SPECULATIVE COMPONENT OF MARKET QUOTATIONS OF FINANCIAL ASSETS

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SPECULATIVE COMPONENT OF MARKET QUOTATIONS OF FINANCIAL ASSETS Magomet Yandiev1 Economic Department of Moscow State University Abstract. In this work the author analyzes the speculative component of market quotations of financial assets. The author specifies the assumptions on which builds a model explaining the cause of the volatility of the market quotations. The author encourages renounce conventional stereotypes, for example, that risk and return are linked. The author explains why the information is not reflected in the market quotations of financial assets during speculative investment. In this work the author presents the financial asset pricing model in which the probability of success of speculative strategy is a key element. (JEL G12, G14)

INTRODUCTION

Among investors there is tremendous demand for models explaining the behavior of market quotations. All scientific articles on this subject can be divided into two main blocks. The first block is the articles in which the quotations of financial assets due based on discounted dividends model. The key article were written by Williams (1938), Gordon M. (1962) and Scott B. (1969). The second block is the articles in which quotations is due based on econometric models. Key works - Sharpe W. (1964), Lintner J. (1965), Mossin J. (1966): the Capital Asset Pricing Model (CAPM), as well as Ross S. (1976, 1984) and Richard Roll (1984): the Arbitrage Pricing Model (APM). All models have been empirical verificated, but none of them has received unconditional recognition. Shiller (1981) tested the quality dividend discount model based on Standard and Poor's Composite Stock Price Index and the Dow Jones Industrial Average. As a result of calculations he finds that this model is not valid. Akdeniz, Salih, Tulug (2003) proof that the findings of previous works are not warranted. Opposite results were obtained Capelle-Blancard (2004): dividends and market quotations are not related. The authors also studied the relationship between the historical return of stocks and market quotation of stocks and also concluded that there is no connection. With regard to verification model CAPM, Roll (1977) claimed that the CAPM model cannot be verified. Fama E. and French K. (1992) came to mixed conclusions. Bali and Cakici (2004) conducted regression analysis of model and concluded that beta coefficients unable to explain the variance return of companies stocks. 1

I wish to express my gratitude to the following colleagues for their help and support at various stages of this study: Renat Bekkin, Yury Danilov, Bella Zlatkis, Alex Kirianov, Maxim Kleymenov, Olda Dittrih, Evgeniy Seredinskiy, Ekaterina Egorova, Maria Volkova, Anna Gnevsheva, Alex Markin and to a great many students of the Lomonosov MGU Department of Economics, who provided ―the testing ground‖ for the author‘s arguments. Author‘s internship in the Czech University of Life Sciences Prague (Czech Republic) contributed to the writing of this study. Internships took place through the Erasmus Mundus - External Cooperation Window program.

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Trying to solve the problem many of authors trying to find a pricing factors, which would explained the arise in the studies. Smith W. (2001) develops the idea according to which "the spirit of capitalism", which means the desire to possess property, affects the price of financial assets through increased risk aversion. To date, the global scientific thought has created a host of financial asset pricing models, but the asset pricing and volatility formation mechanisms as well as parameter relationships in trading remain enigmatic. The key element of this paper is a set of assumptions that simplifies the current situation in the stock market and enables the processes taking place therein to be formalized. The key assumption excluding any investment activity from the analysis is that no new information has come in the market during the analysis. The main conclusions of the research: 1. A financial asset‘s risk and return are not interrelated in speculative trading and thus the portfolio theory does not apply thereto. 2. If N of securities are circulating in the stock market, it means N+1 of finance assets are actually circulating in there. 3. If the mathematical expectation of return on speculation in financial markets is less than the current rate of return in the interbank credit market, a professional participant will close up his financial activities in financial markets and transfer his assets to the interbank market. 4. Financial markets provide the conditions for manipulative transactions when the mathematical expectation of return on speculative transactions goes below the current value of the interbank market return, with no funds flowing from the stock market to the interbank market. 5. The higher the dealer-estimated probability of success of his speculative strategy, the higher the risk he would be willing to assume (the higher quotation he would be willing to offer). 6. Information is not a mandatory component for the dealer to carry out speculative trading. Certainly he may use it but he is basically indifferent to the information flow. 7. The modern exchange trading system accepted globally, including Islamic countries, violates a few fundamental principles of Sharia and cannot be used in Islamic countries. 1. The Securities Credit concept within the market quotations structure 1.1. Assumption underlying the concept Researching an extremely complicated object (which is what a quotation certainly is, its complexity depending on the vast number of influencing factors; part of such factors, such as information, are so far not amenable to formalization) is only possible by simplifying the research object. Any research, 2

therefore, should be started with artificial setting of financial market conditions that will allow logically relevant conclusions as to the behavior of financial asset quotations. To formulate such conditions, we need to know who generates quotations. The answer is obvious and well-known. There are two basic bidder categories – brokers and dealers. We should therefore set assumptions in a way ruling out any unformalized effects that the many factors may have on brokers and dealers and allowing us to identify the basic situation that, on the analogy with physics, may be termed ―an elementary particle of the bidding procedure‖ in which the behavior of professional participants may be objectively investigated. We have formed the following assumptions based on the above considerations. Over the period during which the researcher is watching quotations: 1. no information comes into the market; 2. existing prices reflect all the known information; 3. no information is expected to arrive in future; 4. brokers receive neither purchase nor sales orders; 5. brokers do not have any outstanding purchase or sales orders; 6. no investment inflows and outflows occur in the market; 7. dealers are professionals of about the same level and their asset risk assessments are generally similar; 8. degree of the dealers‘ persistence in increasing the capital under their management is about the same; 9. trading is conducted in similar lots (number of securities); 10.each transaction is conducted at equal time intervals; 11.each particular transaction will be watched in the trading process. In other words:  there are no news updates and even no rumors are rife so that no information urges the traders to revise quotations (macroeconomic, microeconomic, political, image etc.);  there are no orders from customers, including outstanding ones, so the brokers are not involved in trading and therefore their influence on quotations is absolutely ruled out;  accordingly, only dealers stay in the market, who have no objective grounds to revise quotations either. Let us also assume that: 12.the number of dealers operating in the market is not relevant but is sufficient to maintain competition: then any price manipulations are impossible and the price of each subsequent transaction is really unpredictable; 13.of all financial markets (stock, currency, derivative and interbank market), only one exists – the stock market; 14.the stock market is organized as a exchange market; there is no OTC stock market; 3

15.there is only one financial asset – equity shares of a certain company – that is traded. Our starting point in this research will be the following: there is only one financial asset in the market and there are no objective grounds for revision of its current quotation. 1.2. Professional participant’s basic motivation Under the set assumptions, a dealer will actually be isolated finding himself in vacuum-like conditions2. Then what will his motivation be? What will he think about and go by in circumstances where there are no reasons for him to review quotations? As human beings, traders of any dealer may be distracted during their work time by talking to their colleagues, personal Internet correspondence etc. Yet, the basic motivation is a need to manage the funds they are entrusted with. The ―need for management‖ means the need to increase these resources, that is to say the need to raise the capital value. This is the basic motivation that will always matter to professional participants, regardless of whatever we may assume. 1.3. Securities Credit – the key quotation element Now, taking this motive into account, let us discuss the dealer‘s behavior in the perfect ―vacuum‖ environment that we have created by introducing the assumptions. It should be noted that dealers remain face to face with one another. They are almost equally skilled and motivated to derive income3. There are no amateur investors ―around‖ them, i.e. in the market, on whose mistakes they could capitalize. Nor is there an information influx and, therefore, and any reason to revise estimated cash flows within the company. Thus the only way for them to earn is have the funds managed by another dealer redistributed4 for their own benefit. The only tool at their disposal to do it is change the purchase or sale bids that have been put in. Logically, in the above situation a professional player have absolutely no objective grounds to revise quotations. Nevertheless, he will regularly put in purchase or sale bids differing from the current benchmark/fair price, hoping that he will thus be able to have part of the funds managed by other dealers redistributed for his own benefit5.

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Imagine a normal, physically fit person submerged in a bathtub with warm water of 36.6ºC, with the bathroom lights off and its walls soundproof. What will such a person think about? About whatever he has in his memory. But such thoughts will only be the result of his own immediate choice rather than of any external action. 3 Motivations may vary in case some companies offer the trader‘s fee tied to the capital value increase, while others do not. I repeat: motivations are supposed to be equal. 4 Note the point in case is a trite redistribution of another‘s funds for one‘s own benefit rather than earnings or creation of a new value. 5 Note that in practice adjacent transactions (tick quotations) with a liquid paper hardly ever have similar quotations. Incidentally, a second‘s trading period may well be regarded as trading under the conditions extremely close to the preset assumptions. According to the author‘s estimates (source – www.finam.ru), while up to 20-30 transactions per minute are recorded in the Russian market, it is by an order more in global markets.

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Putting it otherwise, the objective reason – motivation (i.e. the need to increase capital) – compels professional players to conduct a multitude of purchase/sales transactions. From the intuitive viewpoint, the situation seems illogical: since there is no reason to revise quotations, then, logically, trading should either be discontinued or conducted at a constant price. But it is not and the price is unstable. In this case the dealer behavior looks more like a game, i.e. a procedure based on win or luck6, than exchange trading, i.e. a procedure relying upon establishment of fair prices. A questing naturally arises: if there are no grounds for quotations to be revised but they are in the course of trading, what is that magic stuff a professional player trades in? Modern financial science recognizes that the quotation comprises a company‘s present value of future cash flows and furthermore asserts that the quotation is a sum of the present value and something else. This ―something else‖ may only be some other finance asset and nothing else (no spices, oil or bricks). Hence, the quotation is a sum of the value of two (or more, theoretically, but we abandon this version) finance assets, each of which may be represented as the present value of its cash flows. The first cash flow is from a specific company whose name is borne by a traded security and the second one is from an unknown object. For maximum possible coverage of the situation, let us consider the ―first‖ asset, i.e. the company‘s present value of future cash flows, to see if it can be traded on a stock exchange (meaning frequent change of the owner, not a oneoff sale). Running ahead, it should be noted that the asset in question cannot be an object of regular trading at all due to its features. This argument may be supported by the following. Let us first consider a standard equitype product, say, a table. May the table be of interest, as regards its multiple purchases and sales, in unchangeable economic conditions? Suppose the table price is 100 rubles and the first buyer buys it for this money. Then the first buyer decides to sell the table. Will he be able to sell it at a higher price and earn some return? He will, if any critical business environment has changed and he will not if no such change has occurred (this is exactly what we have assumed). Nor will he be able to resell the table for the same 100 rubles because a new buyer will realize that the price of this product is unchangeable and will not grow. Besides, it is simpler and less risky for him to buy this table from the original vendor (manufacturer) than to rebuy it from the first owner. You should also be mindful of transaction costs that each bargain involves. Then striving to turn the table into traded merchandise is likely to result in the market price splitting into the purchase price and the selling price, as is, for one, the case with foreign currency retailing. 6

The following key definitions have been found on yandex.ru: Game is a nonproductive activity engaged in for diversion or amusement associated not only with the result, but also with the activity process itself. Game is a physical or intellectual activity lacking in direct reasonable practicality and enabling an individual to selfactualize, going beyond the scope of his current social roles. Game is a type of lottery differing from the traditional one in that it sets a game period during which chances to win vary.

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Let us now move on from the table price to the company‘s present value of estimated cash flows. The situation will be the same. The present value (remember, in our case it is constant since there are no grounds to revise it, including information on a forecast change in the company‘s financial parameters) will be unchangeable, so traders will sustain a loss rather than earn on its purchase and sale. This asset, once its owner has changed, will no longer be in demand. Then we may state that of the two assets comprising the quotation the first one takes no part whatsoever in forming its volatility, hence it is the second one that has to be examined for the reasons for the existing variability. Since the ―second‖ one is in any case a finance asset and various types of assets only differ in the cash flow structure, we need to understand the order of the ―second‖ asset cash flows. Recall that there are three varieties of finance assets, all told (see Fig.1), if they are classified by cash flow structure, viz:  simple credit means repayment of the principal along with charged interest by a single payment at the end of the loan period;  bond means payment of interest during the loan period and repayment of the principal at the end of maturity;  stock means distribution of dividends over an indefinite period. Stocks and bonds are not suitable to play the role of the ―second‖ asset as their structures imply payment of interest or dividends and trading practices provide for no interest to be paid in the intervals between transactions closed in the market. Dividend distribution existing in the market is part of the present value of estimated cash flows, that is, it does not pertain to the ―second‖ asset. Then using the method of elimination, we have the only alternative left – to recognize that by its cash flow structure the ―second‖ asset corresponds to the simple credit.

