previous section, the

148

Trading VolumeandPrice Variability

Table 6.2: Summary of Results Number of Cases in which Significant Relationship Exists

Commodity Year

Number of Contracts

Vol·Var'

Var-Volb

Can't Say

Number of Cases in which no Significant Relationship Exists

1973174 1974175 1975176

4 4 4

0 0 0

4

0

3 0

1 4

0 0 0

Corn

1974 1975 1976

4 4 4

0 0 0

3 0 3

0 04 0

0 0 0

Oats

1973174 1974175 1975176

30 30 30

0 0 0

0

3

0 0 0

1973174 1974175 1975176

4 4 4

0 0 0

Iced broilers

1974 1975 1976

3

4

0 0

Plywood

1974 1975 1976

4 4 4

Soy beans

1974 1975 1976

Wheat

Live cattle

Soybean oil

Soybean meal

Silver

Gold

2

1

0

3

0 0 0

2

1

3

0 0

2

00 02 0

00 0 0

0 0 0

00 0 00

0 03 03

03 00 0

5 5 5

0 0 0

2

4 5

2

0 0

1974 1975 1976

4 5 4

0 0 0

22

0 0 04

0

0 0

1974 1975 1976

4 4 4

0 0 0

01 00 0

3

0 0 0

1974 1975 1976

4 4 4

0 0 0

0

1975 1976

4 4

0 0

4

2

0 03

1

1

4

3

1

0

4 0

2

2

3

0

4

0 0

2

0 0

0 0

1

03

Trading VolumeandPrice Variability OM

Yen

1974 1975 1976

2 2 2

o o o

o o o

o o 2

o

1975

2

o

o

o

2

80

23

136

Total

31

2

149

2 2

Notes: ' Indicates number of cases in which causality is identified as running from trading volume to price variability. b Indicates number of cases in which causality is identified as running from price variability to trading volume.

Table 6.3: Wheat, May 1975 Contract

Dependent Variable Estimated Coefficient

Var,

Var,

x 10·

X 10·

Vol,

13,

-0.7567 (0.4673)

39487.6 (29073.4)

13,

0.9500 (0.4898)

-21017.3 (29798.8)

13,

1.1986 (0.4990)

15185.8 (29487.6)

Vol,

Yo

0.2678 0.8204 40602.5 40606.6 (0.4979) (0.5015) (29054.1) (28631.5)

y,

-0.04779 0.07252 (0.4989) (0.5173)

y, Y3 Y4 Ys F~

Fy

-0.2782 (0.5040)

-0.4566 (0.5325)

79024.1 (28820.0)

77236.8 (28682.7)

66873.9 63528.8 (29005.4) (28618.3)

0.6937 0.8112 -24083.3 -24061.8 (28890.0) (28534.5) (0.4998) (0.5319) -0.3347 -0.3158 22769.9 24088.0 (28790.4) (28491.6) (0.4945) (0.5263) -2500.72 0.3521 0.8365 -3044.35 (28493.1) (28380.1) (0.4921) (0.5167) 3.77'

0.97 0.87

Notes: ' Denotes statistically significant at 5 per cent level. F~ Denotes value of F-statistics for testing 13, - 132 - 13, - O. Fy Denotes value of F-statistics for testing Yo - Y. - ... Ys - O.

2.29'

150

Trading VolumeandPrice Variability

Table 6.4: Gold, March 1977 Contract

DependentVariable EstimatedCoefficient

Vart

Vart

x 10'

X 10'

VOlt

VOlt

133

0.6897 (0.1652)

-83.6890 (1001.30)

13,

-0.01842 (0.1803)

-128.411 (993.513)

13,

0.3655 (0.1787)

44.6761 (1052.87)

Yo

0.2506 (0.1774)

0.2832 (0.1848)

1638.77 (1043.99)

1601.91 (978.823)

Y,

-0.03023 (0.1769)

-0.09688 (0.1900)

1384.61 (1064.68)

140.96 (980.055)

y,

0.2123 (0.1775)

0.1329 (0.1919)

680.007 (1048.25)

697.260 (996.805)

Y3

0.02801 (0.1788)

-0.08402 (0.1918)

3270.66 (1055.21)

3252.72 (998.856)

Y.

0.1003 (0.1769)

0.09573 (0.1904)

1294.90 (1053.79)

1306.65 (1001.90)

Y5

-0.6667 (0.1564)

-0.004908 (0.1846)

-1647.20 (1077.74)

-1602.74 (1003.01)

F~

8.03**

Fy

0.Q1

0.47

3.15*

'Seenotesto Table 6.3

presenceof longer lags is requiredfor the test procedureto be able to identify the direction of causality. Most importantly, of the 33 casesin which the proceduredoes identify the direction of causality,only two show causalityrunning from trading volume to price variability. In all other cases,the evidencesupportsthe hypothesisthat trading volume respondsto price variability ratherthan causesit. The two exceptionsare of some interestalso. They both occur in 'distant' iced broiler contractsin 19747 in which trading activity was particularly thin. In this connection,it is worth noting that the thinnessof the iced broiler contractat the ChicagoBoard of Trade has recently attractedboth trade and academiccomment(Emery, 1896, p. 41; Schrader,1978).

Trading Volumeand Price Variability

151

Table 6.5: Iced Broilers, August 1974 Contract

DependentVariable EstimatedCoefficient

Vart

VOlt

x 105

X 105

Volt

~, VOlt

-0.8161 (3.012)

295.681 (336.133)

~, VOlt

-3.778 (3.307)

735.477 (338.059)

~, VOlt

VOlt

770.979 (336.360)

0.2037 (3.415)

Yo

16.59 (3.343)

15.60 (3.004)

2037.02 (337.656)

1890.48 (351.660)

y,

0.7089 (3.376)

0.6886 (3.315)

526.545 (342.707)

518.702 (357.878)

Y,

1.121 (3.426)

1.025 (3.366)

34.9577 (343.921)

133.968 (360.656)

y,

0.4499 (3.542)

0.6472 (3.448)

-113.348 (345.827)

78.4356 (360.172)

Y4

-0.2991 (3.515)

-0.9272 (3.411)

35.7533 (348.739)

98.3929 (362.995)

Y5

-0.2680 (3.241)

-0.5734 (3.149)

1.30372 (347.531)

-78.0271 (360.355)

Fp

0.74

Fy

4.65' 3.04'

6.00'

'Seenotesto Table 6.3.

5. Conclusions In July 1976, the Commodity Futures Trading Commission Advisory Committee on the Economic Role of Contract Markets reported in the following terms: The Advisory Committee is in general agreement that the current daily trading limits for speculatorsshould be changedto daily limits on net position change. The present flat fixed limit on the number of contracts a speculator can trade during the day may actually cut back participation of speculators at the very time when they are most needed. On active trading days somespeculatorsare forced out of the pit during the later hours of daily trading - reducing liquidity. The Committee feels these daily trading limits are probably more binding on market per-

152

Trading VolumeandPrice Variability

formance than the speculative position limits. (Commodity FuturesTrading Commission,1976, p. 22) The empirical evidencereportedin the presentchaptermust be regarded as providing considerable support for the Advisory Committee'srecommendations.While it does not provide direct evidencethat speculativeactivity stabilizesprices in the short run, it clearly forms the basis for rejecting the alternative view that speculativeactivity destabilizesprice. Finally, it is to be emphasizedthat a good deal of further work along the lines of this chapterremainsto be done. In addition to the more technical extensionsmentionedin Section 4, analysisof additional time periods and commodities would strengthenthe analysis.Nevertheless,the resultsas presenteddo representa contribution to our knowledge about the role of speculation in commoditymarkets.

Appendix: Details of Sample Periods and Contracts Used in Empirical Analysis Exchange

Commodity SamplePeriod

ContractsUsed

Chicago Board of Trade

Wheat

March 1974. May 1974. July 1974. Sept. 1974 March 1975. May 1975. July 1975. Sept. 1975 March 1976. May 1976. July 1976. Sept. 1976

1/11/73-2/28/74 1/11/74-2/28/75 1/11/75- 2/29/75

Corn

1/1/74-4/30/74 1/1/75-4/30/75 1/1/76-4/30/76

Oats

1/11/73-2/28/74 1/11/74-2/28/75 1/11/75-2/29/76

Soybeans 1/1/74-4/30/74 1/1/75-4/30/75 1/1/76-4/30/76

May 1974. July 1974. Sept. 1974. Dec. 1974 May 1975. July 1975. Sept. 1975. Dec. 1975 May 1976. July 1976. Sept. 1976. Dec. 1976 March 1974. May 1974. July 1974 March 1975. May 1975. July 1975 March 1976. May 1976. July 1976 May 1974. July 1974. Sept. 1974. Nov. 1974. Jan. 1975 May 1975. July 1975. Sept. 1975. Nov. 1975. Jan. 1976 May 1976. July 1976. Sept. 1976. Nov. 1976. Jan. 1977

Trading VolumeandPrice Variability Soybean oil

1/1/74-4/30/74 1/1/75-4/30/75 1/1/76-4/30/76

Soybean meal

1/1/74-4/30/74 1/1/75-4/30/75 1/1/76-4/30/76

Silver

2/1/74-5/31/74 2/1/75-5/31/75 2/1/76-5/31/76

Iced broilers

1/2/74-4/30/74 1/2/75-4/30/75 1/2/76-4/30/76

Plywood

1/2/74-4/30/74 112/75-4/30/75

1/2/76-4/30/76

Chicago Mercantile Exchange

Live cattle

10/1/73-1/30/74 10/1/74-1/30/75 10/1/75-1/30/76

Internationa I Monetary Market

Gold

2127/75-5/31/75

2/1/76-5/31/76

Deutsche Mark

Japanese Yen

153

May Dec. May Dec. May Dec.

1974, July 1974 1975, July 1975, Jan. 1976, July 1976

1974, Oct. 1974,

May Dec. May Dec. May Dec.

1974, July 1974, Oct. 1974, 1974 1975, July 1975, Oct. 1975, 1975 1976, July 1976, Oct. 1976, 1976

1975, Oct. 1975, 1976 1976, Oct. 1976,

June 1974, Aug. 1974, Dec. 1974, Feb. 1975 June 1975, Aug. 1975, Dec. 1975, Feb. 1976 June 1976, Aug. 1976, Dec. 1976, Feb. 1977 May Aug. May May Aug.

1974, June 1974, July 1974, 1974 1975, June 1975, July 1975 1976, June 1976, July 1976, 1976

May Nov. May Nov. May Nov.

1974, July 1974, Sept. 1974, 1974 1975, July 1975, Sept. 1975, 1975 1976, July 1976, Sept. 1976, 1976

Feb. 1974, April 1974, June 1974, Aug. 1974 Feb. 1975, April 1975, June 1975, Aug. 1975 Feb. 1976, April 1976, June 1976, Aug. 1976 June 1975, Sept. 1975, Dec. 1975, March 1976 June 1976, Sept. 1976, Dec. 1976, March 1977

2/1/74-5/31/74 211 /75-5/31 /75 2/1/76-5/31/76

June 1974, Sept. 1974 June 1975, Sept. 1975 June 1976, Sept. 1976

211/75-5/31/75

June 1975, Sept. 1975

154

Trading VolumeandPrice Variability

Notes ·SydneyFuturesExchange.This chapterwas preparedwhile the author was Visiting AssociateProfessor,Food ResearchInstitute, StanfordUniversity. 1. For evidenceof a different kind to be presentedin this chapter,which suggeststhat this view is false, seeUS GeneralAccountingOffice (1975). 2. This definition refersto 'unit scalping'in the grain markets.Howeverit applies mutatismutandisto other commodities. 3. The term is Working's, who notesthat in trade practicethis is frequently designated'position trading' (Working, 1967, p. 201). 4. For an interestingillustration of this argumentin the context of the price effectsof futures trading, seeHieronymus(1960), Shepherd(1960). 5. The following discussionis necessarilya somewhatloose summaryof a rathersophisticatedliterature. The interestedreaderis referredto the papersof Grangerand Sims for a more rigorous presentation. 6. As noted above,5 per cent significancelevels have beenused.Use of more generouslevels of significance(say, 10 per cent) doesnot greatly reducethe numberof 'can't say' casesand doesnot alter the balancebetweencolumns2 and 3 in Table 6.2. 7. The two iced broiler contractsinvolved are for July 1974 and August 1974 delivery.

References Baumol, W.J. (1957) 'Speculation,Profitability and Stability', The Reviewof Economicsand Statistics,XXXIX(3) (August), 263-71. (1959) 'Reply', The Reviewof Economicsand Statistics,3 (August) 301-2. Chapman,S.J. and D. Knoop (1906) 'Dealingsin Futureson the Cotton Market', Journal of the RoyalStatisticalSociety,69(2) (June),321-73. Commodity FuturesTrading Commission(1976) Reportof the Advisory Committeeon the EconomicRoleof ContractMarkets, WashingtonD.e., 17 July. Cox, e.e.(1976) 'FuturesTrading and Market Information', Journal of Political Economy,84(6) (December),1215-37. Crouch,R.L. (1970) 'The Volume of Transactionsand Price Changesof the New Analysts York Stock Exchange',Financial 26(4) (July-August), 104-9. Journa~ 104-9. Donnelly, R.A. (1977) 'CommoditiesCorner', Barron's, 12 December,pp. 40-1. Emery, H.e. (1896) Speculationon the Stockand ProduceExchangeof the United States,New York: ColumbiaUniversity Press. Epps, T.W. (1974) 'Security Price Changesand TransactionVolumes: Theory and Evidence',AmericanEconomicReview,LXV(4) (September),586-97. Epps,T.W. and M.L. Epps(1976) 'The StochasticDependenceof SecurityPrice Changesand TransactionVolumes: Implicationsfor the Mixture-of-DistributionsHypothesis',Econometrica,44(2) (March), 305-21. Farrell, M.J. (1966) 'ProfitableSpeculation',Economica,N.S. XXXIII(130) (May), 183-93. Fisher, l. (1930) The StockMarket Crash andAfter, New York: Macmillan. Friedman,M. (1953) Essaysin PositiveEconomics,Chicago: University of ChicagoPress. Granger,e.W.J. (1969) 'InvestigatingCausalRelationsby EconometricModels and Cross-SpectralMethods', Econometrica,37(3) (July), 424-38.

Trading VolumeandPrice Variability

155

Granger,CW.J. and P. Newbold (1977) ForecastingEconomicTime Series,New York: AcademicPress. Gray, R.W. (1960) 'The Importanceof Hedgingin FuturesTrading; and the Effectivenessof FuturesTrading for Hedging',in Futures Trading Seminar,I, Madison: Mimir Publishers,pp. 61-82. (1961) 'The RelationshipAmong Three FuturesMarkets', Food Research Institute Studies,II(l) (February),21-32. (1963) 'OnionsRevisited',Journal of Farm Economics(May), 273-6. (1967) 'Price Effects of a Lack of Speculation',Food ResearchInstitute Studies,VII, Supplement,17-94. Hieronymus,T.A. (1960) 'Effects of FuturesTrading on Prices', Futures Trading Seminar,I, Madison: Mimir Publishers,pp. 121-62. Hooker, R.H. (1901) 'The Suspensionof the Berlin ProduceExchangeand Its Effects upon Corn Prices', Journal ofthe RoyalStatisticalSociety,64 (December),574-604. Huang, CJ. and B.W. Bolch (1974) 'On the Testingof RegressionDisturbances for Normality', Journal of the AmericanStatisticalAssociation,69(346) (June), 330-7. Hume, D. (1888) A Treatiseon Human Nature, ed. L.A. Selby-Bigge,Oxford: ClarendonPress. Johnson,A.C (1973) Effectsof Futures Trading on Price Performancein the Cash Onion Market, 1930-68,USDA, E.R.S. TechnicalBulletin 1470, February. Kemp, M.C (1973) 'Speculation,Profitability and Price Stability', The Reviewof Economicsand Statistics,XL V(2) (May) 185-9. Kent, P.K. (1973) 'A SubordinatedStochasticProcesswith Finite Variancefor SpeculativePrices', Econometrica,41(1) (January),135-55. Osborne,M.F.M. (1967) 'SomeQuantitativeTestsfor Stock Price Generating Models and Trading Folklore', Journal of the AmericanStatisticalAssociation, 62 (June), 321-40. Powers,M.J. (1970) 'Does FuturesTrading ReducePrice Fluctuationsin Cash Markets?',AmericanEconomicReview,LX(3) (June),460-4. Rocca,L.H. (1969) 'Time SeriesAnalysis of Commodity FuturesPrices', unpublishedPhD dissertation,University of California, Berkeley. Schimmler,J. (1973) 'Speculation,Profitability and Price Stability: A Formal Approach', The Reviewof Economicsand Statistics,LV(l) (February),110-14. Schrader,L.F. (1978) 'Pricing Problemsin the Food Industry: Broiler Chickens and Eggs', paperpresentedat Symposiumon Pricing Problemsin the Food Industry, WashingtonD.C, 2-3 March. Shepherd,G. (1960) 'Effects of FuturesTrading on Prices: Discussion',Futures Trading Seminar,I, Madison: Mimir Publishers,pp. 181-91. Sims, CA. (1972) 'Money, Incomeand Causality',AmericanEconomicReview, LXll(4) (September),540-52. Stein, J.L. (1961) 'DestabilizingSpeculativeActivity Can Be Profitable', The Reviewof Economicsand Statistics,XLIII(3) (August),301-2. Suppes,P. (1970) A Probabilistic Theoryof Causality, Amsterdam: North-Holland. Taylor, G.S. and R.M. Leuthold (1974) 'The Influence of FuturesTrading on Cash Cattle Price Variations', Food ResearchInstitute, XIII(l), 29-36. Telser, L.G. (1959) 'A Theory of SpeCUlationRelating Profitability and Stability', The Reviewof Economicsand Statistics,XLI(3) (August), 295-301. Telser, L.G. and H.N. Higinbotham(1977) 'OrganizedFuturesMarkets: Costsand Benefits', Journal of Political Economy,85(5) (October),969-1000. Tomek, W.G. (1971) 'A Note on Historical Wheat Pricesand FuturesTrading', Food ResearchInstitute Studies,X(l), 109-13.

