Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model 1137561386, 9781137561381

Citation preview

Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets

DOI: 10.1057/9781137561398.0001

Other Palgrave Pivot titles Timothy Wood: Detainee Abuse During Op TELIC: ‘A Few Rotten Apples’? Lars Klüver, Rasmus Øjvind Nielsen and Marie Louise Jørgensen (editors): Policy-Oriented Technology Assessment Across Europe: Expanding Capacities Rebecca E. Lyons and Samantha J. Rayner (editors): he Academic Book of the Future Ben Clements: Surveying Christian Beliefs and Religious Debates in Post-War Britain Robert A. Stebbins: Leisure and the Motive to Volunteer: heories of Serious, Casual, and Project-Based Leisure Dietrich Orlow: Socialist Reformers and the Collapse of the German Democratic Republic Gwendolyn Audrey Foster: Disruptive Feminisms: Raced, Gendered, and Classed Bodies in Film Catherine A. Lugg: US Public Schools and the Politics of Queer Erasure Olli Pyyhtinen: More-than-Human Sociology: A New Sociological Imagination Jane Hemsley-Brown and Izhar Oplatka: Higher Education Consumer Choice Arthur Asa Berger: Gizmos or: he Electronic Imperative: How Digital Devices have Transformed American Character and Culture Antoine Vauchez: Democratizing Europe Cassie Smith-Christmas: Family Language Policy: Maintaining an Endangered Language in the Home Liam Magee: Interwoven Cities Alan Bainbridge: On Becoming an Education Professional: A Psychosocial Exploration of Developing an Education Professional Practice Bruce Moghtader: Foucault and Educational Ethics Carol Rittner and John K. Roth: Teaching about Rape in War and Genocide Robert H. Blank: Cognitive Enhancement: Social and Public Policy Issues Cathy Hannabach: Blood Cultures: Medicine, Media, and Militarisms Adam Bennett, G. Russell Kincaid, Peter Sanfey, and Max Watson: Economic and Policy Foundations for Growth in South East Europe: Remaking the Balkan Economy

DOI: 10.1057/9781137561398.0001

Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model Viola Fabbrini Researcher, Bocconi University, Italy

Massimo Guidolin Professor of Finance, Bocconi University, Italy

and

Manuela Pedio Researcher, Bocconi University, Italy

DOI: 10.1057/9781137561398.0001

© Viola Fabbrini, Massimo Guidolin, and Manuela Pedio 2016

Softcover reprint of the hardcover 1st edition 2016 978-1-137-56138-1 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No portion of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, Safron House, 6–10 Kirby Street, London EC1N 8TS. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages. he authors have asserted their rights to be identiied as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2016 by PALGRAVE MACMILLAN Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS. Palgrave Macmillan in the US is a division of St Martin’s Press LLC, 175 Fith Avenue, New York, NY 10010. Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world. Palgrave® and Macmillan® are registered trademarks in the United States, the United Kingdom, Europe and other countries. ISBN: 978-1-137-56139-8 PDF ISBN: 978-1-349-85102-7 A catalogue record for this book is available from the British Library. A catalog record for this book is available from the Library of Congress. www.palgrave.com/pivot DOI: 10.1057/9781137561398

Contents List of Figures

vi

List of Tables

vii

Preface

viii

1 he Background: Channels of Contagion in the US Financial Crisis

1

2 Methodology

13

3 he Data

28

4 Estimates of Single-State VAR Models

38

5 Results from Markov Switching Models

50

6 Estimating and Disentangling the Contagion Channels

68

7 Comparing the US and European Contagion Experiences

94

8 Conclusions

119

References

124

Index

130

DOI: 10.1057/9781137561398.0001

v

List of Figures 5.1 5.2 6.1 6.2 6.3 6.4 7.1 7.2 7.3

7.4

vi

Smoothed probabilities estimated from an MSIH(3,0) model for yields Filtered probabilities estimated from an MSIH(3,0) model for yields MSVAR-yield impulse response functions to a shock to the ABS AA–BBB series VAR-yield impulse response functions to a shock to the ABS AA–BBB series MSVAR-spread impulse response functions to a shock to the ABS AA–BBB series VAR-spread impulse response functions to a shock to the ABS AA–BBB series Smoothed probabilities estimated from an MSIH(3,0) model for European yields MSVAR-yield impulse response functions to a shock to peripheral (PIIGS) sovereign yields Smoothed probabilities estimated from an MSIH(2,0) model for European yields augmented with US ABS yield series MSVAR-yield impulse response functions to a shock to US low-credit quality ABS yields

65 66 73 75 81 88 100 106

113 114

DOI: 10.1057/9781137561398.0002

List of Tables 3.1 Summary statistics for bond and stock yields 3.2 Summary statistics for bond and stock yield spreads 4.1 Model selection results for single-state VAR(p) models 4.2 Estimates of a single-state VAR(2) for yields 4.3 Estimates of a single-state VAR(2) for yield spreads 5.1 Model selection results for Markov switching models 5.2 Estimates of an MSIH(3,1) model for yields 5.3 Estimates of an MSIH(3,1) model for yield spreads 7.1 Summary statistics for European bond and stock yields 7.2 Model selection results for Markov switching models of European yields 7.3 Estimates of an MSIH(3,1) model for European yields 7.4 Estimates of an MSIH(2,1) model for European yields augmented with US ABS yield series

DOI: 10.1057/9781137561398.0003

33 35 41 43 47 52 57 60 97 99 103

111

vii

Preface When a negative price shock – a change in market valuation that is not justiied by the current or expected dynamics of fundamentals (such as dividends, earnings, or the low of mortgage installment payments) – hits one asset market, what is the mechanism through which such a deviation from the expected path is transmitted to other asset markets, if any? Does the strength of the shock, the fact that it cannot be explained either by fundamentals or, more generally, by the state of the economy, impact whether and how the shock propagates from one market to others? hese appear to be key questions in the light of how the recent 2007–09 inancial crisis has unfolded in the US. Before the recent subprime crisis, most contagion studies had focused on episodes of cross-country contagion, while scarce attention had been devoted to cross-asset, cross-market contagion episodes within a country. However, the negative shock that hit the assetbacked security (henceforth, ABS) market in 2007 and then triggered negative efects that rapidly spread to other markets, both in the US and worldwide, has created an ideal background to study the mechanisms that drive cross-asset contagion. Indeed, at irst, only subprime and speculative grade asset-backed security markets were afected. Gradually, the negative shock spread, to all ixed income markets irst and eventually to the equity market (between late 2008 and early 2009; see Dwyer and Tkac, 2009; and Guidolin and Tam, 2013, for a discussion and exact dating of this sequence of events). Interestingly, this contagion occurred in spite of a range of conventional and viii

DOI: 10.1057/9781137561398.0004

Preface

ix

unconventional policy measures adopted by the Federal Reserve (see, for example, Cecchetti, 2009), and therefore proved to be a resilient feature of modern inancial markets. Similar questions have also been posed by both academics and inancial commentators with reference to the way the negative events marking the 2010–11 European sovereign debt crisis have unfolded and spread well beyond its original epicenters, in this case, Ireland and Greece (see Beirne and Fratzscher, 2013; Lauricella, Fidler, and Gonglof, 2010). Also, in the European scenario, the European Central Bank has been extremely active in managing the crisis (see, for example, Papademos, 2009), yet this has not prevented a rather visible spillover efect that has involved credit and debt markets of many countries well beyond Portugal, Ireland, Italy, Greece, and Spain (for instance, at times French government bond prices were afected as well; see Milne, 2011), and of credit, bond, and equity markets more generally. An in-depth understanding of the transmission mechanisms of shocks across asset markets appears to be critical to appreciate how the events unfolded, which is of paramount importance, especially for policymakers, who need to decide which policy measures may be efective in such episodes and to inform important decisions by money and risk managers in the inance industry. herefore, in this book we proceed to specify and estimate, according to state-of-the-art econometric methods, a range of models that capture how shocks from particular markets that played a role in the onset of the US and European inancial crises (of asset-backed and sovereign nature, respectively) dynamically propagate to alter conditions in other, related markets. Importantly, in doing this, we adopt methodologies that recognize the existence of diferent regimes (to be interpreted in an economic as well as in a statistical sense) in which the inancial system may lie. In this book, we propose a quantitative study based on both simple linear (single-state vector autoregressions) and non-linear (Markov switching vector autoregressions) models. Both types of framework are able to capture the efects of co-movements among time-series, and are therefore useful tools to investigate contagion dynamics. In particular, in both linear and non-linear models, contagion occurs because of a simultaneous efect due to non-zero correlations among the innovation terms and a linear efect due to non-zero coeicients of the autoregressive lags of each variable included in the model (the vector autoregression coeficients). Moreover, Markov switching models are able to capture a third, DOI: 10.1057/9781137561398.0004

x

Preface

non-linear contagion channel, which arises because the regime switches in the model occur contemporaneously for all the series included in the system. his form of contagion is independent from all the other patterns and arises because (as a minimum) the intercept terms of all the variables move in the same direction when there is a shit in regimes.

DOI: 10.1057/9781137561398.0004

1

he Background: Channels of Contagion in the US Financial Crisis Abstract: In this introductory chapter, we provide the background material that will help a reader to understand the indings presented in the rest of the book. First, we provide a review of the key facts that characterized the onset and the unfolding of the 2007–09 US inancial crisis. In addition, we explore diferent deinitions of inancial contagion and discuss the key papers published on the topic because they provide benchmarks to our empirical analysis. Keywords: contagion; cross-asset contagion; inancial crisis; sub-prime mortgages Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model. Basingstoke: Palgrave Macmillan, 2016. doi: 10.1057/9781137561398.0005.

DOI: 10.1057/9781137561398.0005





Transmission Channels of Financial Shocks

he core of this book is devoted to the discussion of the contagion channels that contributed to the propagation of a shock in the speculative grade asset-backed securities (henceforth, ABS) market to the other asset markets during the recent US inancial crisis. Consequently, in this chapter, we provide the necessary background to follow the rest of the analysis. In particular, in the irst paragraph, we propose a short synopsis of the main events that have marked the 2007–09 crisis. Our objective is not to exhaustively list all the signiicant developments or to discuss causes of and solutions to the inancial crisis. A number of excellent analyses of these issues have been circulating or are already published; see, for example, Wheelock (2010). On the contrary, we devote special attention to emphasizing the steps through which shocks may have propagated from one market to others during this speciic historical event. Indeed, in the second section, we provide a review of the main deinitions of inancial contagion and a distinction of the different contagion channels that have been explored in the literature. Not only is distinguishing among such channels intellectually rewarding, but also their relative importance and empirical incidence during a speciic period of crisis may be highly informative to policy-makers (who manage and ight the efects of the shock) and investors alike.

1.1 A brief review of the sequence of events during the US inancial crisis he inancial crisis began with a sharp downturn in US residential real estate markets as a growing number of banks and hedge funds reported substantial losses on subprime mortgages and mortgage-backed securities (MBS), the biggest and best-known segment of the ABS market. he crisis had been slowly building up since the early months of 2007. For instance, in late February 2007, the Federal Home Loan Mortgage Corporation (commonly known as Freddie Mac) had announced that it would no longer buy the most risky subprime mortgages and MBS. his meant that a large portion of the process of origination and securitization of subprime MBS would have to be moved over to the private-sector segments of the US residential mortgage market. In April 2007, New Century Financial Corporation, a leading subprime mortgage lender, had iled for Chapter 11 bankruptcy protection. In June 2007, Standard and Poor’s and Moody’s Investor Services had downgraded over 100 DOI: 10.1057/9781137561398.0005

he Background



bonds backed by second-lien subprime mortgages. However, the irst major step towards a spiraling crisis was marked by Fitch Ratings’ decision in August 2007 to downgrade one of the major irms specializing in mortgage intermediation in the subprime segment, Countrywide Financial Corporation. As a result, Countrywide was forced to borrow the entire $11.5 billion available in its credit lines with other banks, which was irst-hand evidence that the crisis was destined to spread from the mortgage market to the inancial intermediaries backing its operators. In terms of pricing and trading volumes, the crisis irst appeared to be spreading beyond the boundaries of the US mortgage market when it spilled over to the interbank lending market in early August 2007. he London Interbank Ofered Rate (LIBOR) and other funding rates spiked ater the French bank BNP Paribas announced that it was halting redemptions for three of its investment funds. By wide consensus among researchers and policy commentators (see, for example, Wheelock, 2010), these two negative developments mark an arbitrary and yet useful onset date for the crisis. Initially, the Federal Reserve’s (henceforth, Fed) reaction was limited to calming markets by reminding banks of the availability of the discount window. his was done by extending the maximum term of discount window loans to 30 days and lowering the Fed fund rate target, initially (between August and September 2007) by 50 basis points.1 Financial strains eased in September and October 2007, but reappeared in November, because many banks found themselves unable to fulill their dollar funding needs. In December 2007, the Fed announced the establishment of reciprocal swap currency agreements with the European Central Bank (ECB) and the Swiss National Bank to provide a source of dollar funding to European inancial markets, and announced the creation of the Term Auction Facility (TAF) to lend funds directly to banks for a ixed term.2 Despite the relatively small size of the ABS market in the US, the shock rapidly triggered negative and widespread consequences in all credit and, eventually, bond markets (see, for example, Gorton, 2010). he irst reason triggering such a chain reaction was the immediate negative response of lenders in the repo market, an episode that has become known as a repo run in the literature (see Gorton and Metrick, 2012).3 Before the crisis, the repo market represented a fundamental source of funding to inancial institutions, and a large part of the collateral requirements were met through securitized ABS products. Ater the DOI: 10.1057/9781137561398.0005



Transmission Channels of Financial Shocks

shock in the ABS market, lenders became uncertain about their ability to quickly liquidate assets other than Treasuries in the event of default of the counterparty of the repo transaction (see, for example, Adrian, Begalle, Copeland, and Martin, 2013). herefore, lenders restricted their inancing to short-term transactions against Treasury bonds, while severe haircuts were applied on other assets, because of their modest liquidity (see, for example, Hördahl and King, 2008).4 Following the changes in the conditions set by lenders on repo transactions, investors’ demand for Treasury bonds rapidly increased, bringing the yield on this asset class as well as the Treasury repo rate to levels close to zero.5 Ater that and throughout the crisis, the repo activity was, in fact, mainly driven by the need to borrow Treasuries that were scarce in the market, rather than to obtain inancing. Moreover, the liquidity shock in the repo market forced inancial institutions to ire sale their asset holdings in order to raise money, so that the shock to the ABS market rapidly spread to the corporate bond and stock markets.6 To address this type of market freeze, in March 2008, the Federal Reserve established the Term Securities Lending Facility (TSLF) to provide secured loans of Treasury securities to primary dealers for 28-day terms, and the Primary Dealer Credit Facility (PDCF) to provide secured overnight loans to primary dealers under Section 13(3) of the Federal Reserve Act, which permits the Federal Reserve to lend to any individual, partnership, or corporation “in unusual and exigent circumstances”. he crisis intensiied during the inal months of 2008. Lehman Brothers, a major investment bank, iled for bankruptcy on September 15. Lehman’s bankruptcy produced an immediate fallout. On September 16, the Reserve Primary Money Fund announced that the net asset value of its shares had fallen below $1 because of losses incurred on the fund’s holdings of Lehman commercial paper and medium-term notes. he announcement triggered widespread withdrawals from other money funds, which prompted the US Treasury Department to announce a temporary program to guarantee investments in participating money market mutual funds, the Asset-Backed Commercial Paper Money Market Mutual Fund Liquidity Facility (AMLF), set up to extend non-recourse loans to US depository institutions and bank holding companies.7 In spite of the strength of these massive policy interventions, inancial markets appeared to be mired in a state of persistent turmoil, worsened by the almost complete freezing of the commercial paper and ABS markets, where the activity of issuance and origination had completely stopped in DOI: 10.1057/9781137561398.0005

he Background



the atermath of the severe losses imposed by Lehman’s default. In particular, while the policy interventions led to some beneicial efects on the short-end of the ixed income markets, the situation remained diicult in most other segments, especially as far as ABS and associated derivative products (for example, collateralized debt obligations written on portfolios of MBS) were concerned. he result was that immense portfolios at several multinational inancial institutions remained extremely illiquid and potentially exposed to tremendous losses upon what are oten called ire sales. In November 2008, the Fed announced the creation of the Term Asset-Backed Securities Lending Facility (TALF). Under this facility, the Federal Reserve Bank of New York provided loans on a non-recourse basis to holders of AAA-rated asset backed securities and recently originated consumer and small business loans. At the same time, the Federal Open Markets Committee (FOMC) announced its intention to purchase large amounts of US Treasury securities and mortgage-backed securities issued by Fannie Mae, Freddie Mac, and Ginnie Mae (the FOMC was to increase the amount of its purchases in 2009). hese interventions helped to propagate the strains to the long-term Treasury market, where prices were lowered by the combined thrust of negative expectations on the economic outlook and the efects of the Fed’s purchases. In early 2009, fears spread that the enormous market for securitized commercial mortgages was on the brink of collapse, similarly to the subprime residential mortgage market in the spring of 2007. Stock markets were severely afected, with heavy losses that – purely for accounting reasons, as irms are slow to adjust dividend pay-outs, which were still to drop, as the US economy had just timidly entered a recession – implied that dividend yields had shot up. he policy-makers explicitly admitted that inancial markets remained strained, and they decided that the extraordinary measures enacted between December 2007 and December 2008 should be extended for as long as necessary. he turnaround and the exit from the crisis seem to have occurred – we claim now in hindsight – between the late spring and the fall of 2009. In fact, while in June 2009 the Fed had still announced a number of extensions and modiications to a number of its liquidity programs, a novel desire to ine-tune the programs had replaced the drive towards expanding them that had dominated policymaking until April 2009. With the situation rapidly improving, and the short-term debt (especially interbank) markets going through an unfreezing cycle opposite to the severe, paralyzing disruptions experienced in September–November 2008, in DOI: 10.1057/9781137561398.0005



Transmission Channels of Financial Shocks

November 2009 the Fed approved a irst reduction in the maximum maturity of the credit it ofered through the discount window. Although the discount window never played a major role in the credit-easing policies of the Fed, this represented the irst oicial acknowledgement that the inancial system was healing and the crisis possibly ending. his was made clear not only by the Fed but by all central banks around the world when – between late 2009 and early 2010 – they ended some or most of the public support measures introduced in response to the inancial crisis. For instance, the Fed completed its purchase of Treasury securities in October 2009.8 In the same month, the ECB conducted a last 12-month euro repo to inance banks, and the Bank of Japan stopped its purchases of commercial paper and corporate bonds; inally, the Swiss National Bank ceased providing Swiss francs through foreign exchange swaps against euros in January 2010. On the demand side, the take-up of many measures drastically declined around the turn of the year. his seems to relect better market access and hence reduced demand for government support. In fact, Guidolin and Tam (2013) use data on US bond yields and spreads to date the end of the US inancial crisis to between June and December 2009. However, what we have ofered represents a simple narrative account of the US inancial crisis, and its power to spread from the ABS market to all other inancial markets was simply presumed. Moreover, speciically how these spillover efects took place remains interesting. he next section analyzes the deinition of contagion and reviews the relevant literature, while Chapters 4 through 6 use modern statistical techniques to tackle exactly the questions we have raised above.

1.2 Modeling alternative cross-market contagion channels Before analyzing the diferent contagion channels, it is useful to review the deinition of the phenomenon. he literature provides a number of alternative and yet complementary deinitions of inancial contagion. Kyle and Xiong (2001) describe contagion as an episode of declining asset prices, tightening of liquidity conditions, and increased volatility and correlations, which rapidly propagates from one market to another. Hence, besides the dynamics of irst- and second-order moments, which has also been discussed elsewhere in the literature (see below), the lack DOI: 10.1057/9781137561398.0005

he Background



of liquidity and its propagation across markets would matter. Dornbusch, Park, and Claessens (2000), Kaminsky, Reinhart, and Végh (2004), and Longstaf (2010) deine contagion as an episode of signiicant increase in cross-market linkages, following a shock to one market. In this perspective, the strength of cross-market connections is the deining feature of contagion. In Pritsker (2001), the most salient trait of contagion is that the negative efects generated by a shock to one market on the value of assets traded in other markets cannot be explained by changes in the fundamentals characterizing these other markets. hese deinitions of the general concept of contagion have been subjected to a number of detailed applications that have further revealed the general nature of the phenomenon. For instance, a large number of existing studies have focused on cross-country contagion to identify episodes of international crisis spillovers, which arise when a shock to one national market triggers signiicant and immediate inancial efects in other countries (see, for example, Kaminsky, Reinhart, and Végh, 2004; Allen and Gale, 2004; Kodres and Pritsker, 2002; King and Wadhwani, 1990). However, in light of the recent subprime crisis, recently researchers have also paid increasing attention to the empirical analysis of cases of cross-asset contagion, that is, within-country, cross-market contagion episodes (see, for example, Longstaf, 2010; Guo, Chen, and Huang, 2011). For instance, scores of recent articles have aimed to identify the contagion channels that are typically active during national, closedeconomy inancial crises (see, for example, Kodres and Pritsker, 2000; Brunnermeier and Pedersen, 2009; Vayanos, 2004; Caballero and Kurlat, 2008; Longstaf, 2010). Recently, researchers have achieved progress by isolating and trying to measure the strength of four distinct propagation channels: the correlated information, light-to-liquidity, light-to-quality, and risk premium channels. Under the correlated information channel, a shock to one market provides information that market forces compound into the equilibrium prices of a range of other markets that are not directly afected by the shock. In this case, contagion occurs rapidly via the pricing mechanism, which represents the engine of market activity: investors immediately adjust their views on the fair value of these “other” inancial assets based on the new information. he correlated information channel has oten been used to explain episodes of simultaneous drops in stock market prices in diferent countries. he idea behind this contagion mechanism is that price changes in one market are perceived as relevant by investors DOI: 10.1057/9781137561398.0005



Transmission Channels of Financial Shocks

for the valuation of inancial assets in other markets. Because investors immediately adjust their beliefs, prices in other markets change as well. Among many others, King and Wadhwani (1990) present a celebrated model in which contagion in equity markets arises as investors attempt to infer information from price changes in other markets. he starting point of their analysis is the simultaneous fall in worldwide stock markets recorded during the October 1987 crash, which occurred in spite of the widely diferent economic conditions prevailing in the geographic areas afected. In King and Wadhwani’s model, investors have access to diferent information sets. Following a shock to one market, because of this underlying, structural information asymmetry, uninformed traders incorrectly update their valuation of all inancial assets. his, in turn, generates contagion efects. hey also show that the equilibrium linkages among stock markets are time-varying. In particular, they observe that correlations across markets are linked to volatility. When the latter increases following a shock, correlations increase as well, thus amplifying contagion efects. Kodres and Pritsker (2000), however, point out that the assumption underlying an information updating-based mechanism – that price movements in one market afect the asset values in others – may be reasonable only for closely linked markets, while it faces serious diiculties in explaining how shocks propagate across markets that are presumably populated by heterogeneous investors. For instance, equity markets are generally more accessible to small investors than sophisticated credit derivative markets are, and yet these two markets have recently appeared to be linked (see, for example, Chakrabarty and Zhang, 2012). A second contagion mechanism is known as the light-to-liquidity channel. In this case, following a shock to one market, agents’ preferences shit towards more liquid securities. Brunnermeier and Pedersen (2009) develop a model in which the negative spiral in market liquidity that follows a shock originates from variations in traders’ funding liquidity. In their model, the ease and speed with which traders can secure funding afects and is afected by asset market liquidity.9 In particular, trading in inancial markets requires capital, and traders can use securities as collateral to borrow funds. Yet, the amount obtained is subject to a haircut (or margin) applied to the value of the collateralized assets. he haircut is the diference between the asset value and the amount borrowed against pledging the asset as collateral, and it must be inanced with a trader’s own capital.10 In the model, Brunnermeier and Pedersen assume that margins are destabilizing, that is, changes in the margins afect the DOI: 10.1057/9781137561398.0005

he Background



availability of funds. When a shock to one market leads to an increase in the volatility of asset prices, the margins required by lenders will increase as well. his reduces the availability of funding to traders, and therefore forces them to trim their positions in capital-intensive securities (that is, requiring higher regulatory and/or prudential margins, such as risky junk bonds and complex derivatives). Because traders’ preferences shit towards liquid assets (accepted as collateral in favorable conditions), the liquidity of other assets noticeably worsens. his triggers a decrease in the overall market liquidity, and therefore funding liquidity considerations become the main driver of a fall in asset prices that follows one initial but isolated (volatility) shock to one single market. Vayanos (2004) has discussed why times of high uncertainty and, thus, high volatility in inancial markets are oten associated with a rational light-to-liquidity phenomenon. He considers fund managers who execute portfolio strategies taking into account the risk of withdrawals by the individuals investing in their funds. herefore, this type of risk afects optimal asset allocation and, during periods of increased uncertainty and volatility, managers are less willing to hold illiquid securities. herefore, the increase in volatility leads to an upward adjustment in the price premium investors recognize to liquid inancial instruments, that is, to a liquidity premium. he light-to-quality channel represents one additional contagion mechanism. Caballero and Kurlat (2008) use the term lightto-quality to identify episodes in which, following a shock to one market, investors attempt to sell assets perceived as risky and, instead, purchase safer assets. hese episodes lead to an increasing risk premium and signiicant disruptions in other asset markets. he literature that discusses light-to-quality episodes has mostly focused on the stock–bond return relation (see, for example, Gonzalo and Olmo, 2005; Baur and Lucey, 2010). Gonzalo and Olmo (2005) describe light-to-quality as an episode of widespread leeing from the stock market to the bond market that typically occurs during inancial crises. hey use indices that are representative of the short- and long-term corporate bond markets, as well as stock market price series, to investigate whether a substitution efect between bonds and equities occurs following a shock.11 hey ind that a light-to-quality from the stock market to the short-term corporate bond market arises during inancial crises. In contrast, this does not occur for the long-term corporate bond market. he fourth contagion mechanism identiied in the literature is the risk premium channel. According to this view, shocks to one market lead to a DOI: 10.1057/9781137561398.0005



Transmission Channels of Financial Shocks

generalized increase in the risk aversion of inancial market participants. his generates, in turn, an increase in the risk premium of all inancial assets. Of course, this mechanism requires either preferences or the quantities of undiversiiable risk to be strongly time-varying in order for this story to help organize the data. For instance, Longstaf (2010) explains the workings of this mechanism with the efects that negative returns in one market have on subsequent returns in other markets by way of time-varying risk premia. In the framework proposed by Vayanos (2004) and already discussed above, the increase in volatility that is caused by inancial shocks may also be a driver of contagion because of the increase of the risk premium in periods of inancial instability. In particular, from the perspective of fund managers, holding riskier portfolios increases the probability that the performance of their funds may fall below the threshold considered by investors for withdrawal decisions. When volatility is low, managers are less concerned with withdrawals, and the component of risk premium rewarding this risk is small. As volatility increases, the contribution of the risk of withdrawals to the risk premium of assets rapidly grows. Kyle and Xiong (2001) have proposed a theoretical framework in which the source of the increase in market risk aversion, and thus of contagion through the increase of asset risk premium, is a net worth efect through the balance sheet of inancial intermediaries. In their framework, inancial intermediaries are “convergence traders”, that is, traders who speculate that the transitory efect of noise trading on asset prices will induce only temporary deviations of prices from their fundamental values.12 When noise trading generates signiicant disruptions in the market, convergence traders sufer trading losses. herefore, convergence traders need to rebalance their portfolio and to liquidate their positions. he massive sales that convergence traders carry out in the market trigger an increase in volatility and thus generate contagion efects.

Notes 1 In addition to the Fed’s rescue operations and programs to stabilize speciic inancial markets described below, the Federal Open Markets Committee would then progressively cut its target for the federal funds rate in a series of moves that lowered the target rate from 5.25 per cent in August 2007 to a range of 0–0.25 per cent by December 2008.

DOI: 10.1057/9781137561398.0005

he Background



2 A strong policy response did not come from the Fed only. During the crisis, all central banks around the world, including the European Central Bank, substantially increased their liquidity provision through extended maturity repos, thus allowing banks to access existing lending facilities cheaply, and relaxed collateral requirements. 3 In a repo transaction, the sale of an asset at a certain price is combined with the agreement to repurchase it at a higher price at maturity, and repo rates paid by borrowers are given by the diference between these two prices. Repo rates are driven by the quality and the liquidity of the assets provided as collateral. 4 High degrees of safety and liquidity are the two key features that diferentiate Treasury bonds from any inancial asset, leaving aside circulating currency (cash) (see, for example, Krishnamurthy and Vissing-Jorgensen, 2012). he safety (sometimes referred to as “quality”) of Treasuries refers to their level of credit risk, which is the lowest in the US economy. Liquidity relates, instead, to the ease and speed with which Treasuries’ assets can be traded without afecting their price, which is traditionally very high. he high quality of Treasury bonds allows borrowers to obtain funding against this asset class at more favorable conditions (that is, at lower haircuts) than those applied to other types of securities, such as corporate bonds. In particular, “on the run” Treasuries (that is, the latest issued and thus the most liquid among the Treasury bonds) possess a premium collateral status and are assigned special repo rates (see, for example, Duie, 1996; Longstaf, 2004; Keane, 1996; Banerjee and Graveline, 2013). 5 here is a broad literature explaining that, because in periods of inancial turmoil investors face the risk of large portfolio losses, as a result they prefer to hold highly liquid securities that can be easily sold when necessary (see, for example, Goldreich, Bernd, and Nath, 2003, and Longstaf, 2004). he recent subprime crisis has revealed another motive that drives similar episodes of altered government bond yields: the fact that traders oten pledge Treasuries in the collateralized lending market (Hördahl and King, 2008; Hrung and Seligman, 2011). 6 Fire sales occur when the need to fund themselves forces inancial institutions to sell a large amount of assets at a price that is far below their intrinsic value. 7 To help alleviate inancial strains in the commercial paper market, the Fed established the Commercial Paper Funding Facility (CPFF) on October 7, 2008. his facility provided inancing for a special-purpose vehicle established to purchase three-month unsecured and asset-backed commercial paper directly from eligible issuers. On October 21, the Fed created the Money Market Investor Funding Facility (MMIFF). Under the MMIFF, the Fed ofered to provide loans to a series of special-purpose vehicles that purchased assets from money market mutual funds.