PVstock PVbond PVcredit

D1 (1 r ) C1 (1 r ) FV (1 r ) n

D3 D5 D2 D4 ... (1 r ) 2 (1 r ) 3 (1 r ) 4 (1 r ) 5 C3 Cn Nn C2 ... (1 r ) 2 (1 r ) 3 (1 r ) n (1 r ) n C N (1 r )

Fig.1. Three basic types of cash flows Since this was the key thesis of the Concept, I will repeat it in other words. In the preset conditions where there is no fresh information and, accordingly, the present value amount of any finance asset, both ―first‖ and 6

―second‖, must be invariable, the quotation amount may only change if one of the assets (it may only be the ―second‖ one) is regularly replaced with a similar new asset of a different value, though. It means, in particular, that the ―second‖ asset‘s life must be extremely limited (tick). We may offer here the only reasonable explanation for what is understood as ―replacement‖: retirement at time point t of the asset issued at time point t-1 and issue of a replacement asset. Since the ―second‖ asset‘s life (i.e. its validity period) is limited, it cannot be a stock a priori. Thus the quotation varies because its ―second‖ component, on which no interest is paid, is regularly renewed. It means the ―second‖ component cannot be a bond and is, therefore, a simple credit. Ultimately, we arrive at the next market quotation structure. It comprises the present value of cash flows expected from the issuer and a short-term credit (Securities Credit, SC) that professional participants extend one other7. Then the return on stocks under each individual transaction may be expressed by the following equation:

r

RPV

RL

[1]

 r is financial asset return;  RPV is return on the company‘s present value of cash flows;  RL is return on (present value) a short-term credit. Let us consider a fictitious example (see Fig.2). Assume that the market quotation of a stock under the last transaction was 100 rubles and the company‘s present value of cash flows is known to be 70 rubles. It means that, while conducting this transaction, the buyer purchased the company‘s present value of cash flows from an anonymous seller at a fair price, i.e. 70 rubles, and granted the seller a credit of 30 rubles. For the seller it means that he sold the company‘s present value of cash flows for the same sum as he had bought it and got back the earlier extended credit of 30 rubles8. Let‘s assume now that the next transaction price was 105 rubles, which implies that the buyer paid the same 70 rubles for the company‘s present value of cash flows, but this time granted a 35 rubles credit. It corresponds to a 5percent market return on the stock, this return being all due to the ―second‖ component – the securities credit. Now as to the above transaction from the seller‘s side: he gets back his 70 rubles plus the earlier extended credit of 35 rubles.

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Theoretically, a reversed situation (with a loan) is possible. If we knew the amount of the credit he granted as he bought this stock we could calculate the return for the seller (he could have extended credits both of 20 rubles (that would mean a positive return) and 40 rubles (negative return)). Since no such information is available we can only talk about market return in this paper, meaning the return resulting from comparing the transactions taking place in the market, irrespective of what exactly dealer has conducted them. 8

7

120

Total Price

100 80 Credit

60

PV

40 20 0

100

105

110

85

95

Credit

30

35

40

15

25

PV

70

70

70

70

70

securities trade

Fig. 2. Quotation structure variations throughout five transactions The third transaction amount was 110 rubles. Like before, the buyer purchased the company‘s present value of cash flows for 70 rubles and extended a credit but this time in the amount of 40 rubles. The market return on this transaction may be estimated at 4.76 percent. And so on. As seen from Fig.2, while the present value remains unchanged, the ―second‖ component varies whereby ensuring stock volatility. It should be reminded that had it not been for the securities credit the asset quotation would have turned into two simple components – the purchase price and the selling price. 1.4. Securities Credit formation mechanism In accordance with the preset assumptions, the basic situation for the stock market is when professional participants are only driven by their motivation. In this case they naturally strive for profit that cannot be made except through another market participant. In the context where none of external factors can affect a stock price, such a factor has to be created artificially. Then all the professional participant‘s efforts, i.e. putting in purchase and sale bids, are akin to a game of chance, nearly like in a casino, because there are no grounds whatsoever, I repeat, for any growth of the asset value in the market. A professional participant will sell and buy in the hopes for a luck-based profit. What may constrain him somehow is the limit amount of loss and transaction costs. The rules of the game are apparent: granting (imposing) a credit to (on) an unknown partner9 ―in a maximum possible amount‖10, for a period determined 9

The partner is unknown in exchange trading.

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by the market11 with repayment ―to the extent possible‖12. More simply, it‘s like invest less, take more. This is a game for and with money. I guess the securities credit formation mechanism is rooted in the collective, subliminal self inherent in humans. An example of my personal observation is how people in a crowd awaiting to step onto the escalator stairs start rocking from side to side synchronously. There was no one who organized these people or gave any commands. It‘s just that every person realizes that when he moves ahead in small steps waddling left-right (such is walking mechanics) he may feel great discomfort if he keeps pushing and being pushed by fellow passengers walking on the right and left, who have the same choice (waddling left-right). So every rational person (long pushing in the subway makes everyone rational) seeks to match the waddling movements of his body to those of people walking alongside him. The result is the wave effect. We can assume, therefore, that professions participants, as they find themselves feeling discomfort (no chance of making profit on trading in the company‘s present value of estimated cash flows and, hence, the risk of a potential decrease in the value of capital under their trust management) will look for ways to coordinate their actions. Obviously, there may be no direct analogy with the above example, because professions participants have different tools available and different goals, too. Yet, they intuitively identify and accept, without agreeing upon, the only possible way of creating volatility in the stock market, i.e. trading in a short-term credit with one another. In fact, the securities credit is the very ―bubble‖ that is said to exist in the stock market in times of crisis. We do argue this bubble exists there at all times. And it is due to its existence that we have the stock market in the speculative form, in which it has operated in different countries and in different times. Trading in actually ―redundant‖ money, supported by nothing, is possible due to the market being a somewhat limited-access area, since becoming an investor for most persons is only possible through buying stock in the secondary market, i.e. by having to accept the rules of the game (extending a credit). A possible credit formation mechanism may be exemplified by the developments after the primary stock issue. Let us assume that a company has placed stocks at the present value of estimated cash flows. This is a fair price that must remain unchanged unless there are reasons for change. But the market equilibrium situation is not something that satisfies a professional participant, as it disables him to earn on speculation. So, as soon as trading starts he will offer the present value along with a credit to the community, estimating 13 that eventually this credit given to him by the first buyer will be repaid to the latter by a second buyer and probably so at a interest rate acceptable enough. By accepting and extending credits, professional participants create volatility ―with 10

It is impossible to know in advance a transaction price in exchange trading. Even if a professional participant does make a competitive bid, it does not necessarily mean the bid will be accepted. 12 I‘d like to say once again that the future price of a transaction is always unknown. 13 Rather ―in the hopes‖, because ―estimating‖ tends to be applied to objective transactions. 11

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their own hands‖. Again, such volatility may not exist when only the present value of future cash flows is traded. 1.5. Securities credit risk and return The amount of the securities credit, I believe, depends on the company‘s present value of cash flows, while the ratio of such dependence, in all appearance, depends on the general market factors (information circulating in the market, supply-and-demand situation etc.) and on the structure and features of a local stock market and market makers. We have derived a rule that will work in the set assumptions environment where, I remind, there are no objective grounds for changing the credit amount (nor is such changing prohibited, though): the average value of return on a securities credit per transaction calculated for the entire trading period will be zero or extremely low.

Rm

r1

r2

r3 ... rm m

0

[2]

 Rm is average return for the period  rm is return on each transaction  m is number of transactions. The above may be substantiated by the following. The securities credit amount may vary due to market unpredictability and professional participant‘s motivation, with every participant aware that any deviation from the real (initial) credit value is artificial, ungrounded. Any professional participant, therefore, will always seek to return to the initial credit value and then the total (accumulated) credit return value for a trading period will be zero or as close to zero as possible. It‘s only natural, then, that the average return on one transaction is an extremely low value. This rule enables a new understanding of asset risk. Let us now discuss a fictitious example (see Fig.3). Assume that the first transaction is conducted at a securities credit return of +3%14. It means that, to restore the balance, the return on the next transaction must be –3%. In this case the credit value (and the stock value as a whole) will return to the natural, initial state. Assume now that the return on the second transaction is –1%. It means that, to restore the balance, the return on the next transaction must be –2%. And so on. This example shows that, while unaware of the actual return on the next transaction, the professional participant will always know the ―expected‖ return15, i.e. the one that helps restore the initial value of an asset quotation. 14

It will be reminded that, according to the set assumptions, the return on the discounted cash flow is zero. In this paper we put the term ―expected‖ return in quotes because it differs from the one traditionally accepted in financial markets. 15

10

4 3 2 1

%

0 -1

1

2

3

4

5

Actual Return Expected Return

-2 -3 -4 -5 -6 -7

Fig.3. Actual and ―expected‖ return Formalization of the above example creates the following expected return formula:

Ri

Ri

ri

1

1

[3]

 r is actual return (always a random value)  R is expected return (calculated value). Considered traditionally as the risk of a finance asset has been deviation of its return from the average return for the period, i.e. the standard deviation. Such a parameter is a risk for the present value of cash flows (naturally, where there are grounds for their volatility). The above traditional approach, however, does not apply to the securities credit because, it will be reminded, the average return for the period is zero. In such circumstances the return deviation from zero cannot pose any risk to a trader (just as in usual calculation of the standard deviation); on the contrary, he needs this deviation to sway the market and create volatility (this stems, I repeat, from the dealer‘s motivation). Each individual transaction risk (RSKi) will be the absolute value of deviation of the actual return from the ―expected‖ one. It is when it deviates from the ―correct‖ value that it takes risk.

RSK i

ri

Ri

[4]

To be precise, we may say that the current transaction risk value will always be equal to the value of the expected return on the securities credit of the next transaction taken by the module: 11

RSK i

Ri

1

[5]

In this case the formula for calculating the period‘s securities credit risk (standard deviation module) remains the same, except that the expected return value (now it will be a new number, Ri, every time) will be inserted instead of the arithmetic average (typically, it is the same value every time): n

Ri ) 2

(ri i 1

n

[6]

Then a description of the parameters of a securities credit traded in the market may be as follows. The return for the period is 0%, volatility – e.g. 25% and risk – e.g. 15%. It implies that the deviation of the actual return on the securities credit from the expected value averages 15%. But then the securities credit turns out to be an asset directly opposed to an asset with risk-free return – it will have an ―unprofitable risk‖. In other words, whatever risk is assumed by the dealer, it will not affect his earnings. Hence the conclusion that is critical for the stock market: securities credit risk and return are not interrelated. Since the securities credit is one of the two quotation components, the stock must not generally have any clearly defined and consistent relationship between risk and return16. In this case, the higher the percentage of the securities credit in a stock quotation, the higher the uncertainty of the stock risk - return relationship.

2. Financial Markets within the Securities Credit concept 2.1. Real number of assets in the market For further analysis we need to ease off the set assumptions. We have previously assumed that only one issuer‘s stocks are traded in the market. Let us ease off assumption 14 and suppose that two issuer‘s stocks (common stocks as before) are now traded in the markets. The increased number of traded assets notwithstanding, the dealer motivation remains the same and, as before, dealers have no grounds to revise quotations (of two common stocks this time). Logically, quotations should be stable but they will keep varying because of the dealers seeking to redistribute part of other dealers‘ capital for their own benefit. Just as before, the dealers will realize that what they do is only deviate prices from the fair price and, just as before, they will abide by the fair price as the 16

There is certainly a relationship between risk and return on the issuer‘s present value of future cash flows, which follows from the discounting formula.

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basic level. Hence, in elaboration of formula 2, the overall result will be the same: the average ―market return‖17 (the sum of average returns on securities credits of two stocks) will be zero: Rm = r1 + r2 = 0

[7]

 r1 – average return of the securities credit of stock No.1 for a period  r2 – average return of the securities credit of stock No.2 for a period. This provides the dealers with an opportunity to devise more complicated trading strategy than those with only one security circulating in the market. Thus, for example, a situation is possible when during or after trading one of the securities has a high return, then another one has a negative return. In this case the average market return will remain zero anyway, subject to the following equality: r1 = - r2 [8] From the viewpoint of devising trading strategies, it means that even in the preset conditions the return on one of securities may grow for some reason unknown, provided that the return on a second stock decreases accordingly. Let us now assume that common stocks of three or more issuers are circulating in the market. According to the above logics, the ―market return‖ will still be zero, with the absolute amount of a securities credit remaining unchanged but redistributed among securities: Rm = r1 + r2 + r3 = 0

[9]

In this case, however, the number of trading strategies increases dramatically and the market loses its demonstrativeness. I will now clarify this idea. In the case of two securities, dealing for an artificial rise of one of the securities would be apparent because the return on the other one would fall accordingly. In the case of a great number of securities circulating in the market, the above will not be apparent and it will be extremely difficult, if at all possible, to visually identify a security involved in coordinated, purposeful speculations for a rise or fall undertaken by a group of dealers. Thus we may conclude that with any number of assets in the market the market return on a securities credit will be zero. In this case each of the assets will have a risk (standard return deviation). Let us continue analyzing. It is important to emphasize that the ratio of the number of transactions conducted with the first, second, third etc. security does not matter: whether there have been more transactions with the first, second or 17

The term ―market return‖ is put in quotes as here we are not talking about the total return on stocks but only about that on their elements, i.e. securities credits. There is a difference because, while calculating the return on a securities credit or the entire stock value, we obtain various digital results. True enough, this difference is not critical.