156

Trading VolumeandPrice Variability

US 69th Congress(1926) 1st Session,Senate,Fluctuationsin WheatFutures, SenateDocumentNo. 135, 28 June. US 71st Congress(1930) 2nd Session,Senate,Reportsby Membersof Grain Futures Exchanges,SenateDocumentNo. 123, 6 January. US 85th Congress(1957) Senate,Hearings Beforea Subcommittee of the Committeeon Agriculture and Forestry, 12 August. US 93rd Congress(1973) 1st Session,House, HearingsBeforethe Subcommittee on SpecialSmallBusinessProblemsof the HousePermanentSelectCommittee on SmallBusiness,25 July. US 93rd Congress(1974) 2nd Session,Senate,Committeeon Agriculture and Forestry, The CommodityFutures Trading Act of 1974, 15 November. US GeneralAccounting Office (1975) ImprovementsNeededin Regulationof CommodityFutures Trading, WashingtonDC, 24 June. Withrow, R.M. (1960) 'Effects of FuturesTrading on Prices: Discussion',Futures Trading Seminar,I, Madison: Mimir Publishers,pp. 163-72. Working, H. (1977) 'Price Effects of Scalpingand Day Trading', in Selected Writings of Holbrook Working, Chicago: ChicagoBoard of Trade, pp. 181-94. (1960) 'Price Effects of FuturesTrading', Food ResearchInstitute Studies, 1(1), 1-31. (1967) 'Testsof a Theory ConcerningFloor Trading on Commodity Exchanges',Food ResearchInstitute Studies,VII, Supplement,5-48. (1970) 'EconomicFunctionsof FuturesMarkets',in Futures Trading in Livestock- Origins and Concepts,ed. H. Bakken, Chicago: Chicago Mercantile Exchange.

7

THE FORWARD PRICING FUNCTION OF THE LONDON METAL EXCHANGE Barry A. Goss*

Futuresprices are rationally formed current prices relating to later delivery dates; they are not forecastsof subsequentspot prices. Yet, if all available information, including economic agents' expectations,is fully takeninto accountin the price formation process,then both currentspot and futures prices may be regardedas market anticipations of subsequentspot prices. This chapter explores the hypothesisthat futures prices (and spot) are prethe predictors of subsequentspot prices in this sense.It assesses dictive performanceof futures prices for four non-ferrousmetals traded on the London Metal Exchange using a simple linear model, the parametersof which are estimatedby ordinary least squaresor instrumentalvariables in the caseof serial correlation (becauseof the presenceof a lagged endogenousregressor).The results suggest that the unbiasednesshypothesis should not be rejectedfor copper,tin or lead, but marginally may be rejectedfor zinc. The chapter begins with a discussion of the functions of futures markets,including a review of the literatureon the forward pricing function. 1. Nature and Role of Futures Trading

Futurescontractsare financial instrumentsdealing in commodities or other financial instrumentsfor forward delivery or settlement, on standardizedterms. They are tradedon organizedexchangesin which a clearing house interposesitself betweenbuyer and seller and guaranteesall transactions,so that the identity of the buyer or seller is a matterof indifferenceto the oppositeparty. The London Metal Exchangehas long been the world's leading metals futures market and trades, inter alia, in futures contractsfor copper,zinc, tin and lead, which are officially quotedfor spot and three months delivery only. Although the analysis of the feasibility conditions for futures 157

158

Forward Pricing Function

trading awaits a comprehensivetheoretical framework, it was customaryuntil around 1973 to distinguishat leastfive conditions which were thought to be necessaryfor futures trading to be possible. Recent experience,however, has shown that some of these conditions are in fact not necessary.The first 'customary condition' is that there must be variation in the price of the actual commodity under consideration; second, there must exist economic agentswith commitmentsin the actualsmarket; and third, it must be possibleto specify a standardgradeof the commodityand to measuredeviationsfrom that grade.As a result of the first two conditions, some economicagentswill face a price risk and there will be a demand for hedging facilities. A futures market establishedspecifically to meet purely speculativedemandsis possible but, as far as the presentauthor is aware, i~ unknown. The third condition, togetherwith standardizationof delivery date and of delivery location and testing procedures,where relevant,means that a high degreeof contractstandardizationis possible.1 Until recently it was customary to distinguish storability and deliverability as feasibility conditions. A consequenceof the former of thesetwo is that the forward premium could not exceed the marginal net cost of storage,and a consequenceof deliverability is that the price of a futures contract at maturity and the cashprice at that date would, theoretically,be broughtto equality. Recentexperiencessuchas trading in shareprice indices(which can be neitherstorednor delivered),and in finished live beefcattle (which may be deliveredbut are virtually non-storable)in Chicago and Sydney,have shown thesetwo conditionsto be unnecessary.2 Further conditions which are thought necessary for the establishmentof futures trading are the presenceof speCUlative capital (see Gray, 1960) and financial facilities for payment of margins and contract settlement (see Goss, 1972). Recently, Powers and Tosini (1977) have emphasizedthe infrastructure required, including financial, legal and communicationssystems. Moreover, they have placedrenewedemphasison the presenceof speculativecapital, drawing attentionto the externalitiesgenerated by that capital and indeedby the exchangeitself (pp. 981-2). The literatureon feasibility of futures trading hasdistinguishedbetween possibility and successof a market, and Gray (1966) has drawn attentionto factors which may lead to a thin market even though the aboveconditionsare fulftlled. Becauseof its limited predictive ability, this 'shopping list' of

Forward Pricing Function

159

commodity prerequisiteshas been supersededin recent years by attemptsto developa comprehensiveframework toanalysefutures market feasibility. Telser and Higinbotham (1977) argue that the degreeof successof futures marketscan be explainedin terms of maximization of a net benefitsfunction, and they found inter alia that the most actively traded commoditieshave the most variable prices. Veljanovski (Chapter 1 in this volume) shows that choice can be made among contractual arrangementson the basis of maximum net benefit, taking account of transactionscosts. He argues that futures markets have a comparativeadvantageover spot markets in the temporary transfer of certain bundles of propertyrights betweentraders. The major functions performed by futures markets are as follows: they facilitate stockholding; they facilitate the shifting of risk; they act as a mechanismfor collection and disseminationof information; and they perform a forward pricing function. We shall consider the first three of these functions briefly, and the fourth in more detail. First, futures markets facilitate stockholding because the forward premiumacts as a guide to inventory control, and may be interpretedas a return on hedgedstock (at leastwherethe hedgeis held to maturity of the future). The forward premium has been interpretedas a price of storage(Working, 1953a),and the holding of inventoriesat times of spot premiumis explicablein termsof the convenienceyield (Brennan,1958). Second,futures markets permit risk-shifting becausethey provide facilities for hedging. Hedging is defined as the holding of a futures market position in conjunctionwith an actualsposition of opposite sign, in pursuit of expectedgain, subject to a risk constraint. Hedgingsubstitutesa basisrisk for a price risk, and hedgers transferall or part of their price risks (dependingon whetherthey are fully hedged)to other market participantswilling to bearthose risks. This is so whether hedging is undertakenprimarily for the purposeof risk-reduction(which Working (1953a)believedto be unimportant in practice) or for some other reason, such as to facilitate product pricing or enhanceprofitability of the overall stockholdingoperation.Hedging has also beenstudiedas a means of reducingbusinessrisks in general,and henceas an instrumentin the managementof a total assetportfolio (Dusak, 1973). The risk-reducing effect of futures trading can of course be obtained by other meansof hedging, such as by use of forward

160

Forward Pricing Function

contracts.Economic agentswho hedge in futures markets do so becausethe net costsof that mediumare less than the net costsof the alternatives.The costsof hedginginclude not only marginsand transactionscosts, which are now being studied as a function of marketliquidity (Telserand Higinbotham,1977; Telser, 1979) but also costs due to changesin price spreads.For example, a spot premium which narrows during the period of a short hedge imposesa cost on the hedger.Suchcostsare likely to be larger the smaller is the volume of trading, other things being equal. From suchcostshave to be subtractedthe benefitsof increasedflexibility which futures contractsoffer comparedwith forward contracts.3 The performanceof futures marketsas a hedging medium has beenthe subjectof considerableempirical work. Generallyspeaking, futures marketshaveperformedwell from the routine hedging point of view (Yamey, 1951; Graf, 1953), in the senseof the supply of storageconcept(Working, 1953b; Brennan, 1958) and also from the portfolio viewpoint (Rutledge, 1972; Ederington, 1979). Thirdly, futures markets also act as centresfor the collection and disseminationof information. If this information, including traders'expectationsabout the future, is fully reflected in current prices, then the price formation processis said to be efficient. Hence,futures marketshavebeensubjectedto weak-formtestsfor efficiency, seeking evidenceof dependencein past prices, using runs tests, serial correlation tests, etc. (Larson, 1960; Stevenson and Bear, 1970). In some markets evidenceof dependencehas beenfound (Cargill and Rausser,1975), while in othersit has not (Praetz, 1975). Tests have recently been employedto investigatewhethercertain marketsare efficient in the senseof using all publicly available information as soonas it is published.This semi-strongform of the efficient marketshypothesishas been addressedby two different means,and has been rejectedfor US hogs, some currenciesand some non-ferrous metals (see Leuthold and Hartmann, 1979; Hansen and Hodrick, 1980; and Goss, 1983). Futures markets also perform a forward pricing function, which is central to the empirical work reportedin this chapterand is discussedin detail in the next section.

Forward Pricing Function

161

2. Forward Pricing Role of FuturesMarkets The literature on futures markets has interpreted the forward pricing function as an extension of Working's (1949) 'price of storage' concept. If all available information is fully taken into account in the processof current price formation, then the best possible anticipation of the price relating to a later date is the current price. Working arguedthereforethat the current spot and futures prices are equally valid anticipationsof the spot price at a subsequentdate, and a current forward premium of Sx is not a prediction that the spot price will rise by Sx, but rather it is a marketestimatedcarrying chargeof Sx. Similarly, a spot premium of Sy is not a prediction of a fall in the spot price of Sy, but is a market estimatedinverse carrying chargeof Sy. This at least was the theory developed for continuously storable commodities (Working, 1942). If spot and futures prices fully reflect all available information, then they may each be regardedas predictorsof subsequentspot prices, although technically they are not forecasts,but are rationally formed prices relating to specific delivery dates.The hypothesis that futures pricesare unbiasedpredictorsof maturity datespot prices has been tested for both continuous and discontinuous inventory commodities,and also for non-inventorycommodities. The evidencesupportsthe view that futures prices are unbiased predictors for continuous inventory commodities such as corn, soybeansand coffee (Tomek and Gray, 1970; Kofi, 1973), but not for discontinuousinventory commoditiessuch as potatoes(Kofi) or non-inventory commodities such as finished live beef cattle (Leuthold, 1974), or in the last case not with lags of more than three monthsprior to delivery. The reasonsfor this phenomenonare still under discussion. Leuthold has linked the efficient prediction period for live beef with the typical hedgingperiod. Kofi seeksan explanationin terms of the quality of information on demand and supply conditions. While thereis somesupportfor this hypothesis,the hypothesisthat the predictiveperformanceof futurespricesvariesdirectly with the degreeof price administrationcan also be supportedon the same evidence.Tomek and Gray attemptto accountfor this difference in predictiveperformance(at leastin the caseof potatoes)with the suggestionthat the futures price represents expectations only (and not a price of storage). This explanation is perhapsincomplete

162 Forward Pricing Function becausetheseexpectationsare always wrong and exhibit no learning process.Elsewhere,Gray (1972) has given a fuller explanation for the potatoescase.4 Other reasonssuggestedfor this phenomenonare that the discontinuousand non-inventory markets are newer and have relatively smallertrading volumes.This hypothesiswas testedby Giles and Goss(1981) for wool on the SydneyFuturesExchange,where the predictive performanceof wool futures prices for 1963-7 (a youthful period for the exchange)was compared with that for 1968-78and found to be inferior. Other suggestionsadvancedare that the absenceor discontinuity of inventoriesitself constitutesa significant gap in the information flow, so that such marketsare at a permanent disadvantagewith continuous inventory markets, other things being equal. Moreover, it is possiblethat the absence of inventories increases the possibility of expectational error, becausethere is less opportunity for arbitrage between the spot and futures markets. 3. The Predictive Ability of Futures Prices for Copper, Zinc, Tin and Lead

The hypothesisconsideredin this chapteris that futures prices are unbiasedpredictorsof subsequentspot prices. The implied relationship may be expressedin linear form as: ~t

=

a + BPt-i + Et

(1)

where ~t Pt t

spot (cashprice) threemonthsfutures price

t

3 monthslag

Et

randomdisturbance

t

time in months.

On the hypothesisa = 0 and B= 1. Equation(1) was estimatedby regression methods using monthly average data from Metallgesellschaftfor copper, zinc, tin and lead for the sample period April 1966 to April 1984, with 55 non-overlappingobser-

Forward Pricing Function

163

vations. As in most other empirical work on this hypothesis,(1) was estimatedby Ordinary Least Squares(OLS) for copper, tin and lead. If, however, all information bearing on At is not summarized in Pt-io equation (1) will be under-specifiedand autocorrelationamongthe residualsis likely, as occurredin the caseof zinc. Hence, the OLS standarderrors would be understated.To allow for this phenomenon,the model for zinc was extendedby assumingthat:

where

+ et

tt

Pft- k

P

a parameterto be estimated

et

a well-behavederror term

k1

t

(2)

An iterative Cochrane-Orcuttprocedurewas employedto estimate a, Band P for zinc. Moreover, the effect of auto-correlatederrors and a lagged endogenousvariable is that the OLS estimatesof a and B will be both biased and inconsistent.Following Giles and Goss (1981), equation(1) (augmentedby (2)) for zinc was thereforeestimated by the instrumental variable technique with an AR1 correction using TSP 4.0 (Hall (1983)), in order to obtain consistentestimates. As we saw in Section 2 above, if current prices fully reflect all available information then current spot prices may also be interpreted as predictors of subsequentspot prices. A variant of the main hypothesistestedhere is that currentspot pricesare unbiased estimatesof spot pricesthree monthshence.The following relation has thereforebeenestimated: A, where

i e;

=

a' + p'At_, + e;

(3)

3 disturbanceterm.

Again, equation (3) was estimatedby OLS for copper, tin and lead, and by IV with an AR 1 correction for zinc becauseof the presenceof serial correlationfor that metal. The parameterestimatesfor equations(1) and (3), augmented

164

Forward Pricing Function

by equation(2) in the caseof zinc, are given in Tables7.1 and 7.2 respectively,togetherwith the relevantstandarderrors,and values of R2 and Durbin Watson test statistics. From theseestimates,it will be seenthat on the basisof individual t testsof the hypotheses a = 0 and B= 1, theseseparatehypothesescan be rejectedfor copperonly at the 5 per cent level (but not at 1 per cent). Yet the definitive test of the unbiasedness hypothesisin this case is a joint test of the hypothesisH: (a = 0, B= 1). For copper,tin and lead this is an F test, and the calculatedF-valuesfor H: (a = 0, B= 1) for thesethreemetalsare given in Table 7.1. When these values are comparedwith the critical 5 per cent F2,6o = 3.15 it is clear that the unbiasedness hypothesiscannot be rejectedfor any of thesethreemetals.In the caseof zinc, the appropriatetest of the joint hypothesisis a X2 test with two degreesof freedom. The calculated X2 value for zinc for the hypothesisH( a = 0, B= 1) is given in Table 7.1; this compareswith the critical 5 per cent X2(2) value of 5.99, at which level the unbiasedness hypothesismust be rejected(when comparedwith the critical 1 per cent X2(2) value of 9.21, the hypothesiscannotbe rejected). Hencethe caseof zinc is marginal, although in line with the suggestionof Arrow (1982) that the more stringent significancelevels should be reservedfor Table 7.1: Spot Prices Regressed on Lagged Futures Prices (1966-84)

.