DOI: 10.1057/9781137561398.0005



Transmission Channels of Financial Shocks

8 In February 2010, a number of liquidity programs (CPFF, ABCP MFLF (Asset-Backed Commercial Paper Mutual Fund Liquidity Facility), TSLF) expired and were not replaced by the Fed. he Fed also announced an increase in the primary credit rate from 1/2 per cent to 3/4 per cent and that, efective on March 18, 2010, the maximum maturity for primary credit loans was shortened to overnight. 9 he occurrence of a negative spiral in market liquidity refers to the fact that, because demand for illiquid assets decreases ater a shock, the illiquidity of these assets worsens. his may originate additional rounds of feedbacks to market liquidity and, again, to the illiquidity of critical assets. 10 A haircut or margin is the diference between the price of a security that is pledged and the amount of money that can be borrowed against it, when used as a collateral. In practice, an α% haircut on a security means that an investor can only borrow (1 − α)% of the market value of the collateral. 11 he indices used are the Dow Jones Corporate 0–2 Years Bond Index (DJBI02) and the Dow Jones Corporate 30 Years Bond Index (DJBI30) for the corporate bond market, and the Dow 30 Industrial Stock Price Index for the stock market. 12 Noise traders are assumed to trade irrationally and not on the basis of fundamentals.

DOI: 10.1057/9781137561398.0005

2

Methodology Abstract: In this chapter, we survey the statistical methods that we subsequently apply in Chapters 5–8. We do not claim that our presentation of the econometric tools and framework is exhaustive; we deploy a more modest efort to provide a reader with the basics to follow the technical aspects of our empirical work. Keywords: Markov switching; vector autoregressions Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model. Basingstoke: Palgrave Macmillan, 2016. doi: 10.1057/9781137561398.0006.

DOI: 10.1057/9781137561398.0006





Transmission Channels of Financial Shocks

2.1 Vector autoregressive models he irst exercise we plan to perform consists of the estimation of singlestate, vector autoregressive (henceforth, VAR) models. hese models are lexible enough to capture complex linear patterns of cross- and own-serial correlations in which estimable coeicients are constant over time. First introduced by Sims (1980), the VAR methodology is applied in the literature to investigate complex multivariate relationships among series. In the following sections, we irst describe the properties and the estimation process for VAR models. Second, we explain how to compute impulse response functions (henceforth, IRFs), which are statistics commonly used in the literature to simulate the dynamic efects of an exogenous shock to one variable on other variables. We refer to Enders (1995) and Lütkepohl (2005) for a more detailed analysis of VAR models and of the IRFs that can be estimated from them.

2.1.1

Reduced vs. structural forms

In a VAR model, the variables included in the system are explained by the lagged values of the other variables as well their own-lagged values. A general VAR(p) model (in standard or reduced form) can be represented as yt  A0  A1 yt 1  z Ap yt p  ut ,

ut ∼ N 0, 3 u ,

(2.1)

where p indicates the number of lags included in the model, that is, the VAR order, yt = (y1,t, ... ,yN,t)9 is an N × 1 random vector of endogenous variables, A0 = (a1,0, ... ,aN,0)9 is an N × 1 vector of intercept terms, Ai for i = 1,..,p are the N × N vector autoregressive coeicient matrices, and ut = (u1,t, ... ,uN,t)9 is an N-dimensional white noise innovation process, such that E(ut) = 0, E(utu9t) = ∑u, and E(utu9s) = 0 for s ≠ t. For simplicity, in our description we shall consider a simple bivariate VAR system with one lag, that is, a model in which, besides its own past, the dynamics of {y1,t}is afected by current and past realizations of the {y2,t} series, and the time path of {y2,t} series is afected by current and past realizations of {y1,t}, besides its own past. In this case, we can re-write the system in reduced form in the following way: y1,t  a1,0  a1,1 y1,t 1  a1,2 y2 ,t 1  u1,t

(2.2)

y2 ,t  a2 ,0  a2 ,1 y1,t 1  a2 ,2 y2 ,t 1  u2,t .

(2.3)

DOI: 10.1057/9781137561398.0006

Methodology



he VAR represented in Equations (2.2)–(2.3) is diferent from a structural VAR (the primitive system underlying the reduced-form VAR). In fact, in its structural representation, a bivariate system with one lag is y1,t  b1,0 b1,2 y2,t  c 1,1 y1,t 1  c 1,2 y2,t 1  e1,t

(2.4)

y2 ,t  b2 ,0 b2 ,1 y1,t  c 2 ,1 y1,t 1  c 2 ,2 y2 ,t 1  e2 ,t .

(2.5)

Unfortunately, because y2,t is correlated with the error term e1,t and y1,t is correlated with the error term e2,t, this representation cannot be directly estimated by standard least squares, as it is well known that they require regressors to be uncorrelated with the error terms (Enders, 1995). Note, however, that one can re-write the system in Equations (2.4) and (2.5) as Byt  ' 0  '1 yt 1  et ,

(2.6)

so that by pre-multiplying both sides of the vector equation by B–1, we can obtain the VAR in standard form. Because in the reduced form the error terms and the regressors are uncorrelated, this has the advantage that it can be directly estimated by standard least square techniques. he two representations are identical only in the case of no contemporaneous correlations among the variables included in the system. Because this is rarely the case, generally the error terms we obtain in the VAR in reduced form will not be the same as the original, structural errors but a composite of them, and therefore they will be correlated (see Enders, 1995).1 In fact, the parameters of the structural system cannot be recovered from the VAR in standard form unless we impose some identiication restrictions on the coeicients, that is, unless we force the innovations of some of the variables in the system not to display contemporaneous efects on other variables. he impossibility of retrieving the structural VAR from the VAR in standard form is due to the fact that the number of parameters to be estimated in the former is higher than in the latter (see Enders, 1995). For example, in the bivariate system shown above, the primitive system requires the estimation of ten parameters, while the VAR in standard form has nine parameters. One possible way to solve the identiication problem is to apply a Cholesky decomposition, that is, a lower triangular decomposition, to the covariance matrix of the residuals of the variables in the VAR system.2 However, the Cholesky triangular identiication scheme introduces obvious asymmetries in the DOI: 10.1057/9781137561398.0006

Transmission Channels of Financial Shocks



model: not all variables are assumed to have contemporaneous efects on others. his aspect will be discussed in additional depth in Section 2.1.3, when we estimate impulse response functions.

2.1.2

Estimation

Taking into consideration the VAR(p) model in its reduced form, yt  A0  A1 yt 1  z Ap yt p  ut ,

ut ~ N 0, 3 u ,

(2.7)

because the error terms are assumed to be serially uncorrelated and with constant variance, we are able to estimate the coeicients of the system by applying multivariate least square (henceforth, LS) estimation. In practice, assuming that we have a sample of size T for each of the N variables, we can now deine: Y   y1 ,z, yT

N rT

(2.8)

N r  Np  1

(2.9)

Zt  1, yt , yt p 1 `



Np  1 r 1

(2.10)

Z   Z 0 ,z, Zt 1

Np  1 r T

(2.11)

U  u1 ,z, ut

N r T.

(2.12)



B  A0 , A1 ,z, Ap





In this case, the LS estimator of the coeicients is Bˆ 

ZZ `

1





‚ 3 u Z ‚ 3 u 1 y ,

(2.13)

where y = vec(Y). he multivariate estimation of B is identical to the result we would obtain through a separated estimation with ordinary least squares (henceforth, OLS). his was irst proven by Zellner (1962), who showed that multivariate LS and OLS estimations in a multiple equation model are identical if the regressors in all equations are the same. Moreover, the OLS estimator is consistent and asymptotically eicient.3

DOI: 10.1057/9781137561398.0006

Methodology

2.1.3



Impulse response functions

he ultimate objective of our analysis is to investigate the dynamics of inancial contagion in periods of inancial turmoil, that is, to study how and when a shock to one market is propagated to other markets. For this purpose, we compute IRFs and we use them to track over time the efects of a shock to a variable on the other variables in the system. Our IRF analysis is performed using the vector moving average (MA) representation of the VAR(p) process (henceforth, VMA(∞)) as shown in Equation (2.1): c

yt  *  £ j  0 A j ut j ,

(2.14)

where * is the unconditional mean of the process.45 However, for the purposes of an IRF analysis, the mean vector can be dropped. herefore, in what follows our description concerns a zero-mean VAR process. Because IRFs will be computed from a vector moving average (henceforth, VMA) representation of the reduced-form process, and only a stationary VAR process can be written as a VMA, an important condition to check when dealing with VAR models is their stationarity.6 Since a stable VAR is always stationary, to check stationarity we are only required to prove the stability of the model. In other words, the stability condition represents a suicient but not necessary condition for the stationarity of the process. For the speciic case of a VAR(1) model, the stability condition requires that all the eigen values of A1 have modulus less than one, or, equivalently, that det(IN – A1z) ≠ 0 for |z| ≤ 1. he condition is similar for a VAR(p) process with p > 1, because all VAR(p) models can be re-written as a VAR(1) (see Lütkepohl (2005) for a detailed analysis of stationarity conditions for general VAR(p) models). As previously discussed, structural and the corresponding reducedform VAR models turn out to be identical only in the case where the contemporaneous correlations among the variables are zero. Because this coniguration rarely occurs in empirical applications, the innovations of a VAR in standard form are in most cases quite diferent from the true innovations of the model; they are, instead, complex weighted averages of structural shocks with correlations diferent from zero. he Cholesky decomposition allows us to re-write a VAR process in such a way that the correlations among the residuals of the variables are zero (see Sims, 1980) and decompose the covariance matrix as ∑u = PP9. In DOI: 10.1057/9781137561398.0006



Transmission Channels of Financial Shocks

fact, by deining a diagonal matrix D that has the same main diagonal as P and by specifying W = PD–1 and ∑e = DD9, we can write the following decomposition of the structural error covariance matrix: 3 u  W 3eW `,

(2.15)

where ∑e is a diagonal matrix with positive diagonal elements and W is a lower triangular matrix. By pre-multiplying Equation (2.1) by B : = W–1 and deining 'i : = BAi, we obtain Ayt  '1 yt 1  z ' p yt p  et ,

(2.16)

where et : = But has a diagonal covariance matrix ∑e = B∑uB9, and the VAR(p) process is a zero-mean process. he ininite order MA representation stated in Equation (2.14) can thus be reformulated in the following way: c

y t  £ j  0 1 j wt j ,

(2.17)

where the elements wt = (w1t, ... , wjt)9 are uncorrelated and have unit variance, that is, ∑w = Ij. he 1j(i) coeicients correspond to the IRF caused by a shock to the orthogonal innovations wt. Because the variance of each such innovation is one, a unit shock to a variable is simply an innovation of size equal to one standard deviation. he VMA representation therefore allows us to trace out the time path of the various shocks to the variables in the VAR system. Because the innovations collected by the wt vector are orthogonal to each other, it is indeed sensible to assume that a shock occurs uniquely to one source of innovations at a time.7 In this respect, the Cholesky scheme seems to provide only advantages, as it allows us to trace out IRFs from non-structural shocks. However, because the Cholesky triangular factorization forces asymmetries into the model, the ordering of the variables becomes crucial to the estimation of the IRF.8 In particular, the importance of the latter depends on the level of the contemporaneous correlations among the innovations (Sims, 1981). A diferent approach consists in deining an appropriately rich set of structural identiication restrictions, that is, imposing contemporaneous correlations to be zero for some variables, on the basis of hypotheses about the true but unknown model underlying the DOI: 10.1057/9781137561398.0006

Methodology



data-generating process. However, because these restrictions should be driven by economic theory, while in this book we want to pursue an agnostic approach to estimating the patterns of dynamic contagion, we shall not pursue them, but rely instead on a more traditional Cholesky scheme. IRFs are computed using coeicients that are estimated and thus are subject to estimation error. herefore, to interpret correctly the values of the estimated IRFs, we need to construct the appropriate conidence intervals. In fact, these conidence bands placed around the point estimates of the IRF allow us to take into account the uncertainty of the estimated values of the parameters. he best way to compute conidence intervals for IRFs is bootstrapping techniques (see, for example, Runkle, 2002; Kilian, 1999). he advantage of these methodologies lies in the fact that they do not require imposing any special assumptions on the distribution of the IRFs and they avoid the complicated computation of precise expressions for their asymptotic variances (Lütkepohl, 2005). Moreover, they produce more reliable estimates than those based on asymptotic normality results (see, for example, Kilian, 1999). he bootstrapping procedure involves the implementation of the following steps. First, the coeicients of each equation are estimated by ordinary LS. A series {ut} of T errors (where T is equal to the sample size) is constructed by randomly sampling with replacement from the estimated residuals. In this way, we are able to construct a simulated series of errors that we assume has the same properties as the true error process. Together with the estimated coeicients, these errors are used to construct a simulated {y ts} process. A new estimation of the coeicients for {y ts} is then carried out. Finally, the new estimated coeicients are applied to compute the IRFs. his process is repeated a suiciently large number of times (in our application we use 10,000 simulation trials), and the resulting IRFs are then used to construct the conidence intervals reported in the chapters that follow.

2.2 Markov switching vector autoregressive models One shortcoming of single-state VAR models is that their parameters are time-invariant, and hence they may not be suicient to properly capture the nature of the statistical relationships among the variables, which is indeed a dynamic one (see, for example, Ang and Timmermann, 2011; Guidolin, 2011). his issue arises because on many occasions inancial DOI: 10.1057/9781137561398.0006



Transmission Channels of Financial Shocks

markets have been demonstrated to be characterized by unstable statistical relationships. his type of unstable behavior of inancial time series can be represented either by assuming the existence of recurring regime changes, such as the alternation between recession and expansion states, or in the form of one-time structural breaks, such as changes in the tenure of the chairmen of central banks (see, for example, Sims and Zha, 2006), that may afect riskless yield curves. For example, in the stock market, we oten observe sequences of periods of high returns and low volatilities, known as bull regimes, and periods of low returns and high volatilities, known as bear phases (see, for example, Pagan and Sossounov, 2003; Ang and Bekaert, 2002). In a similar fashion, ixed income markets typically alternate periods of low rates and periods of high rates (Guidolin and Timmermann, 2009). In particular, regimes in interest rates seem closely linked to the underlying regimes in monetary policy (see, for example, Hamilton, 1988; Bekaert, Hodrick, and Marshall, 2001; Ang and Bekaert, 2002; Bikbov and Chernov, 2008). Models able to capture regime switches in inancial markets may help in the ex-post understanding of the episodes of sudden change in the behavior of inancial markets (see, for example, Guidolin and Timmermann, 2005). For this reason, we estimate a range of Markov switching (henceforth, MS) models. Due to the impossibility of observing in real time the regimes prevailing over a certain period, under this framework states in inancial markets are assumed to be generated by a latent variable with a Markov structure. Regime switching models are able to capture diferences across regimes in terms of volatilities, auto – and cross serial correlations, and covariances of asset returns. Consequently, they are able to capture features of inancial series that a single-state VAR is not able to capture, including fat tails, heteroskedasticity, skewness, and time-varying correlations (Ang and Timmermann, 2011).

2.2.1

he model

As earlier, we model an N × 1 random vector yt that collects the realizations on N diferent assets. Assuming that yt follows a k-regimes Markov switching VAR (henceforth, MSVAR) process with heteroskedastic components, compactly MSIAH(k,p) (Markov switching intercept autoregressive heteroskedasticity), we have the representation yt  A0, St  £ j 1 A j , St yt j  7 S1t/2 et , p

et ^ IIDN 0, I N ,

(2.18)

DOI: 10.1057/9781137561398.0006

Methodology



where St = 1,2, ... , k, k is the number of regimes, p is the number of vector autoregressive lags, A0,St is the N × 1 vector collecting the k regimedependent intercept terms, and A1,St ... Aj,St are the regime-dependent N × N vector autoregressive coeicient matrices. Finally, 7½St is a lower triangular matrix and represents the factors applicable to the regime St in a state-dependent Cholesky decomposition of the covariance matrix 7St. Conditionally on the unobservable state, St, the MSIAH(k,p) model in Equation (2.18) is identical to Equation (2.1), that is, to a VAR(p) model in reduced form. In our speciication of MS models, we assume that alternative states are possible, that is, k > 1, and that regimes are hidden, meaning that at all times, investors fail to observe St. In MSVAR models, the state St is assumed to be generated by a discrete-state, homogeneous, irreducible, and ergodic irst-order Markov chain with transition probabilities



[ ] ,[Y ]

Pr St  j | S j

t 1

j 1

t 1

n

n 1

 Pr S  j | S

t 1

t

 i  pi , j Œ0,1 ,

(2.19)

where pi,j is the generic [i, j] element of the k × k transition matrix P with elements pi , j  Pr St 1  j | St  i ,

£

k j 1

pij  1

i , j Œ[1,z, k].

(2.20)

he Markov chain is discrete because it can assume only a inite number k of values. It is a irst-order chain because the current state is only inluenced by the state prevailing in the previous period. It is ergodic because there exist long-run or unconditional state probabilities, which are col– – lected in a k × 1 vector, r . he property of irreducibility requires r > 0, that is, there are no absorbing states. Finally, homogeneity means that the transition probability matrix P is constant over time. he elements of the main diagonal of the transition matrix, pi ,i  Pr St 1  i | St  i i Œ[1,z, k],

(2.21)

are the so-called stayer probabilities, that is, the probability of remaining in regime i in two consecutive periods. Stayer probabilities allow us to capture a persistence in the data that is not linear and does not depend on the persistence captured through the VAR coeicient matrices. DOI: 10.1057/9781137561398.0006



Transmission Channels of Financial Shocks

he model in Equation (2.18) requires an analyst to estimate a large number of parameters, that is, § ¶ N  N  1 K ¨ N  pN 2   (K 1)· . 2 © ¸

(2.22)

In particular, if the number of variables included in the system is large, the model that is speciied and estimated will be extremely complex and richly parameterized. As an alternative, it is possible to estimate models that require a lower number of parameters than a fully-ledged MSIAH(k,p) framework. For example, in a MSIH(k,0) (Markov switching intercept heteroskedasticity), we have p = 0, and only the intercepts and the covariance matrix of the error terms are regime-dependent: yt  A0, St  7 S1t/2 et .

(2.23)

In a MSIH(k,p), we have p > 0, and the VAR coeicient matrices are not linked to the state variable: yt  A0, St  £ j 1 A j yt j  7 S1t/2 et . p

(2.24)

In principle, we may also consider homoskedastic models, that is, models with regime-independent, constant covariance matrix. However, in the literature the empirical evidence of conditional heteroskedasticity in inancial data (including interest rates) is predominant; therefore, the ability of homoskedastic models to properly it available time series is limited (see, for example, Bollersev, 1986; Nelson, 1991). Due to the introduction of regime switches in the model, an MSVAR is able to capture important statistical features of the data. In particular, in these models the diference in conditional means across regimes afects higher-order moments, including variance, skewness, and kurtosis. For example, when a regime shit occurs, the diference in means contributes to generating volatility: therefore, the variance is not simply the average of the variances across regimes but increases when regimes imply large diferences in state-dependent conditional means. Diferences in means also generate autocorrelation in the data, which would be zero otherwise. Moreover, the persistence in volatility is generated by both the diference in variances and the diference in means across regimes. Furthermore, DOI: 10.1057/9781137561398.0006

Methodology



the stronger the combined persistence, as captured by the diagonal elements of the transition probabilities matrix as well as by the persistence implicit in standard linear components, the higher is the persistence in both means and variances. Finally, similarly to the case of a single-state VAR, we deine the stationarity conditions for the MSVAR processes. he stability of the process represents a suicient, but not a necessary, condition for the process to be stationary also in this framework. For the general case of a MSIAH(k,1), the stability of the vector autoregressive coeicient matrix in each regime is identical to the stability condition for a single-state VAR model. Moreover, the stability of A1 in at least one regime is suficient (but not necessary) for the model to be stationary; see Ang and Bekaert (2001).

2.2.2

Estimation

MS models are estimated by maximum likelihood (henceforth, MLE) (Krolzig, 1997). In particular, estimation is performed through the Expectation–Maximization (henceforth, EM) algorithm proposed by Dempster, Laird, and Rubin (1977) and Hamilton (1990). Given the matrix Yt–1, which collects all lagged values of the variables, and a regime rt, the density function of yt conditional on the realization of the regime k is normal: p  yt |St  i,Yt 1  ln 2.

1/ 2

ln 7

1 2

[





]

exp yt y k ,t `7k 1 yt y k ,t . (2.25)

If we consider that the information set available at time t–1 includes only the pre-sample values collected in Yt–1, the sample observations, and the states of the Markov chain up to St–1, then the conditional density of yt is a mixture of normal distributions: p  yt | St 1

¤ ln 2. 1/2 ln | 7 | 1/2  i,Yt 1  £ j 1 £i 1 pi , j ¥ ¥¦ exp yt y k ,t `7k 1 yt y k ,t k

k

[





³ ´ . (2.26) ´µ

]

he information about the Markov chain is collected in the vector rt.9 Because at time t–1 the only information available is the realized time series, the unobserved regime vector rt needs to be estimated alongside DOI: 10.1057/9781137561398.0006



Transmission Channels of Financial Shocks

the parameters that deine the model. he corresponding estimates are collected in the vector rˆt|n such that § Pr(St  1 | Yn ) ¶ · ¨ ⋮ rˆt|n ¨ ·. ¨Pr(St  k | Yn )· ¸ ©

(2.27)

herefore, rˆt|n includes the probabilities of being in regime k given the information set Yn . If we collect the densities of yt conditional on St and Yt–1 stated in Equation (2.25) in the vector dt, the conditional probability density of yt given by Yt–1 in Equation (2.26) can be written as p(yt|Yt–1) = d9t P9rˆt–1|t–1,

(2.28)

where § p( yt | rt  1,Yt 1 ) ¶ · ¨ ⋮ dt  ¨ ·. ¨ p( yt | rt  k,Yt 1 )· ¸ ©

(2.29)

Following the same derivation process applied to the single observation yt, we can derive the conditional probability density of the whole sample. he joint probability distribution of the observations and the states is p Y |rt  p Y |r Pr r  “t 1 p  yt |rt ,Yt 1 “t  2 Pr rt |rt 1 Pr r1 . (2.30) T

T

he EM algorithm carries out an iterating process to jointly estimate the parameters of the model and the Markov state probabilities. his involves two steps: the expectation and maximization steps. First, we deine the initialization values for r1|0 and the parameter vector h[k l], that is, values that are arbitrarily ixed and that are used in the irst round of the iteration process. Next, the expectation step is started. In this step, the estimated parameters obtained from the maximization step and collected in the parameter vector h[k l] are used to make inferences on the unobserved state rt.10 In particular, the estimated parameters are used to estimate both the time-series sequence of the iltered probability vecT T tors {rˆt|t}t=1 and the smoothed probability vectors {rˆt|T}t=1 (see Hamilton, 11 1994). he smoothed probabilities derived in the last expectation step DOI: 10.1057/9781137561398.0006

Methodology



are the estimates of the conditional regime probabilities. Hence, they are used to estimate the parameters. In the maximization step, the model vector of parameters h is estimated as a solution of the irst-order condition associated with the likelihood function. his vector of parameters h is then used to start the estimation step again and compute new iltered and smoothed probabilities. his process is iterated until convergence, ∼ ∼ that is, until [k l̻∼l]9 ≃ [k l–1̻∼l–1].

2.2.3

Generalized impulse response functions for MS models

In this section, we discuss the estimation process for IRFs in a MS framework. For concreteness, we focus on the case of a MSIH(k,p) model, that is, a model with intercepts and covariance matrices (for errors) depending on the Markov state variable, but with regime-invariant vector autoregressive coeicient matrix. According to the general deinition, an IRF represents the diference between the conditional expectation of yt + h at time t in the case when yt has been subject to a shock and the conditional expectation of yt + h at time t in the case when yt has not been subject to any shock. In practice, we can deine the h-step ahead IRF as follows IR$u h  E §©Yt  h | yt q ` ¶¸ E §©Yt  h | yt q ¶¸ ,

(2.31)

where the sample path yt(q9) difers from the sample path yt(q) because the initial value of yt has been subject to a shock Δu (see Potter, 2000). his general deinition can be extended and adapted to an MS framework. In this case, we obtain the following representation: IR$u h  E §©Yt  h | rt , ut  $ ut ;Yt 1 ¶¸ E §©Yt  h | rt , ut  $ ut ;Yt 1 ¶¸ .

(2.32)

he h-step ahead IRF thus depends on the state prevailing at time t, when the shock occurs. However, when computing IRFs in a MS framework, we need to deal with the additional issue that regimes are not observable, and therefore the prevailing state at time t is unobservable. For this reason, we compute regime-dependent IRFs assuming that the regime prevailing at the time the shock occurs is known. his corresponds to a counter-factual experiment in which investors and/or policy-makers can base their decisions on a knowledge of the current state.

DOI: 10.1057/9781137561398.0006



Transmission Channels of Financial Shocks

MSVAR models are subject to the same identiication problems that we have described for the single-state VAR model in Section 2.1.1. herefore, we apply a Cholesky decomposition to the regime-dependent covariance matrices. Also, in this case, conidence intervals for the IRFs are computed through Monte Carlo simulation techniques. If we consider for simplicity the case of p = 1, that is, the case of a irst-order MSVAR model, we assume that the matrix of the VAR coeicients A1 has the following distribution: ˆ ,∑), A ~ N(A

(2.33)

that is, it follows an asymptotic multivariate normal distribution, where ˆ represents the estimate of the true but unknown coeicient matrix and A ∑ is a diagonal matrix consisting of the squares of the standard errors of the estimated parameters. Note that normality follows as a result under rather weak restrictions (see Krolzig, 1997, for details). he matrix A is extracted from this distribution a suiciently large number of times (for example, 10,000 times) and is used to compute the IRFs. Next, we sort the realizations of the IRFs, and we construct the upper and lower bounds of the 95 per cent conidence interval as those that exclude the highest and the lowest 2.5 per cent, respectively, of the realizations.

Notes 1 For instance, we can compute u1,t and u2,t as u1,t 

e b e and u  e b e . 1 b b 1 a a 1,t

1,2 2 ,t

2 ,t

2 ,1 1,t

2 ,t

1,2 2 ,1

1,2 2 ,1

2 In the general case of an N–variable VAR(1), this type of decomposition forces (N2 – N) / 2 values of the covariance matrix to be equal to zero. 3 In general, an estimator θˆ of a parameter θ is consistent if p limnl∞ (θˆ)θ . An estimator θˆ is eicient if it is the minimum variance estimator of the parameter θ. As a irst approximation, θˆ is asymptotically eicient if this property holds in the limit. 4 In an ininite-order moving average representation, the variables are expressed in terms of the current and past values of the innovations. 5 he unconditional mean can be computed as * = (Im – A1 – ... – Ap)–1A0. 6 A stationary VAR process has time-invariant irst and second moment. 7 his means that because the components are orthogonal, and hence uncorrelated, a change in one component wt has no efect on the other components.

DOI: 10.1057/9781137561398.0006

Methodology



8 his implies that, in principle, we may obtain diferent results when estimating the model with a diferent ordering of the variables in the system. § I (St  1) ¶ ¨ · rt  ¨ ⋮ · , where the indicator function assumes the value of 1 if St = k ¨Pr(St  k )· © ¸ and zero otherwise. 10 In the irst round of the estimation process, the values assumed for the parameters and used in the expectation step are the arbitrarily ixed initial values. In the following rounds, the values used for the expectation step are the ones obtained in the maximization step. 11 A iltered probability is the best assessment of inference on the state at time t on the basis of the information set up to time t. A smoothed probability represents the estimate of the unobservable state at time t based on the entire sample, and hence also on data available up to time T > t. 9

DOI: 10.1057/9781137561398.0006

3

he Data Abstract: In this chapter, we introduce the variables used in this book and present the main features of the data sets actually utilized for the estimation of the models that have been examined in Chapter 2. All the series that we present in this chapter concern the US market. In Chapter 7 we will briely examine the contagion dynamics that has engulfed the European inancial markets in the diferent stages of the subprime and sovereign crises. he data consists of weekly observations covering the period from January 2000 to December 2013 and relates to the following asset classes: asset-backed securities, Treasury overnight repo contracts, Treasury bonds and notes, investment grade and non-investment grade corporate bonds, and stocks. Finally, we present the main statistical features of our series. Keywords: asset-backed securities; corporate bonds; inancial crisis; Treasury bonds Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model. Basingstoke: Palgrave Macmillan, 2016. doi: 10.1057/9781137561398.0007.



DOI: 10.1057/9781137561398.0007

he Data



To investigate the dynamics of the contagion episode that arose from the shock to the asset-backed securities (ABS market) during the 2007 subprime crises, we use data that represents four diferent markets: the ABS market itself and the repo, ixed income (including both Treasury and corporate bonds), and equity markets. We estimate our models on two diferent types of data: a irst set of models is itted on yield series and a second one is itted on spread series. he yield on an asset can be deined as the constant return that makes the current market price of the asset identical to a theoretical price, according to which expected future cash lows are discounted to the present using the yield of the asset. he spread series for each asset class is computed as the diference between the yield on the asset and the one-month Treasury yield. Obviously, a yield spread gives a measure of the additional expected return that a risky asset commands over relatively riskless one-month T-bills; that is, spreads can be interpreted as ex-ante risk premia. Before presenting the key summary statistics concerning our data, we will briely review the nature of the asset classes under consideration in our work and discuss the reasons for their choice, given our stated objectives.

3.1 Asset-backed securities ABS are bonds backed by the cash lows of a variety of pooled receivables or loans. Generally, these products are collateralized by consumer and business loans. hey difer in this from the speciic features of mortgagebacked securities, which are exclusively backed by mortgages, even though mortgage-backed securities can be considered a special type of ABS. In particular, in the securitization process that leads to the creation and the origination of ABS, a set of assets is used by the originator to create several classes of securities, known as tranches, characterized by a diferent level of priority of the claims on the collateral pool (see Agarwal, Barrett, Cun, and De Nardi, 2010). In case of default, the losses are absorbed by the lowest-priority tranches before afecting those of higher priority. Before the subprime crisis, ABS were a class of ixed income securities of growing popularity. In fact, they allowed banks and inancial institutions to reduce the size of their balance sheets and to free up capital.1 Over the years, the investor base for ABS products has

DOI: 10.1057/9781137561398.0007



Transmission Channels of Financial Shocks

changed, moving from banks and institutional investors towards hedge funds and structured investment vehicles (SIV).2 Moreover, before the crisis, ABS were extensively used by inancial institutions as collateral in the repo market, and hence played a crucial role in guaranteeing a continuous availability of funds. To represent this market in our analysis, we collected weekly observations on the yields of two ABS series that correspond to indices prepared and sold by Bank of Afairs Merrill Lynch. he irst series includes AAArated ABS, which are the highest-grade asset-backed securities. he second series covers lower-grade ABS that belong to the rating bracket AA–BBB and represent the lowest-grade asset-backed securities. We do not resort to lower-grade ABS data because before 2007 they were rare (that is, junior tranches resulting from the securitization process were usually held by the originator itself, and only securities with BBB or higher rating were sold to the general public) and therefore time series would be patchy and hardly reliable before 2007, when a wave of downgrades hit this asset class.