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third security. Nor does the trading sequence for these stocks matter: whether a transaction was closed with the first stock, then with the second one etc. The thing is, you may remember, that in our case the dealer does not trade in the issuer‘s present value of cash flows which for the most part depends on each issuer‘s specific factors. He trades, in fact, in a securities credit that only depends on a lucky conjunction. This factor equalizes chances for different stocks, which raises the question: does a dealer trading in a securities credit have any fundamental preferences as to what security to trade: common or preferred stocks or bonds? May it be that one of these securities gives better chances of success in speculative trading? In other words, we now give up the assumption that assets traded in the market are only common stocks18. We now have common and preferred stocks and bonds circulating in the market. Quotation of each security comprises, as before, the discounted cash flow and securities credit. Just as before, the return on the discounted value is zero. While different variability of the discounted value of different asset types may affect the variability of a securities credit, in our case the present value of each security paper is zero and thus it does not affect the securities credit. Then it makes no difference whatsoever to the dealer in what particular instrument (stock or bond) to invest, because variability of all security types will equally depend only on that of the securities credit. A professional participant, therefore, will choose the asset that he believes may best help him implement his speculative strategies. Thus an efficient and rational professional participant trades in all assets in all markets available. In other words, he trades in a securities credit through any security circulating in any of the securities market segments. All the above considerations allow another important conclusion to be drawn: if n securities are circulating in the stock market it means that n+1 finance assets are actually circulating in the market, i.e. n present values and a securities credit. To put it otherwise, we cannot say there are n securities credits in the market by the number of issued securities circulating in the market. In fact, the securities credit is the only asset but traded by all19. 2.2. New content of the market return concept Since the securities credit is the only asset, we need to adjust the traditional term ―market return‖ as a parameter characterizing the market in general and understood as a sum of returns on various securities at one point in time, for example, at closing. The market return parameter, as it is understood today, actually implies that returns of n discounted values and returns of n securities credits are summed up. As we just found out, there are no n securities credits in the market, so multiple summation of securities credits defies logic. 18

Thus we altogether abandon assumption No.14. Going back to §1.4. Securities credit formation mechanism, we may add that the dealer community may supposedly act as the securities credit issuer. Functioning as the securities credit carrier (or securities credit delivery vehicle or securities credit packaging) is the present value of future cash flows of the issuing company. 19

14

Because the securities credit and present value have different qualitative characteristics, it makes sense to consider the term ―market return‖ separately for the securities credit. To determine the content of and the calculation procedure for ―market return‖ for the securities credit, we will take advantage of the well-known enough thesis that, for some reasons, remains yet to be applied to financial markets. The case in point is the statement ―Time is discrete‖20. Simplified to the maximum possible extent, this well-known thesis implies that no event can concur with another. One event always takes place a bit earlier or a bit later than another. This statement correlates with our previous conclusion about the number of assets in the market: in fact, one and the same goods (securities credit in our case) cannot be traded by different traders. Then, in view of the above, “market return” as applied to the securities credit at a specific point in time21 is an accumulated return on the securities credit for all transactions since the trading start. To illustrate the above considerations, let us discuss a fictitious example. Assume that three securities (No.1, 2 and 3) are circulating in the market. Returns on their securities credits22 are shown in Fig.7-9. Pay attention that three horizontal divisions correspond to one second and that the chart is constructed so that no transaction visually concurs with another. Figures 7-9 are specially provided to illustrate how the general market return on the securities credit is formed from individual returns on the securities credit for separate stocks. Доходность фондового кредита 1 Return on the securities creditакции of stock 1 0,4 0,3 0,2 0,1 0 -0,1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

-0,2 -0,3 -0,4

Fig.7. Return on the securities credit of stock 1

20

Discreetness (from Lat. discretus — divided, intermittent) — discontinuity, that is, a property opposite to continuity. Specific point of time – date/time of a specific transaction. No other time intervals are measured in financial markets. 22 Since the return on discounted cash flow is still zero, this is actually the return on a security. 21

15

Доходность кредита акцииof2 stock Return onфондового the securities credit

2

0,04 0,03 0,02 0,01 0 -0,01

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

-0,02 -0,03 -0,04 -0,05 -0,06

Fig.8. Return on the securities credit of stock 2

Return on theфондового securitiesкредита credit акции of stock Доходность 3 3 0,5 0,4 0,3 0,2 0,1 0 1

-0,1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

-0,2 -0,3 -0,4

Fig.9. Return on the securities credit of stock 3 Return onфондового the securities credit for period Доходность кредита за aпериод 0,5 0,4 0,3 0,2 0,1 0 -0,1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

-0,2 -0,3 -0,4

Fig.10. Return on the securities credit for a period

16

Fig.10 shows how the market return on a securities credit is formed from returns on securities credits of different stocks arranged in historical sequence of transactions. Thus, we will have two parameters for each particular point in time (transaction closing time). The first one is a return on the securities credit under a given transaction (specific security) and the second one is the accumulated return on the securities credit by the time of closing a given transaction, which may be considered an equivalent to ―market return‖. Still more illustrative is Fig.11 showing a market return calculated according to the traditional, currently accepted rules. It depicts the market return for each second. To define such a return, two rules should be applied. The first one: if a few transactions have been conducted in the market during a second, only the last one is taken into consideration. The second one: the returns of all the last transactions on each security are summed up. As a result, the set and dynamics of data will considerably differ from those shown in Fig.10. Return on доходность, the securities считаемая credit for a традиционным period, calculated traditionally Рыночная способом 0,6 0,5 0,4 0,3 0,2 0,1 0 -0,1

1

2

3

4

5

-0,2 -0,3 -0,4

Fig.11. Return on the securities credit for a period, calculated traditionally Let us discuss the results of Fig.10 and 11. According to Fig.10, the return of the last transaction is 25%. As seen from Fig.11, the last second‘s return is 35%. To be able to compare both parameters (the return of the last transaction and the last second‘s return), let us bring the first figure into a form consistent with Chart 11. To this end, we will calculate the accumulated last second‘s return using Fig.10. It is 75%. The difference between the two figures is owing to the fact that the traditional method does not take account of all transactions. A similar difference results from calculation of the return for the entire trading period. For the proposed option it is 129%, which means that the speculative component of quotations (securities credit) has increased by this value since the start of trading. Whereas in the traditional calculation (per

17

second returns are summed up) the return for the entire trading period is only 80%. Let us now discuss the term ―market return‖ as applied to the second component of market quotations – the issuing company‘s discounted cash flow. Here, I believe, we should use the traditional calculation of market return as we are now dealing with different assets, not with one (securities credit), as was considered before. Then the market return on a security, according to the new approach, is a sum of two components: the accumulated return on a securities credit and the total return on issuing companies‘ discounted cash flows: Rm = Rfc + RPV

[10]

 Rm is market return  Rfc is accumulated return on a securities credit  RPV is overall return on issuing companies‘ present values of future cash flows. 2.3. New content of the market stability concept Whereas the term ―market stability‖ is not as widely accepted as the term ―market return‖, it is important for description of market conditions. Bearing in mind what we said before, we cannot treat ―stability‖ as a low value of quotation volatility (or more often, asset return), in the way this term is commonly treated. Just as in case of risk related to return (when we said that risk and return are not correlated for the securities credit and are correlated for discounted cash flows) and in this case the term ―market stability‖, as currently treated, should be used separately for these two quotation components. Price volatility for the securities credit is a prerequisite for implementing successful speculative strategies. For the present values of cash flows volatility is evidence of an on-going revision of the company‘s financial parameters, i.e. business instability or doubted business efficiency. Therefore we should find an interpretation of the term ―market stability‖ that would be consistent with logic of both components. This will require the application of another breakthrough thesis23 that will enable the problem to be viewed from a new perspective. The following statement may well serve as such a thesis: ―Rhythmicity is one of the critical performance characteristics of any process‖. To clarify this, I will give another example. When out for morning jogging and doing so at a steady speed, a person has his head ready for any brainwork, i.e. as he jogs he may mull over whatever he wants. But if the person‘s jogging speed varies, his intellectual abilities are dramatically restricted as his attention is distracted by having to ―change gear‖. The stock market situation is similar, I guess. Logic here is as follows: if the trading rhythm is steady, professional participants tend to get accustomed to 23

It will be reminded that the previous breakthrough thesis was ―Time is discrete‖.

18

the time of appearance of every new transaction. Furthermore, they begin getting prepared for the results of every new transaction to be displayed on the PC screen. This preparation may involve working out an action algorithm: if some return is expected I will act this way, if expectations are different I will do so and so. And the idea that a transaction may never have place or that it will not take place soon etc. never occurs to them. If rhythmicity is suddenly broken it will mean that, from the human psychology viewpoint, something unexpected appears in a professional participant‘s trading ―life‖. This brings about confusion and distrust in the on-going process and gives rise to questions such as ―why‖, ―what does it mean‖ and others. As a result, the trading decision making process becomes burdened with reflections that are not directly related to trading. It impairs the trader‘s ability to make fast and effective decisions (both speculative and investment) and, I am sure, increases the number of errors. Thus rhythmic irregularity of transactions tends to impair effectiveness of decisions taken by dealers, which allows the following conclusions: market stability is a situation in trading when transactions are conducted with certain regularity. Here neither the extent of such uncertainty nor quotation volatility matters; market stability is a situation when the trader takes trading decisions in psychological conditions24 that are as comfortable as possible. Market stability may be expressed with the following formula obtained by conversion of the standard deviation formula: s

(ti ti 1 ) 2

[11]

n

 s is market stability  t is time intervals between transactions The market is stable when s is zero. According to formula 11, it is possible when intervals (time t) between transactions are equal: s = 0, if t = const. Market stability should be considered in two versions. The first one is for the securities credit. In this version regularity of transactions should be viewed as general regularity of transactions, i.e. account is taken of any and all securities traded in the market because, as I said before, a professional participant does not care what paper to use (stock or bond) for trading in a securities credit. He is ready to trade in any paper that he believes may help him attain his speculative objectives. Therefore, to reflect the status of speculative activities in the market, regularity should be calculated by all papers in historical sequence of closing the transactions. As far as the discounted cash flow is concerned, to reflect the status of speculative activities in the market, regularity should be calculated by each particular security. 24

Thus we cancel assumption No.10.

19

2.4. Interrelation between the stock and interbank markets To continue our analysis, we will give up the assumption that only one stock market exists. Let us now suppose that financial markets feature the stock market and the interbank market (IM)25. We will first discuss some common and distinctive features of both markets. One common feature is that one asset type (credit) is traded in both markets (in IM it is a credit granted without property pledge, while in the stock market it is a securities credit discussed earlier in this paper, also granted without property pledge). Also, both markets feature the speculative type of trading26 and short-term transactions. Besides, the same dealer banks operate27 in both markets. It should be noted that the investment period in both markets is also the same. Duration of speculative strategies in the stock market almost never exceed one trading day. Similarly, 24 hours‘ (night‘s) crediting is the most ―popular‖ operation in IM. The principal differences between the markets are related to the risk type (in IM, the investor knows in advance the return he will earn, while in the stock market this is not the case in securities credit trading) and trading forms (IM conducts OTC trading). Now we have said enough to formulate the dealer‘s motivation that will drive him in choosing an investment market. A dealer involved in speculative trading does not care in what instrument (we have discussed it earlier) or what market to invest. It is obvious, I believe. What he primarily seeks is to obtain the sought-after return. As to the market where he will earn it, this is something that each professional participant handles on his own using his expertise and skills. Thus, choosing which market to use (stock market or IM) the dealer will think about the maximum return that he could draw. He will transfer his resources to the market (stock market or IM) where he expects to earn the maximum return. The main problem in formalizing the above is that the dealer knows the return he will draw from IM but cannot know the return he will earn in the stock market. Nevertheless, being a professional market maker and using his background of experience, the dealer may intuitively identify his chances to succeed in implementing his speculative strategy. Then the model explaining the rule of selecting a market for speculative investment will be as follows: Re * h > RIM

[12]

 Re is return a professional participant wishes to earn in the stick market by implementing his speculative strategy (―desired‖ return on a securities credit) 25

Thus we ease off assumption No.12. Operations of placing short-term (night, 24 hours), temporary free resources of a bank may not be regarded as capital (investment) operations. 27 May be present if they show a will and make an effort. 26

20

 h is probability of obtaining the ―desired‖ return (in shares, from 0.0 to 1.0), determined by a professional participant subjectively  RIM is return that may be earned through investing in the interbank market. If mathematical expectation of the return which a professional participant anticipates to earn in the stock market is higher than the return he is sure to draw in IM, then the professional participant will transfer his resources to the stock market. And visa versa. Accordingly, the minimum increase of dealers‘ capital in the set assumptions environment (with no information inflow etc.) will be equal to the IM return. The maximum increase will depend on luck in implementing speculative strategies. The dealer may decide to build an investment portfolio, placing part of his funds in IM and using part thereof for speculations in the stock market. Then the model of return on such a portfolio (Rp) may be set as follows:

Rp

We * Re * h (1 We ) * RIM

[13]

We is share of investment in the stock market. Formula 13 allows an intraday limit to be introduced for speculative activities. Such activities must be stopped before the end of the trading day when the absolute return amount expected to be earned in IM is equal to or less than speculation costs (losses from speculation plus transaction expenses). Now, getting back to the risk and return issue. If we present h as h = (1k), then k is a parameter reciprocal to h – failure probability. If risk is to be treated like that (risk as a failure probability), we may then talk about a relationship between risk and mathematical expectation of return on a securities credit. Parameter h – a probability of obtaining the ―desired‖ (or required by the capital owner) return – is the most critical parameter in formula 12. Evidently, this parameter depends on a multitude of forecasting factors, both subjective and objective: h = ∑(Wn * CFn) + ∑(Wm * OFm)     

[14]

W is factor weigh CF is subjective factor value OF is objective factor value n is number of subjective factors m is number of objective factors.