Copper (OLS) Tin (OLS)

P

ex

~

FP

DW

Observations

117.498 (51.765)

0.849 (0.070)

0.729

1.898

55

100.938 (111.342)

1.005 (0.023)

0.973

1.919

55

Zinc (IV)

47.883 0.868 0.367 (42.809) (0.130) (0.128)

0.669

1.784

52

Lead (OLS)

13.569 (10.331)

0.919

1.980

55

0.958 (0.039)

JOINT TEST STATISTICS (H: ex - 0,

fl -

1)

Calculated F-values Copper: 2.577

Tin: 1.991

Calculated X' values Zinc: 6.536

Lead: 0.873

Forward Pricing Function

165

Table 7.2: Spot Prices Regressed on Lagged Spot Prices (1966-84)

cl'

~'

R'

DW

Observations

108.616 (53.779)

0.870 (0.074)

0.719

1.968

55

Tin (OLS)

117.366 (123.164)

0.997 (0.025)

0.967

1.881

55

Zinc (IV)

47.181 (42.643)

0.881 0.341 0.682

1.798

52

2.004

55

Copper (OLS)

Lead (OLS)

16.879 (10.127)

JOINT TEST STATISTICS (H:

p'

(0.132)

(0.129)

0.921

0.951 (0.038)

IX' -

0,

W - 1)

Calculated F-values Copper: 2.205

Tin: 1.169

Lead: 1.451

Calculated X' values Zinc: 6.908

larger samples,there may be groundsfor preferringthe 5 per cent level in this case.With respectto the hypothesisthat spot pricesare unbiasedanticipationsof spot prices three months later, as representedby equation(3), the outcomesare identical. The estimates reported in Table 7.2 suggestthat the unbiasednesshypothesis cannot be rejected for copper, tin and lead, while for zinc this hypothesiscan be rejectedat the 5 per cent level (but not at 1 per cent). The OLS resultsin Tables7.1 and 7.2 are evidentlyfree of firstorder serial correlation, and the samewould appearto be true of the IV estimatesfor zinc, although the DW statisticscan only be informally interpretedwith IV estimation. (A more precise test could be conductedalong the lines suggestedby Godfrey (1976).) The results in this chaptersupport the conclusionsreachedin the original paperin AppliedEconomicsfor copperand tin and in a subsequentreport for lead.5 Agents in thesemarketsusing LME futures priceswould havebeenas well off on averageas if they had known the delivery date spot price in advance.In this respectthe LME has facilitated the intertemporal allocation of economic resources. Rejectionof the unbiasedness hypothesisat the 5 per cent level for zinc does not necessarilyimply that the zinc market is informationally inefficient, becauseof the other key assumptionson

166

Forward Pricing Function

which that hypothesis is jointly conditional. In any case, the marginal result for zinc suggeststhat this case requires further research. Ultimate rejection of the unbiasednesshypothesisfor zinc, if that were to eventuate,may be explicablein terms of the risk nonneutrality of agentsor discountingof the future, in terms of differences in the options available to agents under spot and futures contracts, or in terms of informational inefficiency in the zinc market. In order to investigatefurther the informationalefficiency of the zinc market, and indeedof thesefour non-ferrousmetalsmarkets, Appendix 1 considers the hypothesis that non-ferrous metals futures prices reflect as fully as possible publicly available information. It is assumedthat this information set is measuredby the immediately prior forecast errors for all four "metals and the coefficients of equation(AI) were estimatedby OLS. The hypothesis relating to informational efficiency is testedby the joint F-testthat all coefficients(a, Bl' ... , (3 4 ) are zero. It will be seenthat at the 5 per cent critical F value with (5,49) degreesof freedom,this hypothesiscan be rejectedfor zinc and copper,but not for tin and lead. At the 1 per cent level the hypothesiscannotbe rejectedfor any of the metals. The resultsfor zinc in Appendix 1 are consistentwith those in Table 7.1, suggestingthat, for this metal, rejection of unbiasedness may be due, at least in part, to some inability to reflect information. For tin and lead also, non-rejection of unbiasednessis consistent with non-rejection of this version of the market efficiency hypothesis.In the caseof copper, there would seemto be some ambiguity (at the 5 per cent level) in the two sets of results, becauseability to reflect relevant information as fully as possibleis an assumptionon which the unbiasedness hypothesisis jointly conditional. This ambiguity disappearsat the 1 per cent level. To clarify the ambiguity in the resultsfor copper,the question of multi-collinearity among the regressorsin equation (AI) was considered.The hypothesisthat Hz:rj = 0 (i, j=l, ..., 4, i ~ j) was testedagainstthe alternativehypothesisH3:rjj ~ o. This test was conductedas a t-test of the significance of the partial correlationcoefficientsrjj where

Forward Pricing Function (t1,324

167

rnJn - k 1)

Jl- r~=

1) (t1,324

and v = n-k degreesof freedom, k is the numberof explanatory variables in (AI). These tests of significance of the collinearity among the various pairs of regressorsshowedthat there is a significant relationshipbetweenthe prior forecast errors for copper and zinc (t1,324 = 3.8449comparedwith the critical value 5 per cent tv ~ 40 = 2.02). None of the other relationshipsamong the prior forecasterrorsis significant: thereis somerelationshipbetweenthe prior forecasterrorsfor tin and lead, but this is not significant(t 2,4)3 = 1.7494). The coefficientsof equation(AI) for copperwere thereforereestimatedwith j = 2, 3, 4 only: that is, the prior forecasterror for copper was deleted. These estimatesare given in Appendix 2, together with calculatedF statistics to test the hypothesisH4:(a, ~2,3,4 = 0). It will be seenthat this version of the efficient markets hypothesiscan be rejected at the 5 per cent level of significance but not at the 2.5 per cent level. The implication of theseresultsis that the observedambiguityof the outcomesfor copperdisappears at the 2.5 per cent level of significance.This suggestssome slight informationalinefficiency in the coppermarket. The coefficients of equation (AI) were also re-estimatedfor zinc with j = 2, 3, 4, but the outcomes were the same as in Appendix 1, and so theseresultsare not reportedin Appendix 2. It equation(AI) is re-estimatedfor copper and zinc with the zinc prior forecasterror deletedinsteadof that for copper,the market efficiency hypothesiscannot be rejected, so that deletion of the copperforecasterror resultsin a more relevantspecificationof the set of publicly availableinformation.

4. Conclusions This chapter addressesthe hypothesis that futures prices (and lagged spot prices) are unbiasedpredictorsof delivery date spot prices,on the groundthat they are rationally formed currentprices incorporatingall availableinformation, including economicagents' expectations,and hence may be interpreted as market anticipations. OLS estimatesof the hypothesizedlinear relationship

168

Forward Pricing Function

were obtainedfor copper, tin and lead (IV with a correctionfor first-order auto-correlationfor zinc). Joint tests of the hypothesis of zero intercept and unit slope suggest acceptanceof the unbiasedness hypothesisfor copper,tin and lead, and rejection of that hypothesisfor zinc at the 5 per cent level of significance(but not at the 1 per.cent level). The implications of this result are that agents using London Metal Exchangecopper, tin and lead futures prices for decision purposesare as well off on averageas if they had known the subsequent cashprice in advance.Rejectionof this hypothesisfor zinc, however,doesnot imply that this market is not performingits riskreduction function satisfactorily or that it is informationally inefficient. In view of the marginal rejection of the unbiasedness hypothesisfor zinc, the ability of futures prices for all four metals to reflect publicly available information was considered.It was assumedthat an appropriatespecificationof that information set is the group of immediatelyprecedingforecasterrors for thesefour metals.The efficient marketshypothesiscannotbe rejectedfor tin or lead, and this outcome is consistent with non-rejection of unbiasedness for thesemetals.For zinc the marketefficiency hypothesis is rejectedat the 5 per cent level but not at 1 per cent and this outcome is also consistent with the marginal rejection of unbiasednessfor that metal. In the case of copper, there is some ambiguity in that the efficient marketshypothesisis rejectedat the 5 per cent level. This ambiguity disappearsat the 2.5 per cent level however, where the market efficiency hypothesis cannot be rejected.

Appendix 1: The Informational Efficien~y of the London Metal Exchange

This Appendix is concernedwith the ability of futures prices for copper,tin, zinc and lead on the LME to reflect publicly available information. It is assumedthat an appropriatespecificationof that information set is comprised of the immediately prior forecast errors for these four non-ferrous metals. This version of the efficient markets hypothesis is then addressedby testing the hypothesisthat the current forecast error for each metal is unrelated to the elementsof this information set. The rationalefor this

Forward Pricing Function

169

procedureis that forecast errors contain information becauseof innovationswhich occur in the interval betweenthe time when the futures price is formed and the delivery date of the contract. If, however, the market under considerationis efficient, this information will be utilized very rapidly and there should be no systematic relationship between the current forecast error for an individual metal and any of the immediatelyprior forecasterrors. The existenceof a systematicrelationshipwould be evidenceof a lag in the utilization of information. Hence the relevantestimating equationcan be written

~+k Pt,Hk -

where k 3

~j(At-

Pt,Hk

a

+

4

L

j=l

~j(At-~j(At-

Pt-k,t)j

+ Ut

(A1)

~j(At1, ...,4 for copper,tin, zinc and lead respectively.

The efficient marketshypothesisis testedby the joint test that the coefficientsa, ~j = O. This procedurewas used by Hansenand Hodrick (1980) for currencies,and by Goss (1983) for non-ferrous metals on the LME for the period 1971-9,with overlappingobservations.In this Appendix, however,the resultsare reportedfor equation(A1) for all four metals, for the sample period 1966-84 with 54 nonoverlappingobservations.The coefficients are estimatedby OLS and there is no evidenceof first-order serial correlation in any of the relationships.Theseestimatesare given in Table A1, together with calculatedF valuesto test the hypothesisthat all coefficients a,~I' ••• , ~I' ~4 = O. At the 5 per cent level of significance, this version of the efficient marketshypothesismust be rejectedfor copperand zinc, but cannotbe rejectedfor tin or lead. At the 1 per cent level, the hypothesiscannotbe rejectedfor any metal.

ri

10.396 (1.147)

6.181 (1.187)

Zinc (OLS)

Lead (OLS)

Tabulated 0.01 F5,4o - 3.51

Tabulated 0.05F5,40 - 2.45

Tin: 1.783

Zinc: 2.948

I"', ... , 1\ -

-0.084 (-1.279)

-0.120 (-1.047)

0.214 (0.264)

Calculated F-values to test H, (u,

Copper: 2.829

1\

-0.330 (-1.687)

Notes: • T-values are in parentheses.

123.778 (1.935)

18.079 (1.170)

Tin (OLS)

Copper (OLS)

*

Lead: 1.291

0)

-0.022 (-1.719)

-0.045 (-1.966)

-0.100 (-0.623)

-0.104 (-2.670)

1\

Table A1: Coefficient Estimates for Equation A1

1\

0.194 (1.760)

0.631 (3.291)

1.874 (1.385)

0.849 (2.598)

1\

0.072 (0.394)

-0.232 (-0.733)

-0.047 (-0.021)

0.730 (1.350)

FP

0.033

0.160

0.015

0.155

DW

2.073

1.765

2.027

1.924

54

54

54

54

Observations

Forward Pricing Function

171

Appendix 2: Informational Efficiency of the London Metal Exchange Coefficient Estimates for Equation A1 (with j

13. Copper (OLS)

13.

13.

0.525 18.279 -0.110 (1.162) (-2.781) (1.949)

=

2, 3, 4)*

13.

R'

DW

Observations

0.483 (0.912)

0.124

2.276

54

Notes: • T-values are in parentheses. Calculated F-values to test H.: (0:,

fl"

3,' ~

0)

Copper: 2.725 Tabulated .05F•.4o

-

2.61

Tabulated .025F•.4o

~

3.13

Notes *Monash University, Australia. This is a revisedversion of a paperof the same title publishedin AppliedEconomics,1981, 13, pp. 133-50,reprintedby permissionof the editor and Chapmanand Hall Ltd. The revisionsfollow the introduction of joint testsand extensionof the sampleperiod. I am grateful to David Giles, Max King and Mark Upcher for helpful comments,and to Olive Chin and Gulay A vsar for researchassistancein preparingthe revisions. Remaining errorsare the sole responsibilityof the author. 1. Homogeneityof courseis sufficient but unnecessaryto meet this condition. Seealso Houthakker(1959). 2. Recentlyin the literature on feasibility there has beena tendencyfor the 'commoditycharacteristicsapproach'to be absorbedby a maximizationof net benefitsapproachin which both the costsand benefitsof futures trading are functions inter alia of turnover, open positionsand price variability (seeespecially Telserand Higinbotham, 1977). In the opinion of the presentauthor this change has occurredbecauseof the low predictive power of the earlier approach.[See also the chapterby Veljanovski in this volume. Ed.] 3. In fact, futures contractsare frequently usedin conjunctionwith forward contracts. 4. The evidenceon potatoesis not unambiguous.Yamey (1977) found that the relative inferiority of potatofutures pricesas predictorswas greaterduring intra-seasonalperiods(in the presenceof inventories)than during inter-seasonal periods(when inventorieswere discontinuous). 5. Report preparedin 1982 by the presentauthor for the Commodities Division, World Bank, Washington,DC.

References Arrow, K.J. (1982) 'Risk Perceptionin Psychologyand Economics',Economic Inquiry, vo!. 22, 1-9.

172

Forward Pricing Function

Breeden,D.T. (1982) 'Statement'[on topics and methodologiesfor researchin financial futures], Reviewof Researchin Futures Markets, vo!. 1(2), 175-8 (ChicagoBoard of Trade). Brennan,M.I. (1958) 'The Supply of Storage',AmericanEconomicReview,vo!. 48,50-72. Cargill, T.F. and G.c. Rausser(1975) 'TemporalPrice Behaviorin Commodity FuturesMarkets', The Journal of Finance, XXX, 4 (September),1043-53. Dusak, K. (1973) 'FuturesTrading and Investor Returns:An Investigationof CommodityMarket Risk Premiums',Journal of Political Economy,vo!. 81, 1387-406. Ederington,L.H. (1979) 'The Hedging Performanceof the New FuturesMarkets', Journal of Finance, XXXIV, 1 (March), 157-70. Fama,E.F. (1970) 'Efficient Capital Markets: A Review of Theory and Empirical Work', Journal of Finance, vo!. 25, 383-417. Giles, D.E.A. and B.A Goss(1981) 'The PredictiveQuality of FuturesPrices, with an Application to the SydneyWool FuturesMarket', Australian Journal of Agricultural Economics,vo!. 25, 1-13. Godfrey, L.G. (1976) 'Testing for Serial Correlationin Dynamic Simultaneous EquationModels', Econometrica,vo!. 44, 1077-84. Goss,B.A (1972) The Theoryof Futures Trading, London: Routledgeand Kegan Pau!' (1983) 'The Semi-StrongForm Efficiency of the London Metal Exchange', AppliedEconomics,vo!. 15,681-98. Graf, T.F. (1953) 'Hedging- How Effective Is It?', Journal of Farm Economics, XXXV, 3 (August), 398-413. Gray, R.W. (1960) 'The CharacteristicBias in SomeThin FuturesMarkets', Food ResearchInstituteStudies,1, (November),298-312. (1966) 'Why Does FuturesTrading Succeedor Fail? An Analysis of Selected Commodities',Futures Trading Seminar,vo!. Ill, MIMIR: Madison. (1972) 'The FuturesMarket for Maine Potatoes:An Appraisal', Food ResearchInstituteStudies,vo!. 11, 313-41. Hall, B.H. (1983), Time SeriesProcessorVersion 4.0 ReferenceManual, TSP International,Stanford,California. Hamburger,M.I. and E.N. Platt (1975) 'The ExpectationsHypothesisand the Efficiency of the TreasuryBill Market', The Reviewof Economicsand Statistics,57, 190-9. Hansen,L.P. and L.R. Hodrick (1980) 'Forward ExchangeRatesas Optimal Predictorsof Future Spot Rates:An EconometricAnalysis', Journal of Political Economy,vo!. 88, 829-53. Houthakker,H.S. (1959) 'Scopeand Limits of FuturesTrading', Allocation of EconomicResources,M. Abramovitz et al., StanfordUniversity Press,pp. 141-59. Kofi, T.A (1973) 'A Frameworkfor Comparingthe Efficiency of Futures Markets', AmericanJournal ofAgricultural Economics,vo!. 55 (November), 584-94. Larson, AB. (1960) 'Measurementof a RandomProcessin FuturesPrices', Food ResearchInstituteStudies,1,3 (November),313-24. Leuthold, R.M. (1974) 'The Price Performanceon the FuturesMarket of a Non-storableCommodity: Live Beef Cattle', AmericanJournal ofAgricultural Economics,vo!. 36 (May), 271-9. Leuthold, R.M. and P.A Hartmann(1979) 'A Semi-strongForm Evaluationof the Efficiency of the Hog FuturesMarket', AmericanJournal ofAgricultural Economics,61, 3 (August), 482-9. Powers,M.I. and P. Tosini (1977) 'Commodity FuturesExchangesand the

Forward Pricing Function

173

North-SouthDialogue', AmericanJournal ofAgricultural Economics,59, 5 (December),977-85. Praetz,P.D. (1975) 'Testingthe Efficient MarketsTheory on the SydneyWool FuturesExchange',Australian EconomicPapers(December),240-9. RutIedge,D.l.S. (1972) 'Hedgers'Demandfor FuturesContracts:A Theoretical Frameworkwith Applications to the United StatesSoybeanComplex', Food ResearchInstitute Studies,vo\. 11,237-56. Stevenson, R.A.and R.M. Bear (1970) 'Commodity Futures:Trendsor Random Walks?', Journal of Finance, XXV, 1 (March), 65-81. Telser, L.G. (1979) 'Reasonsfor Having an OrganizedFuturesMarket', Report 7925, Centerfor MathematicalStudiesin Businessand Economics,University of Chicago. Telser, L.G. and H.N. Higinbotham(1977) 'OrganizedFuturesMarkets: Costsand Benefits', Journal of Political Economy,85, (5), 969-1000. Tomek, W.G. and R.W. Gray (1970) 'TemporalRelationshipsAmong Priceson CommodityFuturesMarkets: Their Allocative and Stabilizing Roles', American Journal of Agricultural Economics,52, 3 (August), 372-80. Working, H. (1942) 'Quotationson Commodity Futuresas Price Forecasts', Econometrica,vo\. 10, 39-52. (1949) 'The Theory of Price of Storage',AmericanEconomicReview,vo\. 39 (December),1254-62. (1953a)'FuturesTrading and Hedging', AmericanEconomicReview,vo\. 43, 314-43. (1953b) 'HedgingReconsidered',Journal of Farm Economics,vo\. 35, 544-61. Yamey, B.S. (1951) 'An Investigationof Hedgingon an OrganisedProduce Exchange',The ManchesterSchoolof EconomicsandSocialStudies,vo\. XIX (September), 305-19. (1977) 'ContinuousInventories,FuturesPricesand Self-fulfilling Prophecies', mimeD, London School of Economics.

This pageintentionally left blank

8

AN ANALYSIS OF GOLD FUTURES PRICES IN LARGE AND SMALL MARKETS

c.

Rae Weston and Ross McDonnell*

Gold, for example,is tradedin many countriesand currencies; where daily quotations are available, gold prices in different locations are invariably within transaction costs of equality. (Richard Roll, 'Violations of PurchasingPower Parity and their Implications for Efficient International Commodity Markets', UCLA, May 1978, p. 1) 1. Introduction It is the purposeof this chapterto investigatethe relevanceof the abovepropositionto the gold futures prices in large and small gold futures markets. Despite a number of tests made concerningthe relationship between spot prices across various markets (Booth and Kaen, 1979), very little work hasbeendoneon the connection between the futures markets relationships (an exception is BrendanBrown, 1977). Writing of the gold futures markets in November 1979 the Australian Financial Reviewsaid, 'There is a market open somewhere in the world practically 24 hours a day ... The world clock shows that the gap in official marketsis four hours betweenthe close of the New York Comex and the opening of the Sydney FuturesExchange'(26 November1979). By comparisonwith the New York Comex, both the Winnipeg Commodity Exchange and the Sydney Futures Exchange are marketsof much smaller size, so that even to the extent that they fill in the time gap, they may not have the same depth as the Comex market and market imperfectionsmay arise. There are, in particular, differences between the Sydney Futures Exchange (SFE) arrangementsand those of the other two markets which may be sufficient to reduce the ability of SFE trading to reflect *MasseyUniversity and Australian CommercialComputingPty Ltd.

