The Capital Asset Pricing Model - Coursework Example

The Capital Asset Pricing Model A reaction paper to the ment: The capital asset pricing model (CAPM) is the sterile offspring of advanced mathematics. Introduction Individuals as well as large corporations are prone to suffer the consequences of a poorly studied investment. This compels analysts and theorists to discover workable theories that could be used to forecast future returns of investments and thus minimize the risk. One such theory is the Capital Asset Pricing Model, or CAPM, a widely accepted theory the validity of which noted economists and finance authorities have questioned. Its usefulness as a tool in minimizing risk and maximizing returns has been questioned – or as the statement says, the CAPM is a “sterile offspring” – an unproductive result – of mathematical manipulation. Problem and Objectives Given the general acceptance of the capital asset pricing model, the objective of this essay is to determine authorities’ views on the usefulness of the model as a predictor of returns in investments. To attain this, the paper shall answer the following questions: What is the capital asset pricing model, or CAPM, and how was it formulated? What do noted authorities say about the CAPM’s validity, and what empirical data support these views? Discussion The capital asset pricing model (CAPM) described - The capital asset pricing model is a theory developed by William F. Sharpe for which he received the Nobel Prize for economics. It first appeared in his article “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” which appeared in the September 1964 issue of the Journal of Finance (Brigham and Gapenski 1996, p. 67). It is summed up in the equation: kj = kRF + βj (km – kRF) where: kj = the expected rate of return of an investment kRF = risk-free rate of return βj = the beta of the investment km = the expected rate of return of the market The beta coefficient is a measure of the nondiversifiable risk of the investment. It is “an index of the degree of movement of an asset’s return in response to a change in the market return,” and the market return is “the return on the market portfolio of all traded securities” (Gitman 1995, p. 346). The CAPM is thus the theory that relates expected investment return with the risk free rate and the expected market return, taking into account the systematic risk of the investment. Its usefulness to the investor as an invaluable decision-making tool is immediately apparent. Application of the model is not straightforward. Because it is a theoretical model of a real-world phenomenon, the mathematical model makes eight Basic Assumptions for it to hold true. These are: 1. All investors think in terms of a single period, and they choose among alternative portfolios on the basis of each portfolio’s expected return and standard deviation over the period. 2. All investors can borrow or lend an unlimited amount of money risk-free rate of interest, kRF, and there are no restrictions on short sales of any asset2 3. All investors have identical estimates of the expected values, standard deviations, and correlations of returns among all assets, that is, investors have “homogeneous expectations.” 4. All assets are perfectly divisible and are perfectly marketable at the going price. 5. There are no transactions costs. 6. There are no taxes. 7. All investors are price takers (that is, all investors assume that their own buying and selling activity will not affect stock prices (Brigham and Gapenski 1996, p. 68)). 8. The quantities of all assets are given and fixed. (Jensen M. 1972, 357-398.) The above assumptions are necessary in order to observe tendencies in the behaviour and relationship among the variables expected market return, risk free rate of return, and expected return on the asset, such that a constant beta coefficient is sufficiently determined. The use of such assumptions is not unusual for theoretical models or theories. In fact, pure theories make use of such assumptions in order to minimize the “random noise” that accompany real-world data so that consistent relationships among variables may be observed. What authorities say: Critiques on the CAPM - The constrictiveness of the eight assumptions have not gone without adverse comment. Brigham and Gapenski (1996) state that the CAPM was developed on the basis of “a set of unrealistic assumptions” (p.82). They acknowledge that if the stated assumptions were all true, then by the empirical data and econometric equations of Sharpe, the CAPM would have to be true. But they observe that the assumptions may not realistically be expected in real life. For example, it is impossible for all investors to have the same estimates of the expected values of assets, contrary to the third assumption; or, contrary to the