21

Of the diverse objective factors we may call four that have an apparent effect on the probability of obtaining the ―desired‖ return. First, it is the stock market stability factor. The more stable the market (i.e. the more regular the time intervals between transactions (see formula 11)), the higher the probability of a successful speculative game. Second, it is the amount of the ―desired‖ return. The higher the amount, the harder it will be to earn it and, accordingly, the lower the probability of obtaining it. The relationship is generally28 inverse. Third, any speculative strategy involves conducting some minimum number of securities credit29 purchase and sale transactions and only after that a professional participant may hope for success. Every dealer has a limited amount of resources utilized for speculative trading and so his speculative capital turnover is an important parameter for him. There will be a certain relationship (speculative capital turnover, F) between the total number of transactions closed by the dealer (U) and the amount of his speculative investments (Inv.): U Inv. [15] F We also may calculate a similar parameter characterizing the market in general:

Invm

Um Fm

[16]

Then if the dealer‘s capital turnover is higher than the average market capital turnover, the dealer may implement his speculative strategy making less effort and using fewer resources, and so he stands a better chance of succeeding in his speculative game. The relationship between probability (h) and turnover will be generally direct. Fourth, the probability of securing the ―desired‖ profit will be affected by the value of standard deviation of a securities credit. The higher the volatility in the market, the higher the probability of successful speculation. The relationship between probability (h) and volatility will be generally direct. Given below is a simplified expression of what has been said about the four objective factors affecting the probability of obtaining the ―desired‖ profit: h Wm 4 * f (

e

) Wm 3 * f (

F 1 1 ) Wm 2 * f ( ) Wm 1 * f ( ) Fm Re s

[17]

28

Here ―generally‖ implies that in graphic presentation the line describing the relationship between the two parameters will not be straight. 29 In the simplest case it is: 1. market destabilization in an attempt to deviate prices from fair ones as much as possible, e.g. downward deviation; 2. cornering of as many stocks as possible at cut prices; 3. market destabilization in an attempt to deviate prices from fair ones as much as possible (upward deviation); 4. sales of earlier cornered stocks and profit taking.

22

 Wm-4 is weight of the objective factor related to the securities credit risk  Wm-3 is weight of the objective factor related to speculative capital turnover  Wm-2 is weight of the objective factor related to the ―desired‖ return amount  Wm-1 is weight of the objective (forecasting) factor related to market stability  ƒ is function from a parameter. The integral weight (Wm-4 + Wm-3 + Wm-2 + Wm-1) may be less than one since we do not know exactly all the factors, primarily subjective ones affecting the probability parameter (h). And finally, the last thing that we can draw from formula 12 is signs of emerging conditions for conducting manipulative transactions. The plain fact is that all dealers are rational30 as distinct from private investors, for example, always follow logic, obey common sense and show prudence in actions. Thus we may state that conditions for manipulative transactions emerge in the stock market when the total (for all dealers) mathematical expectation of the return on speculative investments in the stock market drops below the IMB return value, but there in no crossflow of funds from the stock market to IM (change in shares in the structure of the cumulative portfolio of all dealers – see formula 13). In other words, investments must leave the stock market, in whole or in part, but this is actually not the case. So what are they doing there? Why don‘t they leave? Of course, we may answer that some dealers have lost part of their rationality, which is very unlikely. More probably, professional participants expect to earn a return by artificially distorting the market price of an asset (by conducting nonmarket transactions). 2.5. Interrelation between all financial markets Following the logic of formula 12, we may define a relationship between all the financial markets – the stock market, the currency market, the derivatives market and IM. But in order to continue our analysis we need to supplement the assumptions that we have made at the beginning of this paper. Let us assume that no investment transactions (for example, purchase of currency or risk hedging within capital transaction funding) are conducted in the currency and derivatives markets. Suppose that the set assumptions apply both to the domestic and overseas currency markets and that information already reflected in prices contained nothing that would allow forecasting. Then the set assumptions rule out any possibility for clients‘ money to be involved or any grounds for revision of asset prices (securities, currencies or 30

Remarkably, the basic method of success in speculation is to strip the other bidders of rationality, making them succumb to emotions, for instance, craving for revenge or vehemence.

23

derivatives). Accordingly, investing both in the currency market and the derivatives market will only be restricted to short-term investments aimed at earning return by changing the current asset value (speculation). IM will apparently be the ―base‖ market for all the markets as it allows a low but guaranteed return to be derived. Then IM will always be a safe heaven for dealers and each of them will shape his speculative strategy with a view to IM return. As we found out earlier, essentially one and the same asset (credit) circulates in IM and the stock market, which suggests a fairly natural crossflow of funds from one market to the other. Now as to the terms of investing in the currency and derivatives markets. In both cases the investor acquires nonproperty rights: in the currency market it is the right to buy goods and services denominated in a currency; in the derivatives market it is the right to buy/sell in future (option) or the right to certain assets in future (futures). The logic of analyzing the currency and derivatives markets will be similar to that for the stock market. Let us repeat it briefly. In the set assumptions environment there are no grounds for revision of the asset prices established in the two markets. Yet dealer motivation will maintain volatility in both markets, which in the context of stable prices for the basic product (nonproperty rights) may only be created by a speculative addition to the price. Thus we may say that a securities credit equivalent is also used in speculative trading in the currency and derivatives markets. In para.2.1 we concluded that, regardless of the number of securities in the market, the market return on the securities credit will be zero. This conclusion will also hold true for the currency and derivatives markets. Furthermore, because all the three markets (stock, currency and derivatives) are an exclusively speculative environment within the set assumptions, the zero return must be derived after speculative trading for all the three markets in general. It means that the return in each of the markets may differ from zero, provided that the total return in all the markets is zero. This may be expressed as follows, similarly to formula 9: Rm = RSec + RCur + RDer = 0    

[18]

Rm is total return in all the markets for a period RSec is stock market return for a period RCur is currency market return for a period RDer is derivatives market return for a period.

We also may say that a rational and efficient dealer will conduct speculative trading in all the three markets at the same time and place funds in IM using it as a source of a minimum but guaranteed return. Then, in elaboration of formula 13, the dealer portfolio (Rp) may be represented as follows:

24

Rp

WSec * RSec * hSec       

WCur * RCur * hCur

WDer * RDer * hDer

WIM * RIM

[19]

W is share of investment in each specific market R is return the dealer wishes to earn in a specific market h is probability of deriving the ―desired‖ profit in a specific market Sec is stock market Cur is currency market Der is derivatives market IM is interbank market.

We may suppose that the higher the mathematical expectation of return in a specific market (R*h), the higher the share of funds in the dealer‘s portfolio, channeled to this market. Formula 19 shows that in speculative trading it does not matter what particular asset is traded and in which particular market. The amount of return that may be earned in a specific market and the IM return amount are of crucial importance to the trader. It should be noted that if the IM return grows to exceed the return the dealer expects to earn on speculations, it may result in fully discontinued speculative activities.

3. Securities credit pricing model 3.1. Financial parameter correlations As we found before, the risk of (standard return deviation) and return on a securities credit calculated for the trading period (trading day), are not interrelated. Furthermore, since the period‘s return is zero, there is no point in trying to find any links between return and any other trading parameters, all the more so because return will always be a random value. It would be wrong, however, to view trading as utter chaos. Let us look at Table 1 that compares the various financial parameters characterizing the trading process. Let us note again that return on a securities credit for the trading period correlates with no other parameter. The parameters ―market stability‖, ―desired return‖ and securities credit risk for a period‖ correlate by formula 17 with the parameter ―probability of securing desired profit‖. The parameter ―IM rate of return‖ correlates by formula 12 with the parameters ―return desired by the dealer‖ and ―probability of obtaining return desired by the dealer‖. The parameter ―risk-free interest rate‖ correlates with no other parameter (please note this is only true for the terms of the preset assumptions, i.e. for those of speculative trading only), as it is a constant.

25

Table 1. Possible correlations between financial parameters characterizing the financial asset pricing process 3

4

5

1.

Return1 on a securities credit under one-off transaction

2.

Risk of a securities credit under one-off transaction

3.

Return on a securities credit*

4.

Securities credit risk*

5.

Market stability *

6.

Return desired by the dealer *

7.

Probability of obtaining return desired by the dealer *

8.

Risk-free interest rate *

9.

Rate of return on interbank credit*

-

Return desired by the dealer *

Market stability *

Securities credit risk*

Return on securities credit*

Risk of securities credit under one-off transaction

Return on securities credit under one-off transaction

No.

6

7

8

9 Rate of return on interbank credit *

2

Risk-free interest rate *

1

Probability of obtaining return desired by the dealer *

No.

-

-

-

-

?

-

-

-

-

-

-

?

-

-

-

-

-

-

-

-

-

-

+

-

-

-

+

-

-

+

-

+

-

+

-

―*‖ – for a trading period ―–‖ – no correlation ―+‖ – existing correlation ―?‖ – possible correlation

Using the method of elimination and intuition, we will now see if there is an assumed correlation between the parameters ―risk of a securities credit under a one-off transaction‖ and ―probability of obtaining return sought by the dealer‖. Practice has shown that humans tend to be willing to take a higher risk as the goal attainment probability grows31. In other words, the higher the likelihood of a successful speculative strategy, the higher the risk (the risk of a transaction as the author understands it – see formula 4) a professional player is willing to take in closing each particular transaction. Considering the logics of formula 17, we need to specify the following. The probability, as contained in this formula, depends on volatility of a securities credit for the trading period. It means that the higher the entire market 31

For example, an athlete running second (immediately after the leader) on last leg of a distance will make a greater effort at the tape than an athlete running last. As the latter has little hope, if at all, to win he will hardly make any superhuman effort to shoot ahead at finish. But the athlete running second still has a chance to win, sometimes a good one, so he will bend over backwards to come first. He may not win but is sure to do his best.

26

volatility, the higher the degree at which a market player will estimate the probability of attaining his goal. Accordingly, the higher his estimation of this probability, the higher the risk he would be willing to assume in offering his quotations. Let us now discuss the limit values of both parameters to see what kind of relationship exists between the risk of a separate transaction and the probability of successful implementation of a speculative strategy: zero risk, minimum risk and maximum risk as well as a zero probability and 100 percent probability (item 2). We will thereafter be able to make conclusions as to the kind of dependence existing between these two parameters (linear, proportional etc. (item 3)). 3.2. Parameter limit values (maximum, minimum risks) The minimum risk is impossible, which is obvious from the very beginning of our research, i.e. from the dealer‘s motivation who will offer quotations different from the current market prices, even though there are absolutely no reasons for changing the price. It means that even where the probability of success is zero, the dealer will still take some minimum risk. It is also evident that a 100 percent probability is impossible. It follows from uncertainty of future transaction prices, and so the risk will reach its maximum possible level at a probability value close to 100 percent. Table 1.1. 100% probability Probability closest to 100% 0% probability

Zero risk

Minimum risk

–

+

Maximum risk – +

In order to position the maximum risk point on a graph, we need to define whether the maximum risk is a finite number or a value infinitely approximating some value. In other words, it is necessary to calculate the maximum risk value. To this end, let us consider a fictitious example that will help us simulate a situation when the maximum risk occurs in the market. This example will be based on formulas 2, 7, 8 and 9 and the conclusion that the market return on a securities credit for the trading period is zero. Theoretically, the maximum risk may occur in the market when security values fall alternately as low as possible as regard the securities credit. It means alternate complete zeroing of a securities credit for each of the securities. Then the maximum risk, i.e. the maximum deviation of the anticipated return from the actual one, will occur in the transaction with the last security. Let us expand on the above and assume that there are a few equity shares circulating in the market. To simulate a maximum risk situation, we will suppose that all the shares are alternately sold at prices equal to their present

27

value, i.e. lower than the initial quotation level. Then the level of risk assumed by the dealer will increase with each new transaction. So let us assume that a new trading day begins. The following quotations (opening quotations) were recorded during the last transactions in yesterday‘s trading: Table 1.2. No.