175

176 A nalysisof Gold FuturesPrices only the movesin the Comexmarket. First, the size of the contract is different (50 troy ounces in SFE, as opposed to 100 troy ounces);second,the presenceof exchangecontrol regulationsin Australia may deter potential offshore operatorsin the SFE, while there is not the same limit in the other markets (the Australian authorities are in fact sufficiently paranoid about speculationto have limited the recently introducedcurrency futures markets in US dollars to residents only); and third, within the Australian market, clients who are neither Exchangemembersnor members of the Clearing House, may only be unsecuredcreditors with respect to deposits paid by them to a broker; by comparison, clients' funds appearto be fully covered by the Clearing House provisionsof the Comexmarket. The purposeof this chapteris to examinethe daily data of gold futures prices from three markets - Winnipeg, New York and Sydney - over the period April 1978 to April 1979 in order to investigate:(i) the comparativeefficiency of the markets; (ii) the coherencebetweenthe markets;and (iii) the comparativeresponse of individual marketsto the releaseof externalinformation. Thereare interestingdifferencesbetweenthe three markets;for example,Winnipeg, the first of thesegold futures marketsin time, was then a centreof investor interest, but has more recently been of reducedimportancedue to the openingof the US gold futures markets. Both Winnipeg and Sydney (the gold contract of the latter openedin April 1978) have much more localized markets than New York; previously Sydneyhad offered wool futures and cattle futures, and interest in that gold futures market was very slow to develop.That is, Sydneyin its first monthsof gold futures trading was a small thin market, Winnipeg, a small but wellestablishedmarket, while New York was a large well-developed market. The availability of futures trading in gold on successiveinternational markets over approximately20 hours of a 24-hour day reducesthe possibility that market closing changesthe speedof adjustmentof prices, although there is still a gap at weekends. Grangerand Morgenstern,however,(1971, pp. 122-9),in discussing the effect of night and weekendclosing of a market, note three possiblehypotheses:first, that the opening price on day t will be the closing price on day t-l regardlessof the time that passes betweenthem, if price changesare only generatedby the operation of the marketitself; second,that the mechanismthat generatesthe

Analysisof Gold FuturesPrices 177 prices may operatequite independentlyof whether the market is open or not; and third, that the mechanismgeneratingprices will still operatewhen the marketis closed,but at a lower speed(where speedis measuredby the varianceper unit time of the first difference of the price series).The possiblerelevanceof each of these hypotheseswill be discussedin relation to the results presentedin the remainderof the chapter. 2. Methodology and Data

Methodology The statisticalanalysisreportedin this chapterfalls naturally into two parts: first, a test of the weak form of market efficiency; and second,a spectralanalysisof the structure of each of the market seriesconsideredand the relationshipbetweenthe series.It is of assistancein applying the latter analysisif it is possibleto establish that the distribution of gold futures prices is stationary. Accordingly, as the first part of our analysisof the applicability of the weak form of market efficiency, we examine the distribution propertiesof changesin the daily gold futures pricesin the markets considered. For each of the markets consideredthe mean, standarddeviation, skewnessand kurtosis are reported and the KolmogorovSmimov two-sampletest is usedto test whetherthe distribution of price changesought to be regarded as stationary. Next, serial correlation coefficients are estimated. If statistically significant auto-correlationsare not identified it is likely that dependency does not exist in the time series. In the absence of a time dependencyit is appropriateto apply the runs test in order to determinewhetherthe observednumberof runs approximatesthe expectednumber. Spectral analysis is based on the Cramer Decomposition Theoremwhich providesthe result that a stationaryseries~w with a discreteindex set t = 0, 1,2, ... ,andmeanu canbe represented as: ~-u

w

LH exp (iwt) d Z (w)

w

angularfrequency

where

178 and

Analysisof Gold FuturesPrices

w dz(w)

2IIf an independentincrementprocess.

This decompositiontheorem implies that any stationaryseries may be decomposedand studiedon a cycle-by-cyclebasis. In our analysis we use the auto-spectrumto isolate cycles in the series, becausethe value of the auto-spectrumat any frequency is a measureof the contribution of that particular frequency to the total varianceof a series.While we are interestedin the strengthof the relationshipbetweenany two series,that is the coherence,the phaseangle allows us to considerthe leads and lags betweenthe series.

Data The raw data for this study are the per ounce prices for gold futures traded on the Winnipeg, Sydney and New York markets convertedto the US exchangerate (although some use is made later of the unadjustedprices for the New York-Sydney market pairs). As our prime interest lies in identifying the relationships betweenthe prices on large and smaller markets, we analysethe Winnipeg-NewYork and Sydney-NewYork pairings. The log of the first differencesof the per ouncegold futures prices is usedin the subsequentanalysis. Thereis, of course,a problem in identifying a continuousseries of prices,from daily futures trading, that will be comparableacross markets. We have available for the three markets high and low prices for sales during each trading day for all of the contract months traded in each market. In addition, we have the closing prices on the New York market and the opening bids and offers for the Sydneymarket. We are reluctantto use the bid and offer data becauseour investigationsrevealed that these bear no consistent relationshipto the prices at which actual tradesare made. We do, however, in the last test reported for the New YorkSydney market relationships, take the closing price on the US market and the openingbid on the Australian market in order to explore the timing connections. For the remainderof the tests reported,we use the averageof the highs and lows for each future quoted on both markets (for each pair) on each trading day. That is, we concentrateon the pairedfutures.Two separatemethodswere undertakenin attempt-

Analysisof Gold FuturesPrices 179 ing to constructcontinuousseries:the first is to identify all of those futures quotedon both marketson eachday and to take thosein sequence.This producestoo lumpy a sequenceand we abandoned this at an early stage. The secondmethod,which is that applied in this chapter,is to identify a single pairing of futures tradedon eachday; that is, we may take the first quotedfuture tradedin both marketseachday to form a continuoussequence,or the secondquoted future, or the third quotedfuture, and so on. We report here resultsfor both the first and secondtradedfutures. 3. Results

The New York and WinnipegMarkets There is only one hour difference betweenthese two markets, a time-differencethat our data do not allow one to distinguish. In Table 8.1 we report the summarystatisticsfor the distribution of daily log price changesfor the first quoted future in both markets. The New York resultsreveal a negativeskewnessthat is significant at the .01 level, while the Winnipeg results reveal a slight positive Table 8.1: Distribution Statistics for Log Daily Price Change in First Quoted Future (April 1978-April 1979) New York and Winnipeg Statistic

New York

Winnipeg

Mean Deviance Skewness Kurtosis Correlation

0.0012 0.0151 -0.1518 1.3832

0.0012 0.0147 0.0700 1.9984 0.9388

Runs Test: first quoted month: all paired futures Normalized total runs

0.5952

0.3205

Kolmogorov-Smirnov Two·sample Test

2 sample

One side Two side

1st with last section One side Two side

0.1873 0.3020 0.3721 0.5873

0.2402 0.3020 0.4737 0.5873

0.0787 0.1574

0.0787 0.1574

180

Analysisof Gold FuturesPrices

skewnesssignificant at the .10 level. The kurtosis statisticsreveal a tendencyto a platykurtic distribution in both cases. The runs test is the simplesttest of whetherthe past history of these price changesmay be used to predict their future movements, that is, whether the description 'random walk' is relevant. The rationale of the runs test is that unless there is a time dependencywithin the dataspan,both the observedlength and the numberof runs ought to approximatethe expectednumber.If the normalizedtotal runs lie between0 and 1, a weak test of market efficiency is confirmed and we are able to make this confirmation for both markets. In order to apply spectralanalysis to these data we need evidenceof stationarityin the data. Application of the Kolmogorov-Smirnov one-sample test suggeststhat the distributions are normal. The KolmogorovSmirnov two-sample test allows us to test stationarity; and the resultsreportedin Table 8.1 suggestthat the two samples(and the first section with last section comparison) are from the same distribution and, therefore,stationary. Table 8.2: Distribution Statistics for Log Daily Price Change in Second Quoted Future (April 1978-April 1979) New York and Winnipeg Statistic

New York

Winnipeg

Mean Variance Skewness Kurtosis Correlation

0.0011 0.0151 -0.0358 1.6835

0.0011 0.0149 0.0595 0.9817

Runs Test: second quoted month: all paired futures Normalized total runs

0.2274

0.7731

Kolmogorov-Smirnov Two-sample Test

2 sample

One side

0.1873 0.4494 0.2780

0.1072 0.5321 0.2962

Two side

0.3721 0.8188 0.5441

0.2142 0.9107 0.5770

0.0787 0.1574

0.1431 0.2854

1st with last section One side Two side

Analysisof Gold FuturesPrices 181 Stationarity, which is confirmed by these results, allows us to proceed to spectral analysis without any further filtering of the data. Figure 8.1 plots the spectrumsfor the two markets. The patternrevealedis strong evidenceagainstthe randomwalk hypothesis. Becausewe are only observing one quoted future, the earliest,we include in our resultsthosetestsfor the secondquoted future as well. Table 8.2 reports results that are similar to Table 8.1. Referenceto Figure 8.2 suggeststhat the main peaksin the frequencies,revealedin Figure 8.1, are confirmed. Clearestof the peaksis that at three days.

New York-Sydney There is a larger time difference betweenthesemarkets,owing to the fact that Sydney time is 16 hours aheadof New York time. Further,the Sydneyfutures trading in gold openedon the first day of our time period. Accordingly, we might expect trade to be thinner on this market than on the New York market. Australian Figure 8.1: New York-Canadian Spectrums

c-----o Set One

1 20

~----.

Set Two

; 100

~

80

X

60

40

2~LO--~--~10~0--~---2JO-0--~·~3~OO~~--~4.00~--~--5~.0~0--~ Time

In

100

days less no trades (Xl0·')

100

100

182 Analysisof Gold FuturesPrices Figure 8.2: New York-Canadian Spectrums 1.20 0------0 6- _ _ _ _•

Set One Set Two

140

1.20

100

;:

80

x

60

40

20 00

100

200 300 Time In days less no trades ("10")

400

500

exchange control regulations may also have deterred overseas interestin the Sydneymarket. Tables 8.3 and 8.4 report the results for the first and second quoted futures, giving rise to pairs between these markets. It shouldbe notedthat pairedfutures could be identified on lessthan half of the trading days; for example,Table 8.4 reports on only 107 paired futures quotesby comparisonwith the resultsreported for the New York-Winnipeg markets,which have paired futures on every trading day during the sampleperiod. The reduction in the number of observationsreported in Tables 8.3 and 8.4, by comparisonwith Tables 8.1 and 8.2, accountsfor the significant negativeskewnessand kurtosis and for the refutation of the weak test of marketefficiency. Of course,while the changein the New York resultsis due to the selectivesampling causedby the absenceof a Sydneyfutures pair, the results provided for Sydney representas continuousa seriesas it is possibleto identify. Tables 8.3 and 8.4 reveal a dis-

Analysisof Gold FuturesPrices 183 Table 8.3: Distribution Statistics for Log Daily Price Change in First Quoted Future (April 1978-April 1979) New York and Sydney Statistic

New York

Sydney

Mean Variance Skewness Kurtosis Correlation

0.0023 0.0249 -3.8430 31.8844

0.0009 0.0154 -2.9706 23.2452 0.7911

Runs Test: first quoted month: all paired futures Normalized total runs

-1.1443

-0.2861

Kolmogorov-Smirnov Two-sample Test

2 sample

One side Two side

0.2047 0.4059

0.1311 0.2617

0.0642 0.1283

0.1404 0.2801

1st with last section One side Two side

Table 8.4: Distribution Statistics for Log Price Change in Second Quoted Future (April 1978-April 1979) New York and Sydney Statistic Mean Variance Skewness Kurtosis Correlation

New York

Sydney

0.0026 0.0253 1.9709 8.4639

0.0028 0.0255 1.7574 12.4601 0.8249

Runs Test: daily log price changes: paired futures Normalized total runs

-2.0812

-1.6187

Kolmogorov-Smirnov Two-sample Test

2 sample

One side Two side

0.1515 0.3020

0.2837 0.5544

0.0678 0.1356

0.0424 0.0848

1st with last section One side Two side

184

Analysisof Gold FuturesPrices

parity in the skewnessresults; that is, positive skewnessis seenin the first quoted future series, in contrast to significant negative skewnessin the case of the secondquoted future. The kurtosis figures reflect a strongly leptokurtic curve for the distribution. Both seriesalso fail the runs test. With the smaller number of observationsit is unreasonableto put any seriousreliance on the results of spectralanalysis,so we merely note from that analysis that the main frequency cycle revealedby the US-Canadianresultsis not identifiable. Before categorizing the Sydney market as inefficient on the basisof theseresults,it is reasonableto explorethe possiblerole of the exchangerate in thesefigures. Figures 8.3 and 8.4 and Table 8.5 report on the second quoted future series with the data unadjustedfor the exchangerate. The results reported for the exchangerate-adjusteddata in fact confirm those reported in Table 8.5. One further test incorporating Sydney market data, which would enableus to examinethe spectralresultsin particulara little Figure 8.3: New York-Sydney: Log of Prices [unadjustedj

5.50

0-------0

Set One

010-----010

Set Two

5.30

5.30

5.20

510

5000~0--~--~2~0---L--_.4LO---L--~6~0---L--~80~~--~1~0~0--~~1.20 5.30 Time

In

5.30

days less no Hades (X 10-')

5.30

5.30

Analysisof Gold FuturesPrices 185 Figure 8.4: New York-Sydney: First Difference of Log Prices [unadjustedl

160

~SetOneSet 6~

---

-6

Two Set Two

120

120 80

Set Two

120

120

120

120

-800'';;-o----'--~2;;-0

-':-:00:-----' 120 ----'------:40:---"----=60=------''----8:'::0----'----:-1 Time in days less no trades (X 10-')

less tentatively is reportedin Table 8.6. Thoseresults use a combination of the US closing price and the Sydney opening bid to form a seriesof paired futures. This has the effect of more than doubling the number of observationsin the seriesto 225. In this casethe figures are adjustedfor the exchangerate. The skewness for the Sydneyseriesis reducednow to much nearernormal; however, the kurtosis statistic revealsa strongly leptokurtic curve for the distribution. The runs test is now successful and the Kolmogorov-Smimovone-and two-sampletestsdo not reject the hypothesesof normality and stationarity. It is, in these circumstances, more appropriate to consider the results of spectral analysis.Once more, as with the New York-Winnipeg spectrums, there is a significant frequencycycle at three days but it is not the clearestcycle here. Again, as for the New Y ork-Winnipeg spectral analysis, there is considerableevidence that there are sufficient cycles to justify a conclusionof non-randomness.In current work we attemptto test for the possibility of profitable trading strategies

186

Analysisof Gold FuturesPrices

Table 8.5: Distribution Statistics: Second Quoted Future (April 1978-April 1979) New York and Sydney (Not adjusted for exchange rate) Statistic Mean Variance Skewness Kurtosis Correlation

New York

Sydney

0.0026 0.0263 2.3870 11.1875

0.0029 0.0238 2.6479 17.5821 0.8138

Runs Test Normalized total runs

-2.0522

-1.1401

Kolmogorov-Smirnov Two-sample Test

2 sample

One side Two side

0.1346 0.2686

0.4413 0.8080

0.0713 0.1425

0.1089 0.2175

1st with last section One side Two side

in the April 1979-April 1980 period, using the results from the April 1978-April 1979 period to identify reasonablestrategies. It is important to note that the resultsincorporatingthe Sydney opening bids use this artificial non-traded price as a proxy for tradeswhich, our earlier resultssuggest,are not in fact made.We may conclude from the contrast in the results, using bids as opposedto tradedprices, that the traded market is inefficient and the distribution of price changesis skewed.The openingbid series impartsa smoothnessto the trading which doesnot exist in fact. One further differencebetweenthe two setsof Sydneyresultsis the presenceof an expectedtime lag in the close-openingbid results, a lag not reflected in the earlier results. This is inferential evidencethat the two marketsrun independentlyof eachother.

ExternalEffectsand Gold FuturesPrices There are two influences that external effects, for example the Carter budget packageto supportthe US dollar announcedon 1 November1978, might have on the price seriesinvestigatedin this chapter.First, in the caseofthe New York-Sydneypairedfutures, it may well be that price determinationin both markets is coin-

Analysisof Gold FuturesPrices 187 Table 8.6: Distribution Statistics for Log Daily Price Changes for the US Closing Price with Opening Bid Sydney: Second Quoted Future (April 1978-April 1979) New York and Sydney (exchange rate adjusted) Statistic

New York

Mean Variance Skewness Kurtosis Correlation

0.0014 0.0161 -0.0510 1.1329

Sydney

0.0006 1.1393 0.0108 25.0967 0.2367 (with one day lag ~ 0.5647)

Runs Test: US closing price with opening bid Sydney: second quoted future Normalized total runs

0.5292

0.2117

Kolmogorov-Smirnov Two-sample Test

2 sample

One side Two side

0.0567 0.1133

0.1431 0.2854

0.0787 0.1574

0.0787 0.1574

1st with last section One side Two side

cident only in reaction to events occurring outside the markets. There is sufficient unexplained correlation between these two marketsto suggestthat the usual processesof arbitragemay not be working, on the Sydneyside at least. Second,for all three markets, the presenceof external events may well be the influencethat accountsfor the unexpecteddegree of kurtosis in the results. Thesetwo influenceswould allow us to accountfor someof the inefficient elementsthat, accordingto our results, may be present in these markets. The allegation is that there are external effects that bias the normal pattern of price determination in these markets.

