The Relative Merits of the CAPM and Empirical Approaches to Asset Pricing - Coursework Example

The Relative Merits of the Capital Asset Pricing Model (CAPM) and Empirical Approaches to Asset Pricing The capital asset pricing model (CAPM) has proved to be one of the most widely used models by investors in the choice of investments for their portfolio. As much as there are supporters of this theory, however, there are also detractors who argue that empirical evidence does not support the Capital Asset Pricing Model Observing that the Markowitz model fails to account for risk, simultaneous although separate studies by Jack Treynor (1961), William Sharpe (1964), John Lintner (1965), and Jan Mossin (1966) arrived at what eventually became known as the Capital Asset Pricing Model, or the CAPM (Elsas, El-Shaer & Theissen, 2003) where: E(Ri) = the expected return on a stock Rf = the return on a risk-free investment βi = the beta of the stock (i.e., specific risk) E(Rm) = the rate of return of the market portfolio The CAPM is the graphically represented by the security market line (SML), which shows the expected rate of return for the individual security as a function of systematic risk (indicated by the beta of the security). The SML is shown in the following figure. Determination of asset returns through CAPM Suppose an investment was made in a stock with a beta of 1.5. Assuming the return on the market portfolio at 12%, and the return on the one-year treasury bond benchmark rate to be 8%, the rate of return the investor may expect on the stock would be determined by application of the CAPM as: RE = 8% + 1.5 x (12% - 8%) RE = 14% The stock investment is therefore expected to contribute a return of 14% to the investor’s portfolio, which is an improvement over the market return of 12%. The determination of return on the stock is important not only to balance out the portfolio, but also to enable the investor to determine the value of the stock. Knowing the value will enable the investor to decide whether or not he should purchase (or sell) the stock at the current market price. The expected rate of return is useful in the discounted dividend stock valuation method. Assume the stock’s regular per share cash dividend is $1 per annum without further growth, then the stock is priced fairly at: Dividend $1.00 P = ----------------- = ----------- RE 0.14 P = $ 7.14 The price of $ 7.14 is indicative of the value of the investment at the time of consideration, and it may or may not be equal to the price of the stock presently prevailing in the market (exchange). This is then the basis for deciding what investment action to take in the asset. If the market price is presently $9 then the market overvalues the stock, and it would be a good time to sell the stock, but not a good time to buy. On the other hand, if the market price were $6, then the market underprices the stock and it would be a good time to buy, but not to sell, the stock. The CAPM is a theoretical model and like all theoretical models depends on some important assumptions. The following eight assumptions are requisite for the CAPM to hold true (Taylor, 2005; Reilly & Brown, 2006): 1. All the investors agree on the distribution of asset returns. 2. Investors have the same one-period investment horizon. 3. Investors all hold efficient frontier portfolios. 4. All investments are infinitely divisible. 5. The demand for assets equals the supply in equilibrium, and all markets are in equilibrium. 6. All investors have perfect knowledge of all information all the time. 7. All investors hold the risky assets in the same proportions. 8. All investors can always borrow an unlimited amount at risk-free rate. Equilibrium conditions (Jordan, 1998) 1. All investors will hold the same portfolio for risky assets (i.e., market portfolio) 2. Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value. 3. Risk premium on the market depends on the average risk aversion of all market participants. 4. Risk premium on an individual security is a function of its covariance with the market. Shortcomings of the CAPM The CAPM has been the target of criticism, both from academe and practitioners. Some of the more pervasive of these observations are the following: 1. Beta is essentially unstable; since beta is computed as the slope of the regression equation from a time series of past returns. Depending upon the progression and trend of the time series as it continues to be incremented, beta will tend to change periodically (Brooks, Faff & Lee, 1994). For this reason, Ang and Chen (2007) recommend the use of a conditional CAPM with time-varying betas as having greater predictor value for asset returns than the traditional CAPM. 2. CAPM assumes that asset returns are jointly normally distributed random variables; however, this is not supported by empirical data, which shows that large swings (by as much as 3 to 6 standard deviations) from the mean is common in the stock market, and does not follow what is expected from normal distribution (McCracken, 2009). 3. Beta is characterized by ambiguity. Beta is assumed to capture the sum total of risks, based on the notion that the variance of returns adequately measures risk. However, since returns are not distributed normally, then beta finds little basis as the measure of risk, since mean-variance (M-V) loses its validity (McCracken, 2009). 