Challenges of Financial Asset Pricing Models - Essay Example

The field of investment is one of the most serious and focused area of human indulgence due to its potential to chime death bell of financial ruin ifgone wrong. This explains the human aspiration to muster a foolproof model with which risk and returns can be predicted. But even with all these scientific models developed by humans the financial market still remains turbulent and unpredictable so far. The challenges that the financial asset pricing models face are many. Although these models have evolved consistently since its inception in early 1960s the empirical record of these models are not very encouraging to use it in practice. Even then these models would serve as a better guide to the market than the lessons taught by a financial ruin. That is a strong reason for understanding the challenges faced by the financial asset pricing models, so that these models can be used with discretion to understand the market better. Seen from that angle understanding the correlation between risk and returns, by using a tool, in this case the financial asset pricing models is vital. Any pricing errors would affect the valuation models, jeopardize value judgments and therefore give rise to incorrect risk assessment. The challenges faced by the asset pricing models are on the rise due to the intermingling of economies due to globalization. Along with the increase in challenges the number of critics also increases. These pressures and requirements in turn give rise to new models of financial asset pricing. However the scope of this essay is limited to the empirical challenges faced by financial asset pricing models. To make a base for this study I start with comparing and contrasting different financial disasters that made headlines in the past with the more recent ones. In the past all the noted failures were either due to lack of analytical capacity, absence of systems, error in using models or failure to appreciate risks. The inadequate appreciation of yield curves resulted in S&L bailout. Askin Capital management fiasco was as a result of inadequate analytics and Kidder Peaboy tragedy occurred due to the imperfect management risks. In contrast to this is the more recent failures where even the financial entities known for their efficiencies were dragged to take knee jerk reactions to address huge market dislocations like Russia's default and a collapse in liquidity. The problem solving capacity of an investor has increased manifold through the years. Powerful machines today help investors solve problems, which were considered beyond scope, just a few years ago. The right kind of codes put together (software) by a programmer can have a path breaking consequence on the computational capability of an investor. Side by side with this technological breakthrough, there is also a reduction in cost of computation and emergence of better financial theories. Today's investors are much more aware of the market conditions and have a greater capacity to analyze and take logical decisions about investments due to the availability of different computation methods and real time accessibility to information. But paradoxically usage of these refined method for investment have made the markets more risk prone due to the intermingling of the market in a globalized economy. A direct consequence of this is the rise of common risks. Traditionally investors used to diversify their portfolio in an attempt to beat an existing market risk and they were successful in this due to the difference in risk associated with different securities. But now with the increase in awareness about the different tools with which they can make decisions there is a commonality of reaction to a crisis resulting in potential catastrophes. At the time of a crisis the investors try and reduce risk by selling their illiquid positions. But since by now the demand for it would go down due o the similar stance all over by the investors, they try to sell their liquid positions no matter which market they are in. Due to this massive movement the market gets increasingly interconnected giving rise to correlations of asset groups, which are otherwise uncorrelated. This entire process now gets snowballed and makes up the vicious circle of liquidity. The risks of following a similar financial model are explained with the following examples. The portfolio insurance in 1987, as a case study can illustrate the catastrophe that can occur due to adhering to similar practicing of handling securities. Whether the collapse of the market was caused by portfolio insurance singularly or not cant be answered correctly. But it is certain that it imparted the major thrust to the market collapse. Similar practices to avert loss accumulation resulted in massive sell off resulting in market collapse. In 1992 Hedging Mortgages rally even though wall street spend millions in retaining the interest rate the market did not react as per the prediction made with the help of sophisticated financial models and tools. The investors who learned their lessons in the hard way in the preceding years reacted by buying the U.S treasury securities in large numbers which augmented the progress of the rally and resulted in further shortening of mortgages. In 1998 Russia's default on its debts resulted in a similar reaction which would have had catastrophic effect but for the intervention by Federal Reserve. The financial market is a very complex field in which pattern making is a difficult task to achieve. Human