4. Conclnsions Evidencefrom severalsources,reporting investigationof daily or weekly gold prices, supportsthe results of the presentstudy that inefficient elementsmay be presentin gold markets.For example,

188

Analysisof Gold FuturesPrices

Solt and Swanson(1981) examineweekly spot gold price dataand conclude that the market is not efficient; Bird (1983), analysing daily price data from the London gold market between1972 and 1982, not only suggeststhat the random walk hypothesisought to be rejected,but also that there are sufficient dependencies to allow profitable exploitation. Weston(1983) reportslevels of correlation betweenspectrumsof spot marketsfor the April 1979 to August 1980 period that suggestarbitragemay not be effective between thesemarkets.For example,in one pair of markets, onlya 60.30 per cent correlation betweenthe spectrumsof the spot prices in London and Zurich was found. Elsewhere in the same study, spectral tests for the presenceof cycles in spot gold and in gold futures prices,for the period April 1979 to August 1980, revealed no evidenceof short-termcycles. It seemsreasonableto concludethat the resultsreportedin this chapter,to the extent that they suggestthe presenceof inefficient elementsin the gold markets, are consistentwith other evidence from gold marketsgenerally. References Bird, PeterJ.W.N. (1983) 'The Weak Form Efficiency of the London Gold Market', DiscussionPaperin Economics,Financeand Investment,no. 99, University of Stirling, July. Booth, G. Geoffrey and Fred R. Kaen (1979) 'Gold and Silver Spot Pricesand Market Information Efficiency', The Financial Review,EasternFinance Association,Spring. Brown, Brendan(1977) 'The Forward Sterling Market and its Relation to Arbitrage betweenthe Silver Market in London, Chicagoand New York', Oxford EconomicPapers,vol. 29. Cook, W.G. (1980) 'Taxationof CommodityFutures',Conferenceof Taxation Institute of Australia (NSW Branch). Fama,EugeneF. (1970) 'Efficient Capital Markets: A Review of Theory and Empirical Work', Journal of Finance, May. Foster,F.G. and Stuart, A. (1954) 'Distribution-FreeTestsin Time-SeriesBased on the Breaking of Records',Journal of the RoyalStatisticalSociety(b), Part 1. Granger,C.W. and O. Morgenstern(1971) Predictability of StockMarket Prices, Massachusetts:Heath Lexington. Grossman,Sanfordand JosephE. Stiglitz (1976) 'Information and Competitive Price Systems',AmericanEconomicReview,66, 2 (May). Hilliard, Jimmy E. (1979) 'The RelationshipbetweenEquity Indiceson World Exchanges',Journal of Finance, 34, 1 (March). HoIthausen,DuncanM. and John S. Hughes(1978) 'CommodityReturnsand Capital Asset Pricing', Financial Management(Summer). Hooten,J. (1978) 'FuturesTrading in Gold', The Bankers'Magazineof Australasia(June).

Analysisof Gold FuturesPrices 189 Koutsoyiannis,A. (1982) 'A Short-runPricing Model for a SpeculativeAsset, With Data for the Gold Bullion Market', Waterloo EconomicSeries, 126, University of Waterloo, Ontario. Roll, Richard (1978) 'Violations of PurchasingPower Parity and their Implications for Efficient InternationalCommodity Markets', UCLA Study Centerin ManagerialEconomicsand Finance,(May). Solt, M.E. and P.J. Swanson'On the Efficiency of the Marketsfor Gold and Silver', Journal of Business,54 (July). Weston,Rae (1983) Gold: A World Survey,London: Croom Helm; New York: St Martin's Press Winnipeg Commodity Exchange(1979) By-Lawsand Regulationsfor Gold Futuresand Optionson Gold Futures, Winnipeg, Manitoba.

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9

THE DISTRIBUTION OF RETURNS IN SYDNEY WOOL FUTURES Keven Rainbow and Peter D. Praetz*

This chapterstudiesthe empirical frequencydistribution of daily returnson the wool contracton the SydneyFuturesExchangefor the period December 1969 to December 1978. The aim is to determinewhether thesereturnscan reasonablybe approximated by a normal distribution, sinceconsistencywith sucha distribution has desirableeconomicand statisticalproperties. Section 1 summarizesresearchinto the empirical aspectsof return distributions. Section 2 discussesthe theory of competing distributions and the inferential measures which distinguish between them. Section 3 presents the empirical results and discussespossible problemswith the data. Section 4 looks at the implications of the results which are consistentwith non-normal distributions. Section 5 examinesthe limitations of this study and suggestsavenuesfor further research.Section 6 provides a brief conclusion. 1. Some RecentResearchon Return Distributions

The question of the determinationof the distribution that fits a return series must be addressedbefore inferencesmay be drawn about statistical testson thosedata. There appearsto be little evidence available on the distribution of returns on futures markets and even less information about returns on the Sydney Futures Exchange.There has, however, been substantialand continuing researchon the empirical frequency distribution of stock market returns.The evidencefrom this latter areamay be helpful because both futures and stock markets are free exchanges,with similar economic forces underlying price movements,and so the distributions of returns may be expectedto be similar, and often have been assumedto take the sameform. Furthermore,becausedata • MonashUniversity, Australia.

191

192

TheDistribution ofReturns

are more readily available for stock markets than for futures markets,empirical researchon the distribution of returnsis more completein that area.This evidencewill be reviewedbriefly now. This areawas recently discussedby Praetzand Wilson (1978). The studiesreviewedthere used daily, weekly and monthly share prices and indices over differing time periods,and testedfor consistencywith different statisticaldistributions. Evidencehad been found which variously supporteda normal distribution, a student t-distribution, non-normalmembersof the stable Paretianfamily of distributions, a compound events model and a log normal model. Some of these tests were deficient becausethe authors failed to test for alternative distributions. In their researchwith Australian share price data Praetz and Wilson specifically compared the normal distribution with the t-distribution of differing degreesof freedom, and the non-normal stable distribution with variousexponents.On the basisof severalstatisticalteststheir conclusion was (p. 86): This paper has found no evidence to support stable Paretian distributions as a representationfor stock price returns and portfolios. The case for their retention now is very weak. Studentt distributionsprovide a betterfit to the data as well as being easierto handlestatistically. Even normality is not sucha bad representationfor portfolios. . .. non-stationarityin the returns generatingprocessclearly seemsto be the most likely explanationof the typical distribution shapethat we havefound. Interestin this topic was stimulatedby Mandelbrot(1963), who rejected the acceptednormality assumptionand suggestedrather the non-normalstable distributions. This paper will be discussed later in this section. Fama (1965) took up the challenge of Mandelbrot with an extensive study of daily stock returns, for stable distribution with differing exponents. Fama (p. 68) concludes: Even a casualglance ... is sufficient to show that the estimates of a producedby the three different proceduresare consistently less than 2 (that consistentwith a normal distribution). In combination with the results produced by the frequency distri-

TheDistribution ofReturns 193 butions and the normal-probabilitygraphs,this would seemto be conclusiveevidencein favour of the Mandelbrothypothesis. In an attempt to find the reason for the departure from normality, Fama (pp. 55-60) testedfor different distributions for the different days and periodsof the week and for non-stationarity in the parametersof the underlying distribution. The results did not supportnormality. He found no weekendeffect; that is, no difference betweenMonday (close) to Tuesday(close) for example, and Friday (close) to Monday (close). He also found no difference in the behaviourof the distribution with changesin the meanof the distribution. However, when consideringnon-stationarityhe did not test for changesin the varianceof the distribution. Praetz (1969) found stability in the meansof distributions of stock returns over time, but concluded(p. 132) 'we would reject the hypothesisthat the varianceof price changesis constantfrom year to year'. It seems,therefore,that Fama(1965) may not have tested for the appropriatenon-stationarityeffect. Praetz (1972) took accountof the changein varianceand concluded(p. 49): Osborn's Brownian motion theory of share price changesis modified to account for the changing variance of the share market. This producesa scaledt-distribution which is an excellent fit to seriesof shareprice indices. This distribution is the only known simple distribution to fit changesin shareprices. It provides a far better fit to the data than the stable Paretian, compoundprocessand normal distribution. For this reasonthe t-distribution was included in the Praetzand Wilson (1978) study. Among papers in this area, for example, Press(1967), Officer (1972) and Osborn (1974), a major contribution has beenmadeby Blattbergand Gonedes(1974). They too favouredthe studentt-distribution (p. 275): We inferred from our resultsthat the studentmodel providesa betterempirical descriptionthan the stablemodel. This doesnot meanthat the ratesof return do in fact follow a studentmodel. It only indicates that the latter provides a better empirical fit than the stable model. The studentmodel has fat tails as does

194

TheDistribution ofReturns

the stablemodel, but convergesto normality for large sum sizes. The stablemodel doesnot convergeto normality. Although little researchhas been done on the distribution of returns in futures markets, some attention has been paid to the serial correlation of price changes.Praetz(1975) has summarized the resultson this latter issuewhich generallywere consistentwith independenceof price changes. The lack of attention to the distribution of returns in futures markets is surprising becausethe study by Mandelbrot (1963) which stimulated interest in return distributions was on cotton pricesratherthan stock market returns. One of the characteristicsof non-normalstable distributions is infinite variance; that is, the sum of independent, identically distributed, random variables does not convergeto a finite limit but continuesto grow with larger and larger samplesizes. Mandelbrot(p. 308) found: The tails of the distributions of price changesare in fact so extraordinarily long that the samplesecondmomentstypically vary in an erratic fashion. For example, the sample second moment ... does not seemto tend to any limit even though the sample size is enormous by economic standards,and even though the seriesto which it appliesis presumablystationary. Mandelbrot employed sample sizes varying from 1 to 1,300 observations.He also made graphical tests which supportedhis basicconclusionthat (p. 319) 'long seriesof monthly price changes should therefore be representedby mixtures of stable Paretian laws; such mixtures remain Paretian'. The literature began therefore with some evidencefor stable Paretian, non-normal distributions. Cootner (1964), however, queried this evidence.He suggestedthat actual cotton prices are affected inter alia by the level of inventories,which variesthroughout the harvestyear with a consequenteffect on the price variance; when stocks are large, price changesare small and so too is their variance,but when stocksare small, price changesare large with a large variance.He added(p. 334):

TheDistribution ofReturns 195 This can happenin spot prices becausethesechangescannotbe arbitraged away - they would occur in a perfect market. Brownian motion or its Paretianequivalentis only reasonable for prices of futures, and even in this areait will not hold without modification if one accepts... [the] evidencethat futures that expire near the end of the seasonare more variable than those which expire earlier ... this suggeststhat the 'Paretian' behaviourof cotton spot price changesmay really be a result of nonstationarity. Thus we are left with conflicting evidenceon the distribution of price changesin futures markets. Kendall (1953) hasalso examinedthis issue.He observedthat it was the change,not the absolutevalue, which constitutesthe basic elementin price determination,and madetwo significant findings. First, he found (p. 89) the changingvariance that other authors have found, and second,for Chicagowheat futures, he found that the distributionswere nearnormal (p. 91). Clark (1973) used a subordinatedstochasticprocess(i.e. subordinated to a normal distribution) as a model for speculative prices with a generalclassof finite-variancedistributionsfor price changes.He studiedcotton futures price changes,with the process directed by operationaltime which was lognormally distributed, and concluded(pp. 146-7): There is, then, a strongcasefor normality of price changewhen it is adjustedfor operationaltime ... All of the resultsare very strong evidencein favour of the finite-variance subordination model. They also point out that the marginal distribution (unconditionalon operationaltime) of price changesshould be lognormal-normalrather than stable. Hunt (1974) found evidenceof a weak seasonalpatternin daily Sydney wool futures returns during the period 1964-73, but a more recent investigation by Fisher and Tanner (1978) failed to find such a pattern. Although on balancethe evidencefrom both stocksand futures marketsdoesnot supportthe stabledistribution, it is still to be determined which distribution fits futures price changesthe best.

196

TheDistribution ofReturns

2. Inferential Considerations for Retnrn Distribntions Theory

In this chapter we compare the family of stable Paretian and studentt-distributions. Stable Paretian distributions are described by Mandelbrot (1963) and Fama(1963, 1965). They have characteristicfunction (t) given by ~(t) ~(t)

exp (idy - clyl" (1

+ iby tan (a n/2) / Iyl)}

where: d is a location parameterand the meanif a> 1; b(-l';;;; b .;;;; 1) is a measureof skewness;c is the scale parameter;and the exponenta(O .;;;; a .;;;; 2) measuresprobability in the tails of the distribution of returns. With b = 0 we have symmetry;a = 2 gives the normal distribution; and when a = 1 and b = 0 we have the Cauchy distribution. When a is in the interval 0 < a < 2, the extreme tails of the stable Paretiandistributions are higher than those of the normal distribution, and the total probability in the extreme tails is larger the smaller the value of a. Furthermore, these distributions are higher than the density function of the normal distribution in the neighbourhoodof their location parameter'scommon value, zero. Thus for a < 2, stabledistributions havehigher densitiesaroundthe meanand the tails and lesserdensities in the middle than the normal. The most important consequence of this is that the variance exists (is finite) only in the extremecaseof a = 2. The mean, however,exists as long as a > 1. The disagreementbetweenthe hypothesisof the normal distribution and Mandelbrot's hypothesis is over the value of the characteristicexponenta. StableParetiandistributions have two important properties:(i) stability or invarianceunder addition (the distribution of sumsof independent,identically distributed, stable Paretian variables is itself stableParetianand, exceptfor origin and scale,has the same form as the distribution of the individual summands,i.e. a and b are constant);(ii) thesedistributionsare the only possiblelimiting distributions for sums of independent, identically distributed, randomvariables. The stability property is important becausethe price changesof a futures contractfor any time interval can be regardedas the sum of the changesfrom transactionto transactionduring the interval.

TheDistribution ofReturns 197 Thus price changesof daily, weekly and monthly stable Paretian variables will follow a stable Paretian distribution of the same form. If stableParetianvariableshavea finite variance,the limiting distribution of their sum will be the normal distribution. If the basicvariableshave infinite variance,the limiting distribution must be stableParetianwith 0 < a < 2. The student t-distributions, developed as return distribution modelsby Praetz(1972) and Blattberg and Gonedes(1974) have distribution function fey), rem + D/r(m)0(2(m-2)Jt) rem + D/r(m)0(2(m-2)Jt) rem + D/r(m)0(2(m-2)Jt) where: y hasmean ~ and variance02 ; rem) is the gammafunction; and fey) has a t distribution on 2m degreesof freedom, exceptfor a scale factor of [m/(m-1)H. This model follows by combining the normal model for returnswith an invertedgammadistribution; this models the stochastic variance to account for the nonstationarityin variancereportedabove. The studentt-distribution has fatter tails than the density function of a conventional standardizednormal random variable, and it is higher than the standardnormal density in the neighbourhoodof their common mean,zero, when scalingis done by 02 • For the studentmodel with degreesof freedom greaterthan 2, the distribution of sums of random variables convergesto the normal distribution as the number of observationsincreases;that is, the classicalcentrallimit theoremapplies. Parameterestimation proceedsby using the sample mean (x) and sample standard deviation (s) to separatereturns into 16 separateclass intervals. Stable Paretianprobabilities are given in Fama and Roll (1968) for a = 1.0, 1.1, ... 1.95, 2.0. Studentt probabilitiesare calculatedfor degreesof freedomT = 3 to 31 and both setsare comparedwith empirical relative frequencies,giving a chi-squaredstatistic. The best a and T are estimated from the minimum of the chi-squaredvalues. There are 12 chi-squareddegreesof freedom, four being lost due to three estimatedparameters(x, s and either a or T = 2m) and one constraint(for the sum of expectedand observedbeing equal), so an overall goodness-of-fitis testedby the Xi2 statistic.