4. Assumptions unrealistic a. Homogeneous expectations assumption is not viable, as investors have different expectations. b. Taxes and transaction costs exist, contrary to the basic assumptions. c. Investments are not infinitely divisible, as many exchanges have lot sizes. d. The single period time horizon is not a reliable assumption, since investors have investment horizons well into the future in order to secure their lifetime consumption level. 5. Unavailability of time series of historical returns (Washburn and Binkley) 6. CAPM views individual investors as basing investment decisions purely on the risk-return profile, but in fact investors have numerous other bases for selecting investments, many of which are subjective (e.g., such as how they feel about a particular product of the company whose stock they are considering purchasing) (McCracken, 2009). 7. The CAPM should only be based on forward-looking (ex-ante) data (e.g., the expected rate of return and expected beta). However, these variables cannot be estimated with precision and are therefore often historically based (Brigham & Gapenski, 1996, p. 85). Development of Other Asset Pricing Models The shortcomings of the CAPM, as perceived by theorists, spurred the formulation of other models which sought to account for those aspects ignored by the original model. For instance, Stephen Ross developed the Arbitrage Pricing Theory or APT Model, and published his theory in his 1976 article in the Journal of Economic Theory, “The Arbitrage Theory of Capital Asset Pricing.” The APT is founded on the idea that the return of each stock is influenced by a number of independent factors, even while it is founded on the fundamental precepts of the CAPM. According to the APT, the risk premium of an asset depends upon the risk premium of the factors any number of factors identified as relevant to the particular market, and the asset’s own sensitivity to each of the factors (an adaptation of the beta concept in CAPM) (Jagannathan & McGrattan, 1995). Neoclassical models – Traditional asset pricing 1. Asset Pricing Theory (APT) For this example, a theoretical investor is contemplating investment in stock ABC that has a GNP coefficient of 1.6, an inflation coefficient of 1.2, and an investor coefficient of 2.4. Assuming current economic conditions peg inflation at 4%, the GNP growth rate showed 5%, and the increase in investor confidence was estimated by the government economic research agency to be at 18%. Assuming that risk-free rate was 8%, the asset ABC will have and expected rate of return of: RE = 8% + 1.2 (4% - 8%) + 1.6 (5% - 8%) + 2.4 (18% - 8%) RE = 8% - 4.8% - 4.8% + 24% RE = 22.4% 2. Zero-beta CAPM Black’s zero-beta CAPM, formulated in 1972, has been developed to address the concern that the CAPM falls short because there is no risk-free asset. For this model, the following assumptions prevail (Jordan, 1998): • Absence of a risk-free asset • Combinations of portfolios on the efficient frontier are efficient • All frontier portfolios have companion portfolios that are uncorrelated • Returns on individual assets can be expressed as linear combinations of efficient portfolios There are conditions that may be conceived as limiting the effectiveness of Zero-Beta CAPM. An important stipulation in this model is that short-sales are possible; in order for zero-beta portfolios to be attained, it would be necessary to sell some assets short. Constraints in this aspect will cause zero-beta CAPM to fail (Le Sourd, 2010). 3. Introducing taxes and transaction costs The original CAPM specifies that there are no taxes and transactions costs, to avoid the distortionary effect of different tax rates with different types of income. This is an unrealistic assumption, and subsequent models that modified the CAPM took into account the effects of taxes and transaction costs. Tax-CAPM introduces features of the respective personal tax system. In US the Tax-CAPM was introduced by Brennan in 1970 for USA’s income tax system. It was adapted in Germany by Wiese in 2004. (Schmitt & Dausend, 2007, p. 2-5). Other models include transaction costs, e.g. information costs (Hug 1993, pp. 185-187) 4. Three factor model F&F Fama and French (1992) argued that CAPM has no explanatory power as far as cross-sectional expected returns are concerned. They argued, and showed by statistical methods, that adding two more variables to represent firm size and book-to-market ratio are able to better capture the subsequent returns on a stock. The F&F model has been challenged by other later studies (Black, 1993; Kenz & Ready, 1997; Kothari, et al., 1995), however, on the basis of periodic effects, the statistical method, and the data used (Jacoby, Fowler & Gottesman, 2000). 