Share

Quotation, USD

including the emitter’s discounted cash flow, USD

1 2 3 4 5

N1 N2 N3 N4 N5

130 130 130 130 130

100 100 100 100 100

including securities credit USD % 30 30% 30 30% 30 30% 30 30% 30 30%

Let us consider each transaction with stocks, step by step. Suppose the first stock was sold at $100. Return on this transaction is minus thirty percent (– 30%). It means someone of the dealers (the seller in a transaction) has assumed a fairly high risk (the module of deviation of the anticipated return from the actual one is 30%), accepting the fact that share N1 is completely free from a securities credit. Thus the risk of the first transaction is 30%, while the anticipated return on the second transaction is estimated at +30% (see Fig.3 to remember why). Now the market will expect the zero return value to recover in the next transaction. Let us assume, however, that the return on the second transaction with share No.2 is –30%. It means the dealer who has sold the share has taken the risk of –30% (this is an absolute difference between +30% and –30%, i.e. between what was expected and what actually happened). Now we have already two shares ―deprived‖ of a securities credit and the market situation looks as follows. Table 1.3. No.

Share

Quotation, USD

including the emitter’s discounted cash flow, USD

1 2 3 4 5

N1 N2 N3 N4 N5

100 100 130 130 130

100 100 100 100 100

including securities credit USD % 0 0 0 0 30 30% 30 30% 30 30%

Thus the second transaction risk was 60%, as I said before, and the return on the third transaction is estimated already at +60%. The market will expect again the next (third) transaction to recover the market balance. But let us suppose that the third transaction, too, had a return of 28

–30%. That is, now share No.3 has lost a securities credit within the quotation and its value has gone down to the discounted cash flow level. Thus the risk of the third transaction was 90%, and the return on the fourth transaction is estimated at +90% The fourth transaction was conducted with share No.4. Let us suppose that the return on this transaction was –30% as well and share No.4, just as the previous shares, lost a securities credit within the quotation. The risk of this transaction was 120%, with the return on the fifth transaction estimated at +120%. And finally, the last stage of ―growing‖ the maximum risk is the fifth transaction, i.e. the transaction with the last share (No.5). Let us suppose that the return on this transaction was also –30% and share No.4 lost a securities credit within the quotation. The risk of this transaction was the required maximum 150 percent. Risk can grow no higher since the securities credit is exhausted. Hence, as trading progresses it will bring the market (eventually or at once) to the initial balanced state. If it happens ―at once‖, the anticipated return on the sixth transaction will be +150% and, according to our logics, it must recover the market balance. The risk of the sixth transaction will be zero. Actually, our example deals with complete cancellation of the entire amount of the securities credit in securities quotations, rather than with redistribution of the securities credit among the assets. Accordingly, the maximum possible risk represents a value of potential reduction of the securities credit in quotations of all securities: j

RSK max i 1

   

Ri Qi

[20]

RSKmax is maximum risk, in shares; Qi is market quotation of the i-th security, monetary unit; Ri is absolute value of the securities credit of the i-th security, m.u.; j is total number of securities circulating in the market.

We can now formulate the answer to the previously raised question about the nature of maximum risk: the maximum risk of a securities credit under an individual transaction is a finite number. We also can make the following conclusion: the maximum risk cannot be taken at once, there must be a whole chain of transactions with a high risk level that will be growing yet higher with each closed transaction. In other words, a market situation in which the dealer assumes the maximum risk cannot arise within a short time. 3.3. Nature of probability-risk dependence Now getting back to the focal point - determining dependence between the probability of successful implementation of a speculative strategy and individual risk. Now that we know the values of two extreme points of this dependence, let 29

us consider its nature to see if the line between the two points (maximum and minimum risk points) is straight or curved. To see the rate of this line, let us see how the extent of risk changes with varying probability. It is hard to see any direct relationship between probability and risk, except by the intuitive guess made above. But we may deduce this relationship by considering two ―intermediaries‖– the parameter ―share of capital that the dealer needs to obtain from other dealers to earn his desired return‖ and the parameter ―number of dealers in the market‖. To this end, let us look at three graphs that depict relationships:  between probability of successful implementation of a speculative strategy and the capital share the dealer has to ―earn‖ (redistribute for his own benefit) to ensure the required return;  between the above capital share and the number of dealers trading in the market;  between the number of dealers and individual risk. We will obtain three ―equations‖ expressed as graphs. Since these ―equations‖ have two repeated parameters they may be ―cancelled‖ and all the three relationships may be reduced to one: between probability and risk. Let us first discuss the probability-capital share relationship. Assume that we have seen a few situations involving two equally skilled dealers with capital of similar size. Situation 1: One of the dealers (dealer N) needs to redistribute 99.99% of another dealer‘s capital for his own benefit. Situation 2: Dealer N needs to redistribute 0.01% of another dealer‘s capital for his own benefit. Given that professional skills of the dealers are similar, it is apparent that the probability of success in the first case is almost zero and in the second case it is almost 100%. Situation 3: Dealer N needs to redistribute 50% of another‘s capital for his own benefit. Given that professional skills of the dealers are similar, the probability of this event is 50%. Having three points through which the probability-capital share relationship line passes, we may plot a graph (see Fig.12) which shows that probability decreases as the capital share grows.

30

1

Probability, in shares

Вероятность, в долях

0,8

0,6

0,4

0,2

0 0,01 (Point2)2) (точка

0,1

0,2

0,3

0,4

0,5

0,6

(Point (точка 3) 3) Capital share, in shares

0,7

0,8

0,9

0,99

(Point (точка 1) 1)

Доля капитала, в долях

Fig.12. Relationship between the probability of successful implementation of a speculative strategy and the capital share the dealer has to ―earn‖ (redistribute for his own benefit) to ensure the required return Let us now discuss the second relationship – between the capital share and the number of dealers. We will use an example in which initially there are only two dealers in the market. We will then gradually increase the number of dealers to change the numerical value of probability. So let us assume that only two dealers are trading in the market. They have speculative capital of a similar size and an equally high goal of accretion to the capital, i.e. 100% return. So for one of the dealers (dealer N) to implement his speculative strategy, he will have to achieve redistribution of 100% of the other dealer‘s speculative capital for his own benefit (point 1 in Fig.13). Let us now assume that three dealers are trading in the market. To succeed in implementing his speculative strategy, therefore, dealer N needs to redistribute 50% of the speculative capital of each of the dealers for his own benefit (point 2 in Fig.13). It seems to be done easier intuitively than in the first case: taking away 50% of property is always easier than taking away 100%. Suppose now that there are four dealers trading in the market. Hence, to succeed in implementing his speculative strategy, dealer N now needs to redistribute only 33.3% of the speculative capital of each of the dealers for his own benefit (point 3 in Fig.13). It is easier to do it than in the second case: taking away 33.3% of property is always easier than taking away 50%. And so on. As the number of dealers in the market grows it become evident that, even though the scope of work does not reduce (in any case dealers have to earn 100% return on balance), the relative load on the dealer decreases32. 32

One inference from this conclusion is that the greater the number of private investors in the market, that are a priori less skilled than professional participants, the higher the probability for the dealer to succeed in implementing his speculative

31

So the probability of a successful speculative strategy grows, such growth not being linear (see Table 1.4 and Fig.13). Table 1.4. 1. 2.

Number of dealers Capital share, %

0 -

1 -

2 100

3 50

4 33

5 25

6 20

7 16

8 13

9 12

10 11

11 10

As the number of dealers in the market grows the parameter ―capital share‖ decreases. The data from Table 1.4 are used to construct the graph in Fig.13.

Доля капитала, в долях

Capital share, in shares

1

0,8

0,6

0,4

0,2

2

15

14

13

12

11

10

9

8

7

6

5

1 (т о чк 1) 2 (Point а 1) 3 (т 2) 3 (Point оч ка 2) 4 4 (Point (т 3) оч ка 3)

0

Number of dealers Количество дилеров, ед

Fig.13. Relationship between the number of dealers in the market and the capital share of each of them, which dealer N should redistribute for his own benefit to derive the desired return Finally, let us consider the third relationship – between the number of dealers and the risk dealer N is ready to assume. Since all the dealers, according to our assumptions, are equally skilled and have capital of similar size, a simple change in the number of professional participants cannot affect dealer N‘s strategy, including as regards risk 33. Hence we can assert that there is no relationship between the above parameters. strategy, although this time not through redistribution of other dealers‘ funds for his own benefit, just as in our example, but through redistribution of private investors‘ funds. 33 Here is another example from human psychology. In some countries people will entertain themselves engaging in a mass fight in which every person fights only for himself and the winner is the last fighter remaining on his feet. In such a ―game‖ physical endurance is a critical quality for any ―player‖; the more the number of fighters, the higher endurance the winner must have, all other things being equal. It is evident because the winner will have to fight with the greatest number of opponents. If we extend this ―game‖ to a financial market where each trader plays only for himself, we may note that a player‘s ―endurance‖ equivalent is the amount of his speculative capital. Our assumption, however, is that all dealers have an equal amount of capital so they are equally enabled to engage in long speculations. Thus, the number of dealers does not affect the extent of risk.

32

Graphically, it looks like a strictly horizontal line (see Fig.14) (the numerical risk value of 30% has been set arbitrarily).

Размер риска, в долях

risk, in shares shares risk, inof Extent of Extent

0,4

0,3

0,2

0,1

0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Number ofдилеров, dealers ед Количество

Fig.14. Relationship between the number of dealers and the risk dealer N is ready to assume 3.4. Securities credit risk forming model Now let us combine logically the last three figures (Fig.12, 13, 14). ―Reducing‖ the parameters ―number of dealers‖ and ―capital share‖, we will obtain the line of the relationship between the probability of successful speculative strategy and the individual risk the dealer is ready to assume. ―Reducing‖ means the following:  the ―probability‖ parameter remains plotted on the vertical axis, while the ―risk‖ parameter, after ―reduction‖, appears plotted the horizontal axis;  the line shown in Fig.13 remains the relationship basic line;  the basic line will be inverted as the relationship depicted in Fig.12 is inversely proportional;  the line shown in Fig.14 does not affect the final result since it is static/unchangeable. The obtained result is presented in Fig.15. The basic line has been shifted a few divisions to the rightward to allow for the fact that the minimum risk taken by the dealer is always more than zero (see Table 1.1).

33

Probability, in shares Вероятность, в долях

1,0

0,8

0,6

0,4

0,2

R

SK m in

0,0

Risk,вin shares Риск, долях

Fig.15. Line of the relationship between the probability of successful speculative strategy and the individual risk the dealer is ready to assume The relationship line depicted in Fig.15 may be described by the following framework equation: RSK

1 1 h

* RSK min

[21]

 RSK is risk the dealer is ready to assume in the next transaction  h is probability of successful speculative strategy  RSKmin is minimum risk the dealer will take at zero probability value. Coefficient 1/(1-h) showing the line curvature has been obtained by transformation of the relationship shown on Graph 13, using the data of Table 1.4. In accordance with formula 21, if probability is zero, the dealer‘s risk is minimum. Here a 100% probability is impossible because it would render the equation meaningless. The abovesaid meets the conditions of Table 1.1. Application of formula 21 is restricted to the IM crediting rate and the dealer‘s desired return (see formula 12): the IM rate must be less than the desired return value. The RSK parameter must be always less that the maximum risk value (see formula 20). Note that knowing the latter, we may calculate the maximum possible probability value by combining formulas 20 and 21:

34

hmax

1

RSK min j Ri i 1 Qi

[22]

Formula 21 is framework because the minimum risk, as distinct from maximum, is not a clearly specified, single parameter. As a matter of fact, the minimum risk, i.e. the risk the dealer will take even if the probability of success is zero, is a parameter whose value depends on the dealer‘s highly subjective, immediate choice34. Each time before bidding the dealer‘s idea of the minimum risk will be different. To prove it, let us assume that the probability of success for some dealer is zero. If this dealer is bidding guided by a single, formulacalculated or predicted value of maximum risk, which is always the same, then all his bids will be of the same amount and the market will lose its outstanding feature – unpredictability. And we know that even at a zero probability market trading has an intrigue (remember the dealer‘s basic motivation). The minimum risk value should be sought within a certain range whose limits may be defined as follows:  The lower limit of minimum risk depends on the minimum permissible variation of a quotation value, i.e. tiki. It cannot be any lower, technically. Putting in a bid with such a risk value, the dealer will seek to show his presence in the market rather than to close a transaction.  The upper limit of minimum risk depends on the current best quotation. Putting in a bid with such a risk value, the dealer will seek to immediately close a transaction at the best price. Being within the lower and upper limits, the value of minimum risk will always be a multiple of tiki. Adjusted for the lower and upper limits of minimum risk, the graphic presentation of the range of the relationship between the probability of successful speculative strategy and the range of the risk the dealer is ready to assume looks as shown in Fig.16 below.