198

TheDistribution ofReturns

The normal distribution test loses three degreesof freedom since there is no a or T, and so this hypothesis is tested by the xi3 statistic. The test for skewnessand kurtosisis definedby Pearson(1930) ~ = as b l = mVm~ L(~ (kurtosis),where L(~ (skewness),and b2 = m4/m~ L(~ L(~ - x}l/N. With a normal and independentsample,~, L(~ of size N (b2 - 3)(NI24)1/2 are and with constantvariance,(bL(~ L(~ l N/6)1/2 andL(~ unit normal deviates.Statisticsfor skewnessand kurtosisare somewhat imperfectas large samplesizesare needed,but the sampleof 299 observationsper contractin this study shouldbe adequatefor that purpose.The final test conductedwas the StudentizedRange deviation.The SR was found by (SR) where SR = range/standard Famaand Roll (1971) to be the best of a numberof goodness-offit testsof normality againstnon-normalstablealternatives. 3. Results

The data for this study consistof daily closing prices from beginning of December1969 to beginning of December1978 on all wool contractstradedon the SydneyFuturesExchange.Becauseit is desirableto haveas many observationsas possible,the datawere organizedin the following way. Observationsfrom trading in the maturity month of each contract were deleted becausein that period the futures price is affected by delivery month influences. Trading in each contract begins 18 months before it is delisted,but in the first few months most contractsexhibited little open interest and little trading. In order to avoid the 'non-trading' effect likely to result from this scant turnover, observations were deleted from the first two months' trading for eachcontract.Thus data were employedfrom 15 months' trading for each of 40 contracts.In order to facilitate computationthe numberof observationswas standardizedat 299 price changes(300 daily closing buyer prices) for each contract. (This standardizationwas achievedby deletion of observationsat the end of the contracts'trading life, where necessary.)There is a slight seasonalpattern only in wool futures prices, and no adjustment was madefor this, in accordancewith the views of Cootner (1964), noted above. Nevertheless,two adjustmentswere madeto the data. First, there was a change from imperial to metric measurementof quantities in wool-handling during the sample

TheDistribution ofReturns 199 period, and prices in the early part of the period were converted from centsper pound to centsper kilogram, so that all price data employedare on this latter basis. Second,becauserates of return were investigatedby most previous studieson this topic, to facilitate comparisonprice relatives were calculated,and from these, ratesof return were derived as follows: Rit

=

Pit /Plt _i

—

1

=

return on contracti over day t

where-denotesa random variable, i = 1, ... , 40 and t = 2, ... , 300. Although tests were conductedboth with and without natural log transformationof returns,the former resultsare preferred.This is first becausethe changein log prices is the yield, under continuous compounding, from holding a security, and second becausethe variability of simple price changesof a security is an increasing function of the price of that security (Fama, 1965; Praetz, 1969). It should be noted that any positive skewnessof returnswill be reducedby this transformation(seeFama, 1976, p. 31). Resultsfor the log of returnsonly are presentedhere. The various rate of return statisticsare presentedin Table 9.1, including statistics for skewness(gl)' kurtosis (g2)' mean (R.), standard deviation (S), studentized range (SR), chi-squared x;p) and x;p), (X~ statistics for the t and stable ParetiandistributionsL(~ first-order serial correlationcoefficient r 1 and the numberof serial correlationcoefficientsnr out of the first twelve which aresignificant at the 1 per cent level. The r l valuesvary from .19 to -.30 and only five are significant at the 1 per cent level of ± .15. Even the largest -.30 only accountsfor 9 per cent of the varianceof prediction for a simple auto-regressivemodel. The r 1 and nr valuesare includedas a check on marketefficiency and, more important, as a diagnosticfor data errors. The low values of both statisticsare encouragingbecause they suggestthe dataare free of grosserrors(seePraetz,1976). Table 9.2 containsthe actual frequency distribution of returns in standardizedclass interval units, and the frequency expected undernormality for two contracts,March 1974 and July 1978. Table 9.3 contains percentages(and numbers in brackets) of contractswhich are significant at the 1, 5 and 10 per cent levels of chi-squared goodness-of-fit tests of the t, stable Paretian and

200

TheDistribution ofReturns

normal distributions, kurtosis (g2), skewness(gt) and studentized range (SR). The results are discussedbelow, using a 1 per cent level of significance due to the possible violation of test assumptionsand the large numberof contractsstudied. It will be seen from Table 9.3 that the t-distribution is far superior to the stable Paretianbecauseon the former hypothesis only 25 per cent of the sample(10 contracts)result in a significant

Table 9.1: Rate of Return Statistics* R(X10")

Contract

9,

9,

Mar 71

.45

7.0

-15

May 71

.63

3.8

-12

SR

xl

1.41

9.9

1.36

8.5

S(%)

x~pxl

r,

27

92

.18

2

27

63

.10

0 00 0 01

n,

July 71

.60

2.8

-11

1.23

6.8

27

51

.15

Oct 71

.66

3.4

-11

1.25

7.4

13

46

.11

Dec 71

.68

4.0

-9

1.29

7.8

20

48

.03

Mar 72

.11

2.8

0

.98

9.0

19

40

.00

May 72

.23

1.2

5

.83

7.1

6

10

.19

3

July 72

.24

1.5

10

.91

7.2

13

22

.11

0

10 0

-.26

1.9

13

1.00

8.0

8

21

-.03

0

Dec 72

.54

14.9

22

2.15

13.1

54

158

.00

4

Mar 73

-.04

10.5

37

2.34

11.5

21

89

.05

0

May 73

.24

4.8

31

2.84

9.4

30

85

.09

2

July 73

.53

9.4

36

3.40

11.9

27

94

-.08

0

Oct 72

Qct 73

-.20

2.2

28

3.44

7.1

20

31

.06

1

Dec 73

-.03

1.7

20

3.28

7.4

11

21

.11

0

Mar 74

.09

1.2

10

2.89

6.9

12 16 12 16

.13

0

May 74

.13

2.0

0

2.78

6.8

22

37

.06

0

July 74

.25

2.1

-1

2.42

7.8

10

20

.03

1

Qct 74

.61

2.4

-12

1.85

7.5

8

15

.08

0

Dec 74

.67

3.6

-10

1.76

8.3

18

30

.12

0

Mar 75

.05

3.3

-11

1.39

8.9

16

27

.07

May 75

.20

4.0

-8

1.12

9.8

13

28

.06

1 0

July 75

.38

4.3

-5

1.10

9.7

8

27

.06

2

Oct 75

.12

6.3

-5

1.00

10.8

9

39

.09

0 0

Dec 75

-.34

2.7

0

.81

7.6

20

40

.11

Mar 76

-.52

3.7

-3

.81

9.0

18

47

.02

0

May 76

.26

5.9

2

.74

10.7

13

34

-.07

0

July 76

-.24

1.2

2

.68

7.1

.05

0

12 15 12 15

The Distribution of Returns 201 Qct 76

-.31

0.8

3

.64

6.2

16

21

-.01

Dec 76

.06

2.6

3

.69

9.0

11

18

-.04

0

7

.77

11.7

16

35

.10

0

0

Mar 77

2.60 2.60 22.4 22.4

May 77

1.47

9.9

4

.69

10.0

21

32

.11

0

July 77

.32

3.1

1

.66

8.8

18

27

.05

0

Qct 77

1.11

7.9

2

.58

10.5

16

27

.10

0

Dec 77

.39

29.1

2

.54

16.4

13

81

-.17

11

Mar 78

.46

2.7

1

.49

8.3

30

58

-.02

0

May 78

.30

2.5

2

.40

8.4

23

38

.08

0 0

.06

1.8

1

.37

8.2

38

42

.01

Qct 78

-.17

0.3

11

.32

5.8

39

44

-.07

0

Dec 78

.11

20.4

0

.43

14.3

74

185

-.30

1

July 78

Note: • Values of statistics for skewness (g,), kurtosis (g,), mean (R), standard deviation (5), studentized range (SR), chi-squared values for t and stableParetian distributions (X; and X;p), and serial correlation measures (r, and n,) for 299 daily wool future returns for 40 contracts with maturities from March 1971 to December 1978.

Table 9.2: Actual and Expected (Normal) Frequency Distribution Daily Returns Frequency Class

Actual (-)

Expected (Normal)

Actual (+)

(a) March 1974 to '12

66

57.2

64

'12 to 1

44

44.8

46

1

21

27.5

23

11

13.2

6

to 2'12

4

5.0

5

>

4

1.5

5

0

to 1'12

1'12 to 2 2

2'12

(b) July 1978 to '12

55

57.2

73

'/' to 1

41

44.8

47

1

23

27.5

18

16

13.2

17

0

to 1'/,

1'/, to 2 2

to 2'/,

2

5.0

1

>

2

1.5

4

2'/,

of

202

TheDistribution ofReturns

Table 9.3: Goodness of Fit Tests*

x' Significance Level (%) Test 1

5

10

5

25

(10)

30

(12)

Stable Paretian

75

(30)

77'12 (31)

87'/' (35)

45

(18)

Normal

72'/' (29)

82'12 (33)

90

Kutosis

97'/' (39)

97'12 (39)

97'/' (39)

Skewness (+)

37'/, (15)

42'12 (17)

55

Skewness (-)

2'/'

(1)

7'12

(3)

12'/'

(36) (22) (5)

Studentized range (+)

80

(32)

90

(36)

95

(38)

Studentized range (-)

0

(0)

0

(0)

0

(0)

Note:

* Percentages

(and numbers in brackets) of contracts significant at 1, 5 and 10 per cent levels for chi-squared goodness-of-fit measures for testing the t, stable Paretian and normal distributions, kurtosis. skewness and studentized range.

X2 value comparedwith 75 per cent (30) on the latter hypothesis. Kurtosis is very strongwith only one contractnot significant. Some positive skewnessalso emergeswith 15 contractssignificant. This is reflected in the studentizedrange results, which also reject normality at the positive end for 32 contracts. From Table 9.2 it is clear that the actual frequenciesare more peakedthan the expectednormal frequenciesand give the appearanceof possibly having fatter tails; the typical result for actualfrequenciesfrom stocks is of fat tails, the distribution being more peakednearzero and having lower frequenciesin between. It is possiblethat data errors may be responsiblefor someof the resultsindicatedabove- very few errors are neededin a database to produce significant results (see Beedlesand Simkowitz, 1978) - and sucherrorsappearto exist in even the bestlarge databases. After an examinationof the top quality data basesof US stocks, Rosenbergand Houglet (1974, p. 1306) stated:

Since the errors are relatively large, each higher power causes the effect of the errorsto grow proportionallylarger. The errors affect the meansby factors of lessthan 111000,the variancesby factors as great as 5/3, the skewnessby factors as great as 11, and the kurtosis by factors as great as 18 - indeed,the errors ... virtually determinethe skewnessand kurtosis.

TheDistribution ofReturns 203 The extent to which such errors affect the data employedhere is unknown. Both skewnessand kurtosis are strongly significant for someindividual contracts,and data errors may be responsiblefor this result. On the other hand, data errors tend to result in negative first-order serial correlation, which is absent in the results presentedhere. A further possible explanationof the skewnessand kurtosis found may be the 'non-trading'effect of low volumes in the early part of the life of the contracts. Rosenbergand Houglet (1974) have suggestedthe exclusionof outlying observ3tions as a means of reducing skewness and kurtosis, although if this procedure results in support for the normal distribution there is an implication that the resultsare preconceived.In this study, experimentationwith data reducedby the elimination of outliers improved the relative performanceof the normality hypothesis,but did not changethe nature of the results (experimentswith reduceddata are not reportedhere). 4. Economic and Statistical Implications The economic and statistical implications of returns which conform to a stabledistribution have been well documentedby Fama (1963, 1965) and Blattbergand Gonedes(1974). Following Fama (1965, pp. 93-8), thesemay be statedas; 1. In a Gaussianmarket, if the sum of a large numberof price changesacrossa long time period is very large, it is likely that eachindividual price changeduring the time period is negligible when comparedto the total change.In a market that is stable Paretianwith a < 2, however, the size of the total will more than likely be the result of a few very large changesthat took placeduring much shortersub-periods.In other words, whereas the path of the price level of a given security in a Gaussian market will be fairly continuous, in a stable Paretian market with a < 2 it will usually be discontinuous. The discontinuousnatureof a stableParetianmarket has the implication that such a market is inherently more risky than a Gaussianmarket. The variability of a given expectedyield is higher in a stable Paretian market, than it would be in a Gaussianmarket, and the probability of large lossesis greater. Moreover, in a stable Paretianmarket with a < 2 speculators

204

TheDistribution ofReturns

cannotusually protectthemselvesfrom large lossesby meansof suchdevicesas 'stop-loss'orders. 2. In practical terms 'infinite' variancemeansthat the sample variance and standarddeviation of a stable Paretian process with a < 2 will show extremelyerratic behaviourfor very large samples.That is, for larger and larger sample sizes the variability of the sample variance and standarddeviation will not tend to dampennearly as much as would be expectedwith a Gaussianprocess. In this situation the mean-varianceconcept of an efficient portfolio losesits meaning.Moreover, the asymptoticproperties of the parametersin classical least-squaresregressionanalysis are strongly dependenton the assumptionof finite variancein the distribution of the residuals. If the stable Paretiandistribution were upheld, the Capital Asset Pricing Model could not be applied to thesedata. On the other hand, the student distribution has some advantages,in that this model allows the use of well-defined density functions, whereaswell-defined density functions for the stablemodel exist in only two cases,wherea = 1 and a = 2. Moreover, the parametersfor the studentmodel may be estimatedfrom the closed form solution of its likelihood function. This is not possiblefor the stabledistributions,which require approximations, and it is not possibleto estimatea from statisticaltheory.

5. Limitations of this Study No single study can prove returns conform to a particular distribution; the best it can do is provide evidence for or against a particular hypothesis.The results here, of course, are specific to this set of data, and our understandingof returns in the wool futures market would be improved by extending the sample period. A priori it was expectedthat natural log transformations would improve the fit of the distributions testedhere to the data. The resultsappearto supportthis contentionbecause,for all tests, the transformationreducedthe significanceof departuresfrom the modelsfitted. One of the reasons for departurefrom normality using daily data is the 'weekend'effect mentionedearlier. If one attemptsto

TheDistribution ofReturns 205 fit one distribution (e.g. the normal distribution) to all the data, when someof the datacomefrom different distributions,a poor fit for the distribution hypothesizedis to be expected.This point was not investigatedfor thesedata although it may have no effect on the results, as in the case reportedby Fama (1965, pp. 55-6). It has been suggestedin the stock market literature that the use of daily ratesof return may be inappropriatebecausesuchreturnsare all affected by market-wideinfluences. It has been suggestedthat these market-wide influences should be eliminated and a distribution fitted to the residuals.Officer (1971) examinedthis alternative with daily stock prices and found it to make virtually no differenceto the results,mainly becausethe cross-sectionalcorrelation amongdaily returnsis close to zero. It was mentionedin Section2 abovethat stabledistributionsare invariant under addition. That is, daily, weekly and monthly returnswould follow the sameform of distribution if they were in fact stablevariables.Fama(1976, p. 33) pointed out, however,in relation to stock prices, that monthly returns are closer to normality than daily returns. This possibility may be explored with futures market data, but was not testedhere. Tests other than those reportedin this chaptermay be used to find the model that best fits the data. Fama (1965) employed normal probability graphs, double-log and probability graphs, range analysis and the sequential variance method used by Mandelbrot (1963). Blattberg and Gonedes (1974) used a maximum likelihood estimation procedure, and more recently Greeneand Fielitz (1977) used a techniqueto detect long-term dependence,which they claim leads to the conclusion that the distribution of security returns is non-normal stable Paretian as opposedto Gaussian.Saniga and Hayya (1977) have also proposed goodness-of-fittests to discriminate between non-normal symmetric stable distributions on the basis of skewness and kurtosis. In addition to the models mentionedabove which have been tested,Oldfield, Rogalski and Jarrow(1977) havesuggesteda new process,an auto-regressivejump process,which may be fitted to stock returns. The searchfor an appropriatedistribution could thus continue far beyondthe limits of this study.

206

TheDistribution ofReturns

6. Conclusion This chapterhas attemptedbriefly to review the literatureof fitting distributionsto marketreturns,to explain the groundsfor research interest in this topic, as well as to provide some evidenceon the distribution of daily returns on the wool contract on the Sydney FuturesExchange. The rival hypothesesaddressedare that the student t, normal and stable Paretiandistributions best describethe returns on the Sydney wool futures contract for the period December1969 to December1978, with 299 sample price changesfor each of 40 contracts.Using a chi-squaretest, the studentt distribution clearly outperformsthe normal and stableParetiandistributions,and tests for skewness and kurtosis provide further evidence against normality. The first-order serial correlation coefficients do not indicate any significant market inefficiency in the use of past price information, nor do they indicateany seriousdata errors. References Beedles,W.L. and M.A. Simkowitz (1978) 'A Note on Skewnessand Data Errors', Journal of Finance, 33, 288-92. Blattberg, R. and N. Gonedes(1974) 'A Comparisonof the Stableand Student Distributionsas StatisticalModels for Stock Prices', Journal of Business,47, 244-80. Clark, P.K. (1973) 'A SubordinatedStochasticProcesswith Finite Variancefor SpeculativePrices', Econometrica,41, 135-55. Cootner, P. (1964) 'Commentson the Variation of Certain SpeCUlativePrices',in P. Cootner(ed.), The RandomCharacterof StockMarket Prices, revisededn, Cambridge,Massachusetts:MIT Press. Fama,E.F. (1963) 'Mandelbrotand the StableParetianHypothesis',Journal of Business,36, 420-9. (1965) 'The Behaviourof Stock-MarketPrices',Journal of Business,38, 34-105. (1976) Foundationsof Finance, Oxford: Basil Blackwell. Fama,E.F. and R. Roll (1968) 'SomePropertiesof SymmetricStable Distributions', Journal ofthe AmericanStatisticalAssociation,63, 817-36. (1971) 'ParameterEstimatesfor SymmetricStableDistributions', Journal of the AmericanStatisticalAssociation,66, 331-8. Fisher, B. and C. Tanner(1978) 'In Searchof Hunt's Short-runPrice Cyclesin the SydneyWool FuturesExchange',Australian Journal of Agricultural Economics,22, 129-34. Greene,M.T. and B.D. Fielitz (1977) 'Long-termDependencein CommonStock Returns',Journal of Financial Economics,4, 339-50. Hunt, B. (1974) 'Short-runPrice Cycles in the SydneyWool FuturesMarket', Australian Journal of Agricultural Economics,18, 133-43.

TheDistribution ofReturns 207 Kendall, M.G. (1953) 'The Analysis of EconomicTime-Series... Part 1: Prices', in P. Cootner(ed.), pp. 85-99. Mandelbrot,B. (1963) 'The Variation of Certain SpeculativePrices'.in P. Cootner (ed.), pp. 307-32. Officer, R. R. (1971) 'A Time SeriesExaminationof the Market Factorof the New York Stock Exchange',PhD diss., University of Chicago. (1972) 'The Distribution of Stock Returns',Journal of AmericanStatistical Association,67, 807-12. Oldfield, B.S. Jr., R.J. Rogalski and R.A. Jarrow (1977) 'An AutoregressiveJump Processfor CommonStock Returns',Journal of Financial Economics,5, 389-418. Osborn, D.R. (1974) 'The Distribution of Price Changeson the SydneyStock Exchange',Australian Journal of Statistics, 16,44-9. Pearson,E.S. (1930) 'A FurtherDevelopmentof Testsfor Normality'. Biometrika, 22,239-49. Praetz,P.D. (1969) 'AustralianStock Pricesand the RandomWalk Hypothesis', Australian Journal of Statistics, 11, 123-39. (1972) 'The Distribution of SharePrice Changes',Journal of Business,45, 49-55. (1975) 'Testing the Efficient MarketsTheory on the SydneyWool Futures Exchange',Australian EconomicPapers, 14, 240-9. (1976) 'SomeEffect of Errors on the Independenceand Distribution of Stock Price Returns',Australian Journal of Management,1(2),79-83. Praetz,1'.0. and E.J. Wilson (1978) 'The Distribution of Stock Market Returns: 1958-1973',Australian Journal of Management,3, 79-90. Press,S.1. (1967) 'A CompoundEvents Model for Security Prices', Journal of Business,40, 317-25. Rosenberg,B. and M. Houglet (1974) 'Error Ratesin CRSPand CompustatData Basesand their Implications', Journal of Finance, 29, 1303-10. Saniga,E.M. and J.c. Hayya (1977) 'Simple Goodness-of-FitTestsfor Symmetric StableDistributions', Journal of Financial and QuantitativeAnalysis,276-89.