3.2 he Treasury repo and Treasury bond markets In a repo transaction, a sale of securities is combined with an agreement to repurchase them at maturity at a higher price. Such a higher price represents a way to compensate the lender for the time value of money and for any credit risk they may incur. Before the subprime crisis, lenders used to accept several types of securities as collateral, including ABS instruments. However, in the atermath of the inancial crisis, the US repo market has come to be dominated by transactions involving US Treasuries. In our analysis, we include a series corresponding to the Treasury overnight general collateral (GC) repo rate collected from GovPX.3,4 his represents the repo rate charged on the shortest-term transactions against the safest and most liquid type of collateral. he use of overnight rates follows Barclay, Hendershott, and Kotz (2006), who report that 94 per cent of repos consist of overnight agreements. For the Treasury bond market, we include yield series corresponding to both the short and the long end of the yield curve, in the form of weekly observations for one month and the ten-year constant maturity Treasury yields.5 DOI: 10.1057/9781137561398.0007

he Data



3.3 Corporate bonds Following a number of earlier papers (see, for example, Longstaf, 2010; Neal et al., 2001), to include the corporate bond market in our study, we rely on indices of corporate bond yields. In particular, we use indices published by Bank of Afairs Merrill Lynch, consisting of portfolios sorted according to maturities and credit ratings. We collect four series: (1) investment grade short-term bonds; (2) investment grade long-term bonds; (3) non-investment grade short-term bonds; (4) non-investment grade long-term bonds. A bond is classiied as short-term if its residual time to maturity is in the range of one to three years and long-term if it exceeds ten years. As described in Chapter 2, the model used in the analysis implies the estimation of a high number of parameters, thus forcing us to represent each market with the lowest possible number of series. For this reason, we exclude from the sample data from corporate bonds with maturities between three and ten years. A bond is classiied as investment grade if it has an S&P’s rating lower than BBB−. For the same reason speciied above, that is, reducing the number of series to be employed in the analysis, for non-investment grade portfolios our data include corporate bonds with a credit rating of CCC and lower, namely, the highly speculative ones. he series including bonds with an S&P’s rating between BB+ and BB− is not included in the analysis.

3.4 he equity market In the case of the equity market, we include a series of weekly observations on the dividend yield of the S&P 500 Index. here exists an extensive literature that proves the predictive ability of the dividend–price ratio for equity returns; therefore, this metric is comparable and consistent with the use of yield series for the assets that belong to the bond market (see, for example, Pesaran and Timmermann, 1995; Campbell and hompson, 2008). When carrying out analyses at high frequency (weekly series, in our case), the main diiculty in including the dividend yield relates to the cyclical nature of this index. To address this issue, we build our own series of weekly dividend yields for the S&P 500 index following a methodology that allows us to deal with and mitigate the presence of cyclic efects. In particular, we compute the numerator of the ratio as a moving DOI: 10.1057/9781137561398.0007



Transmission Channels of Financial Shocks

average of the dividends paid over a period of three months (see, for example, Ang and Bakaert, 2006; Harman and Zuehlke, 2004; Fama and French, 1989; Lewellen, 2004). he weekly dividends are computed by using the diference between the S&P 500 weekly returns including and excluding dividends. he denominator is the closing value of the stock index as of the end of the previous week relative to time t. In the exercise that uses yield spread data, similar to what we do for other series, we compute a dividend yield spread series as the diference between the dividend price ratio and the one-month Treasury yield, which is an approach oten found in the literature (see, for example, Bansal, Kiku, and Yaron, 2011).

3.5 Summary statistics Before we start discussing the results of our analysis, it is worthwhile to discuss the key features of the data described above, which are summarized in Table 3.1. As discussed earlier in the chapter, the series presented are the weekly observations for ABS AAA, ABS AA–BBB, the Treasury overnight GC repo rate, one-month Treasury, ten-year Treasury, investment grade short- and long-term corporate bonds, non-investment grade short- and long-term corporate bonds, and dividend yields. he means and sample standardized deviations of (annualized, percentage) yields present no surprise: riskier asset imply the highest yields but also the highest risk.6 For instance, non–investment (“junk”) grade corporate bonds show average double-digit yields but also volatilities between ive and eight times the typical volatility of long-term Treasuries. One-month T-bill yields imply instead very low average yields (1.96 per cent per year) but almost no standard deviation (2.06 per cent per year). ABS securities and investment grade bonds occupy an intermediate position. All the series display values of skewness and kurtosis that are inconsistent with normality of the series.7 In particular, with the only exception being the ten-year Treasury yield, they are all characterized by a positive skewness. his implies that the right tail of their empirical distribution is thicker (fatter) than the let tail. As far as kurtosis is concerned, the ABS AAA, the repo rate, the one-month Treasury, the ten-year Treasury, and the investment grade short- and long-term corporate bond yield series show a negative excess kurtosis (such distributions are deined DOI: 10.1057/9781137561398.0007

DOI: 10.1057/9781137561398.0007

Table 3.1

Summary statistics for bond and stock yields

Panel A shows the main statistics for the yield series over the sample period January 7, 2000–December 27, 2013. he data are expressed as annualized nominal yields. For instance, 1.00 stands for 1.00 per cent. Jarque–Bera is a test statistic used to assess whether a series is normally distributed; asterisks denote statistical signiicance at conventional levels. Panel B shows sample correlations. Panel A: Summary statistics

ABS AAA ABS AA–BBB Repo rate One-month Treasury Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield

Mean

Max.

Min.

Std. dev.

Skewness

Kurtosis

Jarque–Bera

3.650 6.644 2.119 1.959 3.909 3.601 6.429 20.399 12.776 1.923

8.575 21.040 6.640 7.280 6.770 8.783 9.271 68.764 38.485 3.941

0.681 2.206 0.010 0.000 1.470 0.816 4.318 10.369 8.250 1.024

2.064 3.503 2.085 2.063 1.164 1.937 1.028 9.263 4.777 0.450

0.200 2.005 0.695 0.836 −0.188 0.342 0.185 1.747 2.588 0.671

1.956 7.858 2.048 2.429 2.548 2.115 2.534 6.550 10.383 4.714

38.000*** 1207.08*** 86.440*** 94.847*** 10.497*** 38.061*** 10.775*** 754.49*** 2472.56*** 144.07***

Panel B: Sample correlations

ABS AAA ABS AA–BBB Repo rate One-month Treasury Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield

ABS AAA

ABS AA–BBB

1 0.646*** 0.787*** 0.776*** 0.768*** 0.984*** 0.822*** 0.588*** 0.381*** −0.296***

1 0.119* 0.107* 0.237*** 0.617*** 0.723*** 0.608*** 0.729*** 0.238***

Repo rate

1 0.990*** 0.799*** 0.801*** 0.485*** 0.240*** −0.045 −0.575***

One-month Ten-year T-bill Treas.

1 0.808*** 0.793*** 0.500*** 0.268*** −0.021 −0.605***

1 0.755*** 0.733*** 0.328*** −0.043 −0.695***

Inv. grade Inv. grade ST LT

Non-inv. grade ST

Non-inv. grade LT

Div. yield

1 0.807*** 0.586*** 0.398*** −0.295***

1 0.772*** −0.143**

1 0.300***

1

1 0.755*** 0.529*** −0.344***



Transmission Channels of Financial Shocks

as platykurtic). his means that the distribution of these series is latter and with thinner tails than a normal benchmark with the same mean and variance. he ABS AA–BBB, the non-investment grade corporate bonds, and the dividend yield series show instead a positive excess kurtosis (and, as such, are deined as leptokurtic). his means that these distributions are more peaked and display fatter tails than a normal benchmark. Table 3.1 (Panel A) also shows the values of the test statistic for the Jarque–Bera test, which is an additional metric useful to formally test whether a series is normally distributed. In our case, it can be seen that the null hypothesis of normality can be rejected for all series at any conventional conidence level. Table 3.1 (Panel B) shows the sample correlation coeicients for pairs of yield series. In general, they display positive pairwise correlations, as one would expect, because changes in the level of the riskless rate tend to be transmitted to all other yields. However, the dividend yield is characterized by a negative correlation with all series, with the exception of ABS AA–BBB and non-investment grade long-term corporate bond yields. his is not surprising: indeed, when the appetite for risk increases, investors tend to reallocate their wealth to riskier assets, such as stocks and lower-grade bonds, and vice versa. Because of a similar mechanism, as the Treasury bonds are typically considered the safest asset if we exclude cash, non-investment grade long-term bonds have negative correlations with the Treasury yields and the repo rate. he ABS AAA series is signiicantly correlated with the corporate bond series belonging to the investment grade bucket, showing correlations of 0.98 and 0.82 with the investment grade short-term and long-term yields, respectively. he ABS AA–BBB series is highly correlated with both the long-term corporate bond yield series. It displays, indeed, a correlation of 0.72 with the long-term investment grade and 0.73 with the noninvestment long-term grade series. Finally, the one-month Treasury and the repo rate display a correlation of 0.98. Table 3.2 completes the picture and reports summary statistics and correlations for yield spreads, constructed as the simple diference between yield series and one-month T-bill yields. As one would expect from an ex-ante risk premium interpretation of spreads, these series range on average between the tiny 16 bp per year for the almost riskless overnight repo rates to as much as 1844 bp for the rather risky non-investment grade long-term corporate bonds.8 Clearly, such risk premia also reward the volatility that is, in general, monotone DOI: 10.1057/9781137561398.0007

DOI: 10.1057/9781137561398.0007

Table 3.2

Summary statistics for bond and stock yield spreads

Panel A shows the main statistics for the spread series over one-month T-bill rates, with reference to the sample period January 7, 2000–December 27, 2013. he data are expressed in annualized terms. For instance, 1.00 stands for 1.00 per cent. Jarque–Bera is a test statistic used to assess whether a series is normally distributed. Panel B shows sample correlations. Panel A: Summary statistics

ABS AAA ABS AA–BBB Repo rate Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield

Mean

Max.

Min.

Std. dev.

1.691 4.685 0.160 1.951 1.642 4.470 18.440 10.817 −0.036

8.555 20.978 1.870 3.950 8.593 9.129 68.754 38.295 3.831

−0.927 0.400 −1.178 −1.958 −1.015 0.803 5.599 3.933 −6.184

1.381 3.871 0.299 1.315 1.294 1.787 8.934 5.244 2.363

Skewness

Kurtosis

2.507 2.409 0.965 −0.672 2.531 −0.283 1.719 2.212 −0.786

10.827 9.046 9.882 2.582 11.238 2.436 7.765 9.957 2.562

Jarque–Bera 2628.05 1818.22 1553.71 60.277 2843.89 19.460 1050.24 2067.84 80.945

Panel B: Sample correlations

ABS AAA ABS AA–BBB Repo rate Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield

ABS AAA

ABS AA–BBB

Repo rate

Ten-year Treasury

Inv. grade ST

Inv. grade LT

Non-inv. grade ST

Non-inv. grade LT

Dividend yield

1 0.907 0.201 0.472 0.962 0.663 0.574 0.679 0.380

1 0.081 0.493 0.899 0.727 0.523 0.783 0.483

1 −0.004 0.174 −0.040 −0.184 −0.148 0.031

1 0.500 0.907 0.062 0.332 0.809

1 0.708 0.560 0.734 0.456

1 0.330 0.641 0.852

1 0.715 −0.043

1 0.458

1



Transmission Channels of Financial Shocks

increasing with average spreads. Also, in the case of ixed income spreads, there is massive evidence against the hypothesis that these are generated from a normal distribution. his derives especially from the fact that spreads show large excess kurtosis statistics. Panel B of Table 3.2 reports, instead, sample correlations for pairs of spreads. With few exceptions, all related to repo rates, spreads tend to show higher correlations than yields do. his is an indication that most risk premia on ixed income securities in the US market tend to co-move over bull and bear markets and diferent phases (see, for example, Guidolin and Tam, 2013).

Notes 1 In a typical process of securitization that follows the originate-to-distribute model, a bank holding consumer loans pools several loans together and issues bonds with cash lows linked to the pool of these loans. hese loans are then transferred to a separate entity and sold. he cash inlow so generated is used by inancial institutions to issue additional loans. 2 Structured investment vehicles are non-bank inancial institutions that earn a proit from the diference between long-term structured inance products, such as ABS, held in their portfolio and the short-term liabilities they issue, usually in the form of commercial paper. 3 In a general collateral repo contract, the particular collateral is not speciied and any given asset within an asset category is acceptable. For instance, a Treasury GC repo admits any Treasury security as collateral. 4 he repo index from GovPX is the most timely and comprehensive source of average overnight repo rates weighted by volume for on-the-run Treasuries. On-the-run Treasuries are the most recently issued securities with a given maturity. 5 Constant Maturity Treasury rates, or CMTs, are obtained by interpolating the Treasury rates from the daily curve, based on the closing market bid yields on actively traded Treasury securities in the over-the-counter market. In this way, it is possible to have a yield for any point of the yield curve, even if there is no outstanding bond with that maturity. 6 here are only two visible exceptions to this principle. First, ten-year Treasuries pay higher average interest rates than one-month T–bills do, even though they are characterized by lower volatility. Second, the stock dividend is on average rather low, but this is because, in the case of equity investments, most of the expected return normally comes from capital appreciation, while stocks typically are long-lived or ininite-horizon assets. 7 A standard normal distribution has skewness of zero and kurtosis of three.

DOI: 10.1057/9781137561398.0007

he Data



8 An exception is the dividend yield, which, however, represents only one of the components of the ex-ante risk premium in the case of equities. With regard to the fact that “junk” short-term corporate bonds are characterized by higher average spreads than the corresponding low-quality long-term bonds, this is presumably due to the higher sensitivity of yields on the former to rating downgrades.

DOI: 10.1057/9781137561398.0007

4

Estimates of Single-State VAR Models Abstract: In this chapter, we estimate two single-state VAR models, one for the yield and one for the spread series described in Chapter 3. First, we describe our model speciication search and identify two as the appropriate number of lags of the VAR for both the VAR-yield and the VAR-spread models. Second, we report the results of the estimation of the two VAR(2) models and comment on the signiicance and economic meaning of the coeicients. Keywords: estimation; single-state vector autoregression; VAR Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model. Basingstoke: Palgrave Macmillan, 2016. doi: 10.1057/9781137561398.0008.



DOI: 10.1057/9781137561398.0008

Estimates of Single-State VAR Models



he irst empirical exercise that we propose consists of the estimation of two single-state vector autoregressive (VAR) models, one itted to yield series and one to spread series. he same class of econometric models is itted to both yields and yield spreads because this represents a strategy to disentangle the diferent contagion channels discussed in Chapter 1. We deine the former type of models as single-state VAR-yield models. his model shall include ten endogenous variables: the AAA-rated asset-backed securities (ABS), the ABS of the AA–BBB rating bracket, the Treasury repo rate, the one-month and ten-year Treasury bonds, the investment grade short- and long-term corporate bonds, the non-investment grade short- and long-term corporate bonds, and the dividend yield series. he second type of model shall be called single-state VAR-spread. he model concerns the spread series computed from the variables listed above, all calculated as the diference between the yield series and one-month Treasury rates. hese spread series have been introduced and described in Chapter 3. herefore, the second model includes nine series, as the one-month Treasury bond is obviously excluded from the analysis.

4.1 Model selection A irst choice to be made when estimating a VAR(p) process is the selection of the number of lags p to include in the system. his speciication is crucial because, if the selected lag length is diferent from the true but unknown one, the estimated VAR model, and the impulse response functions (IRFs) resulting from it, risk being inconsistent and therefore hardly meaningful (see, for example, Braun and Mittnik, 1993). To increase the chances of identifying the appropriate lag order of the VAR, we apply a range of model selection criteria, which employ penalized measures of it. In particular, these criteria may be used to obtain indications as to the most appropriate model and at the same time take into consideration the existence of a trade-of between goodness of it and parsimony. In our analysis, we compute and sort models according to three diferent information criteria: the Akaike Information Criterion (AIC), the Schwarz Criterion (SC), and the Hannan–Quinn Criterion (HQ). For a general VAR(p) model, these sample statistics are computed as: AIC(p) = –2L(kˆ ) + 2(dim(kˆ )/T),

DOI: 10.1057/9781137561398.0008

(4.1)



Transmission Channels of Financial Shocks

SC(p) = –2L(kˆ ) + 2(dim(kˆ )ln(T)/T),

(4.2)

HQ(p) = –2L(kˆ ) + 2[dim(kˆ )ln(ln(T))/T],

(4.3)

where p is the VAR order, kˆ collects the estimated parameters, and T is the sample size.1 he term –L(kˆ ) is the minimum of the negative of the (Gaussian) log-likelihood function for a VAR(p) process. Because we are interested in the VAR order that maximizes the likelihood function, and consequently minimizes its opposite, we select the number of lags that minimizes the criteria. Table 4.1 (Panels A and B) shows the values of the three criteria up to ten lags for the single-state VAR-yield and the single-state VAR-spread models. Under both frameworks, the AIC criterion suggests a richly parameterized model with ten lags, while the SC and HQ criteria select a more parsimonious VAR(2) model. Given the heterogeneous results provided by the information criteria, we face the diicult task of choosing between alternative information criteria. Fortunately, there are a number of simulation studies that have investigated which criterion is the most likely to select the true VAR order. hese analyses suggest that the criterion actually employed to specify the autoregressive order should, irst, depend on the purpose of the application of the VAR modeling approach. In particular, if forecasting is the objective, it is appropriate to choose the order that minimizes the mean forecast error, the average of the squared prediction errors implied by a given model. If, instead, the interest centers on the correct VAR order, a criterion that satisies desirable sampling properties, such as consistency, should be privileged (see, for example, the discussion in Lüktepohl, 2005). In particular, an estimator p of the true VAR order is deined to be consistent if and only if limT lc Pr  psel  ptrue  1,

(4.4)

where psel is the VAR order selected by the criterion and ptrue is the true but unknown VAR order. he results of the literature show that while the SC and HQ are optimal estimators, that is, they are consistent, the AIC criterion does not satisfy this property (see Enders, 2005). his, of course, does not mean that the AIC ought to be discarded as an information criterion, but only that it should not be preferred over other criteria when consistency, and hence the convergence of the selected psel to the true but unknown number of lags, ptrue, becomes a priority. he results of a study by Lüktepol (1993) show that for small samples the AIC could, DOI: 10.1057/9781137561398.0008

Estimates of Single-State VAR Models

Table 4.1



Model selection results for single-state VAR(p) models

his table reports the statistics used to select VAR(p) models of the type





ut ~ N 0, £ u .

yt  v  A1 yt 1  z Ap yt p  ut , Panel A refers to the VAR models for yields, whereas panel B refers to the VAR models for spreads.

Panel A Lag 0 1 2 3 4 5 6 7 8 9 10

No. of parameters 65 165 265 365 465 565 665 765 865 965 1065

Saturation ratio

AIC

SC

HQ

112.3 44.2 27.5 20.0 15.7 12.9 11.0 9.5 8.4 7.6 6.9

24.348 −4.808 −5.474 −5.642 −5.711 −5.809 −5.876 −5.852 −5.864 −5.983 −6.120*

24.411 −4.108 −4.138* −3.670 −3.104 −2.566 −1.997 −1.336 −0.712 −0.196 0.303

24.372 −4.537 −4.958* −4.881 −4.705 −4.557 −4.379 −4.109 −3.875 −3.749 −3.641

AIC

SC

HQ

Panel B Lag

No. of parameters

Saturation ratio

0 1 2 3 4 5 6 7 8 9 10

54 135 216 297 378 459 540 621 702 783 864

135.2 54.1 33.8 24.6 19.3 15.9 13.5 11.8 10.4 9.3 8.4

25.127 −2.062 −2.606 −2.688 −2.745 −2.801 −2.867 −2.840 −2.850 −2.962 −3.127*

25.184 −1.489 −1.519* −1.085 −0.627 −0.168 0.281 0.823 1.328 1.732 2.082

25.149 −1.841 −2.186* −2.069 −1.928 −1.785 −1.652 −1.426 −1.237 −1.150 −1.116

Note: Boldfaced and * indicate the lag order selected by each of the criteria

in fact, give superior results in terms of forecasting precision. However, for low-order VAR processes, the SC criterion performs quite well in terms of ability to select the appropriate VAR order and in providing good forecasting results. In practice, it is common to privilege the most parsimonious model to avoid the problems caused by over-itting and over-parameterization. For this reason, we choose a second-order VAR model, namely a VAR(2), as suggested by the SC and HQ criteria for both DOI: 10.1057/9781137561398.0008



Transmission Channels of Financial Shocks

our yield and spread series. his requires the estimation of 265 and 216 parameters for the single-state VAR-yield and single-state VAR-spread, respectively. Before discussing the results of the estimation, there is a last aspect that need to be examined. As discussed already, when we deal with VAR processes, and especially when we have to compute impulse response functions, it is important to check that the VAR is stationary. In general, a stable process is characterized by time-invariant irst and second moments. In an unreported table, we have examined the inverse of the roots of the characteristic polynomial and their modules for the singlestate VAR matrices of coeicients for both the yield and the spread models. Because all the modules are lower than one, both models satisfy the stability and hence the implied stationarity conditions.

4.2 he VAR(2) model We estimate two unrestricted VAR(2) models, one for the analysis with the yields and one with the spreads. Each model has the following representation: Ym,t  v  £i 1am,iYi ,t 1  £i 1bm,iYi ,t 2  um,t . m

m

(4.5)

Tables 4.2 and 4.3 show the estimation results for the single-state VARyield and the single-state VAR-spread models, respectively. For each intercept term and coeicient, we report in parentheses the p–values for the tests that each parameter is not signiicantly diferent from zero. Before moving on, it is worthwhile to comment briely on the output of the estimation. In the case of the single-state VAR-yield model, approximately 50 per cent of the estimated coeicients are signiicant. First of all, we notice that almost all the intercepts are signiicant at a 5 per cent conidence level or lower. he only exceptions are the intercepts of AAA–BB-rated ABS, the ten-year Treasury, and the non-investment grade long-term corporate bonds. If we consider the two ABS yield series, we notice that, as we should expect, the own lags of the series themselves show the highest predictive ability. Curiously, we observe that the yields of the AAA-rated ABS show a negative relation with the second lag of the ABS

DOI: 10.1057/9781137561398.0008

DOI: 10.1057/9781137561398.0008

Table 4.2

Estimates of a single-state VAR(2) for yields

1. Intercept terms 2. VAR(2) matrix ABS AAA (t−1) ABS AAA (t−2) ABS AA–BBB (t−1) ABS AA–BBB (t−2) Repo rate (t−1) Repo rate (t−2) One-month Treasury (−1) One-month Treasury (−2) Ten-year Treasury (−1) Ten-year Treasury (−2) Inv. grade ST (−1) Inv. grade ST (−2) Inv. grade LT (−1) Inv. grade LT (−2) Non-inv. grade ST (−1) Non-inv. grade ST (−2) Non-inv. grade LT(−1)

ABS AAA

ABS AA–BBB

Repo rate

0.209*

0.063

0.489*

0.249**

0.080

0.261** −0.223* −0.011 0.011 0.488* 0.307* 0.181* −0.031 0.111*** 0.006 −0.302* 0.320* −0.029 −0.144* 0.001 −0.002 0.009

0.157 −0.154** −0.081** 0.070*** −0.037 0.151* 0.999* −0.171* 0.136** −0.037 −0.047 0.088*** −0.099*** −0.015 −0.010* 0.010* 0.015**

0.058 −0.045 −0.017 0.024 −0.031 0.011 0.021 0.0139 0.984* −0.016 0.119* −0.144* 0.272* −0.257* −0.006* 0.005** −0.004

0.939* −0.005 0.084* −0.083* −0.032 0.008 −0.041 0.041*** −0.012 0.032 0.040 0.057*** −0.054 0.010 0.009* −0.010* 0.004

0.122*** 0.057 1.070* −0.116* −0.073*** 0.038 −0.064 0.045 −0.108*** 0.031 −0.101*** 0.048 0.030 −0.011 0.013* −0.010* 0.017**

One-month Treasury

Ten-year Treasury

Inv. grade ST 0.257** −0.233* 0.263* 0.025 −0.024 0.037 −0.050 −0.060 0.062** −0.092** 0.109** 1.182* −0.198* 0.028 −0.073 0.014* −0.015* −0.004

Inv. grade LT

Non-inv. grade ST

Non-inv. grade LT

Dividend yield

0.292*

−2.835**

0.219

0.353*

−0.095*** 0.102** 0.010 −0.006 −0.067* 0.032 0.033 −0.004 −0.132* 0.103** 0.162* −0.144* 0.932* 0.050 0.002 −0.003 0.006

0.505 −0.467 −0.441 0.206 −0.433 0.315 0.151 −0.282 −0.834 0.272 −0.130 0.584 1.478** −0.322 1.058* −0.165* 0.268*

−0.281 0.603 −0.356*** 0.237 −0.467* 0.372** 0.272 −0.444** −0.399 0.126 −0.037 0.163 0.891** −0.656*** 0.066* −0.074* 0.857*

−0.053 0.096** 0.006 −0.012 0.023 −0.039*** −0.003 −0.010 −0.030** 0.062*** 0.040 −0.043 −0.022997 0.011 0.008* −0.011* 0.015* Continued

Table 4.2

Continued ABS AAA

Non-inv. grade LT(−2) Dividend yield (−1) Dividend yield (−2) R-squared Adj. R-squared

DOI: 10.1057/9781137561398.0008

3. Correlations/volatilities ABS AAA ABS AA–BBB Repo rate One-month Treasury Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield

−0.013** 0.093** −0.099* 0.996 0.996

ABS AA–BBB

Repo rate

−0.023* 0.001 0.110*** −0.063 −0.070 0.052* 0.997 0.992 0.997 0.992

0.118*** 0.512** 0.182*** 0.100* −0.009 0.179*** 0.041 −0.054 0.392*** 0.408*** 0.207** 0.032 0.699*** 0.442*** 0.050 0.524*** 0.376*** 0.022 0.012 0.008 −0.052 0.091* 0.079 −0.003 0.054 0.115** −0.007

One-month Treasury

Ten-year Treasury

Inv. grade ST

0.001 −0.036 −0.012 0.993 0.993

0.003 −0.091* 0.073** 0.993 0.993

0.004 0.102** −0.130** 0.994 0.993

0.166*** 0.125** −0.064 0.021 −0.033 0.000 −0.042

0.095*** 0.237*** 0.523*** −0.121** −0.091* −0.039

0.151*** 0.552*** 0.142** 0.197** 0.040

Inv. grade LT −0.010*** 0.020 −0.069 0.988 0.988

0.112*** 0.017 0.090* 0.106*

Note: he boldfaced values are signiicant at least 10%, i.e., every value that is signiicant at conventionally accepted levels is boldfaced. he *, ** and, *** correspond to signiicance at the 1%, 5% or 10% levels, respectively.