mind can understand and predict a phenomenon, which follows certain patterns or rules. But however this area holding the importance that it has, have attracted many outstanding personalities who tried to reason the way the market behaves using scientific tools. Along with the challenge it presents this field also offers the thrill of predicting the real life situations using models based on mathematics. But there lies in the effort to find a pattern in the market behavior its greatest peril. The mathematical models are overtly based on constants and variables, that don't change in their characteristics. In contrast with this is the fundamental behavioral pattern of financial market where a parameter, which is considered constant, might develop a varying value in a different time frame relative to the market conditions. A certain parameter, which is considered to be a constant theoretically, may vary in practice thereby giving a different empirical result. This random behavior of the risk factors magnifies as a result of the investors knowledge about them, which triggers a streamlined action. Thus it is seen that unlike the constants and variables in the physical systems, which is universally, true and unchanging those of the financial world are prone to variations resulting in great complexity. The financial models, which simplifies these complexities to suit their objective of prediction, overlooks the real character of these parameters. Too much of objectiveness in these models makes it "simply a model" having very little practical usage. So there we see that there is a need of constant evolution of the system to accommodate the changing characteristics of the market. A model should have the scope of housing the variable by frequent refinement. It should be subjected to frequent reality checks to weed out the inefficiency. However it is illogical to accommodate more variable to make a precise prediction. There fore it is highly essential to apply market knowledge and intuition while investing. So in addition to having knowledge about yield curves and interest rate risk the systematic risks which are not included in any models also should be considered while doing portfolio level analysis. Refined statistical and financial methods are to be developed to approximate unsteady empirical relationship, lack of which will call for relying upon the subjective judgment for investing. Presently the financial asset pricing models are taking only measurable criterion to address this problem. At times due to the absence of clarity existing in the market it is difficult to have assurance on the spread of their historical time series of credit of a security, which is presented by the models. A security's contact with each risk factor can be calculated separately while fixing others, which corresponds to taking partial derivatives in mathematics. But the shear massiveness of the problem is challenging because there can be thousands of risk factors that can be identified for a portfolio, some measurable and others not. And again this approach, also suffers from the assumption that a risk factor progress in segregation, while all the others are unaffected, which is highly improbable. The challenge doesn't end at identifying the relevant risk factors and calculating the exposure of the portfolio to these risks. The next challenge is to appreciate the joint probability distribution of risk factors. The recent development to address this challenge is the creation of statistical models of financial time series data using applied statistics. Using these methods historical volatilities and interrelation of the risk factors can be appreciated. For giving an insight into the behavior of the market in the past, the financial models are excellent but they frequently falter to correctly predict the upcoming movements. Now applying the time series model to the widening of credit spreads in October 1998 this shortcoming can be easily highlighted. Say in July 1998, relying on the historical swap spread data, time series models wouldn't have forecasted the widening of credit spread in October 1998. Time series models would have returned a standard deviation event of about seven which corresponds to one in 700,000,000,000 chance. This suggests that either the assumptions made were wrong or the standard deviation is wrongly estimated or the approach is faulty. So these models while satisfactorily explains the historical events are not successful in forecasting the forth coming changes due to materialization of some variables which were dormant in the past but would cast its spell in the present. On the other hand some of the factors, which were prominent in the past, may become subdued in the present. For example the factors that dictated the movement of interest rates during 1993 -1997 became dormant in 1998 when Federal Reserve started basing their decision on global market rather than the U.S economy. So this reality check calls for the flexibility that has to be administrated to the financial models by allowing inclusion of new risk factors and removal of those that are irrelevant. Even when managing a single share taking the help of financial models throws up complex calculations the challenges involved in large scale money management is huge due to the computation involved is gigantic and have to be performed regularly. With variety of securities and portfolio to be managed the need of computing a varied number of risk factors arise. Markets are also increasingly adding new types and