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MODELS FOR TRENDS IN 10 CONJECTURED FINANCIAL PRICES, TESTS AND FORECASTS StephenJ. Taylor* 1. Introduction The prices of many financial assets,including stocks,commodities and currencies,changeseveraltimes during a day. Much published researchclaims that the day-to-daychangesin financial prices are either random or differ from a random processin a negligible manner,which cannotbe exploited by speculators.Another viewpoint is that prices contain trends but, previously, there has not been much published evidence to support the idea of trends. Statisticaltestshavebeendone upon the pricesof (i) stockstraded in London (Dryden, 1970; Cunningham,1973), America (Fama, 1965; Grangerand Morgenstern,1971), Australia (Praetz,1969) and Scandinavia (Jennergrenand Korsvold, 1974); (ii) commodities traded in America (Labys and Granger, 1970; Dusak, 1973; Cargill and Rausser,1975) and Australia (Praetz, 1975); and (iii) internationalexchange rates (Cornell and Dietrich, 1978). This chaptergives the first detailed analysisof the daily prices of commoditiestradedat the large marketsin London. It will be argued that price changeshave appearedrandom becausethe alternative hypothesisof trends has been described vaguely. Explicit trend models are conjecturedand tested, with conclusionswhich point to the existenceof trends in the markets studied. Some applicationsof the modelsare given. A time series (~). The return from holding the of daily prices will be denotedby10g(~/~_1)' assetfrom day t-l to day t is defined by10g(~/~_1)' ~ = 10g(~/~_1)'10g(~/~_1)' The logarithmic transformationis now conventional(Fama, 1965, pp. 45-6) and it is the best choice from the Box-Cox set of transformations(Taylor and Kingsman, 1979). A variety of models have been used to describethe apparent random behaviour of financial prices. The random walk model *Departmentof OperationalResearch.LancasterUniversity, England.This paper won the Society'sFrancesWood Memorial prize for the session1979-80(section7 of original paper(pp. 358-60)has beenomitted in this chapter).

209

210

ConjecturedModels

states that the daily returns are uncorrelatedand have constant mean: x,

=

Il + et'

0, E(etet+i )

E(et )

°(i

0).

~

(1.1)

Inflationary factors will causecertain prices to drift upwards.This possibility can be modelledby the positiverandom walk: Xr

Ilt

+ et'

(1.2a)

Ilt> 0, E(et )

0, E(etet+i ) cov(/As,e,)

°(i 0), ° (all s,t).

(1.2b)

~

(1.2c)

Equations(l.2c) statethat the drift terms {Ilt] are all uncorrelated with a white-noiseseries(eJ A specialcaseof (1.2) is the so-called 'weak form' of the efficientmarketmodel, which statesthat prices accurately reflect all past price information and reward rational investorsfor acceptingrisk (Fama, 1970; Jensen,1978). Let RFt be the return from risk-free investmentsand let RP, be the risk premium. The statistical representationof the model will be written: (1.2a,b,c), Ilt

RF, + RP„ RP, > 0.

(1.3)

Models (1.2) and (1.3), and (1.1) for Il> 0, are specialcasesof the sub-martingaleprocess(Fama, 1970): E(xt |allx,_i ,i> 1 ) > 0.

(1.4)

This model, and the precedingspecial cases,can be assessedby evaluatingtrading rules, since(1.4) implies that any methodwhich buys and sells the assetover a specifiedperiod, using knowledgeof the past prices alone, is inferior to the strategyof buying at the beginningof the period and selling at its conclusion.Sometrading rules havebeenclaimedto perform well (Leuthold, 1972), but significance test procedures have only recently been published (Praetz, 1979b). Cargill and Rausser(1975) and Praetz (1976) emphasizethe importanceof applying teststo trading rule results. Price-trendmodelswere first describedin statisticalnotation in Taylor and Kingsman (1978). Formal models are essential,if a

ConjecturedModels 211

price-trendhypothesisis to be investigatedthoroughly. Otherwise, evidence for trends can only be obtained from trading-rule analyses,which lack a satisfactorymethodology.We define formal modelsby (l.2a), (l.2c) and a stochasticprocessfor (!il)' The simplest exampleconsideredis a step-process,in which !It equalseither !It-I with probability p, or a new independentvalue with probability I-p. In this example,the trend !It is constanton each of a sequenceof time intervals, eachinterval having random duration. For eachinterval, log(zl) is expectedto 'move' by a constant amount eachday and this is what we mean by trend. We do not assumethat !It is non-negative(as in l.2b) and, in a trend model, !It is not interpreted as an inflation term or as a riskadjusted,expectedreturn. Rather,we interpret !It as a responseto changesin the anticipateddemandfor, and supply of, the asset;it is then reasonableto permit !It ~ O. Kingsman (1974) offers some insight into the econometric character of demand and supply models for commodities.We cannot hope to identify the beginnings and ends of specific trends. Instead, we conjecture trend models, make theoretical deductions and then test appropriate hypotheses. The structure of the chapter, and the major ideas and results, are as follows. Section 2 containsvarious processesfor the trend (!It), of varying complexities. Our processesare characterizedby the correlation structureimplied for the trend, namely cor(!lt,!it+;) = pi(O < P < 1, all i). Section 3 describesfluctuations in the variance of the returns (Xl)' Standard auto-correlationtests are invalid if the fluctuations are ignored. We describea method of rescalingthe returns, to obtain a serieswl}ose varianceis approximately constant.Also, stochasticprocessesfor the series(var(xt») are conjectured. Section4 focuseson the primary argumentagainstprice trends: the alleged absenceof auto-correlationin the returns. Denoting the theoreticalauto-correlationby Pi = cor(x"xl+i), we define a null hypothesisHo: Pi = O(all i > 0), correspondingto the random walk model. We derive an alternativehypothesis,HI: Pi = Ap'( all i > 0, A > 0, 0 < P < 1), from the price-trendmodels. In the past, Ho has been tested against a general alternative hypothesis, using test statistics whose power is not high when the specific hypothesisHI is valid. It is thereforepossible that many reported conclusionsare erroneous.A new test statistic is given and evaluated on eight (hitherto untested) commodity series and an

212

ConjecturedModels

exchange-rateseries.The randomwalk model is rejectedfor most seriesat the 5 per cent significancelevel, and testsof the positive random walk and efficient market models are also presented.In particular,exchangeratesare not randomwalks. Having establishedthe plausibility of the models, Section 5 describesestimatesof the model parameters.The maximum autocorrelationPI = Ap, is typically less than 0.04. Section 6 gives an optimal linear forecasting method for price-trend models. Although accurateforecastsof future returns are not possible,a reasonable correlation between the forecast and the trendcomponentis demonstrated.Section 7 presentsconclusionsand Section8 discussesdesirabledirectionsfor further researchon price trendsin financial time series. 2. Price-trend Models

2.1 ConstantVarianceModels A price-trendmodel of a price series{Zr} is definedby log(zt) - log (zt_,) E(et )

=

0, E(etet+i ) cov(!-1s,et)

x,

=

!J, + et'

o(i ~ 0), o (alls,t)

(2.1)

in conjunction with a stochasticprocessfor the trend component {!J,}. Initially, it is supposedthat the daily returnsE(!J,). {~} have constant variance.Let 0 2 denotevar(et),v2 denotevar(!J,), and !l = E(!J,). Our simplest example of a trend process is obtained by assumingthat: (1) the trend valuesare determinedby the current information about demandand supply; (2) new information arrives randomly at the market; (3) there is new information on a proportion 1-p of the trading day, 0 < p < 1; (4) the trendvaluechangesonly when new informationbecomes available; (5) whenthe trendvaluechanges,the newvalueis independentof all pastvalues.

ConjecturedModels 213 Theseassumptionsdefine the trend process:

m

probability p,

/1,-1'

ft + TIt'

(2.2)

1 - p.

Throughoutthis section(TIt) denotesa seriesof identicallydistributed randomvariables,having zero means,with eachTIt independentof the past trend values(Il" all s and to calculatethe auto-correlationsfrom x/at. An exponentially weighted moving averageof the past absolute price changesgives a suitableestimate,viz.: 00

a,

YL

i=O

l (1 - Y^k-i-i YYI~-l-il

(1-y)at - 1 +YI~-J Y^k-i-i (3.1)

This method of estimation assumesthat the variancesL; change gradually. It is found that maximum likelihood estimatesof Y are always close to 0.1 for commodity prices. A detailed account of the estimationprocedureis given in Taylor and Kingsman(1979). 3.3 VarianceProcesses

We will calculate auto-correlationcoefficients from the rescaled returns, Yt = ~/at· = ~/at· To assessthe validity of this novel procedure,it is advisableto checkit on simulationsof the series = [~)~/at· using appropriate variances[ L ~). It is thus helpful to find stochasticprocesses for [ L ;} which give y approximatelyequal to 0.1; this subjectis of independentinterestalso. The series[at} has been plotted for seriesof copper and sugar prices,with the following tentativeconclusionsabout[

Lt):

(1) the seriesis stationary; (2) the medianvalue is approximately0.016; (3) the distribution about the median is skewed towards the right; (4) an approximate95 per cent confidenceinterval for L t is from 0.016/J8 = 0.006 to 0.016yi8 = 0.045; note that

ConjecturedModels 217 100 L t is approximately the standarddeviation of the percentageprice change,100(~ 100(z, -—~-1)/~-1. z,_,)/zt _|. Conclusions(3) and (4) led us to consider processesfor the logarithm of Lt. It is arguablethat the plots of (~)(a,) can be modelled by either continuous or discrete processes.The simplest continuous processconsistentwith the plots is the AR( 1) model: log( L /0.016)

~llog( og(

L t_/0.016) + Et

(3.2)

with var (log( L t)} = var(Et)/ (1 - ~2)Et = (0.25 log 8)2 and (Et) white noise. An appropriatesimple discreteprocessis the Markov chain:

Lt hasstates(0.008, 0.016,0.032) and transition matrix, l-n [

n 1-n

n/2

o

n

n~2

n/2 ] 1-n

Extensive simulations have shown that estimatesy = 0.1 occur when ~ = 0.98 or n = 0.02. For these values, the correlation betweenlog( L t) and 10gCJt+;)is10.98)i; this is also the approximate correlationbetweenL ; and L ;+i. 4. Auto-correlation Results

4.1 TheoreticalAuto-correlations a. Random walk models: Various random walk models were describedin Section 1. The model (1.1) has constantmean and zero auto-correlationsat all non-zerolags. This is denotedby the random walk hypothesis: H 0 : Pj

0,

all i

>

O.

(4.1)

Models (1.2) and (1.3) are of the form: ~ = !it + et, (et) is white noise, every pair ~s and et are uncorrelated.Any model of this form hastheoreticalauto-correlations:

218

ConjecturedModels COy c o v(~'~^+i) ,

Pj

var(~) var(|i,)

^)

(4.2)

+ var(ett)

Clearly IPil < var(|i,)/var(e var(~)/var(et) = 0, say. The constraints,(i) ~ ~ 0, (ii) ~ has an interpretationas an inflation or mean-returnterm, ensurethat var(^) var(~) is small. For example,if ~ is always equivalent to an annual return of between0 and 28 per cent, then 0 ,,;;; ~ ,,;;; 0.001 and a reasonablebound for var(fi,) var(~) is obtained from the respectiveuniform distribution, viz. (0.001)2/12.If also var(et) ~ (0.005)2,0is no more than (0.001)2/{12 X (0.005)2} = 1/300. We define further null hypothesesby: all i > 0,

H 0 p : | p ; | < Sp , HOe: IPil ,,;;;

oe'

all i > 0,

~ is consistentwith inflation (model 1.2),

~

(4.3)

is consistentwith an (4.4) efficient market (model 1.3).

h. Price-trend models: Initially suppose that var(x,) var(~) is constantand recall the notationv2 = var(^), var(~), 0 2 = var(e var(et). The general t) price-trendmodel, defined by (2.7), has cov(^)Ml+i )

=

(E(at)}'v 2.

(4.5)

Denoting E(~) E(a,) by p, and substituting(4.5) in (4.2), we obtain:

Pi

=

(4.6)

Psv7(v2 + o2).

We note that the coefficientsdependon p and the ratio V 2/02 = R alone; they are all positive; they are small if R < 1; the values decline slowly if p is almost 1; all the price-trendmodelsdiscussed in Section2 havethe sameform of theoreticalauto-correlation. The last remark indicates that it is impossible to distinguish between the different trend processes by considering autocorrelationcoefficients. At presentthere is no feasible methodof identifying the separateprocesses;this is unimportantin practice, as will be shownin the sectionon forecasting.We define thepricetrend hypothesisto be: H 1:Pi = Api,

someA> 0,

0

< P
0

(4.7)

ConjecturedModels 219 and henceforth interpret the parameterp in the context of the basictrend model (equation(2.2», so that m = (1 - p)-I will refer to the meanduration of the trends. When var("t) fluctuates,equation(4.6) is valid if the ratio R = var(Ilt)/var(et ) is constant; this condition is the pragmatic assumptionstatedin Section2.2. c. An ARMA model: The auto-correlationsof an ARMA(l,l) process: x t - p x t _,

=

9, - q?t_i,

have Pi+1 = PPi' for C!ll i

>

{| t) white noise,

(4.8)

0 (Grangerand Newbold, 1977, p. 27).

It can be shown that an ARMA(l,l) process has the autocorrelationsPi = Api if q is chosento be the solution of:

qZ _ q { 1 + (1 - 2A)pZ) + 1 = 0 (1- A)p

(4.9)

which satisfies0 < q < 1. This result gives a simple method of finding the optimal linear forecastsfor the price-trendmodels. 4.2 TestStatistics Previoustestsof the randomwalk hypothesishave beenperformed without reference to a specific alternative hypothesis. Some researchershave implicitly done this by evaluating: k

Ok

n

L rf,

i=l

where the ri are the sampleauto-correlationcoefficientsof n daily returns and k is chosen subjectively; for Ho true, Ok is asymptoticallydistributed as XZk. Other researchershave assessed individual ri's usingtwo-tailedtests.The former methodlackspower and the latter is haphazard,so that both are unsatisfactory. By considering the likelihood-ratio statistic for tests of Ho against HI' using as 'data' {ri' r z, ... , rk), the author has shown (Taylor, 1980) that a suitable set of statistics for accurately recordedpricesis given by:

220

ConjecturedModels k

i=l i=l

L i=l ~iri

i=l

(0


O)

Series Copper 1 Copper 2 Lead Silver Tin Zinc Sugar Cocoa Coffee Maize Sterling/$

(1 )

k-1

k-2

ExpectedChange(%) k-1, a - 0.016

0.43 0.30 0.52 0.42 0.25 0.46 0.46 0.43 0.43 0.37 0.61

0.70 0.63 0.76 0.68 0.61 0.72 0.72 0.70 0.70 0.67 0.83

0.86 0.75 0.92 0.82 0.71 0.88 0.88 0.86 0.86 0.81 0.97

2.3 0.5 5.4 2.0 0.9 3.9 2.7 2.0 1.5 2.0 10.3

so that ~+N can be forecastby ~ exp (St,N)' If a return p. = ft,1 is forecastover the next day, then a total return of (1 + P + ... + pN-I) P. is predictedover the next N days. Letting N tend to infinity shows that the predicted total return is P./(l - p) = mp.. Thus, when ft,1 = kv., it is predicted that the trend will, on average, changelog(Zt) by: m(kv.)

mkrv

mkra (A/(1 - A)}I/z

(6.9)

Column 4 of Table 10.5 illustratesthe value of (6.9) when k = 1 and 0 = 0.016. The figures are approximatelythe expectedlongterm percentageprice changewhen first the trend estimateequals the standard deviation of its generating random variable and secondlythe daily price changeshavestandarddeviationsof about 1.6 per cent of the price. Thesefigures must be interpretedwith care, since they are sensitiveto the estimatesof A and m. The medianentry in column 4 is 2.0 per cent. As commodityinvestors usually pay only a 10 per cent margin, a naive interpretationof the 2 per cent figure states that an investor could frequently take decisionsfor which the expectedreturn on capital investedwas 20 per cent. It can be shownthat the varianceof St,N is:

ConjecturedModels 239 N var( L xt+J i=l

VN

+ 2mpv2 (N -

N(V2

+ 0 2)

1- pN

__ )

1-p

(6.10)

and that the reduction in the MSE of St,N obtained using linear forecastsequals: 1- pN 2 (_ _) var(ft,l) 1-p

WN

which can be evaluatedusing (6.5). The percentagereduction in MSE is 100WN/VN; typical valueswill be comparedin Section6.2 with the reductionsobtainedin practice. d. Modifications for fluctuating-variance series: Supposenow var(~) fluctuates with time. If the ratio R = var(flt)1 that L/ = var(x, var(et) is constant,as conjecturedin Section 2.2, the optimal linear forecastof ut+1 = ~+I/L+I /I t + ) is u1+1 = L(P - q)qiUt_i' Forecastingxt+1 by L+IU,+I gives, after somerearrangement: X.+1

=

( I « + 1 / L ) { q/Ix t t+ )+ ( p - q ) x , }

(6.11)

as the optimal linear forecast of ~+ 1 • In practice every/ILt + ) is unknownat all times. We define 'Forecastl' by replacingthe ratio a,+1/at where the term ~ is an estimateof EI~I E | Xj made L+/L by ~+/at' at time t-1 and is definedby equation(3.1). This forecastcan also be obtainedby applying the theory for constant-variance seriesto x,/at . The updatingequationsare: the rescaledreturns,Yt = ~/~. X.+1 ~+1 X.+1 ~+I

+ ylxtl, (at+/~){q~ ( W a O l q x, + + (p (1 - y) ~

(6.12) q)~) q)x,}

and we recommendy = 0.1. We define 'Forecast2' by deletingthe multiplier ~+1/~ /a, from equation(6.12) which, essentially,ignores the variancefluctuations. log(zt+N/zt ) it is necessaryto estimatefuture To forecastSt,N = 10g(~+N/~) variancesL;+i' 2 :< i :< N. The only viable procedureis to use the

240

ConjecturedModels

relationshipbetweenSt,N and St,) establishedfor constant-variance series,viz. equation(6.8).