fifth and sixth assumptions, the realities of business transactions is that there will be transaction costs and taxes involved. These would necessarily distort the CAPM relationships, in effect rendering the model useless in predicting asset returns and values. Bodie, Kane and Marcus (2005) have similar concerns. They point out that CAPM has two limitations. The first is that it relies on the theoretical market portfolio which necessarily includes trading in all assets, including real estate, foreign stocks, and so forth. This cannot materialize in actual experience, because many assets are not traded in a secondary market. The second is that the model deals with expected, not actual returns. In real-world experience, expected returns vary among investors, and what can be determined for sure are actual returns. Thus, Bodie et al observe that the theory behind the CAPM rests on a shaky real-world foundation” (p. 173). After the CAPM was published, the first article to expound on the weakness of the new model was by Douglas (1969). In an article that appeared in Yale Economic Essays, Douglas presented empirical proof that countered the basic contentions of CAPM, one of which is that non-systematic risk (risk that could be diversified) do not explain average returns. In seeking to defend CAPM, Miller and Scholes (1972) published a paper showing that statistical problems rendered unreliable a straightforward test like that conducted by Douglas. They were not able, however, to prove positively that CAPM is valid. There were later studies by Black, Jensen, and Scholes (1972), and Fama and MacBeth (1973), which, among other things, tried to test the CAPM using portfolios constructed to lessen the statistical errors which resulted from diversifiable risk. Despite these efforts, the CAPM’s validity as a working model remained unconfirmed. Four years after Fama and Macbeth’s study, the first paper written by a practitioner was published. This was Roll’s (1977) “A Critique of Capital Asset Pricing Tests” which was the first view on the CAPM by a non-academician. In it Roll argued that because the true market portfolio as espoused by CAPM can never be observed, the CAPM is rendered definitely untestable and, thus, unverifiable. The “Roll’s critique” was followed by popular articles such as “Is Beta Dead?” by Wallace (1980). Then in 1990, Fama and French completed a study that if controls were implemented on some characteristics of the firm that are commonly followed (e.g. market to book value ratio), then the beta is not even necessary in predicting the future returns of the asset. This rendered the CAPM even seemingly more pointless. What authorities say: In defense of the CAPM - To overcome the limitations of the CAPM, Bodie et al observe that it should be implemented in the form of an index model and use realized, not expected, returns. An index model makes use of actual portfolios which comprise a particular index, such as the S&P 500 or the DJIA, and thus becomes a workable proposition. The advantage of an index model is that its composition is definite and the rate of return of the index is easily measurable. In short, Bodie et al do not debunk the CAPM. They state that “as in all science, a theory may be viewed as legitimate if its predictions approximate real-world outcomes with a sufficient degree of accuracy.” (p.73). More recent studies have continued to explore the possible use of CAPM for determining implications on other variables. In Copeland (2005) it was mentioned that for the past four decades or more, finance theorists have advocated the use of CAPM to estimate the cost of equity capital of a publicly traded firm. Also, many firms continue to use the CAPM to estimate their required rate of return. A survey of companies in the US conducted at the beginning of this decade determined that 73.5% of them rely on CAPM for forecasting (Graham and Harvey, 2001). In 1992, Levy and Samuelson published an article with a more definitive statement about the usefulness of CAPM.  They state that, assuming portfolio rebalancing is allowed, the CAPM holds in four specific cases that were overlooked in previous studies. They defined these cases in econometric terms that, while too technical for this essay, nevertheless points to the possibility that CAPM may still be proved empirically. Another article which seemingly confirms CAPM’s validity was written in 1998 by Ferson and Locke. They observed that the CAPM continues to be relied on by practitioners as a framework to estimate a firm’s cost of capital or expected return. They attributed its appeal to: (a) its strong theoretical basis which, despite attack, remains undiscredited by its critiques; and (b) its relative ease of use. Were CAPM to be discarded, the closest possible method for estimating cost of