structures of securities into its fold. Treasury Inflation-Protected Securities (TIPS), esoteric types of asset-backed securities, CMBS IOs, 144-As, Brady bonds are some examples. This necessitates improving the financial models to cater for auxiliary systematic risk factors since there is no historical information available to assess it using a model. Some of the most prominent and widely used asset pricing models and their drawbacks are discussed below. In1964 William Sharpe initiated a new theory called the Capital Asset Pricing Model (CAPM) to logically predict and test about risk and return, which revolutionized the modern finance. This was the beginning of asset Pricing Theory and for his pioneering effort William Sharpe got the Nobel Prize in 1990. This theory was developed from first principles and is vastly applied in estimating the cost of equity capital for firms and evaluating the performance of managed portfolios. Although CAPM enjoys wide acceptance due to its convincing but simple logic instinctively satisfying testable predictions regarding measurement of risk and the and the manner in which risk and return are related, the observed record of the model is pathetic enough to quash it to obscurity. There the question rises as to which among the model or the test is false These failings may also be due to major drawbacks of the empirical tests especially due to poor proxy for the market portfolio of investment, which is of utmost importance for the prediction using the model. As per CAPM the expected return from capital asset can be calculated using the formula E(ri) = rf + Bim (E(rm) - rf) Where E(ri) is the expected return on the capital asset, rf is the risk free rate of interest, Bim(beta) is the sensitivity of the asset returns to market returns, E(rm) is the expected return of the market, (E(rm) - rf) is known as risk premium. The vulnerability of CAPM starts with its assumptions, which are 1.Individuals are risk averse 2. Individuals seek to maximize the expected utility of their portfolios over a single period planning horizon. 3. Individuals have homogeneous expectations - they have identical subjective estimates of the means variances, and co-variances among returns. 4. Individuals can borrow and lend freely at a risk less rate of interest. 5. The market is perfect - There are no taxes; there are no transactions costs; securities are completely divisible; the market is competitive. 6. The quantity of risky securities in the market is given. The observed shortcomings of this model are the following. It is based on highly restrictive assumptions. There are serious doubts about its testability. The market factor is not the sole factor influencing stock returns. It doesn't adequately explain the variation in stock returns. It assumes that investor expects higher returns for higher risks taken. It doesn't consider taxes and transaction costs. Empirical evidence (CAPM) Although at the time of its inception beta was discarded and did not generate any interest in the investment community in the early 1970s it started gaining recognition. Even portfolio managers with very little knowledge in mathematics were playing with 'beta'. With the concept of beta gaining popularity the CAPM and its many modifications also attracted limelight and was put under scanner. As a result of it getting tested inside out many questions were thrown up regarding the adequacy of testing model, stability of beta, the existence of other factors that affect returns, the capability of CAPM to assess the correlation between risk and returns etc. The following facts were established as an end result of all these investigations. It was concluded that there is a basic problem in testing the capital asset pricing model. According to Richard Roll "since the true market portfolio can't be measured, the capital asset pricing model cannot be tested adequately". Betas of portfolios remain comparatively stable in comparison with that of individual shares, which vary continuously. The empirical evidences show that, the actual correlation between risk and return is flatter than what is brought out by capital asset pricing model. In addition to beta there exists few more factors, which will have a bearing on the realized rate of return. However it should be appreciated that Beta has got an irrefutable and major bearing on the returns. The capital asset pricing model is inadequate to contain the asset pricing process. As James, Loire Peter Dodd, and Mary Kimpton said "Beta however remains a valuable concept, and the capital asset pricing model remains one of the most powerful developments in modern finance. Arbitrage pricing theory (APT) was the brainchild of Stephen Ross who initiated it in 1976 in which he seeks to overcome the shortcomings of CAPM. It centers on the argument that if the price fluctuates the arbitrage would bring it back into line. It sees the expected return of a financial asset as a linear function of several macro economic agents. It also uses beta coefficient to represent sensitivity to changes as in CAPM. The APT assumes that there is a linear relation between the return on any stock and systematic factors or risk factors. Ri = ai + bi1 I1 + bi2 I2 + .. bij + ei Where Ri is the return on stock (i), ai is the expected return on stock (i) if all factors have a value of zero, Ij is the value of jth factor which influences the return on stock (i) (j = 1,2,..), bij is the sensitivity of stock (i)'s return to the jth factor and ei is the random error term. The model rests on