6.2 Empirical Accuracyo/theForecasts Two assessments have beenmadeof the empirical accuracyof the linear forecasts.The first analysischeckswhetherthe theoretically optimal forecastsachieve the predictedreductionsin MSE when they are used on price data. The parameterestimatesobtainedin Section5 are used,althoughin practicetheseestimateswould not havebeenavailableuntil the whole serieswere observed.A second analysis considersforecasts based on some parameterestimates that could havebeenavailable. by calculatingthe weighted Seriesof forecasts(St,N) are assessed error sum-of-squares: [(St,N - St,N)2/a;.

(6.13)

t

The summationis over all times t which are divisible by N. We denotethis quantity by Fo when St,N = 0 is the randomwalk forecast, by F) when St,N is the optimal linear forecast, and calculate the percentagereductionin MSE as 100(Fo- F)/Fo per cent. The weighted least-squaresmethod once more nullifies the problems causedby the fluctuating varianceof the returns. The percentagereductionsin MSE predictedby the theory and the reductionsactually achievedare given for 'Forecastl' in Table 10.6, for N = 1, 5, 10 and 20. When N = 1, there is a consistent and closeagreementbetweenthe theoreticaland actual reductions and several reductions are statistically significant. For further horizons N, there is an increasein both the theoreticaland actual reductions.Again there is a good agreementand the differences betweenthe theoreticaland actual reductionsare consistentwith the relatively small samplesizes. 'Forecastl' outpedorms'Forecast 2' for four series,is inferior for four seriesand has essentially the sameresultsfor the remainingthreeseries. In the secondanalysis,the five seriesof more than 2,000 prices were each subdivided and estimatesof A and p were obtained from the first sub-seriesand usedto calculatethe forecastsfor the second sub-series. The comparison between the reductions expected after analysing the first sub-seriesand those actually obtainedover the secondsub-seriesis given in Table 10.7, again

Copper 1 Copper2 Lead Silver Tin Zinc Sugar Cocoa Coffee Maize Sterling/$

Series

0.63 0.31 0.69 0.64 0.11 0.37 0.84 0.86 2.22 0.18 1.26

T

A

0.64 0.33 0.67 0.29 0.31 0.38 0.96 1.22 2.57 0.22 1.11

A

2.99

2.26

2.83 2.18 0.43 1.56 2.96 2.72 4.27 0.74 5.19

10 5.79

A

0.89 0.28 0.65

3.11

T

4.54 4.11 2.86 4.94 0.64 1.58 0.843.40 0.79 2.58 0.84 0.79 4.00 4.38 3.70 3.33 4.94 3.21 3.52 1.65 1.46 1.19 2.32 2.83 8.36 7.80

2.32 3.40 1.47 2.18 3.57

0.84 0.79 0.84 0.79

A

ForecastHorizon (Days) T

5

Table 10.6: Reductions in MSE (%), Theoretical (T) and Actual (A)

6.15 2.20 0.77 3.63 4.15 2.99 2.05 1.61 11.53

0.84 0.79

3.29

T

20 A

5.82 0.27 6.11 6.57 1.72 3.83 6.37 3.04 0.65 0.20 14.84

0.79 0.11 -0.18

0.28

0.11

0.43

0.95

1970-4 1975-8

1970-4 1975-8

1970-4 1975-8

1961-7 1968-73

Lead

Tin

Zinc

Sugar

0.82

0.27

0.63

1966-74 1974-8

A

Copper

T

T

Dates

Series

3.52

1.80

0.35

1.21

2.26

T

5

2.98

-0.23

0.72

2.70

0.54

A

Forecast Horizon (Days)

5.07

2.95

0.43

2.01

3.11

T

10

4.79

-0.86

0.90

3.75

0.01

A

5.79

4.12

0.37

2.87

3.29

T

20

9.93

-2.80

1.16

5.63

2.14

A

Table 10.7: Percentage Reductions for Second Analysis, Theoretical Predictions (T) from First Sample, Actual Computed for Second Sample (A)

ConjecturedModels 243 for 'Forecast1'. The prior expectationsare exceededfor lead and tin, are not attained for copper and zinc, and are approximately matchedfor sugar. Overall it appearsthat prices could have been forecastmarginally better by using the price-trendmodelsinstead of randomwalk theory. 7. Conclusions We have defined, testedand studieda new set of statisticalmodels for financial time series.Thesemodelsinclude a price-trendterm flt. By specifyingformal stochasticprocessesfor flt, it is possibleto calculatethe theoreticalauto-correlationin daily returnsdue to the conjecturedtype of trend behaviour.It is then possibleto perform statisticaltestsof the random walk and related hypothesesagainst a price-trendhypothesis. The sample evidence from long series of commodity and currency prices is overwhelmingly against the random walk and related hypotheses.It is concludedthat such models are not adequatedescriptionsof the processgeneratingthe data investigated. We emphasizethat clearcutconclusionswere obtained,and could only have been obtained, by two innovations. First, the consequences of fluctuations in the variance of the returns were neutralized. Without this action, the asymptotic sampling theory appealedto in many earlier articles is seriouslyinvalid. Secondly,a new and powerful test statistic was used, to avoid the fate of the established test statistics: a frequent false acceptanceof the randomwalk hypothesis,as enumeratedin Section4.7. The pricetrend models successfullyexplain the observedpreponderanceof positive auto-correlationscoefficientsand thereforeappearto give a more accuratedescriptionof the prices. It is possible to estimate and interpret the price-trend parameters, to obtain optimal linear forecasts and to assessnaive investment rules. Thus, conveniently, the models are mathematically tractable. It is necessary, of course, to distinguish betweena model of the prices' stochasticprocessand their 'true' stochasticprocess.It would be oversimplistic to say that a pricetrend model generatesobservedprices. Nevertheless,it is asserted that the price-trendmodels describecertain statistical featuresof observedprices which the random walk models cannot explain. Also, it is consideredthat the price-trend models are consistent

244

ConjecturedModels

with the marketforces of supply and demand. Although there is very little auto-correlationin the markets, typically less than 0.04 at all non-zero lags, the economic efficiency or otherwise of the markets studied remains an open question. 8. Further Research

The conclusionsare, at present, only applicable to the London commodity markets and one internationalcurrency market. It is possible that they apply to several other financial markets. Researchersare therefore encouragedto test further price series for price-trend behaviour. It would be particularly interesting to test stock price series.The authorrecommendsthat long seriesare studied, consisting of at least 1,000 and preferably more than 2,000 prices,to give a high test power when a price-trendmodel is valid (cf. Figure 10.1). Daily returns must be checkedfor fluctuating variance and, if necessary,appropriate action should be taken, as illustrated in Section4.3. The test statisticU*, defined in Section 4.2, is recommendedfor a test of the random walk hypothesisagainstthe price-trendhypothesis. There is probably considerablescope for improvementin the method of parameterestimation. It is hoped that the established theory of estimation for ARMA processescan be utilized. For practical applications,it would be useful to assessthe implications of basing forecasts and investment decisions upon incorrect estimatesof the trend parameters. Researchcontinuesinto the efficiency of the futures markets. Trading rules are being constructed,using the prices before 1977, and will be assessedby their performanceon the prices from January1977 to a later date, probablyDecember1979. The conclusionshave important consequences for commodity stabilizationpolicies and it is hopedthat the time-seriesresultswill be usedto makestabilizationresearchmore realistic. Finally, the modelswould be enhancedif the trend terms !It and their stochasticprocesseswere to be linked with an econometric descriptionof price determination.

ConjecturedModels 245 References Anderson,T.W. and A.M. Walker (1964) 'On the Asymptotic Distribution of the Autocorrelationsof a Samplefrom a Linear StochasticProcess',Annalsof MathematicalStatistics,35, 1296-303. Cargill, T.F. and G.e. Rausser(1975) 'TemporalPrice Behaviourin Commodity FuturesMarkets', Journal of Finance, 30, 1043-53. Clark, P.K. (1973) 'A SubordinatedStochasticProcessModel with Finite Variance for SpeculativePrices', Econometrica,41, 135-55. Cornell, W.B. and J.K. Dietrich (1978) 'The Efficiency of the Market for Forward ExchangeUnder Floating ExchangeRates',Reviewof Economicsand Statistics,60, 111-20. Cunningham,S.W. (1973) 'The Predictabilityof British Stock Market Prices', AppliedStatistics,22, 315-31. Dimson, E. and R.A. Brealey (1978) 'The Risk Premiumon UK Equities', InvestmentAnalyst, 52, 14-18. Dryden, M.M. (1970) 'A StatisticalStudy of UK SharePrices',ScottishJournal of Political Economy,17,369-89. Dusak, K. (1973) 'FuturesTrading and Investor Returns:An Investigationof Commodity Market Risk Premiums',Journal of Political Economy,81, 1387-406. Fama,E.F. (1965) 'The Behaviourof Stock Market Prices',Journal of Business, 38,34-105. (1970) 'Efficient Capital Markets: A Review of Theory and Empirical Work', Journal of Finance, 25, 383-417. (1976) Foundationsof Finance, Oxford: Basil Blackwell. Fielitz, B.D. (1971) 'Stationarityof RandomData: SomeImplicationsfor the Distribution of Stock Price Changes',Journal of Financial and Quantitative Analysis,6, 1025-34. Granger,e.W.J.and O. Morgenstern(1971) Predictability of StockMarket Prices, Massachusetts:Heath Lexington. Granger,e.WJ. and P. Newbold (1977) ForecastingEconomicTime Series,New York: AcademicPress. Hagerman,R.L. (1978) 'More Evidenceon the Distribution of Security Returns', Journal of Finance, 33, 1213-21. Jennergren,L.P. and P.E. Korsvold (1974) 'Price Formationin the Norwegianand SwedishStock Markets - SomeRandomWalk Tests', SwedishJournal of Economics,76,171-85. Jensen,M.C. (1978) 'SomeAnomalousEvidenceRegardingMarket Efficiency, an Editorial Introduction', Journal of Financial Economics,6, 95-101. Kingsman,B.G. (1974) 'Forecastingand Researchfor Supply Markets-Commodity Buying Systems',Long RangePlanning, 7, 24-38. Labys, W.e. and e.W.J. Granger(1970) Speculation,Hedging and Commodity Price Forecasts,Massachusetts:Heath Lexington. Leuthold, R.M. (1972) 'RandomWalks and Price Trends: The Live Cattle Futures Markets', Journal of Finance, 27, 879-89. Praetz,P.D. (1969) 'Australian SharePricesand the RandomWalk Hypothesis', Australian Journal of Statistics,11, 123-39. (1975) 'Testingthe Efficient MarketsTheory on the SydneyWool Futures Exchange',Australian EconomicsPapers, 14, 240-9. (1976) 'On the Methodologyof Testingfor Independencein FuturesPrices', Journal of Finance, 31, 977-9. (1979a)'Testingfor a Flat Spectrumon Efficient Market Price Data', Journal of Finance, 34, 645-58.

246 -

ConjecturedModels

(1979b) 'A GeneralTest of a Filter Effect', Journal of Financial and QuantitativeAnalysis,14, 385-94. Rutledge,D.J.S. (1976) 'A Note on the Variability of FuturesPrices',Reviewof Economicsand Statistics,58, 118-20. Taylor, S.J. (1978) 'Time SeriesPropertiesand Models of CommodityPrices',PhD Thesis,LancasterUniversity. - (1982) 'Testsof the RandomWalk HypothesisAgainsta Price-Trend Hypothesis',Journalof Financial andQuantitativeAnalysis,17, 37-61. Taylor, S.J. and B.G. Kingsman(1978) 'Non-stationarityin SugarPrices',Journal of the OperationalResearchSociety,29, 971-80. (1979) 'An Analysis of the Varianceand Distribution of Commodity Price-changes',Australian Journal of Management,4, 135-49. Westerfield,R. (1977) 'The Distribution of CommonStock Price Changes:An Application of TransactionTimes and SubordinatedStochasticModels', Journal of Financial and QuantitativeAnalysis, 12,743-66.

INDEX

ask-bidspread28-9 asymmetricinformation(see inside information) AustralianWool Corporation96, 103, 114 autocorrelation106, 163-5 autocorreIationcoefficients:defined 222; graphs226-7 availablesupply 101, 117 n.4

previolls literature45-6; results55-72; theoreticalequilibria 49-54 feasibility 1-2, 8 n. I; conditions13-16,37 FIML estimates107, 108-115passim financial futures 4 forecasterrors 168-71 forecasting:empirical results240; theory 234 forward contracts26-7, 100 forward premium 98,100,107,114-15, 159 forward price 100 forward pricing 161-2 functionsof futures markets159-60 futurescontracts26-7 futuresmarkets:benefitsfrom 86; 'fundamentalproperties'84-5; price volatility 84-5; public-goodscharacter 86 futuresprices: continuousseries103, 117 n.6, 179, 185; exchangerate-adjusted 184; paired 178-9, 182, 185 futurestrading, evolution of 25

basis,changesin 79-81 benefits,from futurestrading 17-18 betacoefficient 126, 128; stock index 126, 127,129,130,131,133,134,135 n.3; commodityfutures 126, 127, 128,129, 130, 131, 133, 134,135 n.3 broilers, iced 148, 150, 151, 153 Brownian motion 193, 195 Bureauof Agricultural Economics99 cattle, live 148, 153, 161 causability143-5 clearinghouse104, 157 cocoa225 coefficient of variation 124-5 coffee 161, 225 commodityfuturescontracts121 concentrationof futurestrading 34-5 consumptionequation(for wool) 99, 107, 115 contractspecification30-1 contractualinnovation 15, 18-19 convenienceyield 79 copper163-7, 168-71 passim cord 148, 152 corn 161 cost-benefitratio 19

Gaussianmarket 203-5 gold 148, 150, 153, 175-88passim hedging46. 47, 49, 55,60-8,72,73,77-8 passim;anticipatory89 n. 7; carrying-charge79-82; executioncosts of 83-4; insurance-type77-84 passim; long 94, 100, 107, 114-15; operational 89 n.7; portfolio theory 87-8; selective 81; short 94, 98,107,113,114-15 hypothesistesting 217-18

daily closingprices223 dataerrors 199,202,203 Deutschemark149, 153 distribution of returns3-4

impersonalmarkets20-1 independence of price changes194 information6-7 inside information 5, 44, 45,49, 54, 65-8, 71,73 institutional innovation 17 instrumentalvariableestimation163-5 investmenthorizons 120, 122, 125, 127, 129, 130, 133, 135 n.3

efficiency 45, 46, 50-5 passim;semi-strong form 6-8,168-71;weak form 7,177-85 empirical frequencydistribution 191 empirical research209 eventuncertainty45-6, 49, 50, 54, 63-8, 71, 73 expectations95, 96, 97,100-1;adaptive 96-7,107,114;rational 5, 45, 50, 52, 53,54 experimentalmarkets5, 43-73 passim; design46-50; methodology43-4;

Japaneseyen 149, 153 joint testsof hypotheses164-5, 170-1 kurtosis 120, 123, 125, 177,179-83, 198, 199,200,202,203

247

248

Index

lead 163-7, 168-71 passim level of inventories194 limit price movements146 London futuresmarkets224 London Metal Exchange157 long hedging(seehedging) maize 225 margins34 marketmodel 119, 126, 133 net benefits(from futurestrading) 1 non-ferrousmetals162-9 non-stationarity192, 193 non-trading198, 203 normal backwardation,theory of 83 normal distribution 191-3, 195-202,204, 206 oats 148, 152 ordinary leastsquaresestimates164, 165, 170,171 personalmarkets20-1 plywood 148, 153 portfolio theory 3 positiveautocorrelation224 potatoes161-2 prediction,intra-sample109-13 presentvalue 18 price eiasticities, estimated 109

price relatives199 price variability 137, 139, 140-3, 145-52 probability distribution 121 propertyrights in futures markets2, 26-7, 35,37

randomwalk 7 random-walkhypothesis180,181,185; defined 210; rejected228 ratesof return 119, 123, 125, 127,131, 133 rational expectations(seeexpectations) regulationof futurestrading 22, 36 reliability risks 21, 27, 34 returns3 risk premium 5,119,130,132,134 risk-reduction159 risk-return measures120, 130 runs test 177, 180-3 self-regulation22 seller'soption 6 semi-strongform efficiency (seeefficiency)

serialcorrelationcoefficient 179-83 shares4 short hedging(seehedging) silver 148, 153 simultaneousmodel 95-107 skewness120, 123, 125, 179-83, 198-200, 202-3 soybeans148, 152, 161 soybeanmeal 148, 153 soybeanoil 148, 153 spectralanalysis181, 184-5, 188 spectraldensityfunction 229 speculation:destabilizing140-1; effectsof 139-41;long 97,107,114;short lOO-I, 107, 115; stabilizing 139-40, 152 speculators,professional3 speedof adjustment(of prices) 176-7 stableParetiandistribution 192-7, 199-200, 202-6 standardand poor index 121, 126 stationarity177, 179-93 statistics209 stock-marketreturns 191, 192, 194,205, 206 storage:hedged94, 98, 107; unhedged 95-7,104,107,112,114 studentt distribution 192, 193, 196, 197, 199,200,204,206 studentizedrange198, 200, 202 sugar224 Sydney FuturesExchange191, 206 systematicrisk 4,119,127,128 time-seriesanalysis209 tin 163-7, 168-71 passim transactionscosts2, 16-20, 28 trend models212 unbiasedprediction hypothesis6, 162-7 uncertainty (seeeventuncertainty) unsystematicrisk 119, 128 variancechanges215 varianceof price changes193, 194, 195 varianceof returns 124, 125 volume of trading 145, 146-7, 148-51 wheat 148, 149, 152 wool 94,96,99,103-5, 106-16 passim wool futurescontract 191 zinc 163-7, 168-71 passim