34

Imagine an athlete running the last in a race with absolutely no chances not only to breast the tape but even to come off third best. What will he do? Will he fall out? Of course he won‘t because then he will find himself out of the competition. So he will keep running but slowly enough. As soon as the runner realizes that he is standing no chances to win, he will choose a running speed range, the lower limit of which will enable him to keep the spectators‘ respect and the upper limit will keep him from overdoing it so as to be fit for the heats to come.

35

1,0

Probability Вероятность

0,8 0,6 0,4 0,2

3 R

2 R

SK m in R

R

1

0,0

Lower risk limitриска Нижняя граница

Верхняя граница Upper risk limit риска

Fig.16. Graphic presentation of the limits of the relationship between the probability of successful speculative strategy and the range of the risk the dealer is ready to assume Both lines – the lower and upper limits of minimum risk (R1 и R2) – cross at the maximum risk point (R3). The relationship line itself will lie in between these two limits and start at point R2 at a zero probability. Since we needed to specify the minimum risk value (RSKmin) in framework equation 21, then following the logic of Fig.16, the range of risk the dealer is ready to take in the next transaction may be described as follows: 1 1 h

* RSK tiki

RSK

1 1 h

* RSK high

[23]

 RSKtiki is the lower limit of minimum risk determined by the tiki value  RSKhigh is the upper limit of minimum risk determined by the best bids of those put in on a stock exchange. Pay attention that coefficient 1/(1-h) does not describe the upper limit of minimum risk (the right-hand part of equation 23) with complete accuracy. This is because the two lines cross at one point (maximum risk) and therefore cannot be parallel and described by the same coefficients. See Fig.17 for details.

36

А1

h

А2

1,0

R1

R2

R3 (RSKmax; hmax)

Fig.17. Adjusted position of the upper limit of minimum risk  Blue: lower limit of minimum risk (R1-A1).  Red: upper limit of minimum risk (R2-A1).  Gray: line R2-A2 close to the upper limit of minimum risk and designated with coefficient 1/(1-h) in formula 23.  Turquoise (shaded area): area of deviation of the actual upper limit value from the line described with coefficient 1/(1-h). The deviation amount (i.e. the value by which the right-hand part of formula 23 is to be corrected) varies within a range from zero (at point h=0) to difference Rhigh – Rtiki (at point hmax). This variation is linear and may be expressed as follows: z

   

h hmax

RSK max

RSK h ig h

[24]

Equation 24 has been obtained by performing the following steps: A rhomb was constructed by points R1, А1, R2 and А2. Line R2-А1 was constructed to determine the time history of the difference between the upper and lower limits of minimum risk (blue and gray lines). The angle of inclination of line R2-А1 to line R2-А2 is described by the known function y=a*b. The limiting points (RSKmax; hmax) and (RSKhigh; 0) were used to define the coefficient ―a‖: a=y/b or, in the terms as applied in this work, a=h/RSK, then:

37

a

hmax RSK max RSK high

[25]

 Function y=a*b should be rearranged in the applied terms as h=a*RSK, and since we are discussing the risk-probability relationship, as RSK=h/a.  Then the correction value will be defined by formula 24. Now that we have defined the deviation value, we may deduce a more accurate version of formula 23: 1 1 h

* RSK tiki

RSK

1 1 h

* RSK high z

[26]

Equation 26 may be presented in another form: RSK

1 1 h

[27]

* RSK tiki

 ώ is a trader-determined variable lying within the range from 0 to q which, in turn, is defined as follows: q

RSK high

RSK tiki

z

[28]

A specific value ώ is defined intuitively by the trader each time immediately before bidding. Let us discuss three distinctive features of this parameter. If the trader bids not really expecting that his bid will be accepted (passive bidding), he will choose the ώ value in the range from R1 to R2. If the trader wants to immediately close a transaction at the exchange‘s best price he will choose the ώ value equal to R2. If the trader‘s aim is to bring about uncertainly or create an intrigue in the market, his bidding may be one of the elements of his market swaying strategy (active bidding). Then the trader will choose the ώ value higher than R2 but lower than Rmax. See Fig.18.

38

А1

h

А2

1,0

Active bidding

Passive bidding

R2

R1

R3 (RSKmax; hmax) Immediate transaction closing

Fig.18. Bidding ranges According to the obtained simulation model (set of formulas 24, 26, 27 and 28), the speculative asset risk depends on two parameters: on the probability at which the dealer whose bid has been accepted in the market has estimated his chances to earn and on the upper limit of minimum risk set by the dealer for himself. As the probability (h) increases the range where the variable (ώ) lies will be decreasing down to zero. This will happen when the probability reaches the maximum possible value (see formula 22). At zero probability the variable (ώ) will be the highest possible as will the dealer‘s decision volatility (spread of risk values for him to choose from). The simulation model apparatus may be applied both to the future and the past. As applied to the future, it shows the extent of risk the dealer is prepared to assume (explains the bidding risk amount). As applied to the past, it explains how the last transaction risk has been formed. 3.5. Securities credit pricing model The set of formulas 24, 26, 27 and 28 enables us to develop a securities credit pricing model. It will be remembered that its risk, for the purposes of this paper, is a deviation of the actual asset return from the expected return on the same asset taken by the module (see formulas 4 and 5). It means that deviation may be both ways. So each calculation will produce two values of return on a speculative asset for positive and negative risks. Give the above, the securities credit return may be expressed as follows: r f rex RSK [29]  rf is actual asset return  rex is expected asset return. 39

Formula 29 represents a securities credit pricing model. Since its parameter rex is a constant, actual return variations will be subject to the logic of formula 27, adjusted for the sign . Then the model will be represented graphically as follows. h 1.0

Return on asset, r

Fig. 19. Graphic presentation of the relationship between the probability of a successful speculative strategy and the actual return on a securities credit As distinct from Fig.16 showing one ―wing‖, Fig.19 depicts two ―wings‖, which is due to allowance for the sign from formulae 29. Besides, the ―wings‖ are not located strictly symmetrical about the Y-axis (probability) due to the correction rex. 3.6. Portfolio theory for development of the securities credit pricing model The key method for analyzing the stock market assets is consolidation of assets in a securities portfolio to explore risk and return variations. This method is used in Markowitz portfolio theory, CAPM and the binominal option valuation model. This method, however, does not apply to the securities credit, as no asset portfolio can be built with only one speculative asset circulating in the market. Even so, there is a possibility to build two securities portfolio equivalents. In the first case the role of assets will be played by the traders employed with a dealer company and relatively independent of one another. In the second case the portfolio will be built through the dealer‘s work on different trade floors each having its own securities credit. Let us discuss the first case. Assume that the dealer has only one trader conducting speculative transactions in accordance with the dealer‘s internal regulations. This is a basic situation. Let us now suppose that the dealer has hired another trader to work independently of the first trader and has established 40

for him special regulations differing from those for the first trader. For example, the second trader has to meet easier risk taking requirements and has a greater amount of capital to handle. Given that both traders only coordinate their actions in dealing with a small number of issues of corporate importance, while otherwise they trade independently, calculation of their earning capacity (obtained return), from the dealer‘s perspective, will be similar to that of the portfolio return: Rp

W1 RT1 W2 RT2

[30]

 Rp is traders‘ earning capacity for the dealer  W is trader‘s capital share in the overall amount of capital allocated by the dealer for speculative trading; W1 + W2 = 100%  RT is return derived by the trader  1, 2 is No. of traders. It‘s worth remembering here a dice game, specifically, a probability of rolling the needed number. If the player only uses one dice, the probability that he rolls a 1, a 2 etc. is always the same. However, if the player uses two dice the probability starts changing and, if depicted graphically, it is bell-shaped: for example, the probability that he rolls a 6 is higher than that of his rolling a 2. In statistics it is termed the Gaussian distribution. Similarly, if the dealer has one trader the probability of deriving a certain value of return will always be one and the same. If the dealer has two or more traders the Gaussian distribution logic will work. A graph reflecting the Gaussian distribution will include the dealer‘s earning capacity (weighted average earning capacity of all his traders) and return earning probability. Since earlier (see Fig.19) we have also considered a combination of probability (success of the dealer‘s speculative strategy) and asset return, we may join the graphs together adding the Gaussian distribution line to Fig.1935. Then, if the dealer has two or more relatively independent traders, the distribution of the dealer‘s total return will be represented graphically as follows.

35

The case in point is a need for two different probabilities (success of speculative strategy and return distribution) to be plotted on the ordinate of the next graph.

41

h 1.0

B C hi

F

E A

D R‘i

Ri

Return on securities credit, r

Fig.20. Points at which the Gaussian distribution line (A, B, C, D) cross the ―wings‖ of the relationship between asset return and speculation success probability Portions A-B and C-D (Fig.20) are of critical importance to dealers. They show the most probable values within the range corresponding to the probability chosen by the dealer. For instance, if the dealer estimates the probability of his speculative strategy success as hi, then Ri and R‘i values will be the most probable ones of the entire range of asset return values on line E-F. Employing a great number of traders may help enhance the company‘s performance but also is fraught with certain risks. Let us consider the following example. One of the most unlikely situations is when there is only one dealer remaining in the market, who has many traders operating, and that creates an illusion of market. Assume that 10 dealers are operating in the market, each having only one trader, except for dealer No.1 who has 10 traders. Thus a total of 19 dealers are playing this market. Let us now suppose that all the dealers, except for dealer No.1, stop bidding and trading. Then only 10 traders of dealer No.1 will eventually remain playing the market. Let us imagine that, because they operate in general independently of one another or for other reason, it took them some time to learn that theirs is the only company operating in the market. This situation may be regarded as completely loss making since the speculative capital will have to be redistributed within one dealer company. Accordingly, the dealer will be unable to increase his capital and will incur transaction costs and lose capital with every new transaction. The higher the traders‘ activity and the more transactions they close, the higher the loss sustained by the dealer. Irrespective of the number of traders, dealer motivation may be affected by some apparent and logical rules. First: the dealer goes out of trading before the end of a trading session if he has exhausted his limit of loss for the current day. Second: the dealer fixes the profit and goes out of trading before the end of 42

a trading session as soon as he earns the desired return. These rules reveal reasonable treatment of risk inherent in most of institutional investors. In the first case it is staying and taking the risk of losing still more and in the second it is staying and losing what has been earned. For example 10 dealers are playing the market. As soon as the fist one of the dealers exceeds the set limit of loss36, he will drop out of the game, guided by logic and common sense. Then the second, third etc. dealers will follow suit. As the losing dealers sustain more and more losses the ―prize fund‖ will grow as will the profits of some luckier dealers. As soon as the profit exceeds a certain level set by the dealer, he will fixes the profit and drop out of the game. This is to say that during the trading day both losing and profit-making players will drop out and those who stay in will have to start from scratch. There may be situations in the market when the ―prize fund‖ is either large or small. The fund size may affect dealer activity: the larger the fund the more prepared the dealer may be to assume risk. Furthermore, a change in the number of dealers playing the market will affect the configuration of the Gaussian distribution line in Fig.20. In the second portfolio building option the dealer will work on various trade floors worldwide and his overall return will be defined with a formula similar to formula 30, which has the return obtained from various trade floors instead of that derived by a team of traders.

4. Discounted value in the structure of financial asset quotation 4.1. Risk-free interest rate in open trade One of the best-known instruments used in the stock market is a risk-free interest rate. A risk-free financial instrument has a zero standard return deviation. In practice, an instrument with the lowest return volatility is considered more risk-free. From the viewpoint of the Securities Credit Concept and in the set assumptions environment, a risk-free instrument is the one whose quotation includes no securities credit. As we said earlier, the securities credit emerges because the dealer buying a security at a price exceeding the company‘s discounted cash flow is confident (he believes) that he will have back the funds paid in excess and even in a greater amount. In the case of a risk-free instrument, however, he chooses not to do it (not to pay in excess of the discounted value) because he does not believe his funds will be returned. He assesses the probability of a speculative gain as zero or nearly zero. The reason, I think, lies in the peculiarities of the bond cash flow structure. The thing is the discounted value of a bond increases daily by a certain amount. Hence, within a trading day the highest addition to the bond value 36

The amount of losses may be calculated with VaR formula whose structure, I believe, is best suited for the purpose.