Non-inv. grade ST

Non-inv. grade LT

Dividend yield

−0.227* −0.655 0.408 0.969 0.968

0.096** −0.073 −0.046 0.967 0.966

−0.010** 0.843* 0.043 0.954 0.954

1.634*** 0.449*** −0.013

0.872*** −0.010

0.097***

Estimates of Single-State VAR Models



in the AA–BBB rating bucket. Possibly, this means that, when a negative shock hits the yield of the lowest-rated ABS, investors slowly adjust their preferences and move their wealth to less risky ABS. In addition, the one-month Treasury yields, the corporate bond yields (with the exception of investment grade long-term ones), and the dividend yield seem to have some predictive ability for the yields of AAA-rated ABS. Instead, the repo rate, the ten-year Treasury, the corporate bond yields (with the exception of investment grade long-term ones), and the dividend yield help forecast the yields of AA–BBB-rated ABS. Looking at the sign of the relationship, we notice that, while the safest ABS show a positive relationship with the majority of the other assets, the yields of the ABS in the AA–BBB rating bucket tend to imply negative coeicients with many other yields, and especially with their second lags. In contrast, the lowest-rated ABS have a positive relationship with the equity market. his is consistent with the fact that ABS are perceived to be a very risky asset class. Also in the case of the repo rate, the lags of the repo itself show the highest forecasting power. In addition, the yields of AAA-rated ABS seem to have a strong predictive power for the repo rate. Interestingly, this relationship is positive if we look at the irst lag and negative if we look at the second lag. Indeed, we expect the general collateral (GC) Treasury repo rate to be low when there is a negative shock to the ABS market, albeit it is conceivable that the adjustment may need some time to be completed. Finally, the repo rate shows a positive relationship with Treasury bond and the dividend yield and a negative one with investment grade corporate bond rates. In contrast to what one might expect, the one-month and ten-year Treasury yields display heterogeneous relationships with the other assets. Indeed, while almost all the yield series are useful to forecast the yields of one-month T-bills, only corporate bonds (with the exception of the non-investment grade long-term ones) and the dividend yield show some explanatory power for ten-year Treasury yields, if we exclude its own lags. Short-term and long-term corporate bonds show a similar behavior. In particular, they present a positive pairwise relationship, and for both of them the ten-year Treasury bond is the asset with the highest predictive potential. In the case of the noninvestment grade corporate bonds, we notice that few variables seem to have forecasting power, especially if we consider only coeicients that are signiicant at a 5 per cent or lower conidence level. Indeed, only yields on other corporate bonds have predictive power for short-term DOI: 10.1057/9781137561398.0008



Transmission Channels of Financial Shocks

non-investment grade yields, while the repo rate and the one-month Treasury yields are also useful to forecast the long-term ones. Finally, the dividend yield, in addition to being explained by its own lags, shows a small but positive predictive relationship with the irst lag of the yields on non-investment grade corporate bonds and the lowest-rated ABS. his is not surprising, as these securities are the riskiest assets in the ixed income market. In addition, the dividend yield shows a negative predictive relationship with the ten-year Treasury and the repo rates. Overall, we conclude that, although tracking these multi-faceted and complex cross-serial correlation patterns is never trivial, the adjusted R-squares in Table 4.2 show that with two multivariate lags, the quality of the it obtained is extremely high, even though not all estimated coeficients are statistically signiicant. As for the single-state VAR-spread model, even more than 50 per cent of the estimated coeicients are signiicant in Table 4.3. For this model, we only comment on the coeicients when there are relevant diferences from what we discussed for the single-state VAR-yield model. A irst noticeable, but not surprising, diference is that in the case of the VARspread models, only two intercepts (for the repo rate and for short-term non-investment grade yields) are signiicant at a conidence level of 5 per cent or lower. As mentioned above, another diference worth noting is that the number of signiicant coeicient is higher for this model than for the VAR-yield one. his result suggests that the relationships between the risk premia of the diferent assets are much stronger than the ones between their yields. his is conirmed when we consider the values of the correlation estimates presented at the bottom of Tables 4.2 and 4.3. Indeed, pairwise correlations between spreads are generally higher than those for yields. his stronger relationship for the spreads compared with the yields is particularly prominent for the ixed income market: for instance, in the case of investment grade corporate bond yields. Indeed, almost all the coeicients are signiicant, including the lowest-rated ABS, which do not seem to have any predictive power for the yields of these securities in the VAR-yield model. In particular, the spreads of the investment grade short-term bonds show a positive relationship with the irst lag of the AA–BBB ABS spreads and a negative relationship for the second lag. Finally, we note that the adjusted R-squares are high in this model also, always exceeding 95 per cent. DOI: 10.1057/9781137561398.0008

DOI: 10.1057/9781137561398.0008

Table 4.3

Estimates of a single-state VAR(2) for yield spreads ABS AAA

1. Intercept terms 2. VAR(2) matrix ABS AAA (t−1) ABS AAA (t−2) ABS AA–BBB (t−1) ABS AA–BBB (t−2) Repo rate (t−1) Repo rate (t−2) Ten-year Treasury (−1) Ten-year Treasury (−2) Inv. grade ST (−1) Inv. grade ST (−2) Inv. grade LT (−1) Inv. grade LT (−2) Non-inv. grade ST (−1) Non-inv. grade ST (−2) Non-inv. grade LT(−1)

0.087*** 0.784* 0.153** 0.168* −0.155* 0.003 −0.145* −0.152** 0.069 0.087 −0.028 0.039 0.021 0.019* −0.017* −0.011

ABS AA–BBB 0.038 −0.030 0.214** 1.156* −0.189* −0.036 −0.118** −0.239* 0.0559 −0.053 −0.036 0.119 −0.006 0.024* −0.021* 0.001

Repo rate 0.287* 0.133 −0.099 0.076*** −0.0615*** 0.550* 0.137* 0.082 −0.065 −0.243* 0.216* 0.079 −0.142*** 0.012* −0.012* −0.005

Ten-year Treasury −0.039 −0.119 0.136*** 0.063*** −0.046 −0.015 −0.128* 0.763* 0.103*** 0.156* −0.216* 0.357* −0.238* 0.004 −0.006 −0.021*

Inv. grade ST

Inv. grade LT

Non-inv. grade ST

Non-inv. grade LT

Dividend yield

0.067

0.028

−2.041*

−0.250

−0.098***

0.382 −0.308 −0.335 0.120 −0.391 0.136 −0.916*** 0.219 −0.074 0.511 1.531** −0.357 1.070* −0.178* 0.252*

−0.404 0.711** −0.272 0.168 −0.394** 0.200 −0.389 0.024 0.026 0.046 1.017* −0.647*** 0.077* −0.083* 0.844*

−0.198** 0.228* 0.086** −0.080 0.075** −0.197* −0.166** 0.046 0.094*** −0.146** 0.093* 0.028 0.018* −0.020* 0.000

−0.388* 0.417* 0.108** −0.095** 0.074*** −0.202* −0.226* 0.142*** 1.229* −0.285* 0.125 −0.060 0.024* −0.025* −0.019**

−0.243* 0.245* 0.093** −0.076** −0.021 −0.126* −0.231* 0.104*** 0.213* −0.239* 1.036 0.063 0.012* −0.013* −0.009

Continued

Table 4.3

Continued

Non-inv. grade LT(−2) Dividend yield (−1) Dividend yield (−2) R-squared Adj. R-squared

DOI: 10.1057/9781137561398.0008

ABS AAA

ABS AA–BBB

Repo rate

Ten-year Treasury

Inv. grade ST

Inv. grade LT

Non-inv. grade ST

−0.013*** 0.110** −0.010** 0.996 0.996

0.02197** 0.126** −0.094 0.997 0.997

−0.001 0.101** −0.075*** 0.992 0.992

0.004 −0.177* 0.174* 0.993 0.993

0.003 0.134** −0.128** 0.994 0.993

−0.012 0.104** −0.101** 0.988 0.988

−0.222* −0.669*** 0.209 0.969 0.968

0.181 0.727 0.849 0.053 0.108 0.718

0.231 0.829 0.192 0.268 0.669

0.198 0.120 0.205 0.746

3. Correlations/volatilities ABS AAA 0.200 ABS AA–BBB 0.780 Repo rate 0.448 Ten-year Treasury 0.810 Inv. grade ST 0.883 Inv. grade LT 0.838 Non-inv. grade ST 0.117 Non-inv. grade LT 0.203 Dividend yield 0.712

0.253 0.356 0.671 0.733 0.726 0.099 0.185 0.639

0.192 0.403 0.424 0.422 0.032 0.095 0.442

1.647 0.462 0.107

Non-inv. grade LT 0.092** 0.171 −0.186 0.967 0.966

0.887 0.160

Dividend yield −0.013*** 0.977* 0.008 0.954 0.953

0.196

Note: he boldfaced values are signiicant at least 10%, i.e., every value that is signiicant at conventionally accepted levels is boldfaced. he *, ** and, *** correspond to signiicance at the 1%, 5% or 10% levels, respectively.

Estimates of Single-State VAR Models

Note ¤ N  N  1 ³ 1 he number of parameters to be estimated is equal to, ¥ N  pN 2  ´, 2 ¦ µ where N is the number of endogenous variables and p the number of lags. he saturation ratio is the ratio between the number of observations used in estimation and the number of estimated parameters, that is, ¤ N  N  1 ³ N ¥ N  pN 2  ´. 2 ¦ µ

DOI: 10.1057/9781137561398.0008



5

Results from Markov Switching Models Abstract: In a symmetrical approach to what we do in Chapter 4, in this chapter, we estimate two MSVAR models, one for the yields and one for the spreads. First, we present our speciication search, which in this case concerns not only the appropriate number of lags, but also the most adequate type of Markov switching model and the appropriate number of regimes. We identify the MSIH(3,1) model as the most adequate to it the data. Furthermore, we try to provide an economic interpretation of the three regimes that we identify. Finally, we discuss the results of the estimation of these models and their economic interpretation. Keywords: Markov switching; regimes Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model. Basingstoke: Palgrave Macmillan, 2016. doi: 10.1057/9781137561398.0009.



DOI: 10.1057/9781137561398.0009

Results from Markov Switching Models



Our second empirical exercise consists in the estimation of Markov switching vector autoregressive (MSVAR) models itted on both yield and spread series. In line with our approach for single-state VAR models, we deine the two frameworks as MSVAR-yield and MSVAR-spread, respectively. As for the single-state models, the MSVAR-yield includes ten endogenous variables: AAA- and AA–BBB-rated ABS yields, one-month and ten-year Treasury yields, investment grade and noninvestment grade short- and long-term corporate bond yields, the repo rate, and the dividend yield. he MSVAR-spread includes the spreads of the same assets, with the exclusion of the one-month Treasury, whose yield is subtracted from the others to obtain the spread.

5.1 Model selection As already mentioned in Chapter 4, when one intends to model a phenomenon of interest through VAR models, whether Markov switching or single-state, it is necessary to specify the appropriate number of vector autoregressive lags to include. In addition, in the case of MSVAR models, we also need to specify an adequate number of regimes, and to deine exactly which parameters are regime-dependent (if one rules out that all parameters, that is, intercepts, autoregressive coeicients, variances, and covariances, ought to be a function of the state). Similarly to the single-state VAR, we experiment with a number of model selection criteria. Table 5.1 shows the results of our selection process. Panel A refers to the MSVAR-yield model and Panel B to the MSVAR-spread. In our speciication search, we investigate the it provided by three alternative models: an MSI(k,p), which requires only the intercept terms to be regime-dependent; an MSIH(k,p), where both the intercept terms and the covariance matrix are linked to the state variable; and an MSIAH(k,p), where the intercept terms, the covariance matrix, and also the autoregressive parameters are assumed to be regime-dependent.1 he decision to extend the analysis beyond the classical case of two regimes (k = 2) and therefore to investigate the possibility of three regimes relates to the indings of Guidolin and Timmermann (2009), who show that, when dealing with ixed income market data, a number of regimes k > 2 is necessary. In an MSVAR framework, we limit the test of the number of lags to the cases where p ≤ 2, instead of p ≤ 10, which DOI: 10.1057/9781137561398.0009



Transmission Channels of Financial Shocks

Table 5.1

Model selection results for Markov switching models

his table reports the statistics used to select multivariate MSVAR models of the form

yt  *St  £ j 1 A j , St yt j  7 S1t/2 et p

et ^ IID N 0, I N .

Panel A refers to the yield-MSVAR, whereas panel B refers to the spread-MSVAR. Panel A LR test Hannan– No. of Saturation Logfor Akaike Quinn Schwarz Model (k,p) parameters ratio likelihood linearity criterion criterion criterion Baseline model: Two-state, Markov switching MSI(2,0) 77 94.81 −8135.79 MSIA(2,1)

277

26.32

2124.33

MSIA(2,2)

477

15.26

2406.05

MSIH(2,0)

132

55.30

−6224.25

MSIH(2,1)

232

31.42

4465.88

MSIH(2,2)

332

21.93

4759.88

MSIAH(2,1)

332

21.96

4633.53

MSIAH(2,2)

532

13.68

5003.21

1599.55 (0.000) 633.61 (0.000) 552.44 (0.000) 5422.61 (0.000) 5316.73 (0.000) 5260.10 (0.000) 5652.02 (0.000) 5746.75 (0.000)

Baseline model: hree-state, Markov switching MSI(3,0) 91 80.22 −7737.36 2396.40 (0.000) MSIA(3,1) 391 18.65 2674.92 1734.81 (0.000) MSIA(3,2) 691 10.54 3408.22 2556.78 (0.000) MSIH(3,0) 201 36.32 −4590.10 8690.92 (0.000) MSIH(3,1) 301 24.22 5058.24 6351.07 (0.000) MSIH(3,2) 401 18.16 5295.67 6331.68 (0.000) MSIAH(3,1) 501 14.55 5054.37 6493.69 (0.000) MSIAH(3,2) 801 9.09 5461.11 6662.56 (0.000)

22.50

22.69

22.99

−5.07

−4.40

−3.32

−5.30

−4.14

−2.29

17.41

17.74

18.25

−11.62

−11.05

−10.15

−12.17

−11.36

−10.07

−11.80

−10.99

−9.71

−12.28

−10.99

−8.93

21.45

21.67

22.02

−6.27

−5.32

−3.80

−7.47

−5.78

−3.10

13.13

13.61

14.39

−13.05

−12.32

−11.16*

−13.45*

−12.47*

−10.92

−12.49

−11.28

−9.34

−12.80

−10.85

−7.75 Continued

DOI: 10.1057/9781137561398.0009

Results from Markov Switching Models

Table 5.1



Continued

Panel B

Model (k,p)

LR test Hannan– No. of Saturation Logfor Akaike Quinn Schwarz parameters ratio likelihood linearity criterion criterion criterion

Baseline model: Two-state, Markov switching MSI(2,0) 65 112.31 −8491.93 MSIA(2,1)

227

32.12

1062.53

MSIA(2,2)

389

18.72

1850.14

MSIH(2,0)

110

66.36

−7055.09

MSIH(2,1)

191

38.17

3279.50

MSIH(2,2)

272

26.77

3492.79

MSIAH(2,1)

272

26.80

3425.25

MSIAH(2,2)

434

16.77

3731.20

1467.41 (0.000) 557.07 (0.000) 1609.11 (0.000) 4341.09 (0.000) 4991.01 (0.000) 4894.41 (0.000) 5282.51 (0.000) 5371.24 (0.000)

Baseline model: hree-state, Markov switching MSI(3,0) 78 93.59 −8019.55 2412.15 (0.000) MSIA(3,1) 321 22.71 1459.85 1351.70 (0.000) MSIA(3,2) 564 12.91 1351.70 1956.36 (0.000) MSIH(3,0) 168 43.45 −5059.44 8332.39 (0.000) MSIH(3,1) 249 29.28 3760.43 5952.87 (0.000) MSIH(3,2) 330 22.06 3970.30 5849.44 (0.000) MSIAH(3,1) 411 17.74 3722.88 5877.77 (0.000) MSIAH(3,2) 654 11.13 4040.17 5989.17 (0.000)

23.44

23.60

23.85

−2.29

−1.74

−0.86

−4.01

−3.07

−1.56

19.63

19.90

20.32

−8.47

−8.01

−7.27

−8.85

−8.19

−7.13

−8.65

−7.99

−6.94

−9.06

−8.00

−6.32

22.19

22.37

22.68

−3.12

−2.34

−1.10

−4.01

−2.64

−0.45

14.32

14.73

15.38

−9.63

−9.03

−8.07*

−10.00*

−9.20*

−7.92

−9.09

−8.09

−6.50

−9.30

−7.71

−5.18

Note: * Boldfaced and * indicate the lag order selected by each of the criteria

was used in the single-state VAR model. his decision is due to the fact that MSVAR models introduce a second source of persistence that is not represented by the traditional VAR components, but is due instead to persistence in the data captured by the diferences in mean returns DOI: 10.1057/9781137561398.0009



Transmission Channels of Financial Shocks

and in variances across regimes (see also Section 2.2.1). In essence, the introduction of regimes into the model allows us to reduce the number of lags required to model the persistence of the data, typical of interest rates. he irst model selection criterion we entertain is based on sequentially performing likelihood ratio (LR) tests, which allow us to test the null of k = 1 against the alternative of k > 1, that is, to test whether it is appropriate to select a number of states greater than one. In Table 5.1, we present the values for the LR test and in parentheses the Davies’ p-values. For both the MSVAR-yield (Panel A) and MSVAR-spread (Panel B), the values of the relevant LR tests and of Davies’ p-values allow us to reject the null of k = 1 at any conventional conidence level. herefore, we conclude that it is appropriate to assume k > 1. Equivalently, these tests formally show that the empirical results in Chapter 4 need to be supplemented by an MSVAR analysis in which at least a few of the model parameters are allowed to switch with the Markov state. he information criteria used to perform model selection are the same as those employed in Chapter 4 and applied to single-state VAR models: the Akaike (AIC), Schwartz (SC), and Hannan–Quinn (HQ) criteria. For both the MSVAR-yield and the MSVAR-spread applications, the SC selects an MSIH(3,1), while the HQ and AIC suggest a more richly parameterized MSIH(3,2) model. For the MSVAR-yield model, an MSIH(3,1) would require the estimation of 301 parameters, leading to a saturation ration of 24.2. An MSIH(3,2), instead, would require us to specify 401 parameters, implying a saturation ratio of only 18.2, which fails to exceed the typical requirement of at least 20 observations per parameter, typical of the non-linear econometrics applied literature. We thus decide to select the most parsimonious MSIH(3,1) for both the MSVAR-yield and the MSVAR-spread cases. his implies a VAR order lower than the one selected in the single-state VAR framework. However, as discussed above and in Chapter 2, the MS models typically require a lower lag order than a single-state VAR model, as there are two sources of persistency instead of one (see Guidolin, 2012, for additional discussion). As already discussed in Chapter 4, once we select the appropriate model, it is crucial to check the stationarity of the process. If we consider again the case of p = 1, in the MS framework, the stability of the coeicient matrix A1, at least in one of the regimes, represents a suicient but not a necessary condition for the process to be stationary.

DOI: 10.1057/9781137561398.0009

Results from Markov Switching Models



Moreover, because in our case the coeicient matrix is regime-independent, the stability condition is the same as in single-state VAR models. Unfortunately, in this case, both the MSVAR-yield and MSVAR-spread models have some of the eigenvalues of the coeicient matrix A1 with a modulus greater than one. herefore, the suicient (but not necessary) stability condition for stationarity is not satisied. For this reason, we apply a diferent methodology in order to check the stationarity of the models: Monte Carlo simulation techniques. We simulate a large number of times (m = 50,000) the series from the estimated multivariate model using the estimated parameters and inspect the properties of the resulting series. To reinforce the general idea that stability is not necessary for stationarity, the Monte Carlo experiment conirms the stationarity of the series, in the sense that the key properties of the simulated densities do not appear to depend on the speciic (simulated) subsample over which such properties are assessed. For instance, the unconditional moments of the simulated series (such as means and standard deviations, but also skewness and kurtosis coeicients that provide indications on the overall shape of the density of the series) appear to be independent of the speciic block of simulated data considered.2 Of course, as an additional pay-of, such experiments also allow us to compute the unconditional moments of the series implied by MSVAR models. he values of the unconditional means are shown in Table 5.2 (Section 5.2) and Table 5.3 (Section 5.3) for the MSVAR-yield and MSVAR-spread, respectively.

5.2 A three-regime MSVAR model In an MSIH(3,1) framework, we specify regime-dependent intercept terms and covariance matrices, while the vector autoregressive coeficient matrix remains constant across the three regimes. Before investigating the interpretation of the coeicients of the MSVAR-yield and MSVAR-spread, it is worthwhile to stress again that in such models, the co-movement of the series is captured in three diferent ways: (i) a simultaneous efect due to the of-diagonal elements of 7½St, which are able to capture the dynamics across regimes of non-zero correlations among the innovation terms; (ii) a linear efect captured through the VAR coeicients, which in our case are not regime-dependent; and

DOI: 10.1057/9781137561398.0009



Transmission Channels of Financial Shocks

(iii) a dynamic non-linear efect due to the contemporaneous switches to the same regime (or regimes characterized by similar conditional irst moments) of all the variables. For this reason, it is not surprising that a lower number of coeicients is signiicant, as some of the cross-asset relationships are explained through channels (i) and (iii), which were not included in the single-state models. he estimation results of the MSVAR-yield model are presented in Table 5.2. As in the single-state case, most of the intercepts are signiicant in every regime, with the exclusion of the one-month and ten-year Treasury yields, and the non-investment grade long-term yield, which do not have a signiicant intercept in any regime. As for the vector autoregressive coeicient matrix, slightly fewer than 50 per cent of the coeicients are statistically signiicant at conventional levels, but only one third of them are signiicant at a conidence level lower than 10 per cent. In the case of the ABS market, we note that, in contrast to the results of the single-state model, the ixed income market does not seem to have any predictive power for the yields of these securities, with the sole exception of the long-term investment grade corporate yields, which show a negative relationship with both the highest- and the lowest-rated ABS. Another relevant diference is that the yield of each corporate bond class does not show a signiicant forecasting power for the yields of others, with the exception of the non-investment grade long-term yield, which helps predict the short-term yield. his lack of linear forecasting power is probably due to the fact that the co-movements of these assets are already well explained by the fact that they share the same regimes. he repo rate, the Treasury rate, and the dividend yield tend to show limited diferences vs. the single-state case. In particular, the dividend yield continues to show a negative and signiicant predictive relationship with the rest of the asset classes, excluding low-rated ABS and non-investment grade long-term bonds, with which it has a positive relationship. he estimation results of the MSVAR-spread model are presented in Table 5.3. First of all, we notice that there is much more homogeneity between the yield and the spread models in the Markov switching framework than in the single-state one. here are some diferences that are worthwhile to mention. First, while in the case of yield almost all the intercepts are signiicant in all the regimes, when it comes to spread, fewer than half of the intercept terms are signiicant. Second, while the DOI: 10.1057/9781137561398.0009

DOI: 10.1057/9781137561398.0009

Table 5.2

Estimates of an MSIH(3,1) model for yields ABS AAA

ABS AA–BBB

Repo rate

One-month Ten-year Inv. grade Inv. grade Non-inv. Treasury Treasury ST LT grade ST

Non-inv. Dividend grade LT yield

1. Intercept terms Regime 1 (Low volatility) Regime 2 (High volatility) Regime 3 (Crisis)

0.210* (0.000) 0.220* (0.000) 0.197* (0.001)

0.179** (0.010) 0.168** (0.011) 0.303* (0.000)

0.154* (0.005) 0.144* (0.009) 0.082 (0.132)

0.015 (0.336) 0.024 (0.255) −0.049 (0.831)

−0.022 (0.621) −0.032 (0.669) −0.064 (0.799)

0.226* (0.000) 0.267* (0.000) 0.264* (0.000)

0.315* (0.000) 0.345* (0.000) 0.349* (0.000)

0.198 (0.333) 0.266 (0.289) 0.287 (0.312)

0.370** (0.012) 0.418* (0.008) 0.432** (0.041)

0.244* (0.000) 0.243* (0.000) 0.265* (0.000)

2. VAR (1) Matrix ABS AAA (t−1) ABS AA–BBB (t−1) Repo rate (t−1) 1-m Treasury (t−1) 10-y Treasury (t−1) Inv. grade ST (t−1) Inv. grade LT (t−1) Non-inv. grade ST (t−1)

1.019* (0.000) −0.004 (0.109) −0.026*** (0.059) 0.005 (0.369) 0.012 (0.132) 0.016 (0.139) −0.044* (0.001) 0.000 (0.358)

0.060* (0.005) 0.981* (0.000) −0.019 (0.174) 0.000 (0.499) 0.002 (0.434) −0.018 (0.173) −0.025*** (0.070) −0.000 (0.423)

0.028*** (0.058) −0.004 (0.105) 0.852* (0.000) 0.114* (0.000) 0.018** (0.045) 0.025** (0.047) −0.05* (0.000) 0.000 (0.362)

0.001 (0.423) 0.000 (0.457) 0.013*** (0.059) 0.984* (0.000) 0.016* (0.002) 0.005 (0.231) −0.021* (0.001) −0.000 (0.192)

0.030** (0.035) −0.004 (0.169) −0.030** (0.038) 0.031** (0.029) 0.932* (0.000) −0.010 (0.239) 0.064* (0.000) −0.004* (0.000)

0.040** (0.031) −0.011* (0.005) −0.012 (0.279) −0.004 (0.425) 0.019*** (0.069) 0.991* (0.000) −0.05* (0.001) −0.000 (0.359)

0.018 (0.167) −0.001 (0.390) −0.035** (0.032) 0.023 (0.106) −0.011 (0.198) 0.015 (0.191) 0.959* (0.000) −0.000 (0.427)

0.168 (0.172) −0.104* (0.001) −0.056 (0.359) −0.127 (0.203) −0.045 (0.312) 0.102 (0.230) 0.043 (0.351) 0.994* (0.000)

0.033 (0.309) −0.021** (0.038) −0.039 (0.232) −0.035 (0.248) −0.031 (0.176) 0.088** (0.043) −0.019 (0.315) −0.002 (0.216)

0.030** (0.028) 0.005*** (0.071) 0.007 (0.318) −0.025*** (0.051) 0.002 (0.427) −0.007 (0.296) −0.026** (0.038) −0.002** (0.027) Continued

Table 5.2

Continued ABS AAA

Non-inv. grade LT (t−1) Dividend yield (t−1) 3. Unconditional mean

−0.002 (0.213) −0.012 0.170 1.246

ABS AA–BBB

Repo rate

−0.000 −0.001 (0.484) (0.358) −0.020*** 0.016 0.094 0.123 1.848

0.598

DOI: 10.1057/9781137561398.0009

4. Correlations/volatilities Regime 1 ABS AAA 0.059** ABS AA–BBB 0.929*** 0.073*** Repo rate 0.000 −0.020 0.067*** One-month Treasury 0.026 0.000 0.250** Ten-year Treasury 0.410*** 0.476*** −0.017 Inv. grade ST 0.923*** 0.904*** −0.021 Inv. grade LT 0.657*** 0.696*** 0.018 Non-inv. grade ST 0.073 0.085* 0.068 Non-inv. grade LT 0.079 0.083* 0.080 Dividend yield 0.080 0.043 −0.071 Regime 2 ABS AAA 0.124*** ABS AA–BBB 0.695*** 0.185*** Repo rate −0.031 0.034 0.079*** One-month Treasury 0.198** 0.265** 0.154**

One-month Ten-year Inv. grade Inv. grade Non-inv. Treasury Treasury ST LT grade ST 0.001*** −0.003*** 0.001 (0.065) (0.067) (0.373) 0.013*** −0.020 −0.010 0.070 0.111 0.246 1.333

2.318

0.066*** 0.053 0.087*** 0.043 0.437*** −0.036 0.531*** −0.036 −0.058 0.041 0.000 −0.072 −0.055

0.024***

Non-inv. Dividend grade LT yield

−0.002 (0.164) −0.038 0.012

0.003 (0.421) −0.108 0.132

0.992* (0.000) −0.082* 0.009

0.007* (0.000) 0.922* 0.000

0.891

1.191

9.739

8.341

0.926

0.071*** 0.644*** 0.117* 0.122* 0.066

0.085*** 0.073 0.003 0.075

0.418*** 0.378*** 0.087*

0.149*** 0.021

0.063***

DOI: 10.1057/9781137561398.0009

Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield Regime 3 ABS AAA ABS AA–BBB Repo Rate One-month Treasury Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield 5. Transition Matrix Regime 1 (Low volatility) Regime 2 (High volatility) Regime 3 (Crisis)

0.502*** 0.312*** 0.826*** 0.520*** 0.611*** 0.454*** −0.099 −0.101* −0.066 −0.025 −0.012 0.004 0.222*** 0.362*** 0.384*** 0.110* −0.017 0.005 −0.056 0.203** −0.078 0.559*** 0.291*** 0.429*** 0.228** 0.114* 0.053 0.164* 0.159* 0.216** 0.305*** Regime 1 0.745*** 0.400*** 0.071

0.044 0.048 0.031 0.034 0.006 0.010

0.431*** 0.402*** −0.014 −0.005 0.003 −0.050 0.017 −0.046

0.321*** 0.114*** 0.187*** 0.333*** 0.131*** 0.170** 0.457*** 0.627*** 0.120*** −0.103* −0.224* 0.006 −0.092* 1.344*** −0.045 −0.313*** −0.005 −0.001 0.255*** −0.031 −0.139* −0.006 0.038 −0.008

0.636*** 0.049

0.132***

0.392*** 0.140* 0.131*** −0.141* 0.110* 0.000 0.427*** −0.040 −0.106* 0.003 −0.081 −0.102* 0.064

0.305*** 0.555*** 0.200* 0.244** 0.188**

1.943*** 0.000

0.120***

Regime 2 0.212** 0.485*** 0.251**

Regime 3 0.042 0.115 0.679***

0.165*** 0.119* 0.537*** 0.343***

3.629*** 0.479*** 0.099

Note: he boldfaced values are signiicant at least 10%, i.e., every value that is signiicant at conventionally accepted levels is boldfaced. he *, ** and, *** correspond to signiicance at the 1%, 5% or 10% levels, respectively.

Table 5.3

Estimates of an MSIH(3,1) model for yield spreads ABS AAA

ABS AA–BBB

DOI: 10.1057/9781137561398.0009

1. Intercept terms Regime 1 (Low volatility) Regime 2 (High volatility) Regime 3 (Crisis)

0.035 (0.165) 0.037 (0.189) 0.154** (0.017)

2. VAR (1) Matrix ABS AAA (t−1) ABS AA–BBB (t−1) Repo rate (t−1) 10−y Treasury (t−1) Inv. grade ST (t−1) Inv. grade LT (t−1) Non-inv. grade ST (t−1)

1.009* 0.045*** (0.000) (0.057) 0.001 0.990* (0.461) (0.000) −0.018083 −0.010 (0.219) (0.353) −0.004191 −0.019 (0.386) (0.122) −0.029*** −0.061* (0.081) (0.005) 0.0038584 0.027*** (0.407) (0.070) 0.001 0.000 (0.302) (0.442)

−0.011 (0.392) −0.026 (0.289) 0.267* (0.001)

Repo rate

Ten-year Treasury

Inv. grade ST

Inv. grade LT

Non-inv. grade ST

Non-inv. grade LT

Dividend yield

0.138* (0.000) 0.131* (0.001) 0.168* (0.009)

−0.123* (0.001) −0.139* (0.001) −0.034 (0.294)

0.056*** (0.081) 0.086** (0.030) 0.269* (0.001)

0.032 (0.227) 0.0529 (0.137) 0.203* (0.003)

−0.345*** (0.064) −0.279 (0.146) −0.230 (0.341)

−0.068 (0.235) 0.015 (0.447) 0.111 (0.352)

−0.091* (0.007) −0.090** (0.016) 0.058 (0.208)

0.038*** (0.052) 0.002 (0.295) 0.783* (0.000) 0.002 (0.447) −0.0113 (0.296) −0.030** (0.030) −0.000 (0.488)

0.038*** (0.058) −0.001 (0.454) −0.026 (0.137) 0.912* (0.000) −0.060* (0.003) 0.102* (0.000) −0.003** (0.018)

0.036*** (0.090) −0.008*** (0.075) −0.014 (0.291) 0.004 (0.394) 0.940* (0.000) −0.002 (0.458) 0.000 (0.447)

0.022 (0.191) 0.001 (0.426) −0.032*** (0.0915) −0.030** (0.037) −0.047** (0.019) 1.020* (0.000) 0.001 (0.304)

0.211 (0.112) −0.108* (0.000) −0.143 (0.206) −0.128*** (0.089) −0.020 (0.441) 0.193** (0.032) 0.995* (0.000)

0.007 (0.457) −0.021*** (0.051) −0.117** (0.040) −0.048*** (0.093) 0.024 (0.334) 0.072** (0.030) −0.004*** (0.088)

−0.025 (0.140) 0.004 (0.189) 0.023 (0.149) −0.015 (0.145) −0.022 (0.135) 0.042* (0.006) −0.001 (0.315)

DOI: 10.1057/9781137561398.0009

Non-inv. grade LT (t−1) Dividend yield (t−1) 3. Unconditional means 4. Correlations/volatilities Regime 1 ABS AAA ABS AA–BBB Repo rate Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield Regime 2 ABS AAA ABS AA–BBB Repo rate Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield

−0.003 (0.157) −0.001 (0.448)

−0.003 (0.157) 0.015* (0.009)

−0.006** (0.010) −0.012** (0.0465)

−0.001 (0.323) 0.007 (0.154)

1.955

5.377

0.287

3.755

2.141

4.813

0.0062 0.0067 0.0022 0.0049 0.0066 0.0065 0.0037 0.0032 0.0035

0.0080 0.0022 0.0056 0.0073 0.0075 0.0046 0.0035 0.0035

0.0049 0.0020 0.0022 0.0024 0.0041 0.0023 0.0023

0.0101 0.0053 0.0069 0.0001 0.0019 0.0028

0.0078 0.0071 0.0052 0.0041 0.0036

0.0113 0.0057 0.0052 0.0042

0.1660 0.0269 0.0050

0.0262 0.0035

0.0082

0.0227 0.0231 0.0009 0.0131 0.0204 0.0147 0.0071 0.0017 0.0073

0.0414 0.0036 0.0129 0.0196 0.0156 0.0101 0.0073 0.0085

0.0213 0.0009 0.0009 0.0022 0.0183 0.0062 0.0008

0.0179 0.0111 0.0111 −0.0067 −0.0082 0.0061

0.0239 0.0153 0.0221 0.0060 0.0072

0.0180 0.0171 0.0077 0.0083

1.9687 0.2596 0.0324

0.3739 0.0139

0.0134

−0.004*** (0.090) 0.005 (0.240)

−0.0060** (0.031) 0.009 (0.126)

−0.001 (0.471) −0.040 (0.149)

0.993* (0.000) −0.019 (0.133)

−0.001 (0.370) 0.985* (0.000)

15.288

12.242

0.278

Continued

Table 5.3

Continued ABS AAA

Regime 3 ABS AAA ABS AA–BBB Repo rate Ten-year Treasury Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield

DOI: 10.1057/9781137561398.0009

5. Transition Matrix Regime 1 (Low volatility) Regime 2 (High volatility) Regime 3 (Crisis)

0.2646 0.2499 0.1336 0.1941 0.2688 0.2195 0.4095 0.3252 0.2108

ABS AA–BBB

Repo rate

Ten-year Treasury

Inv. grade ST

Inv. grade LT

Non-inv. grade ST

Non-inv. grade LT

0.4218 0.1205 0.1870 0.2699 0.2245 0.3717 0.4160 0.2390

0.2419 0.1055 0.1380 0.1126 0.0599 0.1238 0.1215

0.2001 0.2129 0.2007 0.1875 0.1512 0.1898

0.3665 0.2557 0.6250 0.4542 0.2322

0.2352 0.3564 0.2728 0.2093

18.5779 5.0788 0.2816

5.7531 0.2102

Regime 1 0.7495 0.3510 0.0303

Regime 2 0.2402 0.5315 0.3707

Dividend yield

0.2608

Regime 3 0.1174 0.0103 0.5990

Note: he boldfaced values are signiicant at least 10%, i.e., every value that is signiicant at conventionally accepted levels is boldfaced. he *, ** and, *** correspond to signiicance at the 1%, 5% or 10% levels, respectively.