the assumptions that E (eiej) = 0 for all (i) and j where (i) is not equal to j and E (ei (Ij - I _j ) = 0 for all stocks and factors. Apt doesn't specify the factors I1, I2,.Ij, that affect the stock returns. Empirical evidence (APT) Empirical testing of APT has been done using two methods. In one approach a statistical technique called factor analysis is applied to the returns to unearth the basic factors. These factors, which are identified, are investigated to determine the type of variables they fall into that is economic or behavioral variables. The results of these empirical tests reveal that there is no consistency in the terms of the number of basic factors, the interpretation that may be put on these factors and the stability of these factors from test to test. In the next method a priori factors rather than the ones identified by analyzing stock returns are considered. Roll and Ross took the same approach in their classic work. The four factors employed in this approach are industrial production, inflation rate, term structure on interest rates, and default risk premium. In this method variations in the expected return of stocks are explained by the sensitivity to unanticipated changes. Some argue that in comparison to CAPM, the APT model is superior in explaining the stock returns better while others maintains that there is no appreciable difference between the two. Further there is also difference in opinion among researchers n the approach to be followed in identifying the systemic factors and the methodology to be employed in testing APT. Modern portfolio theory (MPT) is based on CAPM beta coefficient; efficient frontier, the capital market line and the securities market line. It argues that an investor will be rational while investing to get the optimum output from the portfolio and towards this he would diversify his investment. It also proposes the methods to price an asset considering the risk relative to the market. As per MPT there is an expected value and a variance for the return of an asset and a portfolio, which is a weighted combination of assets since it suggests return of an asset as a random variable. It suggests that investors would go in for diversification of their portfolio to reduce the risk in having limited securities in their possession. This theory is based on efficient frontier, Capital Asset Pricing Model, beta coefficient; the capital market line and the securities market line. Since beta is commonly used in all the models it has to be explained. The sensitivity to market movements is called beta. Though not perfect, beta represents the most widely accepted measure of the extent to which the return on a security fluctuates with the return on the market portfolio. By definition, the beta for market portfolio is 1. A security, which has a beta of, say 1.5 experiences greater fluctuation than the market portfolio. More precisely, if the return on market portfolio is expected to increase by 10 percent, the return on the security with a beta of 1.5 is expected to increase by 15 per cent. On the other hand, a security that has a beta of, say, 0.8 fluctuates lesser than the market portfolio. If the return on the market portfolio is expected to rise by 10 per cent, the return on the security with a beta of 0.8 is expected to rise by 8 percent individual security betas generally fall in the range of 0.50 to 1.80 and rarely, if ever assume a negative value. For calculating beta of a security the following market model is employed. Rj = aj + BjRm + ej Where Rj is the return of security j, aj is the intercept term alpha, Bj is regression coefficient, beta, Rm is the return on market portfolio and ej is the random error term. Time series analysis has been widely used in economics due to their simplicity and better forecasting capability. The financial models work out the price as a function of a large number of variables, which varies randomly. So more than the accuracy, the general pattern of distribution of future returns is preferred. This requirement is sufficiently met by time series method even though it is less sophisticated. The first and second order approximation using tailor series expansions where first order approximation is known as delta and the second order is known as delta-gamma is not very good forecasters of price variations when risk factors are many. As a general rule a nonlinear yield function would give a substandard estimate. The scenario analysis, which does a number of estimations of a security in various economic conditions, is also unsuccessful when the number of variables is very large. The final triumph of the financial asset pricing models is achieved when they gain the confidence of the populace as a tool to be used for daily investment purposes and are used successfully to forecast the trends of the market. References Bennett W. Golub & Leo M Tilman, 15 Jun 2000, Risk Management: Approaches for Fixed Income Markets, John Wiley & Sons Inc, Canada. Capital Asset Pricing Model, 14 Jan 2006, [Online], Available from: 17 Jan 2006 Chandra Prasanna, 1997, Financial Management Theory and Practice,Tata Mcgraw- Hill Publishing Company Limited, New Delhi. Sources Bennett W. Golub & Leo M Tilman, 15 Jun 2000, Risk Management: Approaches for Fixed Income Markets, John Wiley & Sons Inc, Canada. Bernd Meyer, 1999, Intemporal Asset Pricing, Springer, Germany Bob Litterman, 2003, Modern Investment Management: An Equilibrium Approach, John Wiley & Sons, Inc., New Jersey. 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