5. Multi-period models Several studies have sought to develop models that went beyond the single-period assumption of the CAPM (Kürschner, 2008). In a survey and investigation of these models, Blume (1983) arrived at the conclusion that for multiperiod models to be more realistic than the CAPM, it is still constrained to make some assumptions of one or more of the following areas: (a) state variables which condition the one-period utility function derived from the multiperiod problem; (b) departures from normality; and (c) feasibility constraints. The Blume study showed how assumptions about these areas may directly be incorporated into a pricing equation for the expected returns of individual assets. Support for the CAPM Even as the detractors of CAPM protest that the model is little more than rhetoric, there have nevertheless been studies that tended to confirm the validity and usefulness of the tenets of CAPM. In the appendix of this paper is a summary, prepared by Levy (2008), of criticisms of CAPM and solutions to these criticisms defending the CAPM position. In another article, Taylor (2005) conducting an empirical evaluation of the CAPM. It estimated the beta coefficient by regressing estimated expected excess stock returns on the estimates of beta, and constructed the SML to verify if its coefficients supported the CAPM validity. Three conditions were sought to be satisfied in order to confirm CAPM validity, that is: 1. There is no risk premium for bearing non-systematic risk; 2. The product of beta and the excess market return yields the excess stock return; and 3. The expected excess return is independent of non-systematic risk. Upon testing the foregoing hypotheses, subsequent results showed that the hypotheses could not be rejected at the 95% level. It was thus concluded that the CAPM fairly successfully predicted the price of individual assets, as none of the three necessary conditions for a valid model were rejected at the 95% level. Taylor (2005) thus explained that although CAPM could not be perfectly accurate, the model still presents a cogent explanation for asset price behaviour, that their expected returns are still proportional to their systematic risk and the expected excess return to the market. Accuracy of the model’s application may be improved by searching for better proxies for the market and risk free fates, and more refined econometric techniques (Taylor, 2005). References: Ang, A & Chen, J 2007 “CAPM over the long run: 1926-2001”, Journal of Empirical Finance, vol. 14, pp. 1-40. Bergman, Y Z 1985 “Time Preference and Capital Asset Pricing Models”. Journal of Financial Economics, vol. 14, pp. 145-159. Black, F 1972 “Capital market equilibrium with restricted borrowing.” Journal of Business, vol. 45, pp. 444-455. Blume, M E 1983 “The Pricing of Capital Assets in a Multiperiod World”, Journal of Banking and Finance, vol. 7, pp. 31-44. Brooks, RD; Faff, RW; & Lee, J H H 1994 “Beta Stability and Portfolio Formation”, Pacific-Basin Finance Journal, vol. 2, pp. 463-479. Cervino Institute of Economic Studies 2010 “Using a Zero-Beta Asset for Measureing Variance”, 7 April 2010. Accessed 6 November 2010 from http://www.facebook.com/note.php?note_id=394252669144 Fama, E F, French, K R 1992 “The cross section of expected stock returns.” Journal of Finance, vol. 47, pp. 427-465. Jacoby, G; Fowler, D J; & Gottesman, A A 2000 “The capital asset pricing model and the liquidity effect: A theoretical approach”, Journal of Financial Markets, vol. 3, issue 1, February, pp. 69-81 Jagannathan, R & McGrattan, E R 1995 “The CAPM Debate”. Federal Reserve Bank of Minneapolis Quarterly Review, vol. 19, no. 4, pp. 2-17 Jordan, S D 1998 Capital Asset Pricing Model, Lecture Notes. Fall 1998. Accessed 9 November 2010 from http://www.uky.edu/~sjordan/fin650/chapt9/sld001.htm Kenz, P J & Ready, M J 1997 “On the robustness of size and book-to-market in cross-sectional regressions”. Journal of Finance, vol. 52 Kothari, S P; Shanken, J; & Sloan, R G 1995 “Another look at the cross-section of expected stock returns.” Journal of Finance, vol. 50, pp. 185-224. Kürschner, M 2008 Limitations of the Capital Asset Pricing Model (CAPM): Criticisms and New Developments. GRIN Verlag, Norderstedt, Germany Le Sourd, V 2010 “The Impact of Constraints on Short Sales and on Borrowing on the Effiiency of the Market Portfolio”, Risk Review, EDHEC-Risk Institute, July 2010. Accessed 5 November 2010 from http://www.edhec-risk.com/research_news/choice/RISKReview.2010-03-16.3815 Levy, H 2008 The CAPM: Alive and Well? A Review and Synthesis. September 2008. Accessed 8 November 2010 from http://www.kenesbiz.com/_Uploads/4299haim_levi.pdf Lintner, J 1965 “The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets.” Review of Economics and Statistics, vol 47, pp. 13-37. McCracken, M 2009 “CAPM – The Capital Asset Pricing Model”, Teach Me Finance. Accessed 8 November 2010 from http://www.teachmefinance.com/capm.html Pastor, L & Stambaugh, R F 2000 Comparing asset pricing models: an investment perspective. Journal of Financial Economics, vol. 56, pp. 335-381 Reilly, F K & Brown, K C 2006 Investment Analysis and Portfolio Management. Thomson South-Western Ross, S A 1976 “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory, December 1976, pp. 341–360 Sharpe, W F 1964 “Capital asset prices: a theory of market equilibrium under conditions of risk.” Journal of Finance, vol. 19, pp. 425-442. Taylor, B 2005 “An Empirical Evaluation of the Capital Asset Pricing Model”, Economics.Fundamental Finance.com., 8 December 2005. Accessed 3 November 2010 from http://economics.fundamentalfinance.com/capm.php Washburn, C L & Binkley, C S (undated) “Some Problems in Estimating the Capital Asset Pricing Model for Timberland Investments”, Sponsored research. Accessed 3 November 2010 from http://www.ifiallc.com/PDFs/capitalasset.pdf Appendix Support for CAPM and Rebuttal of Criticisms (Levy, 2008) Read More