Results from Markov Switching Models



dividend yield shows signiicant (negative) relationships with most of the other asset classes, only the investment grade long-term yield seems to have some explanatory power on the equity risk premium, if we do not consider its own past values. Finally, each corporate bond spread seems to have more explanatory power on the others than in the case of yields. In particular, the spread of investment grade long-term bonds is helpful to forecast non–investment grade bond spreads, in addition to its own.

5.2.1

Economic interpretation of the regimes

In this section, we discuss the economic interpretation of the three regimes identiied in our earlier analysis, for both the yield-MSVAR and the spread-MSVAR models. Table 5.2 shows estimated conditional mean parameters (intercepts and VAR coeicients), the correlations, the volatilities, and the transition matrices for the former, while the results for the latter model are presented in Table 5.3. he estimated models allow us to distinguish three diferent states or regimes, which are mainly identiied by corresponding, heterogeneous levels of volatility. In the discussion of the results, we refer to the three regimes as low-volatility, high-volatility, and crisis regimes. he latter regime is diferent from the high-volatility state because it implies variances that are one order of magnitude higher than in the former regime. In the MSVAR-yield, the low-volatility regime is the most persistent, with a stayer probability of 0.75.3 he average duration, which is the average time spent in this regime, is 3.9 months, and the implied ergodic probability is 0.52.4 he probabilities of shiting from this state to the regime of high volatility and crisis are 0.21 and 0.04, respectively. he high-volatility regime is the least persistent state, with a stayer probability of only 0.49. he average duration of the regime is 1.9 months, while its ergodic probability is 0.30. Such a probability is non-negligible, in spite of the low persistence of this regime, because it can be accessed rather easily (frequently) from both regimes one and three. In this case, the probability of a shit from high volatility to the regime of low volatility is 0.40, whereas the probability of a shit to the regime of crisis is 0.11. Finally, the regime of crisis has a stayer probability of 0.68, an average duration of 3.1 months, and an ergodic probability of 0.18. his regime has a higher average duration compared with the high-volatility regime. Moreover, the probability that a shit

DOI: 10.1057/9781137561398.0009



Transmission Channels of Financial Shocks

to the regime of high volatility or low volatility occurs is 0.25 and 0.07, respectively. We obtain similar results for the MSVAR-spread. In particular, the regime of low volatility is the most persistent one in this model also. It is marked by a stayer probability of 0.75, and the estimated probabilities of a shit to the regimes of high volatility and crisis are 0.24 and 0.01, respectively. Moreover, the average duration of this regime is 4.0 months, while its ergodic probability is 0.52. Also in this case, the lowvolatility regime is the least persistent, with a stayer probability of 0.53 and an average duration of 2.13 months only. he ergodic probability of this regime is 0.36. he probability of observing a shit from this state to the regime of high volatility or crisis is 0.24 and 0.01, respectively. For the crisis regime, we obtain a stayer probability of 0.60, an ergodic probability of 0.12, and an average duration of 2.49. Moreover, while a shit from the crisis regime to the high-volatility regime is quite likely (the probability is 0.37), the probability of a shit to the regime of low volatility is only 0.03. Figures 5.1 and 5.2 show the smoothed and iltered probabilities for the MSVAR-yield model, respectively. he smoothed probabilities represent the estimate of the probability of the unobservable state at time t based on the entire sample, whereas iltered probabilities are the best assessment on the unobservable state at time t on the basis of the information set available up to time t. he smoothed probability plots for the three regimes show that economic phases mainly alternate between a lowvolatility regime and a high-volatility one. However, the model is able to capture three crisis phases over our sample period. he irst starts in 2000, corresponding to the bursting of the high-tech bubble in the US, and characterizes a large percentage of our data up to mid-2002; the second starts in the second half of 2007, corresponding to the subprime crisis, and lasts throughout 2008; the third starts in the second half of 2008, ater Lehman Brothers’ collapse. here is, in fact, little or no discontinuity between the two stages of the great inancial crisis in the US (see, for example, Dwyer and Tkac, 2009). Moreover, it is worth noting that iltered and smoothed probabilities assume similar values and recognize the regime switches almost contemporaneously, even though the former display slightly more uncertainty than the latter in the identiication of the regime. Of course, similar plots can be derived and plotted with reference to the MSIH(3,1) model estimated on ixed income spreads, as per the DOI: 10.1057/9781137561398.0009

Results from Markov Switching Models



1 0.8 0.6 0.4

Jan-09

Jan-10

Jan-11

Jan-12

Jan-13

Jan-09

Jan-10

Jan-11

Jan-12

Jan-13

Jan-09

Jan-10

Jan-11

Jan-12

Jan-13

Jan-08

Jan-07

Jan-06

Jan-05

Jan-04

Jan-03

Jan-02

Jan-00

0

Jan-01

0.2

Low volatility 1 0.8 0.6 0.4

Jan-08

Jan-07

Jan-06

Jan-05

Jan-04

Jan-03

Jan-02

Jan-00

0

Jan-01

0.2

High volatility 1 0.8 0.6 0.4

Jan-08

Jan-07

Jan-06

Jan-05

Jan-04

Jan-03

Jan-02

Jan-00

0

Jan-01

0.2

Crisis

Figure 5.1

Smoothed probabilities estimated from an MSIH(3,0) model for yields

estimates shown in Table 5.3. However, these were rather similar to those in Figure 5.1 and 5.2, and are therefore omitted for reasons of space. In any event, the crisis state is clearly recognizable and characterizes periods and market phases that are very similar to those commented on above with reference to Figures 5.1 and 5.2. DOI: 10.1057/9781137561398.0009

Transmission Channels of Financial Shocks

 1 0.8 0.6 0.4

Jan-09

Jan-10

Jan-11

Jan-12

Jan-13

Jan-09

Jan-10

Jan-11

Jan-12

Jan-13

Jan-09

Jan-10

Jan-11

Jan-12

Jan-13

Jan-08

Jan-07

Jan-06

Jan-05

Jan-04

Jan-03

Jan-02

Jan-00

0

Jan-01

0.2

Low volatility 1 0.8 0.6 0.4

Jan-08

Jan-07

Jan-06

Jan-05

Jan-04

Jan-03

Jan-02

Jan-00

0

Jan-01

0.2

High volatility 1 0.8 0.6 0.4

Jan-08

Jan-07

Jan-06

Jan-05

Jan-04

Jan-03

Jan-02

Jan-00

0

Jan-01

0.2

Crisis

Figure 5.2

Filtered probabilities estimated from an MSIH(3,0) model for yields

Notes 1 In an MSIH(k,p) model, the p matrices of vector autoregressive coeicients are therefore constant over time and fail to depend on the regime. 2 For instance, ater discarding 2000 burn-in values, the 50,000 simulated series have been divided into ten blocks of 5000 simulations each to compute DOI: 10.1057/9781137561398.0009

Results from Markov Switching Models

within-subsample moments and check whether these depend on the exact blocks over which the calculation has been performed. 3 A stayer probability is the probability of remaining in a given regime when starting from that regime. 4 Given a regime j = 1, 2, 3, ..., i and the estimated stayer probability pˆjj < 1, the estimated average duration is computed as duration(j) = 1/(1 – pˆjj)

DOI: 10.1057/9781137561398.0009



6

Estimating and Disentangling the Contagion Channels Abstract: In this chapter, we present the key empirical results of this book. First, we explain how our estimation exercises in Chapters 4 and 5 are used to identify diferent inancial contagion channels. Second, we discuss the results and their economic as well as policy implications. We start by examining how and whether contagious patterns across diferent markets are characterized by regime dynamics. We then quantify the existence and extent of each contagion channel. Keywords: contagion channels; correlated information; light-to-liquidity; light-to-quality; risk premium channel Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model. Basingstoke: Palgrave Macmillan, 2016. doi: 10.1057/9781137561398.0010.



DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



he study proposed by Longstaf (2010) represents the starting point of our work. In particular, our objective is to carry out an analysis of cross-asset contagion in the US inancial markets similar to Longstaf ’s (2010), while using some econometric tools that will hopefully allow us to better identify and characterize the contagion dynamics during a inancial crisis. We do not simply perform an ex-post analysis of the efects of the subprime crisis; on the contrary, we set up the methodological apparatus to perform a simulation of a shock in the asset-backed securities (ABS) market similar to the one that actually occurred during the subprime crisis. Indeed, we estimate the impulse response functions (IRFs) generated by a negative shock to the lower-grade ABS market (in our case represented by the ABS AA–BBB series) in the single-state vector autoregressive (VAR) and Markov switching VAR (MSVAR) over an interval of 26 weeks. In this way, we can investigate the contagion from the ABS lower-grade market to the ABS higher-grade, Treasury repo, Treasury bond, corporate bond, and stock markets. In particular, in the MSVAR model we compute regime-dependent impulse response functions, which allow us to evaluate separately the reactions of the series to the shock when the markets are assumed to be in the low-volatility, highvolatility, and crisis regimes, respectively. In particular, the crisis regime is the most appropriate to capture the efects generated by a shock to the ABS market during the subprime crisis. As this is the ultimate objective of our analysis, we will place major emphasis on this regime when discussing our results. In addition to yield and spread series, following Longstaf (2010), we have also performed a preliminary analysis using return series. In this case, we approximate the returns of the bonds with changes in yields (that is, –Δyieldt). Unfortunately, our model shows that when one moves from yields to changes in yields (as a way to approximate bond returns), there is a substantial loss of information and, consequently, this approximation does not allow us to fully capture contagion dynamics. For this reason, this set of results will not be presented.

6.1 A methodology to identify contagion channels In this section we devote our eforts to understanding which of the contagion channels examined in Chapter 1 – namely, the light-to-liquidity, risk premium, light-to-quality, and correlated information channels DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks

– were active in 2007–08, and to which extent each of them contributed to the spread of the subprime crisis to the ixed income, credit, and equity markets. As discussed above, to perform this task, we compute the impulse response functions of the ixed income and equity yield series to a shock to the lower-grade ABS market. To identify each inancial contagion channel, we perform qualitative comparisons of the IRFs obtained from the diferent models. As a result, the irst issue to tackle in order to study these mechanisms empirically is bringing together the theoretical deinitions of the contagion channels and the efects actually observed in the inancial markets during periods of crisis. his is not a trivial endeavor, because, even though in principle the contagion channels are clearly diferent, in practice these may appear to be poorly deined and overlapping. In our analysis, we therefore exploit the diferent information captured by the MSVAR-yield and the MSVAR-spread models, as well as the single-state VAR and MSVAR models, along with the theoretical background ofered by the existing literature on inancial contagion, to distinguish the efects due to diferent propagation mechanisms. he irst contagion mechanism that we address is the light-toliquidity channel. In this case, a shock to one market triggers an increase in the demand of highly liquid securities. his leads to an appreciation of liquid assets and a contemporaneous decrease in the liquidity of other markets (see, for example, Vayanos, 2004). However, in practice, lightto-liquidity episodes manifest themselves in an increase in the demand of Treasury bonds, which investors perceive as one of the few liquid assets let in the market during periods of inancial turmoil. In Chapter 1, we have surveyed the literature that discusses the reasons why investors assign a higher value to Treasury bonds during inancial crises. he main inding is that this phenomenon is driven by liquidity concerns. In particular, because in periods of inancial crisis investors face an increased risk of losses, they therefore prefer to hold highly liquid securities that can be easily sold when this is necessary. For this reason, in our analysis we use the IRFs computed under the MSVAR-yield model for one-month and ten-year Treasury yields to study the light-to-liquidity channel. In particular, we interpret a negative efect on Treasury yields generated by a shock to the lowest-grade ABS yields as being due to a light-to-liquidity phenomenon. Moreover, we strive to achieve a better understanding of this channel by studying the efects of the shock on the Treasury general collateral (GC) overnight repo rate. Our reason for DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



performing this additional analysis lies in the fact that transactions in the repo market can be security-driven, that is, motivated by the need to borrow a speciic security (see, for example, Banerjee and Graveline, 2013).1 In this case, the repo rate demanded/charged by the providers of funding depends on the demand for the speciic asset, in this case liquid Treasuries. When such a demand is high, the asset becomes scarce, and thus the repo rate may be lower just during crisis periods, because funding providers are also hunting for liquid securities (see, for example, Hrung and Seligman, 2011). herefore, the efect on the Treasury repo rate generated by a shock to the ABS AA–BBB yield allows us to capture an increase in the demand of Treasury bonds. Under the risk premium channel, contagion occurs because shocks to one market lead to an increase in the risk aversion of inancial market participants. his triggers an upward adjustment of the risk premia on all the risky assets in the economy (see, for example, Longstaf, 2010; Vayanos, 2004). In a similar way, according to a light-to-quality channel, following a shock to one market, investors attempt to sell risky assets and purchase safer assets. Consequently, the risk premium of the former climbs, while that of the latter declines (see Caballero and Kurlat, 2008). Both the risk premium and the light-to-quality channel trigger efects on the credit spread required by investors, but these are distinct phenomena. A light-to-quality leads to an increase in the risk premium of the riskiest asset classes, such as stocks and lower-grade bonds, while that of the safest ones, such as high-grade corporate bonds, decreases. In contrast, under a risk premium channel, the risk premium of all assets increases. We therefore study the IRFs computed from the MSVAR-spread model and generated by a shock to the ABS AA–BBB yield spread series, because both channels entail an adjustment of the risk premium required by investors.2 We apply this analysis to the corporate bond, the equity (through the implied dividend yield), and the ABS AAA markets. Furthermore, we distinguish which of the two channels drives the efects on the risk premia. For example, a positive efect on the non-investment grade bond spread and the dividend yield spread that is contemporaneous with a negative efect on the investment grade corporate bond spread can be interpreted as a light-to-quality phenomenon. In this case, indeed, the safer assets appreciate, while riskier ones lose value. In contrast, we interpret a contemporaneous increase in the spreads on all series as an efect due to the risk premium channel. DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks

Under the correlated information channel, contagion occurs because the negative shock to one market immediately conveys information that investors perceive as relevant for the pricing of other assets (see, for example, King and Wadhwani, 1990; Longstaf, 2010; Kodres and Pritsker, 2002). his generates an immediate efect because the evidence of a shit to a crisis state in one market triggers an adjustment of investors’ beliefs concerning other asset prices, which instantly record losses caused by the trading activity of investors as they revise their expectations on the state of the markets. We therefore identify this form of contagion with the non-linear and immediate efect captured by the MSVAR framework, due to the possibility that the intercept terms of the inancial variables may move in the same direction when a shit to a given regime occurs, as was noted in Chapter 5. In particular, because we aim to model contagion during inancial crises, we are interested in the efect generated by a switch to the crisis regime. As already mentioned, the time-invariant nature of the single-state VAR fails to capture a similar efect. herefore, we can isolate and measure the contribution of the correlated information channel through the diference between the values of the IRFs computed under the MSVAR and the single-state VAR frameworks. Because this efect is immediate, we will limit our discussion to the values of the IRFs estimated in the two frameworks to the irst week ater a shock hits within the crisis state.3

6.2 Overall patterns of inancial contagion he results of our impulse response analysis show that a shock to the low-grade ABS market generates signiicant and persistent efects on the ABS (including highly rated ones), Treasury repo, Treasury bond, corporate bond, and stock markets. his applies to both yields and yield spreads. Contagion is captured both by the single-state VAR and by the MSVAR empirical exercises. However, due to the introduction of regimes in the model, a MSVAR framework is presumed to be able to provide more accurate results than a time-invariant single-state VAR. In particular First, the regime-dependent IRFs that we obtain from the MSVAR framework are substantially diferent in the three regimes (low-volatility, high-volatility, and crisis regimes). Figures 6.1 and 6.2 show that the magnitude, the patterns, and in some cases the signs of the efects change according to the initial regime. For instance, in Figure 6.1 we observe DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



that for the ABS AAA yield, the repo rate, and the one-month Treasury yield, the values of the IRFs are approximately zero in the low-volatility and high-volatility regimes, whereas they show an efect signiicantly diferent from zero in the crisis regime. Moreover, the (absolute value of the) efects in the crisis regime are always of larger magnitude than those in the other regimes. In particular, the MSVAR framework uncovers an important pattern: inancial contagion mainly occurs during inancial Low-volatility

Crisis

High-volatility

ABS AAA yield

Basis points

0 –2 –4 –6 –8 –10

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

17

19

21

23

25

17

19

21

23

25

ABS AA–BBB yield

Basis points

40 30 20 10 0

1

3

5

7

9

11

13 15 Periods Repo rate

2 Basis points

0 –2 –4 –6 –8

1

3

5

7

9

11

13 15 Periods

One month Treasury yield

Ten year Treasury yield

Basis points

Basis points

3 0 –3 –6

1

3

5

7

9 11 13 15 17 19 21 23 25 Periods

1 –2 –5

1

3

5

7

9 11 13 15 17 19 21 23 25 Periods

Figure 6.1 MSVAR-yield impulse response functions to a shock to the ABS AA–BBB series DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks Low-volatility

Crisis

High-volatility

Non-investment grade short-term yield

Basis points

0 –20 –40 –60 –80

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

19

21

23

25

19

21

23

25

Investment grade short-term yield

Basis points

4 0 –4 –8 –12

1

3

5

7

9

11

13 15 Periods

17

Investment grade long-term yield

Basis points

1 –1 –3 –5

1

3

5

7

9

11

13 15 Periods

17

Non-investment grade long-term yield

Basis points

25 15 5 –5 –15

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

17

19

21

23

25

Dividend yield

Basis points

3 1 –1 –3

Figure 6.1

1

3

5

7

9

11

13 15 Periods

Continued

DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



crises, while non-crisis regimes are subject to weak efects (see, for example, Guo, Chen, and Huang, 2011). his is not as obvious as it may seem, because at one point in time large shocks may hit one speciic market even though the system is not initially in a crisis regime. Of course, such shocks may rapidly plunge the system into a state of crisis.4 Second, the estimates of the IRFs that we obtain from the single-state VAR model are simply similar to those estimated in the low-volatility and high-volatility regimes in the MSVAR. his means that a single-state VAR fails to capture the magnitude of contagion efects during periods of crisis. his

Basis points

ABS AAA yield 5 4 3 2 1 0 –1

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

17

19

21

23

25

17

19

21

23

25

ABS AA–BBB yield

Basis points

20 15 10 5 0

1

3

5

7

9

11

13 15 Periods Repo rate

Basis points

0 –2 –4 –6

1

3

5

7

9

11

13 15 Periods

One month Treasury yield

Ten year Treasury yield 3 Basis points

Basis points

0 –2 –4 –6

1

3

Figure 6.2 series

5

7

9 11 13 15 17 19 21 23 25 Periods

2 1 0 –1

1

3

5

7

9 11 13 15 17 19 21 23 25 Periods

VAR-yield impulse response functions to a shock to the ABS AA–BBB

DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks Investment grade short-term yield 4 Basis points

3 2 1 0 –1

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

19

21

23

25

21

23

25

Investment grade long-term yield 4 Basis points

3 2 1 0 –1

1

3

5

7

9

11

13 15 Periods

17

Non-investment grade short-term yield

Basis points

20 0 –20 –40

1

3

5

7

9

11

13 15 Periods

17

19

Non-investment grade long-term yield

Basis points

15 5 –5 –15

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

17

19

21

23

25

Dividend yield

Basis points

2 1 0 –1

Figure 6.2

1

3

5

7

9

11

13 15 Periods

Continued

DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



makes sense, because the single-state nature of a simple VAR forces it to measure purely average efects, which may, however, severely bias the economic implications derived from the analysis. In particular, in Figure 6.1 it is clear that in the crisis regime, a onestandard deviation shock to low-grade ABS produces important and statistically signiicant efects on non-investment grade, long-term corporate bonds, whose yields are altered by at least 10 bps for up to three months ater the shock. his occurs in the direction one would expect in the presence of contagion – their yields are pushed up. Also, equity valuations decline, although to a modest extent, as shown by the fact that the dividend yield declines by a few basis points only. Of course, efects on low-grade ABS yields are strongly persistent: three months ater the shock, the increase in yields still exceeds 30 bps, and it is highly statistically signiicant. Such efects are absent in the single-state, VAR-yielddriven IRFs depicted in Figure 6.2, when, apart from some persistency of the shock to the low-grade ABS yields themselves, no other efects are large or statistically signiicant. Finally, Figure 6.1 shows that with a few exceptions, no economically large or precisely estimated impacts from an ABS shock may be detected in the two non-crisis regimes.5 Of course, a one-standard deviation shock is completely arbitrary, just corresponding to the economic notion of a “non-negligible” shock. During the actual subprime crisis, several shocks occurred, possibly with an overall size exceeding the one we have imputed here. Our goal is, then, not to assess the precise extent of markets’ reactions, but to track the qualitative efects of the shock and to evaluate their statistical signiicance. he MSVAR framework also provides evidence of an increase in volatilities and correlations in the crisis regime relative to the low-volatility and high-volatility regimes. he values shown in Tables 5.2 and 5.3 refer to the yield model and spread model, respectively. For example, considering the results from the MSVAR-yield model, Table 5.2 shows that the volatility of the ABS AA–BBB series in the low-volatility regime is 5.3 bps, while in the crisis regime it is 147 bps. he diference is also marked for the non-investment grade short-term series. In this case, the estimate of the volatility in the low-volatility regime is 17.5 bps, whereas in the crisis regime it is 132. he results from the MSVAR-spread model capture, instead, noticeable changes in the value of the correlations across the three regimes. For example, Table 5.3 shows that in the low-volatility regime, the pairwise correlations of the ABS AA–BBB with the investment grade short-term corporate bond and the dividend yield spread DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks

series are 0.007 and 0.004, respectively. In the crisis regime, instead, the correlations are 0.27 and 0.24, respectively. his inding is consistent with a large part of the literature that has extensively discussed the increase in volatilities and correlations among inancial returns that occur in periods of crisis (see, for example, King and Wadhwani, 1990; Baig and Goldfajn, 1998; Longin and Solnik, 2001; Ang and Chen, 2002; Ang and Timmermann, 2011; Guidolin and Timmermann, 2006).

6.3 he liquidity channel As already discussed, in a light-to-liquidity, following a shock to one market, investors prefer to hold highly liquid securities (see, for example, Beber, Brandt, and Kavajecz, 2009; Vayanos, 2004). his leads to an increase in the value of liquid instruments and a contemporaneous decrease in the liquidity of the other assets. As previously mentioned, we study the efects generated by a shock to the ABS AA–BBB yield series on the Treasury GC overnight repo rate, the one-month Treasury yield, and the ten-year Treasury yield. his analysis refers to the IRFs computed from the MSVAR-yield model as shown in Figure 6.1. In the crisis regime, a positive shock to the ABS AA–BBB yield generates a similarly sized, of modest magnitude (approximately 3 bps), negative efect on all the three series under examination. As for the repo rate and the one-month Treasury yield, the IRF declines steadily but slowly, and remains statistically signiicant for almost all the 26 weeks we consider. For the ten-year Treasury yield, the efect starts decreasing ater week 11 and assumes a value close to zero by the last period. However, the efect remains statistically signiicant until week 17. In the high-volatility regime, the positive shock to the ABS AA–BBB yield generates weak contagion efects. he value of the IRF is positive for the repo rate and the one-month Treasury yield (around one bp in Period 1), while it is negative and roughly equal to 1 bp in the case of the ten-year Treasury yield. For the three yield series under investigation, the efects are statistically signiicant up to Periods 4–6. Similarly, in the low-volatility regime the contagion efect produced by the shock is also of modest-to-zero magnitude. he IRFs of the repo rate and the one-month Treasury yield are nearly zero and, in fact, slightly negative, whereas the IRF for the ten-year Treasury yield is positive and of approximately 2.5 bps. hese efects remain stable and statistically signiicant over all the 26 periods under investigation. DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



he results of our analysis show that, while in the crisis regime a shock to the lower-grade ABS yield generates a noticeable downward pressure on the Treasury yields, in the other regimes the efects are negligible. his inding conirms that during the subprime crisis, a light-to-liquidity channel of contagion was active. In fact, on the basis of Figures 5.1–5.2, recall that most of the August 2007–June 2009 sample is captured by the crisis state. he irst explanation for the high demand of Treasuries in periods of inancial crisis that emerges from our results is the eagerness of institutional investors to hold highly liquid instruments, which can be easily sold when market conditions turn severely distressed. Moreover, the recent subprime crisis has uncovered another reason that drives similar episodes: the use of Treasuries as securities to be pledged in the collateralized lending market (see Hördahl and King, 2008; Hrung and Seligman, 2011). Ater a negative shock to lower-grade ABS, lenders in the repo market signiicantly increased the margins required on any category of collateral except Treasuries (see Gorton, 2010). Other inancial assets were accepted at disadvantageous conditions because of their low liquidity. In particular, lenders were uncertain about their ability to quickly turn into cash any other asset than Treasuries by disinvesting it in case of default of the counterparty in repo transactions (see, for example, Adrian, Begalle, Copeland, and Martin, 2011). herefore, as happened following a shock to the ABS market that actually occurred in summer 2007, repo transactions quickly became conined only to short-term borrowings against Treasury bonds. As a result, the demand for these instruments signiicantly increased, their price followed in an upward direction, and the corresponding yields fell. his is fully consistent with the crisis-regime IRFs in Figure 6.1. he negative efect observed in the crisis regime on the Treasury repo rate provides further conirmation that during the subprime crisis, contagion in inancial markets also (not exclusively) occurred through the light-to-liquidity channel. In particular, the value of the IRF of Treasury repo rates shows that the yield required by lenders to lend against Treasury notes actually decreased ater the shock to the ABS market that allegedly triggered the inancial crisis and that represents the shock underlying Figure 6.1. A lower repo compensation required by lenders in a period of inancial crisis may appear surprising if one considers that investors’ willingness to lend usually decreases in periods of crisis. However, this negative efect on the Treasury repo inds an explanation in the fact that transactions in the repo market may suddenly be DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks

security-driven (Hördahl and King, 2008), that is, motivated by the demand for a speciic security. It is possible that the negative value of the IRF for this category of asset may be driven by the investors’ high demand for Treasuries during the subprime crisis. In particular, repos became a means to borrow Treasury bonds, which were scarce in the market, and this drove repo rates to values signiicantly lower than before the crisis.