capital would be the Asset Pricing Theory of Ross (1976). This method replaces the market beta with a number of factor betas. Recent studies suggest, however, that multiple-beta models such as the APT is a wieldy method that aggravates the problems encountered with the CAPM. It is more difficult to estimate several betas and risk premiums, which has led to the limited appeal of the APT among practitioners (Lehmann and Modest 1988; MacKinlay 1995). Ferson and Locke further state that sources of errors in the use of the CAPM to determine the cost of equity capital may be reduced by changes in the practices that accompany application of the model. They found that errors in the cost of equity capital may be reduced by approximately 40 percent, when applied to small stocks in most industries, when the usual practice of employing historical averages to estimate the premium on a market index is discarded, and instead replaced with a simple estimate using current market indicators. Using this, it was found that errors due to using the “wrong” beta have a much smaller impact on the computational result. Overall, while the CAPM has not yet been entirely verified using empirical data, academicians and practitioners are in agreement that the model has nevertheless persisted from 1964 until the present day. Its lack of confirmation does not totally discount it either. Conclusion This paper set out to determine whether the capital asset pricing model was a “sterile offspring of advanced mathematics”. This writer adheres to the position that this statement is not true. Were the CAPM an empty theory developed by advanced mathematics but yielding no useful application, it would have been ignored by practitioners and faded away. The real world has no compulsion to pay empty homage to the altar of the academe. It employs what it finds useful and discards what it does not. The CAPM has been around for more than four decades. Despite academic hesitancy in confirming it, practitioners have gone ahead and made it their own (Brigham and Gapenski 1996, p. 177). This is not difficult to rationalize. It is not important to those who employ the model whether it is absolutely accurate or not. Usage has shown that CAPM is capable of reducing uncertainties and minimizing losses. As Ferson and Locke (1998) point out, all theoretical models are in some sense “wrong”. The important consideration, from a practical perspective, is whether the use of a particular model leads its user to make systematically poor decisions, and whether another model can lead to consistently better results. The CAPM guides practitioners in making better decisions. That is sufficient basis to confirm its usefulness for the purpose it was meant to serve. References Journals Black F., Jensen M., and Scholes M. (1972), “The capital and asset pricing model: some empirical tests,” in Studies in the Theory of Capital Markets, Michael C. Jensen (ed.), Praeger. Douglas G. (1969), “Risk in equity markets: an empirical appraisal of market efficiency,” Yale Economic Essays, IX. Fama, E & Macbeth, J (1973) ‘Risk Return and Equilibrium: Some Empirical Tests’, Journal of Political Economy. Fama, E & French, K (1992) ‘The Cross Section Of Expected Stock Returns’, Journal of Finance, 47, 427-465 Ferson, W. and Locke, D. (1998) “Estimating the Cost of Capital Through Time: An Analysis of the Sources of Error,” Management Science, Vol. 44, No. 4 (Apr., 1998), pp. 485-500 Graham J. and Harvey C. (2001), “The theory and practice of corporate finance,” Journal of Financial Economics. Jensen M. (1972), “Capital Markets: Theory and Evidence,” Bell Journal of Economics and Management Science. Levy H. and Samuelson P. (1992), “The Capital Asset Pricing Model with Diverse Holding Periods,” Management Science. Miller M. and Scholes M., “Rate of return in relation to risk: a re-examination of some recent findings,” in Studies in the Theory of Capital Markets, Michael C. Jensen (ed.), Praeger, 1972. Roll, R (1977) ‘A Critique of the Asset Pricing Theory’s Test’, Journal of Financial Economics, 4, 129-176 Sharpe, W.F (1964) ‘Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk’, Journal of Finance 19, 425-442 Wallace A. (1980) “Is beta dead?,” Institutional Investor 14 (July 1980), pp 22-30. Books Brigham E., Gapenski L. (1996) Intermediate Financial Management, Harcourt Brace College Publishers, Orlando, FL Bodie, Z., Kane, A., and Marcus A. (2005) Essentials of Investment, Richard D. Irwin, Inc., Chicago Copeland T., Weston J. and Shastri K. (2005), Financial Theory and Corporate Policy (4th edition), Pearson Addison Wesley, Boston. Gitman, L. (1995), Basic Managerial Finance, Harper and Row, New York. Grinblatt M. and Titman S. (2002), Financial Markets and Corporate Strategy (2nd edition.), McGraw-Hill Irwin, Boston. Read More