43

(securities credit) the dealers can afford must not exceed the daily bond value increment. For example, we have a zero coupon bond whose value increases daily by 10 ruble. If the dealer seeks an increment in excess of 10 rubles it means that his strategy goes beyond the trading day limits. As this involves an extreme risk the dealer is least likely to ever take, because any efficient speculative strategy is only designed for the current trading day. Then the lower the bond yield increment (accrued coupon yield and market value variations), the smaller the securities credit included in a bond quotation and, accordingly, the more risk-free this paper is. We may assume, therefore, that an absolutely risk-free bond is the one whose daily yield increment is equal to or less than the overall transaction costs, because in this case it will be unprofitable for the dealer to conduct any speculative transactions with such a bond in the first place. 4.2. Present value behavior on various trade floors The currently prevalent practice is issuing depositary receipts. It allows issuers‘ securities to be brought to overseas trade floors. In this case we have a situation when one and the same present value of cash flows of an issuer (adjusted for the exchange rate and costs related to exchanging stocks for receipts), but along with different securities credits, is circulating on two different trade floors. Then we may assert that in a situation when the market lacks any news concerning the issuer, i.e. PV is stable, the difference between returns on a stock and receipt will reflect the one between speculative activities on two trade floors. A particular case of the situation when information comes in the market is a varying return on securities owned by companies manufacturing branded products. Let us dwell on it assuming that a manufacturer of branded products has a share and DR markets and the brand does not go beyond the borders of the manufacturer‘s country. If we take as a basis the definition of the brand as a homotypic emotion produced commercially, we may say that a branded product is, in fact, a set of two goods. The first one is an emotion produced for sales and not existing physically; the second one is a physical object designed to deliver the emotion to the consumer. But then we can elaborate on this idea as follows: a company manufacturing branded products is a combination of two relatively independent ―shops‖. The first one produces emotions and the second one – physical products. In this case the common stock of a brand-owing company is a portfolio comprising two conditional securities, the first one of which has been issued for the emotion shop and the second one – for the actual product shop. Then, given that domestic investors are under the impression of the brand and foreign investors are not, we may conclude that the response of domestic and foreign investors to one and the same corporate event will have a different 44

return. We can now determine a brand return, i.e. percentage variations of a company‘s brand in response to a certain information message. In a simplified form it is a difference between the stock return (portfolio return) and the DR return (DR being one of the elements of this portfolio). The following should be taken into account in practical calculations. First, you may run into the problem of lack of quotations, for instance, when trading was active on one exchange and extremely stagnant on another one. Second, calculations should allow for the Russia brand producing an impression on foreign investors. This brand may be calculated following the above logic and additionally using data on quotations of Eurobonds and federal bonds of the central government. Third, the speculative activity level varies from exchange to exchange. It is necessary, therefore, to reduce the quotations of both papers to a ―common denominator‖, make them comparable, i.e. exclude a speculative factor. Fourth, taking into consideration the large amount of assumptions and adjustments made in calculations, we should abandon numerical assessments and switch to qualitative ones (―The brand value has grown‖, ―The brand value has reduced‖). This will help make the final assessment both clearer and specific. And finally fifth, not every return variation should be used for calculations. Some of them, staying within a certain range, should be ignored. As a matter of fact, individual investors may sometimes initiate conversion of stocks into depositary receipts and back. This operation is associated with costs and so long as return stays below cost in the course of trading, there will be no difference in understanding an information message. 4.3. Effect of information messages on the discounted value Effects exerted by information messages on speculative trading (trading in securities credits) seem secondary in relation to a speculative strategy chosen by the dealer. In other words, professional participants hardly ever pay any attention to news when conducting speculative trading. This can be accounted for by the following. In our set assumptions environment, where no information is available, the dealer may trade fairly well and even succeed in trading. Yet, if any information comes in the dealer may use it in trading (actually, he may only use this information to adjust his trading strategy) or he may not – it all depends on how he estimates the probability of success of his strategy. I‘d like to emphasize once again that whether or not information is available will not affect the course of speculative trading. So the widely accepted concept of effective markets will not explain speculative trading. On the other hand, it is quite obvious that information messages do affect trading in the company‘s present value of cash flows. While duration of such an effect is not long, it is intensive enough. Duration and intensity are related to the reflection of news in the present value. This is an oscillating process as it reflects a search by the market for a new fair asset price. Let us consider the following example. Information coming in the market suggests that the issuer‘s financial standing has changed in a way influencing his 45

present value of cash flows. Responding to this event, each of the professional participants will immediately put in new bids for purchase or sale of this issuer‘s securities. It is evident in such a situation that they suspend speculative trading since it is impossible to carry it on when the amount of the first quotation component is not defined and thus the securities credit amount cannot be monitored. In these circumstances the dealers focus entirely on trading in the present value in order to determine as soon as possible its new value, fix it at the new level and resume speculative trading. Naturally, each professional participant will have his own expert opinion as to how exactly (in figures) a news event has affected the discounted value, so bidding will cover a wide range. Let us assume now that a transaction has been conducted at the price PV+15, i.e. 15 monetary units higher than the previous present value price. Two scenarios are possible here: either the market will view this price as underestimated and then the next quotation will have a price exceeding PV+15, or as overestimated and then the price will be less than PV+15. Suppose that the market has found the price overestimated. It means that the market now has the first benchmark – the upper limit that the quotation will never exceed. Now the market is to identify the lower limit of the range within which a new fair price of the present value should be searched (―felt‖) for. Let us assume that the next transaction price is PV+7. Two scenarios are possible here: either the market will find this price as overestimated or underestimated. Suppose the market has found the price underestimated, which implies that the market now has the second benchmark – the lower limit that the quotation will never exceed. As soon as the market identifies the range limits it will take another step to narrow it because it cannot be satisfied with a range of values and needs a precise present value. So the market will again start looking for the highest value (but no higher than the similar value of the first range) and, once it is found, the market will begin searching for the lowest value. And so the market will keep raising and lowering the quotation (each time with a smaller spread) until it finds the best present value that suits most of the professional participants. This process represents damped oscillations known from mathematics, which may have the following graphic representation.

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Fig. 21. Schematic representation of oscillatory motion In our case damped oscillations result in a changed quotation, so the quotation – before a piece of news appears in the market, i.e. prior to start of oscillations – will differ from the one that will be established after the oscillations end. This may be represented graphically as follows:

quotation

S1

S0

t0

t1

time

Fig.22. Schematic representation of the process of market identification of a new asset price after a piece of news has come in the market (in this case the news resulted in an increased quotation) Many traders say that, in practice, the average time for reflection of news in an asset quotation (difference between t0 and t1) is no more than 10 to 15 minutes. This statement may be additionally supported by the fact that trade organizers provide online trading data for a charge, while those with a delay of 10 to 15 minutes or more are offered free.

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4.4. Implications of the two-component structure of market quotation for the procedure of trading in finance assets The two-component structure of market quotation looks quite natural from the perspective of the modern western system of values. But things are different if we look at this fact from another standpoint. The steadily growing segment of world finances – Islamic finances – is subject to a number of very stringent restrictions and bans established by Sheriat. Thus, in particular, it is prohibited to trade in borrowed shares because, according to Islamic law, a trader may not trade in assets he does not own. Neither is it acceptable to invest in shares whose issuers engage in business at variance with Islamic moral norms, for example, producing alcoholic and tobacco products. However, the main prohibition existing in Islam is related to charging interest on a loan. Riba (usury) is forbidden in any of its forms and so involvement of Islamic investors in transactions of which Riba is a component, although not a visible one, is unacceptable practice in any event. Our earlier analysis shows that a quotation of any financial instrument contains an asset similar to a credit (securities credit). We may assert, therefore, that the current trading system, accepted in Islamic countries as well, creates an environment for violation of Sheriat requirements. It means that Islamic financial institutes and private investors must completely withdraw from trading transactions in financial markets, regardless of what particular financial instrument they invest in. The last remark is not relevant, though, because the trading system itself has a major flaw – Riba. Apart from violation of the usury prohibition requirement, we may see that two more Sheriat prohibitions are broken. First, it is a prohibition of groundless risk (Garar). The fact is an investor playing the market assumes a risk not supported by return (see the conclusion about risk and return not being interrelated) so he conducts transactions in which risk and return are incommensurable). Second, it is a prohibition of gambling (Maisir). As we have found, speculative trading in finance assets is essentially a game of chance having nothing to do with investment. Thus, the current trading system containing elements of Riba, Garar and Maisir, is only outwardly acceptable for Islamic financial markets. Without a fundamental change in the trading procedure and bringing it into line with the established bans any investment activity of Islamic financiers, even if they invest in the ―right‖ assets, will be a gross violation of the underlying principles of Islam.

5. Practical application of the Securities Credit Concept 5.1. Refinements to the postulates of the classical financial theory

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5.1.1. Risk of and return on financial assets. While supporting the division of all transactions into two types – investment and speculative, the Securities Credit Concept argues that there is no relationship between risk and return. This thesis holds true both for assessment of trading results over a period when quotation return volatility is taken as risk and for assessment of individual transactions when risk is measured by deviation of the actual return from the expected return. 5.1.2. Investors‘ rationality. In the context of the assumptions made in this paper we may say that dealers are rational at all times. The thing is purchase and sale of assets at prices differing from fair (fundamental) ones only look irrational on the face of it. As they close individual irrational (clearly loss making) transactions during the day the dealers, in fact, expect to derive return from trading. And their temporary ―irrationality‖ is nothing else but a separate element of their speculative strategy. 5.1.3. On the theory of effective markets. This would no certainly a true theory if we only dealt with trading in the issuer‘s present value of cash flows. But in open trade, according to the Securities Credit Concept, ―prices do not reflect all the information available‖. Just as all other market makers, dealers read news updates and hear rumors but, as we could see based on the assumptions made herein, they may well do without information as it is not a prerequisite for speculative trading. 5.1.4. On the CAPM model. According to the Securities Credit Concept, the higher the speculative component (securities credit) of quotations, the lower the efficiency of practical application of this model. The Concept provides for the CAPM model to be applied only for assessment of the issuer‘s present value of cash flows, not for assessment of the speculative component of quotations. 5.1.5. Crisis emergence and development. Quotation division into two components allows a better understanding of the essence of financial crises: ―A financial crisis, as applied to the stock market, is a repeated short-term revision and, accordingly, rapid reduction of the issuer‘s present value of cash flows due to the discounting rate growth caused, in turn, by professional participants assessing the country risk as increased‖. In other words, a financial crisis does not lead to reduction of the speculative component of asset quotation, moreover, panic breaking out in the stock market has to do with the issuer‘s present value of cash flows rather than to the securities credit. Against the backdrop of growing country risk, the risk premium increase will vary from issuer to issuer. That is to say a fall of quotations for individual securities will not be proportional. In its turn, panic occurring in the markets during a crisis is not necessarily caused by the crisis. It is no more than a rise in speculative activity of professional participants who truly believe that in the context of a global review 49

of the country risk they stand better chances than usual to succeed in implementing their speculative strategies. 5.2. Practical proposals 5.2.1. New market index The index of speculative activity (ISA) designed to assess speculative activity of professional participants has been introduced in addition to the existing standard market indices. To calculate ISA, we suggest collecting information from professional participants as regards their expert evaluation of the current amount of issuing companies‘ present value of cash flows and updating it regularly. With such information available, a trading organizer may calculate a securities credit value both for the market in general and for individual companies. The securities credit value data are then used to calculate the ISA index subject to the standard procedure. Actually, we divide the existing market index into two components – investment (to characterize the investment aspect of trading) and speculative. Keeping an eye on the values of both indices, the investor will be able to make a more accurate assessment of the stock market status and to manage his trading strategy more efficiently. 5.2.2. New instrument for state market control The new instrument for state control of financial markets is based on managing the number of transactions conducted on a stock exchange per time unit. For this purpose, the trading system is modified in a way allowing a financial regulator to manually change the minimum permissible time interval between transactions. In case panic starts or is thought to start on a stock exchange, this scheme will enable the regulator to smoothly restrict the number of transactions per time unit and prevent a snowballing growth of trading volumes and transactions. This will help avoid suspension or complete termination of trading. Such regulation will cover both the entire market and individual securities, serving as a fast-operation tool controlled directly from the financial regulator‘s office. Additional measures may include the monitoring of the number of transactions per second and creation of a special indicator for all the market makers. Knowing the limit number of transactions per second set by the financial regulator, they will be able to better evaluate the current market situation. 5.2.3. Market manipulation prevention model This is a framework model designed to identify the points in time at which to conduct manipulative transactions actions. The model is based on monitoring the crossflow of resources from the stock market to the interbank market (IM) and is subject to the following rule: the stock market will have conditions for conducting manipulative transactions when the overall (for all dealers) 50