6.4 he risk premium and light-to-quality channels According to the risk premium channel story, contagion occurs because shocks to one market lead to a generalized increase in investors’ risk aversion. his generates an upward adjustment of the risk premium of all assets. Consequently, all assets are subject to a loss of value (see, for example, Vayanos, 2004; Kyle and Xiong, 2001). In the light-to-quality channel, instead, contagion occurs because investors try to sell assets perceived as risky and purchase safe assets (see, for example, Caballero and Kurlat, 2008). his generates an increase in the risk premium on the riskiest products, while that on the safest ones declines. As already discussed, to separately identify these channels, we study the IRFs of the spread on the ABS AAA yield, on corporate bond yields, and on the dividend yield generated by a positive shock to the ABS AA–BBB yieldspread, to mimic the onset of the 2007 subprime crisis.6 he IRFs are plotted in Figure 6.3. As for the investment grade corporate bond market, in the crisis regime, the shock to the ABS AA–BBB spread series generates a positive efect on the yield spreads of both the short- and long-term series. he efect on the spread of the short-term series is 4 bps in Period 1 and decreases in the following periods. he reaction turns negative but statistically insigniicant ater Period 8. Similarly, the IRF of the spread of the long-term series is 4 bps in Period 1, but it slightly increases in the following periods and assumes a value of nearly 6 bps in Period 26. However, this IRF is not statistically signiicant ater week 19. In the high-volatility regime, the efect on the spread of the short-term corporates is negative (even though only by 1 bp). his efect remains stable and signiicant in all the following periods. In contrast, the efect on long-term corporate spreads is positive; it is nearly zero in Period 1 and slowly increases to reach approximately 3 bps by the last period. his DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels Low-volatility

Crisis

High-volatility

ABS AAA yield 6

Basis points

4 2 0 –2 –4 –6 –8

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

17

19

21

23

25

17

19

21

23

25

19

21

23

25

ABS AA–BBB yield 45

Basis points

35 25 15 5 –5

1

3

5

7

9

11

13 15 Periods Repo rate

4

Basis points

3 2 1 0 –1 –2 –3

1

3

5

7

9

11

13 15 Periods

Ten year Treasury yield 10

Basis points

8 6 4 2 0 –2

1

3

5

7

9

11

13 15 Periods

17

Figure 6.3 MSVAR-spread impulse response functions to a shock to the ABS AA–BBB series

DOI: 10.1057/9781137561398.0010





Transmission Channels of Financial Shocks Low-volatility

Crisis

High-volatility

Investment grade short-term yield 5 Basis points

3 1 –1 –3 –5 –7

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

19

21

23

25

21

23

25

Investment grade long-term yield

Basis points

12 10 8 6 4 2 0 –2

1

3

5

7

9

11

13 15 Periods

17

Basis points

Non-investment grade short-term yield 10 –10 –30 –50 –70 –90 –110 –130

1

3

5

7

9

11

13 15 Periods

17

19

Basis points

Non-investment grade long-term yield 27 22 17 12 7 2 –3 –8

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

17

19

21

23

25

Dividend yield 23 Basis points

18 13 8 3 –2

Figure 6.3

1

3

5

7

9

11

13 15 Periods

Continued

DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



efect remains statistically signiicant over the 26 weeks under investigation. In the low-volatility regime, the value of the IRF computed for the short-term investment grade series is positive, but barely reaches 1 bp, and it fails to be signiicant ater Period 13. For the long-term spreads, the efect generated by the shock under examination is positive and approximately of 2 bps. he response remains stable and signiicant in the 26 periods. hese results reveal that a positive shock to the ABS low-grade spread generates efects on the spreads of the investment grade corporate bonds that are positive and noticeable in the crisis regime. In contrast, in the other regimes, we observe only weak contagion efects. his inding conirms that during the subprime crisis, the negative efects triggered by the shock to the ABS market were also transmitted to the corporate bond market through a risk premium channel.7 his result is not completely surprising if one thinks about the episodes that characterized the subprime crisis. Gorton (2010) comments that following an initial shock to the ABS market, the investment grade corporate bonds were subject to immediate losses of value. his was not due to a deterioration in the quality of the assets, but, rather, to an increase in the risk aversion of lenders in the repo market, which were no longer willing to accept assets other than Treasuries as a collateral to their transactions. As discussed before, this quickly reduced the availability of funds for inancial institutions. In an attempt to meet their inancing needs, inancial institutions executed massive sales of highly rated corporate bonds, and this placed an upward pressure on corporate bond spreads that was not related to the deterioration of fundamentals and quality of these bonds. herefore, the upward pressure on corporate bond spreads occurred for two reasons: the increase in the risk aversion of lenders in the repo market, who started accepting these assets at disadvantageous conditions, and the increase in the risk aversion of investors, who were reluctant to acquire in the market assets other than Treasuries. In the case of the investment grade short-term corporate bonds, our results imply the possibility that ater a few periods, the efect of a low-grade ABS yield shock may become negative over the simulation horizon. In particular, the IRF turns negative, even though not statistically signiicant, ater eight periods. Moreover, if we move back from the MSVAR-spread to the MSVAR-yield model (Figure 6.1), we observe that

DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks

the efect on the yield of this asset class generated by a positive shock to the ABS AA–BBB yield is initially positive but assumes a negative value ater Period 7.8 herefore, the MSVAR-yield and MSVAR-spread models jointly indicate that ater a few periods, the values of the yield and of the spread are lower than what we would observe in the absence of the shock. hese indings reveal the possibility that ater a certain number of weeks, a light-to-quality phenomenon may occur in the investment grade short-term corporate bond market. his means that, while in the irst few months ater a shock investors react by also selling high-quality corporate paper, gradually, as the price of Treasuries climbs and their yield moves down towards zero, the search for yield brings investors at least back to purchasing short-term corporate bonds. In the existing literature, several studies discuss light-to-quality episodes that involve an increase in demand of corporate bonds relative to stocks (see, for example, Caballero and Kurlat, 2008; Gonzalo and Olmo, 2005; Baur and Lucey, 2010). In particular, Caballero and Kurlat (2008) describe the light-to-quality phenomenon that occurred in the months following the shock to the ABS market during the subprime crisis, which became particularly intense in the second half of 2007. Our model reveals the possibility of a light-to-quality efect uniquely for the short-term corporate bond market, while in the case of the longterm corporate spreads, the impact of a subprime-style shock remains positive over 26 weeks (but signiicant only up to week 19). A similar result is obtained by Gonzalo and Olmo (2005), who show that during a inancial crisis a light-to-quality efect from the stock to the bond market occurs uniquely for short-term corporate bonds, and not for long-term ones. As far as non-investment grade corporate bonds are concerned, Figure 6.3 shows that the shock to the spread of the lower-grade ABS series generates an efect on the spread of the non-investment grade short-term class that is negative and statistically signiicant in both the high-volatility and crisis regimes. In both cases, the value of the IRF is increasingly negative across the 26 periods; by the last week of the impulse-response exercise, it reaches approximately 20 bps in the highvolatility regime and 90 bps in the crisis regime. In the low-volatility regime, the efect is nearly zero over all periods. In contrast, a shock to the low-grade ABS spread generates an immediate, positive efect on the spread of the non-investment grade long-term corporate bonds in both

DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



the high-volatility and the crisis regime. In the regime of high volatility, the value of the IRF is roughly 5 bps, and rapidly decreases, assuming negative values by Period 9. In the crisis regime, the value of the IRF is 25 bps in Period 1; aterwards, the recorded response slowly decreases and reaches 10 bps by the last week under simulation. Similarly to the short-term rates, in this case also the efect of a shock in the low-volatility regime is nearly zero. he analysis of the non-investment grade corporate bond market shows that only long-term bonds are subject to contagion efects through the risk premium channel.9 In contrast, the spread on short-term bonds decreases, and as a result, it converges towards values that are lower than those we would observe in the absence of the initial shock. A irst reason for a negative efect on the short-term low-quality paper spreads lies in the dynamics that afects the high-yield corporate bond market in times of inancial turmoil. In particular, we expect the worst companies in the non-investment grade class to be the irst to default, while the surviving companies will be those of higher quality, in relative terms.10 hus, ater a shock, the non-investment grade class will gradually contain a declining number of companies, but with proportionally higher credit standings, within each selected bracket, either because the issuers withstand the impact of the crisis, or because the issuers enter the bracket because of downgrades from initial, high-quality standings. Because of the increasing proportion of high-grade companies in the class, both yields (see Figure 6.1) and spreads (see Figure 6.3) on the short-term non-investment grade class may shrink.11 A second rationale for the empirical results concerning low-grade short-term corporates lies in the portfolio strategies favored by speculative investors during inancial crises. his is complementary to the previous account, and it may explain why we observe efects of opposite sign for short- and long-term series. High-yield bonds are mainly held by hedge funds, while institutional investors are oten not allowed to invest in this asset class. It is plausible that speculative investors hold in their portfolios a certain number of non-investment grade short-term and long-term corporate bonds that matches their desired level of credit risk exposure. When a shock to the ABS market occurs, speculative investors sufer losses and consequently need to liquidate their positions. herefore, they re-balance their portfolios towards safer assets and assets with lower duration.12 In particular, a low duration allows fund managers

DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks

to reduce the exposure of their portfolios to losses generated by a sudden increase in the level of (risky) yields. We therefore expect that, in order to achieve higher returns, speculative investors may keep holding risky assets such as non-investment grade bonds, but with a lower duration (that is, relatively short-term) to reduce the risk of losses generated by changes in yields. his leads to a negative pressure on the yields and spreads of non-investment grade short-term corporate bonds relative to long-term ones, which instead tend to increase. In the case of the stock market, Figure 6.3 shows that in the crisis regime a shock to low-grade ABS spreads generates a signiicant and positive efect on the dividend yield spread. In Period 1, the estimated IRF is 10 bps, and a further increase occurs in the subsequent periods (it reaches 15 bps by week 26). Moreover, the efect remains statistically signiicant over the 26 weeks. In the regime of high volatility, the efect is positive but of smaller magnitude than in the crisis regime. he IRF has a value of 1 bp and slowly increases to assume a value of approximately 5 bps by the last week. he efect is signiicant over all the 26 weeks. In contrast, in the low-volatility regime the IRF assumes a negative value. However, the magnitude of the efect is small (1 bp in the irst period, declining towards zero over time). he irst inding revealed by the study of the stock market is that, following a shock to the ABS market, a signiicant contagion occurs in the crisis regime, whereas in the high-volatility regime we observe only weak responses. his means that during the subprime crisis, contagion was transmitted to the stock market through the risk premium channel. It is interesting, but not surprising, that contagion takes place but is not particularly severe, given that our study simulates the shock to the ABS market that occurred in the irst half of 2007, while severe disruptions in the stock markets arose in 2008–09. All in all, shocks to credit markets spill over to stock markets through a risk premium channel, but rather slowly and to a moderate extent. he last market we analyze in this framework is the high-grade ABS market (ABS AAA). In this case, the value of the IRF turns out not to be statistically signiicant in all the 26 periods and across the three regimes.13 his result is rather interesting, because, given the close relationship between this asset class and low-grade ABS, we would expect an immediate increase in the risk premium of this asset class. However, our study reveals that during the subprime crisis the ABS AAA class was

DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



not afected through the risk premium channel, although, as we have discussed, other channels were in motion that led to the empirical results in Figure 6.1. To conclude, it is important to emphasize that the efects generated by a negative shock to the ABS market on the spreads of the remaining series are generally driven by two opposite forces. he irst driver is the positive efect on yields due to an increase in risk aversion. he second one is the negative efect on Treasury yields, which is not associated with a contemporaneous downward adjustment of the overall level of yields.14 herefore, part of the efect on the spread series is trivially explained by the downward pressure on the one-month Treasury yield, which follows a shock to the ABS market. To better understand the balance between these two efects, we now provide some examples of comparisons between the efects observed in the crisis regime in the MSVAR-spread model and the efect on the one-month Treasury yield. Figure 6.1 shows that the negative efect on the one-month Treasury yield in the MSVAR-yield model is approximately 3 bps and remains stable over the 26 periods. he efect on the high-grade corporate bond spread series shown in Figure 6.3 is, instead, approximately 4 bps (in Period 1). his reveals that – at least in this case – the efect on the spread is mainly explained by the downward pressure on the Treasury yield. In contrast, for the non-investment grade long-term corporate class, the efect on the credit spread is 25 bps (in Period 1); therefore, the efect on the one-month Treasury yield makes a small contribution to the total contagion efect. Similarly, for the dividend yield, we observe an impact on the spread (10 bps in Period 1) that is larger than that on the one-month Treasury yield. For completeness, Figure 6.4 shows plots of the IRFs obtained for the VAR-spread case, that is, when the model is misspeciied to include one single regime. In fact, the point of Figure 6.4 is that there is, in fact, nothing or very little to be seen or commented on. A few IRFs are not only economically negligible, but also statistically insigniicant, and therefore they cannot be distinguished from a zero, that is, the complete absence of a response. his is the case for all non-investment grade corporate spreads and repo rates. Other responses are precisely estimated; they carry the expected sign (positive, consistently with a risk premium channel), but are economically tiny. his is the case for investment-grade corporate and equity spreads, which increase by a few bp only ater a subprime-type shock to relatively low-grade ABS.

DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks ABS AAA yield

Basis points

8 6 4 2 0

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

17

19

21

23

25

17

19

21

23

25

17

19

21

23

25

19

21

23

25

ABS AA–BBB yield

Basis points

20 15 10 5 0

1

3

5

7

9

11

13 15 Periods Repo rate

4 Basis points

3 2 1 0 –1 –2

1

3

5

7

9

11

13 15 Periods

Ten year Treasury

Basis points

7 5 3 1 –1

1

3

5

7

9

11

13 15 Periods

Investment grade short-term yield

Basis points

7 5 3 1 –1

1

3

5

7

9

11

13 15 Periods

17

Figure 6.4 VAR-spread impulse response functions to a shock to the ABS AA–BBB series

DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



Investment grade long-term yield

Basis points

7 5 3 1

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

21

23

25

Non-investment grade short-term yield

Basis points

30 10 –10 –30

1

3

5

7

9

11

13 15 Periods

17

19

Non-investment grade long-term yield

Basis points

15 10 5 0 –5 –10 –15

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

17

19

21

23

25

Dividend yield

Basis points

6 4 2 0

Figure 6.4

1

3

5

7

9

11

13 15 Periods

Continued

6.5 he correlated information channel As we have discussed in Chapter 1, under the correlated information channel, contagion occurs because a negative shock to one market immediately provides information that investors perceive as relevant DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks

for the pricing of other assets. herefore, the prices in other markets immediately adjust downward. As mentioned above, we investigate this channel by comparing the IRFs in the crisis regime for the MSVAR-yield model with those observed in the single-state VAR-yield for Period 1, that is, in the immediate atermath of a shock. In practice, to investigate this last contagion channel, we compare the IRFs presented in Figures 6.1 and 6.2. In the case of the one-month Treasury yield, the efect is negative and roughly 3 bps in the MSVARyield model, while it is 1.5 bps in the single-state VAR. herefore, a small portion of the contagion efect on this asset is due to the correlated information channel. Similar conclusions can be drawn for the repo rate. For the ten-year Treasury yield, the efect is negative and roughly 3 bps in the MSVAR framework, while it is positive, but not statistically signiicant, in the single-state VAR framework. herefore, for the tenyear Treasury yield, the analysis reveals a noticeable contribution of the correlated information channel. As for investment grade corporate bonds, there is a small diference between the responses obtained in the two frameworks for both the short- and the long-term yield series. In particular, for investment grade short-term corporate bonds, the positive shock to the ABS lowergrade yield generates a positive efect of 4 bps on the yield series in the MSVAR, and 1.5 bps in the single-state VAR. For the investment grade long-term corporate bonds, the efect is positive and equal to 1.8 bps in the MSVAR-yield and 1.5 bps in the single-state VAR. his result reveals that during the subprime crisis, the investment grade short-term corporate bond market was subject to contagion efects through the correlated information channel, while the contribution of this channel for the longterm bonds was roughly zero. In the case of the non-investment grade corporate bond market, the IRFs of both the short-term and long-term series in the single-state VAR model have a value in Period 1 that is not statistically signiicant. In contrast, in the MSVAR model, the efect is positive and close to 2 bps for the short-term series, while it is positive and equal to 22 bps for the long-term series. herefore, for the non-investment grade long-term series, we ind that a large portion of the immediate positive efect on the yield generated by the shock to the lower-grade ABS market is due to the correlated information channel. In contrast, we fail to detect a noticeable efect of this channel on the short-term

DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



non-investment grade series. his is economically sensible: many speculative investors are likely to perceive low-quality credit and ABS investments as homogeneous asset classes, so that poor news concerning the prospects of the latter is likely to be interpreted as being informative of the state of the economy afecting the merit of credit of “junk” corporate bonds. In the case of dividend yield, the efect is positive and of similar magnitude in the two frameworks. In particular, in the MSVAR, the value of the IRF in Period 1 is 3 bps, whereas in the single-state VAR it is approximately 1 bp. herefore, our analysis shows that the correlated information channel slightly contributes to the immediate contagion efect generated by a negative shock to the lower-grade ABS AA–BBB market. As for the high-grade ABS market, in both frameworks the value of the IRF in Period 1 is null, and thus any responses occur with a lag. herefore, we ind that during the sub-prime crisis, contagion within diferent rating ABS buckets could not have been triggered by the correlated information channel. his inding is important: it is not the fast spreading of news compounded into rational prices by eicient markets that accounts for the spillovers from the low-grade ABS market to the investment grade that explain the events of the 2007 crisis. Finally, it is worth noting that the analysis carried out up to this point on the ABS AAA market reveals additional indings of some relevance. First, neither the risk premium nor the correlated information channel is accountable for any contagion efects in this market. his is rather interesting, because given the close relationship between the investment grade ABS segment and the market where the shock is simulated to occur (lower-grade ABS), we would expect to observe a positive contribution of both channels. Second, in Figure 6.1, we observe that in the MSVAR-yield model the value of the IRF is negative and statistically signiicant ater week 7. Moreover, the magnitude of the efect tends to slowly grow over time (the value of the IRF is nearly 4 bps by week 26). As discussed in Section 6.4, even if it may seem puzzling at irst glance, the negative efect generated by a shock to the lower-grade ABS market on the ABS AAA yield series does not represent a surprising result if one considers the credit rating crisis that hit the ABS market at the end of 2007 (see, for example, Gorton, 2010; Agarwal, Barrett, Cun, and De Nardi, 2010).15

DOI: 10.1057/9781137561398.0010



Transmission Channels of Financial Shocks

Notes 1 A repo transaction can take two diferent conigurations according to the goals of an investor: it can be either cash- or security-driven. In the former case, the repo contract is motivated by the desire to borrow funds; in the latter case, the purpose is to borrow a speciic security through the repo (Hrung and Seligman, 2011). 2 We compute the spread of our inancial variables as the diference between their yields and the one-month Treasury yield, and interpret it as the (ex-ante) risk premium required by investors on these types of securities. 3 he Cholesky ordering that we impose in our exercise is the natural one that puts the riskiest markets on top (that is, ABS lower-rated, BBB corporate paper, and stocks) and more liquid, less risky assets at the bottom of the ordering. However, our results proved to be qualitatively robust to many types of ordering. 4 In this case, an analyst may want to limit her use of our results to investigate only the few weeks immediately ater a shock is simulated, starting from a non-crisis regime. 5 Apart from a modest increase in ten-year Treasury yields, this is the case with the low-volatility state. In the high-volatility regime, there are some visible efects on low-grade corporate yields, including a negative efect on short-term corporate yields, which are discussed in detail later in the chapter. 6 Any efects on the spreads are due to two forces. he irst is the positive efect on the yields of the series generated by the shock. he second is due to the negative efect generated by the shock to the ABS lower-grade series on the Treasury yields. his is discussed later in the chapter. 7 Also, the fact that the efects we observe on the credit spreads of high-grade corporate bonds are similar to those in Figure 6.1 (from the MSVAR-yield model) supports this hypothesis. herefore, the efects on the yields are mainly driven by the efects on the spreads. 8 he value of the IRF is not statistically signiicant in Periods 7–11. It is again signiicant ater week 12. 9 Similarly to the case of high-grade corporate bonds, the efect on the yields in the MSVAR-yield model in Figure 6.1 is almost identical to the spread series. his conirms that the risk premium contagion channel afects the long term corporate bond series. 10 It may be instructive to provide some igures to give an idea of the magnitude of the credit rating crisis. Prior to the crisis, more than half of the structured inance securities rated by Moody’s had a credit rating of AAA. Following the events of 2007–08, almost 40,000 Moody’s rated tranches were downgraded, of which approximately one third bore the AAA rating (see Agarwal, Barrett, Cun, and De Nardi, 2010). DOI: 10.1057/9781137561398.0010

Estimating and Disentangling the Contagion Channels



11 he long-term non-investment grade class is not subject to a similar efect, because among the irms with the same credit rating in the non-investment grade cluster, the safer ones tend to issue long-term bonds (see Helwege and Turner, 1998). herefore, the long-term non-investment grade cluster includes companies of higher quality than those contained in the short-term class, which therefore are less subject to defaults during inancial crises. 12 A strategy consisting in a long position in short duration assets and in a short position in long duration assets is known as a short duration strategy. hese are typically implemented in periods of high volatility to reduce the exposure of a portfolio to sudden increases in interest rates. 13 A similar efect is observed for the ABS AAA yield series in the MSVARyield model in the regime of low volatility. In the regimes of high volatility and crisis, the efect is instead negative and signiicant. 14 A negative shock to Treasury yields that is not contemporaneous with an increase in risk aversion should leave the level of spreads unchanged and thus lead to a decrease in the level of yields on risky assets in the economy. 15 Given the complex nature of securitized products, the valuation of this asset class was mainly driven by their credit rating. he instability generated by valuations shocks to the low-grade ABS market revealed the inadequacy of the pricing models applied by rating agencies, thus generating uncertainty about the real value of these assets.

DOI: 10.1057/9781137561398.0010

7

Comparing the US and European Contagion Experiences Abstract: In this chapter, we extend our work to European data, addressing two key questions. First, we investigate whether contagion channels similar to the ones observed in the US subprime crisis were also active during the European sovereign crisis. Second, we assess whether, in addition to cross-market contagion, there is evidence of cross-country contagion from US to Europe during the 2007–09 inancial crisis, that is, whether shocks to low-grade ABS did spill over to European ixed income and equity markets, and through which channels. Keywords: contagion channels; European inancial markets; sovereign crisis Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model. Basingstoke: Palgrave Macmillan, 2016. doi: 10.1057/9781137561398.0011.



DOI: 10.1057/9781137561398.0011

Comparing the US and European Contagion Experiences



his chapter extends our empirical work so far in this book on contagion channels based on US data from the subprime, 2007–09 crisis to encompass European data and test the existence and strength of similar channels with reference to both the 2008–09 Great Financial Crisis and the 2010–11 European sovereign crisis. Even though our data are adapted to take into account the speciic nature of the European sovereign-driven hardships, when possible we try to preserve the same series analyzed in Chapters 2–6. In particular, we also perform tests of whether shocks to low-grade ABS did spill over to European ixed income and equity markets, and through which channels. Because it is impossible for us to follow exactly and in detail the same steps as in Chapters 3–6 with reference to new data, this chapter is based on a sequence of short sections that document only key facts and indings in a compact fashion.1

7.1

A European data set

We collected weekly data for a March 23, 2007–December 19, 2014 sample. Similarly to the US case, these data concern sovereign bond, corporate bond, ABS, repo, and stock market (Euro STOXX 600) yields. he sovereign bond yields are collected in two equally weighted portfolios concerning core vs. periphery/low-quality (high credit risk) countries, respectively. he yields concern ten-year government bonds. he core countries are Austria, Belgium, France, Finland, Germany, and the Netherlands. he periphery (in an economic as well as a geographic sense) consists of Portugal, Ireland, Italy, Greece, and Spain (henceforth, abbreviated as PIIGS). he repo rate has a deinition similar to that illustrated in Chapter 3, but in this case it concerns long-term German Bunds. When needed, the repo rate has been used as a euro-denominate riskless rate. Corporate bonds data are prepared by Bank of America (BofA) Merrill Lynch and concern high-quality (Aaa) short vs. long (ten-year) portfolios and low-quality (Bbb) short vs. long (ten-year) European Monetary Union (EMU) corporate portfolios, for a total of eight diferent asset classes.2 One of the analyses that follow is also based on high- vs. low-credit quality US-issued ABS, of which we measure the yields. As in the previous chapters, equity market data are converted into trailing three-month dividend yields in standard ways. Table 7.1 reports summary statistics in panel A and sample correlations in panel B. Data fail to show any surprising features: PIIGS yields are DOI: 10.1057/9781137561398.0011



Transmission Channels of Financial Shocks

on average much higher (6.37 per cent) than core sovereign yields, even though this spread relects periods (2007–09 and 2013–14) that are not afected by the sovereign crisis. his implies that during the crisis, spreads between PIIGS and core yields climbed even higher, beyond the 324 bps that Table 7.1 implies on average (for example, the maximum yield of the PIIGS portfolio is 15.25 per cent). Peripheral government bond yields are also characterized by a volatility that is almost three times larger than for core yields. High-quality corporate bonds always yield on average in excess of low-quality ones, for both short-term (4.64 per cent vs. 2.65 per cent) and long-term securities (5.39 per cent vs. 3.80 per cent), and these diferences in mean yields are also matched by corresponding diferences in volatilities. he European (STOXX 600) dividend yield is considerably higher (3.77 per cent) than the US one (1.92 per cent). All series are characterized by pervasive non-normalities, although in this case more on account of the widespread right-skewness of the data than on their fat tails. As discussed in Chapter 3, this is consistent with the possibility of the data containing regime shits. Finally, in Panel B of Figure 7.1, we can see that most series are positively and signiicantly correlated with each other, with the only exception being PIIGS rates, which seem to follow a process of their own and, in particular, to negatively correlate with investment grade corporate yields, and the repo rate, that is, with the highest-quality assets. his may represent an early indication of light-to-quality efects.

7.2 Alternative channels of contagion in the European sovereign crisis We start our analysis by asking whether, in the face of the peripheral sovereign yield shocks recorded during 2010 and 2011 in Europe, contagion channels similar to the ones that we have characterized in Chapters 1 (theoretically) and 4–6 (empirically) were also active in Europe. A positive inding would validate the notion that the four channels isolated early on (and in the work by Longstaf, 2010) represent a general structural feature of the way inancial systems absorb and propagate shocks. Note that our investigation concerns the same spillover channels, presumably triggered in Europe by an alternative shock (a PIIGS sovereign debt crisis) and over a slightly diferent period, which follows the Great Financial Crisis properly deined.3 DOI: 10.1057/9781137561398.0011

DOI: 10.1057/9781137561398.0011

Table 7.1

Summary statistics for European bond and stock yields

Key summary statistics for weekly yield series over the sample period March 23, 2007–December 19, 2014. he data are expressed in terms of annualized nominal yields. For instance, 1.00 stands for 1.00%. Jarque–Bera is a test statistic used to assess whether a series is normally distributed; asterisks denote statistical signiicance at conventional levels. EW stands for “equally weighted.” Panel A: Summary statistics

Inv. grade corp. ST Inv. grade corp. LT Non-inv. grade corp. ST Non-inv. grade corp. LT Dividend yield Repo rate (on bunds) EW core sovereign EW PIIGS sovereign

Mean

Max.

Min.

Std. dev.

Skewness

Kurtosis

2.647 3.797 4.639 5.392 3.769 1.104 3.013 6.370

5.823 6.280 9.554 8.498 6.848 4.362 4.834 15.254

0.661 1.569 1.502 2.792 2.835 −0.163 0.765 2.915

1.370 1.106 1.900 1.382 0.775 1.544 1.024 2.958

0.425 −0.133 0.413 0.258 1.814 1.216 −0.166 1.416

1.972 1.940 2.843 2.681 6.183 2.721 1.905 4.084

Jarque–Bera 30.014*** 20.173*** 11.913*** 6.221** 393.1*** 101.2*** 22.092*** 155.2***

Panel B: Correlations

Inv. grade ST Inv. grade LT Non-inv. grade ST Non-inv. grade LT Dividend yield Repo rate (on bunds) EW core sovereign EW PIIGS sovereign

Inv. grade ST

Inv. grade LT

Non-inv. grade ST

1.000 0.940*** 0.796*** 0.791*** 0.490*** 0.883*** 0.953*** −0.266***

1.000 0.853*** 0.860*** 0.492*** 0.712*** 0.949*** −0.233***

1.000 0.989*** 0.769*** 0.526*** 0.789*** 0.053

Non-inv. grade LT

1.000 0.744*** 0.518*** 0.804*** 0.063

Div. yield

Repo rate (on bunds)

EW core sovereign

EW PIIGS sovereign

1.000 0.320*** 0.412*** 0.005

1.000 0.782*** −0.316***

1.000 −0.178**

1.000



Transmission Channels of Financial Shocks

Similarly to our approach to the US case, for the European yield and spread series we estimate a single-state vector autoregressive (VAR) model selected in standard ways, that is, by minimizing classical information criteria. However, no strong evidence of cross-market contagion emerges in this model. However, as argued in Chapter 2, it remains possible that a simpler, single-state model may not display suicient lexibility to capture the strength and patterns of contagion across European markets. Consequently, for the sake of brevity, we do not report the results of this exercise, and proceed to estimate Markov switching VAR (MSVAR) (k,p) models. Similarly to Table 5.1 in Chapter 5, an unreported table indicates that an MSIH(3,1) model (that is, with three regimes but time-invariant VAR matrix) is selected for European ixed income yields. In fact, both the Hannan–Quinn and the Schwarz (SC) criteria imply that an MSIH(3,1) model with 160 parameters and a moderate saturation ratio of 17.7 shows that this model optimally trades of in-sample it with the promise of out-of-sample predictive accuracy. he Akaike information criterion (AIC) points instead towards a more richly parameterized model (258 parameters and a saturation ratio of 11) that, however, appears to lack suicient reliability because of the excessive number of parameters. As one would expect in the light of the literature on the presence of regimes in interest rates (see Guidolin, 2013), the null of a single regime is also always rejected when the issues caused by nuisance parameters are taken into account, using Davies’ (1977) correction of the standard chi-square test. Table 7.2 reports estimated parameters from the MSIH(3,1) model just selected. Interestingly, the regimes have a similar interpretation to the one analyzed in Chapter 5 with reference to US data, and are therefore mostly identiied by the volatility of innovations to yields. However, intercepts are not always diferent across regimes, which indicates – in the presence of a time-invariant matrix of VAR coeicients – that irst moments hardly help in the deinition of states. Yet, unlike in Chapter 5, the three regimes are considerably more persistent than those previously isolated. In particular, the low-volatility regime has a duration of six weeks, and Figure 7.1 shows that it characterizes several periods, but it becomes particularly persistent ater the summer of 2012, when the European sovereign crisis was eventually tackled with force by the European Central Bank (ECB) with measures such as the European Financial Stability Facility (EFSF), the European Stability Mechanism (ESM), and the Securities Market Program (SMP), and ater the end of DOI: 10.1057/9781137561398.0011

Comparing the US and European Contagion Experiences

Table 7.2



Model selection results for Markov switching models of European yields

his table reports the statistics used to select multivariate MSVAR models of the form

yt  *St  £ j 1 A j , St yt j  7S1t/2 et p

et ^ IID N 0, I N .

he speciication search is applied to weekly yield series over the sample period March 23, 2007–December 19, 2014. LR test No. of Saturation Logfor Model (k,p) parameters ratio likelihood linearity Baseline model: Two-state, Markov switching MSI(2,0) 54 60.000 −2245.21 866.9594 (0.000) MSIA(2,1) 182 17.758 2486.385 397.0678 (0.000) MSIA(2,2) 310 10.400 2583.249 403.1568 (0.000) MSIH(2,0) 90 36.000 −1201.57 2954.237 (0.000) MSIH(2,1) 154 20.987 2917.791 1259.881 (0.000) MSIH(2,2) 218 14.789 3005.372 1247.401 (0.000) MSIAH(2,1) 218 14.826 2908.249 1240.797 (0.000) MSIAH(2,2) 346 9.318 2923.372 1083.402 (0.000) Baseline model: hree-state, Markov switching MSI(3,0) 66 49.091 −1700.060 1957.256 (0.000) MSIA(3,1) 258 12.527 2662.209 748.7161 0.000 MSIA(3,2) 450 7.164 2870.205 977.0681 (0.000) MSIH(3,0) 138 23.478 17.090 5391.557 (0.000) MSIH(3,1) 202 16.000 3123.962 1512.223 (0.000) MSIH(3,2) 266 12.120 3136.381 1509.421 (0.000) MSIAH(3,1) 330 9.794 3101.773 1627.844 (0.000) MSIAH(3,2) 522 6.176 3333.459 1903.576 (0.000) Note: *Model selected by the criterion in the header.

DOI: 10.1057/9781137561398.0011

Hannan– Akaike Quinn Schwarz criterion criterion criterion 11.354

11.565

11.888

−11.408

−10.694

−9.605

−11.282

−10.064

−8.206

6.378

6.730

7.268

−13.682

−13.078

−12.157*

−13.833

−12.977

−11.670

−13.318

−12.463

−11.159

−12.791

−11.432

−9.358

8.721

8.980

9.374

−11.902

−10.891

−9.347

−12.011

−10.243

−7.546

0.597

1.137

1.961

−14.269* −13.277* −12.068 −14.245

−13.200

−11.606

−13.722

−12.428

−10.453

−13.953

−11.902

−8.773

Transmission Channels of Financial Shocks

 1.0 0.8 0.6 0.4

Jul-14

Nov-13

Mar-13

Jul-12

Nov-11

Feb-11

Jun-10

Oct-09

Feb-09

Jun-08

Jan-07

0.0

Sep-07

0.2

Low volatility 1.0 0.8 0.6 0.4

Mar-13

Nov-13

Jul-14

Mar-13

Nov-13

Jul-14

Jul-12

Nov-11

Feb-11

Jun-10

Oct-09

Feb-09

Jun-08

Jan-07

0.0

Sep-07

0.2

High volatility 1.0 0.8 0.6 0.4

Jul-12

Nov-11

Feb-11

Jun-10

Oct-09

Feb-09

Jun-08

Jan-07

0.0

Sep-07

0.2

Crisis

Figure 7.1 Smoothed probabilities estimated from an MSIH(3,0) model for European yields

DOI: 10.1057/9781137561398.0011

Comparing the US and European Contagion Experiences



the subprime crisis in the US.4 Table 7.2 also shows that the low-volatility regime is marked by below-average correlations among innovations to yields, and in particular to core and peripheral equally weighted sovereign yields and all innovations vs. the equity dividend yield. his means that in this regime, high- and low-quality sovereign bonds, as well as equity vs. ixed income market yields, are segmented. he high-volatility regime is highly persistent (28 weeks on average), and, as we can observe in Figure 7.1, apart from a couple of isolated spikes in 2011, it basically characterizes the 2007–08 period, when the inancial crisis was mainly afecting the US and was still perceived in continental Europe as an episode of turbulent markets. In fact, it is in early 2009 that the crisis spreads from the US corporate and ABS markets to international stock markets. his regime is, indeed, characterized by volatilities of innovations to yields that are between two and ten times larger than in the irst regime. For instance, the volatility of the STOXX 600 dividend yield increases from 7 bps per week to 20 bps. In this state, shocks to core and peripheral sovereign yields become highly correlated (0.90), an indication that general, non-sovereign inancial crises do move all sovereign bond yields in the same direction (presumably, down) as a light-to-quality (although of varying level of creditworthiness) phenomenon occurs. Anecdotal evidence suggests that Italian and Spanish government bonds were subject to heavy purchases in 2008 as much as German bunds, efectively inlating what was to be perceived ex-post as a ixed income bubble in European government paper at large. Because this regime is marked by the Great Financial Crisis spreading to international stock markets, dividend yield innovations now appear to be positively correlated with most other series. As is typical of situations of inancial turmoil, innovations to repo rates are negatively correlated with many other yields, an indication of a second layer of light-to-quality within European markets, where it is plausible that investors may unload positions in risky assets (especially long-term and junk corporate bonds) to enter into relatively safer, short-term (overnight) cash positions. Finally, the third regime also represents in this case a local, European sovereign crisis state characterized by high volatility in the sovereign bond markets, especially peripheral ones, the volatility of which shoots up to a stunning 60 bps per week (that is, 4.35 per cent in annualized terms). However, the volatility of other yield series is comparable to (or occasionally lower than) the one recorded for the second regime, in which market turmoil is not speciically originating from Europe. he DOI: 10.1057/9781137561398.0011



Transmission Channels of Financial Shocks

regime is also moderately persistent (with an implied average duration over four weeks). On the basis of Figure 7.1, we appreciate that this state did start to occasionally appear around mid-2009, corresponding to rising doubts on the sustainability of the debt burden of a few peripheral European countries (at irst Ireland and Greece, and later also Portugal), although the regime efectively characterizes most of the weeks falling between early 2010 and the spring of 2012, corresponding to the worst bouts of the European jitters. Moreover, pairwise correlations between innovations decline relative to the high-variance regime, and in particular core and peripheral bond yield innovations now become negatively correlated (−0.10, although this coeicient is not precisely estimated), which is consistent with our expectations on sovereign market-induced disorders. Table 7.3 also shows that states may not be accessed in a completely random fashion: from the good low-volatility state, one can fall into the local, speciic crisis. However, once in a crisis, the high-variance regime may also be accessed. he time-homogeneous vector autoregressive matrix of coeicients estimated in Table 7.3 reveals that AAA corporate bond, repo contract, and peripheral sovereign rates are particularly predictable, in the sense that most of the VAR(1)-type lagged coeicients are precisely estimated. Of course, as is commonly found in the VAR literature, all own- (partial) irst-order serial correlation coeicients are estimated to be large and highly signiicant. Yet, similarly to what is reported in Chapter 5, capturing non-linear dynamics through a MSVAR framework does not imply that linear predictability stops being estimable. In particular, lagged values of the peripheral government bond and the dividend yield accurately forecast subsequent movements of the yields paid by most of the other series. Interestingly, lower dividend yields today, presumably deriving from higher equity valuations, forecast higher yields on ixed income securities. herefore, equity and bond markets tend to move inversely with each other, which probably relects simple and yet popular switching asset allocation strategies. Figure 7.2 shows the impulse response functions (IRFs) resulting from a one-standard deviation positive shock to peripheral sovereign yields, to simulate the efects of a sovereign crisis.5 he overall efects shown by the igure are the ones we would expect: all other “risk-on” assets are hit by a contagion from a low-credit quality sovereign shock in the crisis state, when the shock may be interpreted to be large enough to have caused a switch in the regime characterizing the system, and when the shock itself DOI: 10.1057/9781137561398.0011

DOI: 10.1057/9781137561398.0011

Table 7.3

Estimates of an MSIH(3,1) model for European yields Repo rate (German bunds)

EW core country yields

0.363*** (0.000) 0.494*** (0.000) 0.370*** (0.000)

0.010 (0.749) 0.058 (0.248) −0.015 (0.650)

0.044 (0.540) 0.039 (0.665) 0.034 (0.630)

0.041 (0.713) 0.083 (0.534) 0.091 (0.463)

0.022 (0.472) −0.005 (0.817) 0.064 (0.004) 0.885 (0.000) −0.023 (0.194) −0.012 (0.507) 0.010 (0.709) 0.005 (0.059)

0.002 (0.950) −0.034 (0.106) 0.032 (0.143) −0.015 (0.618) 0.904 (0.000) −0.004 (0.837) 0.000 (0.991) 0.003 (0.310)

0.036 (0.002) 0.007 (0.183) −0.016 (0.007) 0.016 (0.047) −0.021 (0.031) 0.969 (0.000) −0.023 (0.019) 0.004 (0.000)

0.070 (0.016) 0.024 (0.215) −0.016 (0.449) 0.041 (0.128) −0.039 (0.014) −0.011 (0.471) 0.893 (0.000) 0.001 (0.697)

0.025 (0.525) 0.075 (0.029) 0.001 (0.974) 0.007 (0.869) −0.051 (0.006) −0.018 (0.356) −0.075 (0.025) 0.996 (0.000)

5.392

3.769

1.104

3.013

6.370

AAA corp. short

AAA corp. long

BBB corp. short

0.171** (0.012) 0.151* (0.086) 0.179*** (0.007)

0.197** (0.017) 0.203** (0.042) 0.231*** (0.004)

0.241*** (0.002) 0.385*** (0.000) 0.251*** (0.001)

0.279*** (0.000) 0.374*** (0.000) 0.289*** (0.000)

0.890 (0.000) 0.000 (0.983) 0.034 (0.059) −0.016 (0.507) −0.044 (0.018) 0.059 (0.000) 0.056 (0.021) −0.004 (0.079)

−0.023 (0.479) 0.916 (0.000) (0.021) 0.380 (0.001) 0.980 −0.031 (0.085) 0.022 (0.200) 0.069 (0.012) −0.008 (0.005)

0.033 (0.299) 0.003 (0.854) 1.022 (0.000) −0.072 (0.009) −0.034 (0.100) −0.016 (0.439) −0.001 (0.970) 0.007 (0.016)

3. Unconditional mean

2.647

3.797

4.639

4. Correlations/volatilities Regime 1 AAA corporate short

0.064***

1. Intercept terms Regime 1 (Low volatility) Regime 2 (High volatility) Regime 3 (Crisis) 2. VAR (1) matrix AAA corporate short (t−1) AAA corporate long (t−1) BBB corporate short (t−1) BBB corporate long (t−1) STOXX 600 dividend yield (t−1) Repo rate (German bunds) (t−1) EW core yields (t−1) EW PIIGS yields (t−1)

BBB corp. STOXX 600 long div. yield

EW PIIGS country yields

Continued

Table 7.3

Continued

DOI: 10.1057/9781137561398.0011

AAA corporate long BBB corporate short BBB corporate long STOXX 600 dividend yield Repo rate (German bunds) EW core yields EW PIIGS yields Regime 2 AAA corporate short AAA corporate long BBB corporate short BBB corporate long STOXX 600 dividend yield Repo rate (German bunds) EW core yields EW PIIGS yields Regime 3 AAA corporate short AAA corporate long BBB corporate short BBB corporate long STOXX 600 dividend yield Repo rate (German bunds) EW core yields EW PIIGS yields 5. Transition matrix Regime 1 (Low volatility) Regime 2 (High volatility) Regime 3 (Crisis)

Repo rate (German bunds)

EW core country yields

EW PIIGS country yields

0.073*** −0.057 −0.171* 0.196**

0.015*** 0.066 0.139*

0.075*** −0.014

0.194***

0.142*** 0.411*** −0.289*** 0.057 0.175*

0.203*** −0.178** −0.372*** 0.142*

0.164*** 0.097 −0.037

0.121*** 0.898***

0.133***

0.130*** 0.258** −0.031 0.210** 0.156*

0.107*** −0.236** 0.071 0.172**

0.177*** 0.070 0.062

0.117*** −0.104*

0.603***

AAA corp. short

AAA corp. long

BBB corp. short

0.417*** 0.549*** 0.559*** 0.006 0.264** 0.269** 0.100

0.099*** 0.487*** 0.615*** 0.084 0.012 0.325*** 0.096

0.063*** 0.748*** 0.070 0.169** 0.257** 0.203**

0.071*** 0.118* 0.154* 0.326*** 0.184**

0.183*** 0.774*** 0.612*** 0.514*** 0.309** −0.228** 0.278*** 0.358***

0.154* 0.635*** 0.654*** 0.338*** −0.358*** 0.183** 0.308***

0.182*** 0.812*** 0.544*** −0.255*** −0.033 0.131*

0.079*** 0.853*** 0.368*** 0.561*** 0.132* 0.067 0.376*** −0.039

0.104*** 0.250** 0.589*** 0.142* −0.012 0.475*** −0.013

0.153*** 0.632*** 0.281** −0.030 0.060 0.215**

Regime 1 0.833*** 0.000 0.208

BBB corp. STOXX 600 long div. yield

Regime 2 0.000 0.964*** 0.026

Regime 3 0.167 0.036 0.766***

Note: he boldfaced values are signiicant at least 10%, i.e., every value that is signiicant at conventionally accepted levels is boldfaced. he *, ** and, *** correspond to signiicance at the 1%, 5% or 10% levels, respectively.

Comparing the US and European Contagion Experiences



is large (almost 60 bps) and very persistent. In the remaining two regimes, the responses are muted and hardly distinguishable from zero, as revealed by 90 per cent conidence bands that generally include zero response efects. In general, and apart from crisis phases, European markets appear to be largely disconnected from each other, and contagion does not represent a irst-order concern. herefore, also to be consistent with the analysis performed in Chapter 6, in the following we limit our comments to IRFs that pertain to the crisis state. In particular, BBB corporate bonds (both short- and long-term) and equities (as signaled by the dividend yield they pay) are somewhat hit by contagion, although the overall efect tends to be moderate. For instance, a shock that increases PIIGS sovereign yields by approximately 60 bps on a given week causes an increase in short-term BBB yields that is precisely estimated, starting out at less than 1 bp but gradually increasing to 3 bps ater six months. However, conidence bands tend to remain wide, and efects as large as 7 bps cannot be ruled out. As one would expect, the efect on core sovereign yields tends to be modest, it is not precisely estimated, and it declines to show negative efects (that is, as a result of a “light-to-quality” dynamics) rather quickly. Yet, the true “light-to-quality” seems to concern AAA corporate yields, which tend to decline as the result of a sovereign peripheral crisis.6 Finally, we proceed to identify and measure the alternative channels of inancial contagion. he evidence in favor of a light-to-liquidity channel in these data is positive but also weak. If we take AAA corporate bonds and equities (because here we are dealing with the constituents of the STOXX 600) as instances of highly liquid assets, and BBB corporate bonds as examples of illiquid securities, then we ind evidence of a liquidity channel only insofar as the diferential between AAA and BBB corporate bonds is concerned. Over a long horizon, such a channel accounts for 4–5 bps in the case of short-term securities and in excess of 5 bps for long-term ones.7 Under the risk premium channel, contagion occurs because shocks to one market lead to an increase in the risk aversion of inancial market participants. his triggers an upward adjustment of the risk premia on all the risky assets in the economy. To perform this analysis, we have computed and inspected the regime-speciic IRFs for European yield spreads, computed as the diference between the yields in Table 7.1 and the overnight repo rate, when German bunds are pledged. Also in this case, IRFs are tiny in the irst and second regimes and slightly wider in the crisis regime. We obtain weak evidence that no risk premium channel would be working in Europe: the spreads of most DOI: 10.1057/9781137561398.0011



Transmission Channels of Financial Shocks Low-volatility

Crisis

High-volatility

AAA corporate, short-term yield 0.5 0

Basis points

–0.5 –1 –1.5 –2 –2.5 –3 –3.5 –4

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

19

21

23

25

19

21

23

25

19

21

23

25

AAA corporate, long-term yield 0.5 –0.5 Basis points

–1.5 –2.5 –3.5 –4.5 –5.5 –6.5

1

3

5

7

9

11

13 15 Periods

17

BBB corporate, short-term yield 7 6 Basis points

5 4 3 2 1 0 –1

1

3

5

7

9

11

13 15 Periods

17

BBB corporate, long-term yield 6 5 Basis points

4 3 2 1 0 –1

1

3

5

7

9

11

13 15 Periods

17

Figure 7.2 MSVAR-yield impulse response functions to a shock to peripheral (PIIGS) sovereign yields DOI: 10.1057/9781137561398.0011

Comparing the US and European Contagion Experiences Low-volatility

Crisis

High-volatility

STOXX 600 dividend yield 5

Basis points

4 3 2 1 0 –1

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

19

21

23

25

19

21

23

25

21

23

25

Repo rate (on German bunds) 5

Basis points

4 3 2 1 0 –1

1

3

5

7

9

11

13 15 Periods

17

Core countries sovereign yields 2

Basis points

1 0 –1 –2 –3 –4

1

3

5

7

9

11

13 15 Periods

17

Peripheral (PIIGS) countries sovereign yields 60

Basis points

50 40 30 20 10 0

Figure 7.2

1

3

Continued

DOI: 10.1057/9781137561398.0011

5

7

9

11

13 15 Periods

17

19





Transmission Channels of Financial Shocks

series actually decline as a result of a PIIGS sovereign yield shock. Rising yields (as implied by a light-to-quality channel) and declining spreads are compatible when the underlying, baseline riskless rate climbs, as turns out to be the case for the repo rate on German bunds. he only, limited exception is represented by non-investment grade corporate bonds, for which, even though the immediate impact is a reduction of the spreads, over time we estimate an increase in spreads of up to 2 and 3 bps (hence very modest) for long- and short-term paper, respectively. Of course, a local risk premium efect propagates considerable alterations within the peripheral sovereign government bond markets, because an immediate jump in the spread equal to more than 60 bps still persists at an estimated value of 43 bps ater six months. On the contrary, Figure 7.2 shows that European contagion was mostly driven by a light-to-quality channel, by which, following a shock to one market, investors attempt to sell risky assets and purchase safer assets. Consequently, the risk premium of the former climbs, while that on the latter declines. Indeed, as already noted, while the yields of investment grade, AAA corporate bonds and (at least eventually) core European government bonds decline, the yields of “junk”, BBB corporate bonds and equities increase. For instance, looking at short-term corporate bonds and considering the BBB–AAA diferences in IRFs, we estimate the importance of the light-to-quality channel at 4–7 bps, cumulated over time. Finally, we test the presence of a correlated information channel (sometimes called a “wake-up call” spillover; see, for example, Beirne and Fratzscher, 2013) by measuring the non-linear and immediate efect captured by the MSVAR framework, due to the possibility that the intercept terms of the inancial variables may move in the same direction when a shit to a given regime occurs, vs the short-term IRF estimated under a single-state VAR framework. We discover that during the European PIIGS crisis, this last channel was certainly at work, and that it explains some portion of yield responses in the case of short-term BBB corporate bonds and equities, in the sense that their medium-term IRFs increase by 1–2 bps, which appears to represent 20–40 per cent of the overall contagion efect that we reported earlier.8 Interestingly, this efect – of the order of 1–2 bps and equal to almost 50 per cent of the overall efect – also extends to the repo rate increase. his would imply that a PIIGS shock would contain information useful to support an upward revision of short-term, essentially riskless repo rates. DOI: 10.1057/9781137561398.0011

Comparing the US and European Contagion Experiences



All in all, we conclude that the mild evidence of contagion from a positive (crisis) shock to peripheral European yields is mostly explained by a light-to-quality channel being active a few times during 2010 and 2011, when – while the yields of investment grade, AAA corporate bonds and (at least eventually) core European government bonds declined – the yields of “junk”, BBB corporate bonds and on equities increased. Moreover, there is also some evidence of light-to-liquidity and correlated information channels being active during the European sovereign crisis –assumed to be characterized as an instance of the third regime – although these account for 50 per cent at most of the (already modest) size of the contagion efects. We ind no evidence of a risk premium channel having been at work in Europe. Interestingly, the fact that the 2010–11 European crisis was characterized by only very minor contagion outside the low-quality, peripheral government bond market has received little, if any, attention in the literature. Even though an analyst may be tempted to interpret this evidence as an indication of successful intervention policies having been implemented by the ECB (for instance, the SMP), the possibility remains that other, more structural features of the European inancial markets (for instance, a superior degree of segmentation) may have, by and large, prevented more widespread and damaging contagion efects.

7.3 Cross-country, cross-market shocks: did the subprime crisis spill over to Europe? Our inal empirical exercise further extends the eight-series estimation exercises of Sections 7.1 and 7.2 to a richer data set composed of ten series: the same eight series introduced in Section 7.1, augmented with two US series already used in Chapters 3–6: two ABS yield series prepared by BofA Merrill Lynch. he irst series concerns AAA-rated ABS, and the second collects data on lower-grade ABS that belong to the rating bracket AA–BBB. he series are, of course, expanded to cover the full sample up to December 19, 2014. We use this longer data set (compared with the one in Chapters 3–6) to investigate whether and how subprime (mortgage-related, a speciic kind of ABS) shocks that occurred between 2007 and 2008 may have spilled over to European markets.9 For the sake of brevity, for this exercise we also omit detailed discussion of the estimation of the single-state VAR model and the results DOI: 10.1057/9781137561398.0011



Transmission Channels of Financial Shocks

obtained by the analysis of the IRFs in this framework. In general, also in this case there is little, if any, evidence of the shock to the US lowquality ABS market passing through to European ixed income and equity markets. Indeed, the efects of the shock are small and generally not statistically signiicant, with the exception of PIIGS sovereign bonds; the yield of these declines over time by almost 20 bp, and their response turns statistically signiicant ater four weeks. We therefore move to the estimation of an MSVAR model for these ten yield and spread series. A standard speciication search similar to the one discussed in Chapter 5 leads to specifying an MSIH(2,1) model (which has two regimes and one VAR lag). In this case, information criteria do pose some uncertainties as to whether the VAR matrix ought to be time-homogeneous or should be allowed to follow a regime switching dynamics, that is, whether one ought to select an MSIH(2,1) over a more richly parameterized MSIAH(2,1). here is no empirical evidence in favor of three-regime models. However, because the number of the series has expanded from eight to ten, this may simply derive from our failure to obtain suiciently long time series to support the estimation of a higher number of parameters, as three-state models would naturally imply. herefore, we settle for a relatively parsimonious MSIH(2,1) model, in which the VAR matrix is constant across regimes. his model implies the estimation of 232 parameters and hence an acceptable saturation ratio of 17.4, which should guarantee some reliability to the estimates shown in Table 7.4, where, in fact, a majority of the estimated coeicients appears to be statistically signiicant, at least in tests with size of 10 per cent or lower. Also in this case, as throughout this book, one of the regimes may be branded as a high-volatility, high (average) correlations regime that characterizes periods of turbulent markets and inancial crisis. Figure 7.3 visually conirms this intuition: the second, high-variance crisis regime captures most of the 2007–09 period, extending approximately to the end of summer 2009, in a manner consistent with the empirical results in Guidolin and Tam (2013). Additionally, the smoothed (ex-post) probabilities of this second regime frequently spike up in correspondence to the spring/summer of 2010 and then to the fall of 2011, marking wellknown bouts of European sovereign crisis. Figure 7.4 investigates the existence and strength of contagion from US risky markets – speciically from low-grade ABS yields – to European markets in the atermath of a classical, one-standard deviation shock that one may think of as a stylized way to capture the onset DOI: 10.1057/9781137561398.0011

DOI: 10.1057/9781137561398.0011

Table 7.4

Estimates of an MSIH(2,1) model for European yields augmented with US ABS yield series

1. Intercept terms Regime 1 (Low volatility) Regime 3 (Crisis)

AAA corp. short

AAA corp. long

0.190*** (0.006) 0.167** (0.028)

0.175** (0.047) 0.148 (0.122)

0.137 (0.129) 0.124 (0.207)

−0.014 (0.692) 0.945*** (0.000) 0.054** (0.038) −0.016 (0.641) −0.014 (0.450) 0.044*** (0.007) 0.025 (0.380) −0.012** (0.021) −0.032** (0.021) 0.000 (0.975)

2. VAR (1) matrix AAA corporate short (t−1)

0.903*** (0.000) AAA corporate long (t−1) 0.008 (0.684) BBB corporate short (t−1) 0.060*** (0.002) BBB corporate long (t−1) −0.046* (0.092) STOXX 600 dividend yield (t−1) −0.027 (0.131) Repo rate (German bunds) (t−1) 0.075*** (0.000) EW core yields (t−1) 0.040* (0.090) EW PIIGS yields (t−1) −0.007* (0.090) BBB (low rating) US Yields (t−1) −0.036*** (0.009) AAA (high rating) US Yields (t−1) 0.007 (0.243) 3. Unconditional mean

2.647

3.797

BBB corp. short

BBB corp. long

STOXX 600 div. yield

Repo rate (German bunds)

0.286*** (0.001) 0.311*** (0.001)

0.313*** (0.000) 0.312*** (0.000)

0.029 (0.721) 0.081 (0.355)

−0.124* (0.096) −0.151* (0.060)

−0.047 (0.803) 0.037 (0.856)

−0.052 (0.289) −0.086 (0.115)

−0.294*** (0.000) −0.478*** (0.000)

0.014 −0.007 (0.705) (0.843) 0.045* 0.043* (0.087) (0.096) 1.071*** 0.112*** (0.000) (0.000) −0.115*** 0.827*** (0.002) (0.000) 0.019 0.002 (0.388) (0.918) 0.026 0.021 (0.167) (0.178) −0.030 −0.021 (0.321) (0.452) −0.001 0.003 (0.801) (0.539) −0.012 −0.010 (0.475) (0.458) −0.004 0.001 (0.537) (0.933)

0.024 (0.443) −0.028 (0.187) 0.029 (0.182) −0.037 (0.238) 0.924*** (0.000) −0.011 (0.558) −0.013 (0.621) 0.007 (0.127) 0.034** (0.034) 0.000 (0.967)

0.008 (0.807) −0.024 (0.259) 0.005 (0.817) 0.004 (0.907) −0.016 (0.481) 0.934*** (0.000) 0.032 (0.255) −0.001 (0.807) 0.048*** (0.005) −0.018** (0.013)

0.064** (0.031) 0.026 (0.211) −0.020 (0.351) 0.118*** (0.000) −0.013 (0.455) 0.010 (0.508) 0.860*** (0.000) −0.015*** (0.002) −0.019 (0.150) −0.014** (0.017)

−0.013 (0.842) 0.108* (0.096) 0.197*** (0.001) −0.066 (0.341) −0.009 (0.753) 0.007 (0.774) −0.123** (0.022) 0.977*** (0.000) −0.036* (0.093) −0.046*** (0.000)

0.045** (0.016) 0.004 (0.771) −0.009 (0.466) 0.023 (0.231) 0.017 (0.257) 0.004 (0.758) −0.045*** (0.008) −0.004 (0.163) 0.995*** (0.000) −0.008 (0.102)

0.109*** (0.000) 0.022 (0.180) −0.028* (0.093) 0.048* (0.057) 0.070*** (0.000) −0.028 (0.136) −0.121*** (0.000) −0.002 (0.503) 0.116*** (0.000) 0.955*** (0.000)

4.639

5.392

3.769

1.104

EW core country yields

3.013

EW PIIGS BBB (low AAA (high country rating) US rating) US yields yields yields

6.370

2.509

6.281

Continued

Table 7.4

Continued AAA corp. short

DOI: 10.1057/9781137561398.0011

4. Correlations/volatilities Regime 1 AAA corporate short AAA corporate long BBB corporate short BBB corporate long STOXX 600 dividend yield Repo rate (German bunds) EW core yields EW PIIGS yields BBB (low rating) US yields AAA (high rating) US yields Regime 2 AAA corporate short AAA corporate long BBB corporate short BBB corporate long STOXX 600 dividend yield Repo rate (German bunds) EW core yields EW PIIGS yields BBB (low rating) US yields AAA (high rating) US yields 5. Transition matrix Regime 1 (low volatility) Regime 3 (high volatility/crisis)

AAA corp. long

BBB corp. short

0.068*** 0.652*** 0.104*** 0.465*** 0.384*** 0.099*** 0.626*** 0.594*** 0.740*** 0.009 0.064 0.077 0.176* 0.069 −0.008 0.413*** 0.373*** 0.196** −0.033 −0.014 0.175** 0.173** 0.240** 0.261*** 0.179** 0.283*** 0.190**

BBB corp. long

0.100*** 0.103* 0.015 0.242** 0.123* 0.147* 0.174**

STOXX 600 div. yield

EW core country yields

EW PIIGS BBB (low AAA (high country rating) US rating) US yields yields yields

0.076*** −0.064 0.073*** −0.101 0.132* 0.081*** 0.211** 0.001 −0.207** 0.444*** −0.027 −0.065 0.429*** −0.007 −0.033 −0.058 0.375*** 0.010

0.160*** 0.760*** 0.138*** 0.522*** 0.489*** 0.174*** 0.459*** 0.599*** 0.731*** 0.131*** 0.302*** 0.333*** 0.524*** 0.430*** 0.180*** −0.181** −0.278** −0.108* −0.152* −0.177* 0.248*** 0.262*** −0.039 0.131* 0.029 0.254*** 0.229** 0.193** 0.176** 0.129* 0.240** 0.184** 0.389*** 0.415*** 0.161** −0.045 −0.008 0.120* 0.032 0.131* Regime 1 0.925*** 0.113

Repo rate (German bunds)

0.192*** 0.058 0.130*** 0.073 0.620*** 0.177*** 0.069 0.097 0.055 0.057 −0.076 −0.087

0.042*** 0.824***

0.054***

0.187*** 0.334***

0.311***

Regime 2 0.075 0.887***

Note: he boldfaced values are signiicant at least 10%, i.e., every value that is signiicant at conventionally accepted levels is boldfaced. he *, ** and, *** correspond to signiicance at the 1%, 5% or 10% levels, respectively.

Comparing the US and European Contagion Experiences



1.0 0.8 0.6 0.4

Jul-12

Mar-13

Nov-13

Jul-14

Jul-12

Mar-13

Nov-13

Jul-14

Nov-11

Feb-11

Jun-10

Oct-09

Feb-09

Jun-08

Jan-07

0.0

Sep-07

0.2

Low volatility 1.0 0.8 0.6 0.4

Nov-11

Feb-11

Jun-10

Oct-09

Feb-09

Jun-08

Jan-07

0.0

Sep-07

0.2

High volatility/crisis

Figure 7.3 Smoothed probabilities estimated from an MSIH(2,0) model for European yields augmented with US ABS yield series

of the 2007 subprime crisis. As has now become typical of our presentation of results, each panel in the igure focuses on response efects in each of the markets in the two diferent regimes. However, it is immediately clear that propagation efects in the irst, low-volatility regimes are modest and hardly ever statistically signiicant. In contrast, a more interesting story emerges with reference to the second, high-volatility regime. Surprisingly, there is evidence of spillover efects from a US ABS shock to European markets, but no evidence of contagion in an economic sense. he fact is that a few European markets do react to US crisis shocks, but moving in an opposite direction, as if, during a crisis regime, money would regularly low out of “risk-on” US markets DOI: 10.1057/9781137561398.0011



Transmission Channels of Financial Shocks Low-volatility

Crisis

High-volatility

AAA corporate, short-term yields 2

Basis points

1 0 –1 –2 –3 –4

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

21

23

25

21

23

25

21

23

25

21

23

25

AAA corporate, long-term yields 2

Basis points

1 0 –1 –2 –3 –4

1

3

5

7

9

11

13 15 Periods

17

19

Basis points

BBB corporate, short-term yields 1 0 –1 –2 –3 –4 –5 –6 –7 –8

1

3

5

7

9

11

13 15 Periods

17

19

BBB corporate, long-term yields 1

Basis points

0 –1 –2 –3 –4 –5 –6

1

3

5

7

9

11

13 15 Periods

17

19

Basis points

STOXX 600 equity dividend yield 1 0.5 0 –0.5 –1 –1.5 –2 –2.5 –3 –3.5 –4

1

3

5

7

9

11

13 15 Periods

17

19

Figure 7.4 MSVAR-yield impulse response functions to a shock to US low-credit quality ABS yields

DOI: 10.1057/9781137561398.0011

Comparing the US and European Contagion Experiences Low-volatility

Crisis

High-volatility

Basis points

Repo rate (on German sovereigns) 1 0 –1 –2 –3 –4 –5 –6 –7

1

3

5

7

9

11

13 15 Periods

17

19

21

23

25

21

23

25

21

23

25

21

23

25

23

25

Basis points

Core countries sovereign yields 1 0.5 0 –0.5 –1 –1.5 –2 –2.5 –3 –3.5 –4

1

3

5

7

9

11

13 15 Periods

17

19

Peripheral (PIIGS) sovereign yields

Basis points

–3 –8 –13 –18 –23 –28

1

3

5

7

9

11

13 15 Periods

17

19

ABS BBB (Low rating) US sovereign yields 30

Basis points

25 20 15 10 5 0

1

3

5

7

9

11

13 15 Periods

17

19

ABS AAA (High rating) US sovereign yields 1

Basis points

0 –1 –2 –3 –4 –5

Figure 7.4

1

3

Continued

DOI: 10.1057/9781137561398.0011

5

7

9

11

13 15 Periods

17

19

21





Transmission Channels of Financial Shocks

to a few European markets, and in particular the short-term cash and government bond markets, including peripheral ones. Some have speculated that a market perception of an implicit European-wide bailout guarantee, or simply ignorance among inancial market participants of country-speciic fundamentals, may have been the main explanation for this co-movement between core and PIIGS yields in 2007–09 (see, for example, Beirne and Fratzscher, 2013). In particular, while there is no (or very weak) spillover to both AAA and BBB corporate bond and stock markets, efects are robust and precisely estimated in the case of the repo market and peripheral sovereign bond markets. For instance, in the case of PIIGS sovereign yields, these decline immediately by a nonnegligible 5–10 bps in a matter of a few weeks, but the efect persistently extends over time, reaching almost 20 bps within six months. Further evidence indicates that the efect levels of and starts being re-absorbed only over horizons that exceed the year. here is also an efect on core Europe sovereigns, which is, however, weaker, of the order of 1–2 bps and signiicant only up to three months from the shock. Interestingly, European repo rates also appear to be massively hit by a subprime-type US shock, but in the sense that the time value of essentially riskless overnight cash investments is signiicantly lowered by up to 6 bps. his represents an obvious light-to-quality and light-to-liquidity efect that occurs across diferent regions of the world as well as across markets.10 Once more, these efects are the opposite of the standard notion of contagion, although they represent a case of spillover in a quantitative sense. It appears that one bubble bursting in the US may travel over to Europe, fueling an increase in sovereign bond prices, especially peripheral ones.11 In the case of an MSVAR framework, the sign of the efect not only helps us to make sense of widespread anecdotal evidence from the years 2007–09, but now delivers a reaction that is of a nonnegligible magnitude: a decline of 20 bps in peripheral sovereign bonds and a spread compression by roughly 10–15 bps (obtained, as a irst approximation, as a diference from the analogous efect recorded by repo rates). All in all, this evidence that European inancial markets are more insulated from shocks – of both internal (Section 7.2) and external origin (Section 7.3) – appears to be a new empirical result so far unexplored in the literature. Of course, our econometric analysis only allows us to measure the size of the phenomenon and to assess its statistical signiicance; it is mute on the causes of this higher degree of insulation among DOI: 10.1057/9781137561398.0011

Comparing the US and European Contagion Experiences



diferent markets, whether these may be related to European policymaking or to the very structure and segmentation features of markets. Future research will need to shed light on this phenomenon.