mathematical expectation of return on speculative investments in the stock market goes down below the IM return values, but there is crossflow of resources from the stock market to IM. Implementation of this model will require that additional information be collected from market makers, concerning the structure of investments in the stock market and IM. 5.2.4. Proposals on classification of financial information Considering the double nature of quotation comprising the issuer‘s present value of cash flows and the fact that securities credit trading needs no information, we suggest dividing the existing single news line of information agencies into three different lines. The first one will only include direct information on specific issuers. Such information affects the amount of cash flows, discounting rate and dividend payment frequency and may chance the present value. The second news line will offer news related to the system risk (country risk) and capable of changing the present value discounting rates for all or most of issuers. And finally, the third line will be intended for all other news updates including full texts of press releases, corporate reporting forms and annual statements etc. A quote from any document made public (annual or quarterly statements, press releases etc.) may not be regarded as a piece of news and is thus not subject to placement in a news line. 5.2.5. Proposals on improvement of the trading procedure The market pricing issue is central to improvement of financial markets. According to the Securities Credit Concept, trading comprises two concurrent processes – investment and speculation. Some argue that speculation has a positive effect on the trading process since it creates volatility in the market. But this is a feeble argument because the possibility of selling or buying an asset depends on the relationship between investment supply and demand rather than on the number of transactions in general. Combining investment and speculation leads to a situation when the asset market quotation no longer characterizes the asset from the investment viewpoint. But then the market no longer serves its initial purpose of attracting investment to the real sector of the national economy. A combination of speculative supply and demand results in a distorted real value of a financial asset. Besides, it is really unacceptable (from the moral perspective, above all) to involve in the ‗game‖ less professionally trained players (private investors) alongside professional participants. Here we are dealing not only with some complex financial instruments which only may be traded by so-called qualified investors, but with any assets in general. So in order for financial markets to serve their intended purpose properly, they must be released from speculation to the maximum possible extent. This will require the creation of an environment in which no credit can emerge. Practically, it may mean the creation of a double-level securities trading system. The first level is what may be tentatively called ―wholesale‖, 51

traditional trading in securities within a restricted circle of authorized dealers. The second level is ―retail‖ trading in assets for a wide circle of investors, which involves building a market maker institution based on authorized dealers who sell and buy assets with a certain lag. In this case the over-the-counter trading may remain unchanged, as an alternative. All the more so because prohibitive measures are ineffective anyway. What has to be done in this situation is to have all Forex trading systems licensed as gambling sites. An equivalent of the proposed system has proven itself in the currency market: it is currency trading by authorized dealers and an exchange office network. Basically, the double-level trading system is expected to result in dramatically diminished volatility of financial asset quotations and considerable growth of their dependence on the issuer‘s performance. It should also be noted that the possibility to manipulate market quotations will be substantially decreased. Besides, the money authorities will have a chance to make fast and effective interventions in the securities market, similarly to regulation by the Central Bank of the currency market. Furthermore, let us highlight another important aspect of the double-level trading system, concerning religious restrictions. The fact is the modern trading system appears to violate three fundamental restrictions established by Sheriat, a Mohammedan law system. These are prohibitions of usury, groundless risk and gambling that are all violated by securities credit practices. So trade floors operating in Islamic countries have to revise their operation procedures. A trade floor meeting the above Sheriat requirements, opened in any country, will attract a great number of not only issuers, but also a host of investors from Islamic countries. 6. Conclusions 6.1. The market quotation of any risk asset in free circulation in the market is a sum of values of two independent finance assets. The first one is the market‘s composite rating of the issuer‘s discounted cash flow. The second one is the value of the equivalent commercial loan which investors have to extend one another under a tacit term of investor admission to bidding (it is what is known as a Securities Credit, SC). 6.2. Financial asset volatility results from regular renewal of one of the market quotation components. 6.3. Apart from traditional definitions, the financial asset risk may also be defined as a difference between the actual return and the expected return on a financial asset, i.e. the return required to recover the balanced state of the market (zero asset volatility). 6.4. A financial asset‘s risk and return are not interrelated in speculative trading and thus the portfolio theory does not apply thereto. 6.5. Speculative trading in finance assets is, in fact, sort of a luck-based game of chance.

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6.6. The ―bubbles‖, which experts believe tend to emerge in the stock market during crises, do actually exist there at all times. 6.7. If N of securities are circulating in the stock market, it means N+1 of finance assets are actually circulating in there. An additional asset is the securities credit. 6.8. If the mathematical expectation of return on speculation in financial markets is less than the current rate of return in the interbank credit market, a professional participant will close up his financial activities in financial markets and transfer his assets to the interbank market. 6.9. Financial markets provide the conditions for manipulative transactions when the mathematical expectation of return on speculative transactions goes below the current value of the interbank market return, with no funds flowing from the stock market to the interbank market. 6.10. An efficient and rational dealer chooses not to focus his speculative activities on one or more finance assets. He trades simultaneously in all assets in all accessible markets. 6.11. A basically new content is put into the widely accepted terms: market return (i.e. the accumulated return on all transactions since the bidding start), market stability (a bidding situation when all transactions are carried out with certain regularity). 6.12. There is a correlation between the parameters ―return on a securities credit‖ and ―probability for a dealer to succeed in speculative trading‖. This is generally a directly proportional dependence described by a curve with an infinitely decreasing increment. 6.13. The higher the dealer-estimated probability of success of his speculative strategy, the higher the risk he would be willing to assume (the higher quotation he would be willing to offer). 6.14. The ―financial asset risk‖ parameter has been found to have limit values – maximum and minimum risks. 6.15. A finance asset (bond) on which the annual return increase is equal to or less than the overall transaction costs should be regarded as a maximum riskfree asset (bond). 6.16. Information is not a mandatory component for the dealer to carry out speculative trading. Certainly he may use it but he is basically indifferent to the information flow. 6.17. Return on a brand-owning company‘s stock and that on a depositary receipt issued for the same stock reflect a different amount of information. This allows you to calculate the ―return‖ on a brand, i.e. a percentage change in the absolute brand value in response to some information message. 6.18. Graphically, a change in the company‘s discounted cash flow in response to some information message represents damped oscillations. 6.19. The modern exchange trading system accepted globally, including Islamic countries, violates a few fundamental principles of Sharia and cannot be used in Islamic countries. 53

References 1.

Burmeister E. and Wall KD., The arbitrage pricing theory and macroeconomic factor measures, The Financial Review, 21:1-20, 1986

2.

Barsky, Robert B & De Long, J Bradford (1993) Why Does the Stock Market Fluctuate? / The Quarterly Journal of Economics, MIT Press, vol. 108(2), pages 291-311, May.

3.

Bong-Soo Lee (1996) Comovements of earnings, dividends, and stock prices / Journal of Empirical Finance, No 3 (1996), pp. 327-346

4.

Black, Fischer., Michael C. Jensen, and Myron Scholes (1972). The Capital Asset Pricing Model: Some Empirical Tests, pp. 79-121 in M. Jensen ed., Studies in the Theory of Capital Markets. New York: Praeger Publishers.

5.

Bruner R.E., Eades K.M., Harris R.S., Higgins R.C. Best Practices in Estimating the Cost of Capital//Financial Practice and Education, 1998

6.

Banz R. The Relationship between Return and Market Value of Common Stocks// Journal of Financial Economics. 1981. March 9.

7.

Cohen, R.D. (2007) "Incorporating Default Risk Into Hamada's Equation for Application to Capital Structure", Wilmott Magazine (download paper)

8.

Chen, N.F, and Ingersoll, E., Exact pricing in linear factor models with finitely many assets: A note, Journal of Finance June 1983

9.

Aswath Damodaran 2006 Valuation Approaches and Metrics: A Survey of the Theory and Evidence / Stern School of Business

10. Ehrbar A. EVA: The Real Key to Creating Wealth. New York, Willey, 1998 11. John Y. Campbell & Albert S. Kyle (1988) Smart Money, Noise Trading and Stock Price Behavior/ NBER Technical Working Papers 0071, National Bureau of Economic Research, 12. John Y. Campbell, Robert J. Shiller (2001) Valuation Ratios and the Long-Run Stock Market Outlook: An Update / Cowles Foundation Discussion Paper No. 1295 13. Gregory C. Chow (1999) Shanghai Stock Prices as Determined by the Present Value Model / Journal of Comparative Economics. №27, pp. 553–561 14. Graham J.R., Harvey Campbell R. The Theory and Practice of Corporate Finance. Evidence from the Fields, May 2000. 15. Fama, Eugene F. (1968). Risk, Return and Equilibrium: Some Clarifying Comments. Journal of Finance Vol. 23, No. 1, pp. 29-40. 16. Fama, Eugene F. and Kenneth French (1992). The Cross-Section of Expected Stock Returns. Journal of Finance, June 1992, 427-466. 17. French, Craig W. (2003). The Treynor Capital Asset Pricing Model, Journal of Investment Management, Vol. 1, No. 2, pp. 60-72. Available at http://www.joim.com/ 18. French, Craig W. (2002). Jack Treynor's 'Toward a Theory of Market Value of Risky Assets' (December). Available at http://ssrn.com/abstract=628187 19. John Heaton, Deborah Lucas (2000) Stock prices and fundamentals / Journal Proceedings (Federal Reserve Bank of San Francisco) 20. James J. McNulty, Tony D. Yeh, William S. Schulze, Michael H. Lubatkin. What"s your real cost of capital?//Harvard Business Review, Boston, October 2002. Volume 80, Issue 10 21. Kamstra, Mark (2003) Pricing Firms on the Basis of Fundamentals/ Federal Reserve Bank of Atlanta, Economic Review. First Quarter 2003, p. 55 22. Kleidon, Allan W. (October 1986) Variance Bounds Tests and Stock Price Valuation Models./ Journal of Political Economy №94 (October 1986): 953-1001. (a) 23. Koedijk K.G., Kool C., Schotman P. C., van Dijk M.A. The cost of capital in international financial markets: local or global? Journal of International Money and Finance. 2002. № 21. 24. Lintner, John (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47 (1), 13-37.

54

25. Michael H. Lubatkin, William S. Schulze, James J. McNulty, Tony D. Yeh. But Will it Raise My Share Price? New Thoughts About an Old Question//Long Range Planning, Volume 36, Issue 1, February 2003. 26. Merton H. Miller and Franco Modigliani (Oct., 1961) Dividend Policy, Growth, and the Valuation of Shares / The Journal of Business, Vol. 34, No. 4, (Oct., 1961), pp. 411-433 27. Merton R. An intertemporal capital asset pricing model. Econometrica. 1973. № 41 (September) 28. Mullins, David W. (1982). Does the capital asset pricing model work? Harvard Business Review, JanuaryFebruary 1982, 105-113. 29. Markowitz, Harry M. (1999). The early history of portfolio theory: 1600-1960, Financial Analysts Journal, Vol. 55, No. 4 30. Mehrling, Perry (2005). Fischer Black and the Revolutionary Idea of Finance. Hoboken: John Wiley & Sons, Inc. 31. Alireza Nasseh , Jack Strauss (2004) Stock prices and the dividend discount model: did their relation break down in the 1990s? / The Quarterly Review of Economics and Finance, No 44 (2004), pp. 191–207 32. Pindyck, Robert S & Rotemberg, Julio J (1993) The Comovement of Stock Prices / Quarterly Journal of Economics, Vol. 108, рр. 1073-1104. 33. Qin J. Human-capital-adjusted capital asset pricing model // Japanese Economic Review. Oxford: Jun 2002, Vol.53, Iss. 2. 34. Roll, Richard and Stephen Ross, An empirical investigation of the arbitrage pricing theory, Journal of Finance, Dec 1980, 35. Roll R. A Possible Explanation of Small Firm Effect// The Journal of Finance. 1981. Vol. 36. № 4 (September). 36. Ross, Stephen, The arbitrage theory of capital asset pricing, Journal of Economic Theory, v13, issue 3, 1976 37. Ross, Stephen A. (1977). The Capital Asset Pricing Model (CAPM), Short-sale Restrictions and Related Issues, Journal of Finance, 32 (177) 38. Rubinstein, Mark (2006). A History of the Theory of Investments. Hoboken: John Wiley & Sons, Inc. 39. Salih, Aslihan Altay, Akdeniz, Levent and Ok, Suleyman Tulug, (June 2006) "Are Stock Prices Too Volatile to be Justified by the Dividend Discount Model?" 40. Shiller, Robert J. (June 1981) Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends? / The American Economic Review, Vol. 71, No. 3, PP. 421-436. 41. Summers, Lawrence H. (July 1986) Does the Stock Market Rationally Reflect Fundamental Values? Journal of Finance. Vol. 41, No. 3, pp. 591-601. 42. Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3), 425-442 43. Stone, Bernell K. (1970) Risk, Return, and Equilibrium: A General Single-Period Theory of Asset Selection and Capital-Market Equilibrium. Cambridge: MIT Press. 44. Stulz R.M. Globalization, Corporate Finance, and the Cost of Capital// Journal of Applied Corporate Finance. 1999. № 12(1). 45. Solnik B. An Equilibrium model of the International Capital Market// Journal of Economic Theory. 1974. № 8. 46. Sandahl G. and Sjogren S. Capital budgeting methods among Sweden"s largest groups of companies. The state of the art and a comparison with earlier studies //International Journal of Production Economics, Volume 84, Issue 1, April 11, 2003. 47. Yandiev M. The Company‘s Brand Evaluation on the Base of the Financial Markets‘ Instruments. Finance, № 7, 2007. Available at SSRN: http://ssrn.com/abstract=1412085

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