Notes 1 We do not attempt to provide a chronological synopsis of the key events that have characterized the European iscal and sovereign debt crisis. See Lane (2012) for an account and balanced commentary on the most important developments between 2007 and 2011. 2 All data are downloaded from Datastream. Irish government bonds fail to be characterized by market–driven yield data between October 2010 and March 2013. For this period, the PIIGS equal weighting concerns the remaining four peripheral countries. 3 Section 7.3 further extends the analysis to study whether a US-originated low-credit quality ABS shock may also have propagated throughout European bond and equity markets. 4 he European Financial Stability Facility was created in May 2010 as a temporary facility to provide loans to euro area member states. he European Stability Mechanism was set up in June 2011 as a permanent crisis-handling mechanism. he share of the countries guaranteeing the EFSF’s debt is proportional to the capital share of each country in the European Central Bank, adjusted to exclude countries with EU/International Monetary Fundsupported programs. 5 he Cholesky ordering that is adopted is natural one, which puts the riskiest markets on top (that is, BBB corporate paper, stocks, and PIIGS sovereign rates) and more liquid, less risky assets towards the bottom of the ordering. 6 Even though the efect remains economically small, the impact on the repo rate is precisely estimated to be positive, which is rather puzzling. 7 Because the repo rate on German Bunds moderately increases as a result of a low-credit quality sovereign yield shock, we fail to ind the same liquidity efects as in the analysis of cross-market contagion with US data. his signals a much less compelling need by traders to borrow government securities. Of course, it is easy to speculate that the scarcity of Treasury notes caused by the large-scale asset purchases pursued by the Federal Reserve in the US found no match in the policies pursued by the European Central Bank. 8 In this case, the correlated information is measured over a horizon of 6–12 weeks from the original shock because, by construction, our Cholesky ordering implies that a peripheral yield shock must imply very limited efects on other risky yields in the very short run. DOI: 10.1057/9781137561398.0011



Transmission Channels of Financial Shocks

9 Switching to a 2007–14 sample (from the 2000–13 sample used in Chapters 3–6) does not radically afect the summary statistics for ABS yields in Table 4.1. For instance, in the new sample, the mean yield for AAA (BBB) ABS is 3.65 (6.64) per cent, vs. 2.51 (6.28) per cent in Table 7.1. Both series are non-normal and characterized by large excess kurtosis. 10 We have conirmed the robustness of these results to the case in which the one-standard deviation shock is applied simultaneously to both the US AAA and BBB asset-backed security markets. he efects are qualitatively homogeneous even though they are slightly weaker. 11 Interestingly, while in a single-state model, investors seem also to replace low-quality US ABS with risky European corporate bonds, this stops being the case in a MSVAR model.

DOI: 10.1057/9781137561398.0011

8

Conclusions Abstract: In this chapter, we summarize the indings of our analysis on contagion episodes in US and European markets. In particular, we emphasize the results that are most relevant to policy-makers, who have to address crises with appropriate measures, and to investors, as contagion has strong implications for portfolio diversiication. Keywords: contagion; crisis; policy-making; transmission channels Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model. Basingstoke: Palgrave Macmillan, 2016. doi: 10.1057/9781137561398.0012.

DOI: 10.1057/9781137561398.0012





Transmission Channels of Financial Shocks

In this book, we have pursued the identiication and measurement of cross-asset contagion channels that we estimate were active during the recent subprime crisis that hit US inancial markets between 2007 and 2009. Some earlier studies have investigated inancial contagion on the basis of the empirical evidence on the behavior of asset prices during this episode (see, for example, Longstaf, 2010; Guo, Chen, and Huang, 2011). However, our approach substantially difers from previous papers. In our analysis, we simulate the shock that, according to recent empirical literature (for example, Dwyer and Tkac, 2009; Gorton, 2010), hit the ABS market during the subprime crisis with the objective of understanding the ensuing cross-asset contagion efects to other asset markets. In particular, we exploit impulse response function (IRF) analysis techniques to evaluate the reaction of high-grade ABS, Treasury repos, Treasury bonds, corporate bonds, and stocks to a negative shock to the low-grade ABS market. Firstly, our analysis shows that a shock to the low-credit quality ABS market causes signiicant and persistent efects on the remaining yield and spread series. Furthermore, the estimation of regime-dependent impulse response functions in a Markov-switching vector autoregressive (MSVAR) framework allows us to draw one important conclusion. he values of the regime-dependent IRFs substantially difer across the three regimes that our model selection analysis is able to isolate: the low-volatility, high-volatility, and crisis regimes. In particular, the efects obtained in the crisis regime are always of larger magnitude than those in the other states. With a considerably higher frequency than in the case of other regimes, such responses are oten also statistically signiicant. his means that – as it is sensible to expect – contagion episodes mainly occur during inancial crises, while in non-crisis regimes, our time series fail to display signiicant spillover efects with suicient consistency. Second, our study of the contagion channels emphasizes that following a shock to the (low-credit quality) ABS market, negative efects are transmitted to other markets through distinct and empirically identiiable light-to-liquidity, light-to-quality, risk premium, and correlated information channels. In particular, the results concerning the light-toliquidity channel show that following a shock to the ABS low grade market, a signiicant negative efect on the one-month and ten-year Treasury yields as well as the Treasury repo rate occurs, signaling an increase in the demand for liquid US Treasuries. As for the risk premium and light-to-quality channels, we evaluate the reactions of the credit spread on AAA ABS, on corporate bonds, DOI: 10.1057/9781137561398.0012

Conclusions



and on the equity dividend yields triggered by a shock to lower-grade ABS yields. Our key inding is that most yield series are subject to an increase in the implied spread. his is consistent with the notion that the risk premium channel represents the contagion mechanism through which a shock propagates throughout the inancial system. In particular, the markets that experience a positive efect, and are, as such, victim of a risk premium-driven contagion, are: the investment grade corporate bond, the non-investment grade long-term corporate bond, and the stock markets. In contrast, the spreads on non-investment grade short-term corporate bonds are subject to a negative efect, that is, they seem to be positively inluenced by the ABS shock. We explain this as a result of speculative investors (for example, hedge funds) re-balancing their portfolios towards assets with lower duration, that is, the presence of pervasive short duration strategies. his type of re-balancing usually occurs in periods of high volatility, and is implemented to reduce the exposure of managed portfolios to increases in the levels of (risky) interest rates. he spread on the ABS AAA series is, instead, subject to a negligible efect over the 26 weeks investigated in Chapter 7 and across the three regimes. herefore, the risk premium channel is unlikely to represent the key contagion mechanism through which a shock to the ABS lower-grade market is propagated to higher-grade ABS. Finally, when the IRF analysis is limited to one period ater the shock, the efect on the spread of the investment grade short-term corporate bonds is negative, even though it is never statistically signiicant. his shows that it is possible that, ater a certain number of weeks, a lightto-quality phenomenon that lowers the yield on this category of asset occurs. he fourth mechanism we study is the correlated information channel. In the crisis regime, this channel triggers small contagion efects on the Treasury repo, the one-month Treasury, the investment grade corporate bond, the non-investment grade short-term corporate bond markets, and the dividend yield. An efect of consistent magnitude is obtained instead in the case of non-investment grade long-term corporate bonds. he study of the reactions of the AAA ABS market to the shock shows that contagion did not occur through either the risk premium or the correlated information channel. he reason for this result lies in the sequence of events that characterized the subprime crisis. In particular, in the atermath of the shock to the lower-grade ABS products in the second half of 2007, the whole ABS market was hit by a credit rating DOI: 10.1057/9781137561398.0012



Transmission Channels of Financial Shocks

crisis, which led to numerous downgrades, mostly concerning AAArated products. We have also extended our analysis to European data to investigate two questions. First, we examine whether shocks diferent from those that arose in the ABS market in the US would propagate in the inancial system in ways similar to what we have uncovered in the case of the US. In particular, we perform simulation experiments in which the key driver of the crisis event is represented as a shock to peripheral, low-credit quality sovereign rates. Second, we study whether the same low-grade ABS shock recorded in the US may have caused important efects in the European corporate bond and equity markets as well. In other words, we investigate the patterns of cross-country (region) and cross-asset contagion. On European data that are of similar nature to those used for the US application, however, we ind weaker evidence of contagion. In the case of a few markets – in particular sovereign bonds – we report that yields may be lowered by a severe shock to riskier asset classes, such as low-grade ABS. When contagion did occur, in the European case, a light-to-quality efect seems to have played a dominant role, at least in a quantitative sense. Whether such diferent indings may derive from the diferent institutional setup that characterizes European markets, or whether they are in the data and driven by diferences in policy responses during the inancial crisis (in particular, by the European Central Bank), remains an interesting issue to be explored in future research. Our results have important policy and portfolio management implications. If shocks to low-quality ABS and risky credit securities have the power to quickly spill over to other markets, including classical bond and equity markets, thus impairing the capability of irms to raise funds to inance their investment projects, then policy-makers ought to remain extremely vigilant towards negative and unforeseen developments in such markets. Although reaching a clear-cut conclusion remains dificult, this does not appear to have been the case in 2007 in the US, even though the strength of the subsequent policy interventions during 2008 and 2009 is beyond doubt. he fact that such shocks produce rather different efects across diferent regimes – with a particular role played by a crisis state – indicates the existence of a deep and resilient asymmetry between positive and negative shocks to ABS, where the latter clearly trigger greater concerns. We document another aspect that should be carefully taken into account, that is, the existence of strong linkages across apparently DOI: 10.1057/9781137561398.0012

Conclusions



independent markets, which clearly arise when a shock occurs. For this reason, our results may have important implications for investors’ decisions as well. Investors should consider the recurring nature of inancial crises and changes in regimes when implementing their portfolio strategies. In particular, choices of asset allocation should take into account the possibility that the statistical relationships among the categories of assets included in inancial portfolios may change over time. In this sense, our study sheds light on the reasons that drive similar changes, and under which market conditions investors can expect similar efects to arise. Finally, at least with reference to US data, we ind that the most important and robustly estimated contagion channel is, beyond doubt, the light-to-liquidity channel, which depresses the yields of Treasuries and repo rates, while increasing required yields of other ixed income securities and of equities. However, the risk premium, light-to-quality, and correlated information channels – even though these were at work during the crisis of 2007–09 – lead to weaker and less precisely estimated results. Although a literature exists that has emphasized the role played by liquidity dry-ups during the subprime crisis (see, for example, Gefang, Koop, and Potter, 2011) and the resulting damage to the functionality of the US inancial system, the conclusion of our book, that liquidity occupies a key role in the way shocks spill over across diferent security markets, seems novel and important in terms of policy measures (see Fleming, 2012) as well investment advice (see, for example, Lou and Sadka, 2011).

DOI: 10.1057/9781137561398.0012

References Adrian, T., Begalle, B., Copeland, A., and Martin, A. (2013). Repo and securities lending. Federal Reserve Bank of New York. Agarwal, S., Barrett, J., Cun, C., and De Nardi, M. (2010). he asset-backed securities markets, the crisis, and TALF. Federal Reserve Bank of Chicago. Allen, F. and Gale, D. (2000). Financial contagion. Journal of Political Economy, 108, 1–33. Ang, A. and Bekaert G. (2001). Stock return predictability: is it there? Unpublished paper, Columbia University. Ang, A. and Bekaert G. (2002). Regime switches in interest rates. Journal of Business and Economic Statistics, 20, 163–82. Ang, A. and Bekaert, G. (2006). Stock return predictability: is it there? Review of Financial Studies, 20(3), 651–707. Ang, A. and Chen, J. (2002). Asymmetric correlations of equity portfolios. Journal of Financial Economics, 63(3), 443–94. Ang, A. and Timmermann, A. (2011). Regime changes and inancial markets. Annual Review of Financial Economics, 4(1), 313–37. Baig, T. and Goldfajn, I. (1998). Financial market contagion in the Asian crisis. No. 98–155. International Monetary Fund. Banerjee, S. and Graveline, J. (2013). he cost of shortselling liquid securities. The Journal of Finance, 68, 637–67. 

DOI: 10.1057/9781137561398.0013

References



Bansal, R., Kiku, D., and Yaron, A. (2011). An empirical evaluation of the long-run risks models for asset prices. Unpublished paper, Duke University and University of Pennsylvania. Barclay, Michael J., Hendershott, T., and Kotz, K. (2006). Automation versus intermediation: evidence from treasuries going of the run. Journal of Finance, 61(5), 2395–414. Baur, Dirk G. and Lucey, Brian M. (2010). Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financial Review, 45(2), 217–29. Beber, A., Brandt, Michael W., and Kavajecz, Kenneth A. (2009). Flight-to-quality or light-to-liquidity? Evidence from the euro-area bond market. Review of Financial Studies, 22(3), 925–57. Beirne, J. and Fratzscher, M. (2013). he pricing of sovereign risk and contagion during the European sovereign debt crisis. Journal of International Money and Finance, 34, 60–82. Bekaert, G., Hodrick, Robert J., and Marshall, David A. (2001). Peso problem explanations for term structure anomalies. Journal of Monetary Economics, 48 (2), 241–70. Bikbov, R. and Chernov, M. (2008). Monetary policy regimes and the term structure of interest rates, working paper. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31 (3), 307–27. Braun, Phillip A. and Mittnik, S. (1993). Misspeciications in vector autoregressions and their efects on impulse responses and variance decompositions. Journal of Econometrics, 59(3), 319–41. Brunnermeier, Markus K. and Pedersen, Lasse H. (2009). Market liquidity and funding liquidity. Review of Financial Studies, 22(6), 2201–238. Caballero, R. and Kurlat, P. (2008). Flight to quality and bailouts: policy remarks and a literature review. Working paper series, Massachusetts Institute of Technology. Campbell, John Y. and hompson, Samuel B. (2008). Predicting excess stock returns out of sample: can anything beat the historical average? Review of Financial Studies, 21(4), 1509–31. Cecchetti, S. G. (2009). Crisis and responses: he Federal Reserve in the early stages of the inancial crisis (digest summary). Journal of Economic Perspectives, 23, 51–75. Chakrabarty, B. and Zhang, G. (2012). Credit contagion channels: market microstructure evidence from Lehman Brothers’ bankruptcy. Financial Management, 41, 320–43. DOI: 10.1057/9781137561398.0013



References

Davies, R. B. (1977). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 74, 33–43. Dempster, Arthur P., Laird, Nan M., and Rubin, Donald B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 39(1), 1–38. Dornbusch, R., Park, Y. C., and Claessens, S. (2000). Contagion: understanding how it spreads. The World Bank Research Observer, 15(2), 177–97. Duie, D. (1996). Special repo rates. The Journal of Finance, 51 (2), 493–526. Dwyer, G. P. and Tkac, P. (2009). he inancial crisis of 2008 in ixedincome markets. Journal of International Money and Finance, 28, 1293–316. Enders, W. (1995). Applied econometric time series. New York: Wiley. Fama, E. and French, K. (1989). Business conditions and expected returns on stocks and bonds. Journal of Financial Economics, 25, 23–49. Fleming, M. J. (2012). Federal Reserve liquidity provision during the inancial crisis of 2007–2009. FRB of New York Staf Report 563. Gefang, D., Gary K., and Simon M. Potter. (2011). Understanding liquidity and credit risks in the inancial crisis. Journal of Empirical Finance, 18(5), 903–14. Goldreich, D., Bernd H., and Nath, P. (2003). he price of future liquidity: time-varying liquidity in the US Treasury market. Review of Finance, 9(1), 1–32. Gonzalo, J. and Olmo, J. (2005). Contagion versus light to quality in inancial markets. Universidad Carlos III de Madrid Working Paper 05–18. Gorton, Gary B. (2010). Questions and answers about the inancial crisis. NBER working paper No. 15787, 2010. Gorton, G. and Metrick, A. (2012). Securitized banking and the run on repo. Journal of Financial Economics, 104(3), 425–51. Guidolin, M. (2011). Markov switching models in empirical inance. Advances in Econometrics, 27, 1. Guidolin, M. (2012). Markov switching models in empirical inance. Working Paper No. 415, Innocenzo Gasparini Institute for Economic Research. Guidolin, M. (2013). Markov switching models in asset pricing research. Handbook of Research Methods and Applications in Empirical Finance. Cheltenham, UK: Edward Elgar Publishing, 3–44. DOI: 10.1057/9781137561398.0013

References



Guidolin, M. and Tam, Y. M. (2013). A yield spread perspective on the great inancial crisis: break-point test evidence. International Review of Financial Analysis, 26, 18–39. Guidolin, M. and Timmermann, A. (2005). Economic implications of bull and bear regimes in UK stock and bond returns*. The Economic Journal, 115 (500), 111–43. Guidolin, M. and Timmermann, A. (2006). An econometric model of nonlinear dynamics in the joint distributions of stock and bond returns. Journal of Applied Econometrics, 21, 1–22. Guidolin, M. and Timmermann, A. (2009). Forecasts of US short-term interest rates: a lexible forecast combination approach. Journal of Econometrics, 150 (2), 297–311. Guo, F., Chen, Carl R., and Huang, Y. S. (2011). Markets contagion during inancial crisis: a regime-switching approach. International Review of Economics and Finance, 20(1), 95–109. Hamilton, J. D. (1988). Rational-expectations econometric analysis of changes in regime: an investigation of the term structure of interest rates. Journal of Economic Dynamics and Control, 12 (2), 385–423. Hamilton, J. D. (1990). Analysis of time series subject to changes in regime. Journal of Econometrics, 45, 39–70. Hamilton, J. D. (1994). Time series analysis. Princeton: Princeton University Press. Harman, Yvette S. and Zuehlke, homas W. (2004). Duration dependence testing for speculative bubbles. Journal of Economics and Finance, 28(2), 147–54. Helwege, J. and Turner, C. (1998). he slope of the credit yield curve. The Journal of Finance, 54, 1869–1884. Hördahl, P. and Michael R. King. (2008). Developments in repo markets during the inancial turmoil. BIS Quarterly, December, 37–53. Hrung, Warren B. and Seligman, Jason S. (2011). Responses to the inancial crisis, treasury debt, and the impact on short-term money markets. FRB of New York Staf Report 481. Kaminsky, Graciela L., Reinhart, Carmen M., and Végh, Carlos A. (2004). When it rains, it pours: procyclical capital lows and macroeconomic policies. NBER Macroeconomics Annual, 19, 11–82. Keane, F. (1996). Repo rate patterns for new treasury notes. Federal Reserve of New York. DOI: 10.1057/9781137561398.0013



References

Kilian, Lutz. (1999). Finite-sample properties of percentile and percentile-t bootstrap conidence intervals for impulse responses. Review of Economics and Statistics, 81 (4), 652–60. King, M. and Wadhwani, S. (1990). Transmission of volatility between stock markets. Review of Financial Studies, 3(1), 5–33. Kodres, Laura E. and Pritsker, M. (2002). A rational expectations model of inancial contagion. Journal of Finance, 57(2), 769–99. Koop, G., Pedersan, M., and Potter, S. (1996). Impulse responses in nonlinear multivariate models. Journal of Econometrics, 74, 119–47. Krishnamurthy, A. and Vissing-Jorgensen, A. (2012). he aggregate demand for treasury debt. Journal of Political Economy, 120(2), 233–67. Krolzig, H.-M. (1997). Markov-switching vector autoregressions: modeling, statistical inference, and application to business cycle analysis. Berlin: Springer-Verlag. Kyle, Albert S. and Xiong, W. (2001). Contagion as a wealth efect. Journal of Finance, 56(4), 1401–40. Lane, P. R. (2012). he European sovereign debt crisis. Journal of Economic Perspectives, 26, 49–67. Lauricella, T., Fidler, S., and Gonglof, M. (2010). Fears of domino efect pervade Europe. Wall Street Journal, November 24. Lewellen, J. (2004). Predicting returns with inancial ratios. Journal of Financial Economics, 74, 209–35. Longin, F. and Solnik, B. (2001). Extreme correlation of international equity markets. Journal of Finance, 56(2), 649–76. Longstaf, F. (2004). he light-to-liquidity premium in U.S. treasury bond prices. Journal of Business, 77, 511–26. Longstaf, F. (2010). he subprime credit crisis and contagion in inancial markets. Journal of Financial Economics, 97, 436–50. Longstaf, Francis A. (2002). he light-to-liquidity premium in US Treasury bond prices. NBER working paper No. 9312. Lou, X. and Sadka, R. (2011). Liquidity level or liquidity risk? Evidence from the inancial crisis. Financial Analysts Journal, 67, 51–62. Lütkepohl, H. (1993). Testing for causation between two variables in higher-dimensional VAR models. In: Studies in Applied Econometrics. Physica-Verlag HD, 75–91. Lütkepohl, H. (2005). New introduction to multiple time series analysis. New York: Springer. Milne, R. (2011). French bond trading soars on contagion worries. The Financial Times, August 15. DOI: 10.1057/9781137561398.0013

References



Neal, R., Rolph, D. S., and Morris, C. (2001). Interest rates and credit spread dynamics. Working paper, Indiana University. Nelson, Daniel B. (1991). Conditional heteroskedasticity in asset returns: a new approach. Econometrica: Journal of the Econometric Society, 59(2), 347–70. Pagan, Adrian R. and Sossounov, Kirill A. (2003). A simple framework for analysing bull and bear markets. Journal of Applied Econometrics, 18 (1), 23–46. Papademos, L. (2009). he role of the ECB in inancial crisis management. BIS Review 65, 1–16. Pesaran, M. Hashem and Timmermann, A. (1995). Predictability of stock returns: robustness and economic signiicance. Journal of Finance, 50(4), 1201–28. Potter, Simon M. (2000). Nonlinear impulse response functions. Journal of Economic Dynamics and Control, 24 (10), 1425–46. Pritsker, Matt. (2001). “he channels for inancial contagion”, International inancial contagion. Springer, 67–95. Runkle, David E. (2002). Vector autoregressions and reality. Journal of Business & Economic Statistics, 20 (1), 128–33. Sims, Christopher A. (1980). Macroeconomics and reality. Econometrica: Journal of the Econometric Society, 48(1), 1–48. Sims, Christopher A. and Zha, T. (2006). Were there regime switches in US monetary policy? The American Economic Review, 96(1), 54–81. Vayanos, D. (2004). Flight to quality, light to liquidity, and the pricing of risk. NBER Working Paper No. 10327. Wheelock, D. C. (2010). Lessons learned? Comparing the Federal Reserve’s responses to the crises of 1929–1933 and 2007–2009. Federal Reserve Bank of St Louis Review, March, 89–108. Zellner, Arnold. (1962). An eicient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American statistical Association, 57 (298), 348–68.

DOI: 10.1057/9781137561398.0013

Index ABS, viii, 2–4, 6, 29, 30, 32, 34, 36, 39, 42, 45, 51, 56, 69, 70–72, 77–80, 83–87, 90–95, 101, 109, 110, 117, 118, 120–22 asset-backed security. See ABS autoregressive, ix, 14, 19–21, 23, 25, 40, 51, 55, 56, 66, 102, 125, 127 bear phases, 20 bubble, 64, 101, 116 bull regimes, 20 Choleski, 15, 17, 18, 21, 26, 92 collateral, 3, 8, 11, 12, 29, 30, 36, 79, 83 contagion, viii, ix, 1, 2, 6–10, 17, 19, 28, 29, 39, 68, 69, 71–73, 78–80, 83, 85–87, 89–91, 94–96, 98, 102, 105, 108–10, 117, 119–28 crisis, viii, ix, 1–7, 11, 29, 30, 63–65, 69, 70, 72, 77–80, 83–87, 90–96, 98, 101, 102, 105, 108–10, 113, 117, 119–28 cross-asset, viii, 7, 56, 69, 120, 122 cross-country, viii, 7, 94, 122 cross-market, viii, 6, 7, 94, 98, 109, 117 dividend yield, 31, 32, 34, 37, 39, 45, 46, 51, 56, 63, 71, 77, 80, 86, 87, 91, 96, 101, 102, 105, 121



duration, 63, 64, 67, 85, 93, 98, 102, 121 ECB, 6, 11, 98, 109, 117, 122, 128 EM algorithm, 24 equity markets, viii, ix, 8, 29, 31, 45, 70, 94, 95, 110, 117, 122 Federal Reserve, ix, 3–5, 10–12, 117, 124–27, 129 financial instability, 10 fire sale, 4 fixed income, viii, 5, 20, 29, 36, 46, 51, 56, 64, 70, 94, 95, 98, 101, 102, 123 flight-to-liquidity, 7–9, 69, 70, 78, 79, 105, 109, 116, 120, 123, 125 flight-to-quality, 7, 9, 69, 71, 80, 84, 96, 101, 105, 108, 109, 116, 120–23 funding, 3, 8, 11, 71, 125 hedge funds, 2, 30, 85, 121 information channel, 7, 70, 72, 89, 90, 91, 108, 120, 121 institutional investors, 30, 79, 85 interest rates, 20, 22, 36, 54, 93, 98, 121, 124 least squares, 15 liquidity, 4–6, 8, 9, 11, 12, 70, 78, 79, 105, 117, 123, 125, 126, 128, 129

DOI: 10.1057/9781137561398.0014

Index

long-term, 5, 9, 31, 32, 34, 36, 37, 39, 42, 45, 51, 56, 63, 77, 80, 84, 85, 87, 90, 92, 93, 95, 96, 101, 105, 121 margin, 8, 12 market freeze, 4 Markov switching, ix, 19, 20, 22, 125, 126, 127, 129 maximization step, 25, 27 mortgage-backed securities, 5, 29 MSVAR, 20–23, 26, 50, 51, 54–56, 63, 64, 69, 70–72, 77, 78, 83, 87, 90–93, 98, 102, 108, 110, 116, 118, 120, 127 multivariate Least Square, 16 noise, 10, 14 not linear, 21 OLS, 16 on-the-run Treasuries, 11, 36 policy, ix, 20 policy measures, ix, 123 policy-makers, ix, 2, 5, 119, 122 portfolio, 9–11, 36, 85, 93, 96, 119, 122, 123 propagation, 2, 7, 70, 113 reduced form VAR, 15 regime shift, 22, 96 repo rate, 4, 30, 32, 34, 39, 45, 46, 51, 56, 70, 73, 78, 79, 90, 95, 96, 105, 108, 117, 120, 123 repo run, 3 returns, 9, 10, 20, 29, 31, 32, 36, 53, 69, 86, 124, 126, 128 risk aversion, 10, 71, 80, 83, 87, 93, 105

DOI: 10.1057/9781137561398.0014



risk premium, 7, 9, 10, 34, 37, 63, 69, 71, 80, 83, 85, 86, 91, 92, 105, 108, 109, 120, 121, 123 risk premium channel, 9, 71, 80, 83, 85–87, 105, 109, 121 shock, viii, 2, 3, 7–9, 12, 14, 17, 18, 25, 29, 45, 69, 70–72, 78–80, 83–87, 89–93, 96, 102, 108–10, 117, 118, 120–23 short-term, 4, 5, 9, 31, 34, 36, 37, 45, 46, 56, 77, 79, 80, 83–85, 90, 93, 96, 101, 105, 108, 116, 121 spread, viii, ix, 3–6, 29, 32, 38, 39, 40, 42, 46, 51, 54–56, 63, 64, 69, 70, 71, 77, 80, 83–87, 92, 96, 98, 108, 110, 116, 120, 121, 126 standard form, 15, 17 stayer probability, 63, 64, 67 stock, 4, 7, 9, 12, 20, 28, 32, 36, 69, 72, 84, 86, 95, 101, 116, 121, 124, 126, 127 structural VAR, 15 sub-prime, viii, 2, 5, 7, 28, 29, 30, 64, 69, 70, 77, 79, 80, 83, 84, 86, 87, 90, 91, 101, 113, 120, 121 switch, 54, 72, 102 time-varying, 8, 10, 20 transition matrix, 21 transmission mechanisms, ix Treasury bonds, 4, 11, 28, 30, 34, 39, 45, 69, 70, 79, 120 VAR, 14–19, 21–23, 26, 38–40, 42, 46, 51, 53–55, 63, 69, 70, 72, 90, 98, 102, 108–10 volatility, 6, 8–10, 22, 32, 34, 36, 63, 64, 69, 72, 77, 78, 80, 84–86, 92, 93, 96, 98, 101, 110, 113, 120, 121, 127