The Relevance of Portfolio Theory and the Capital Asset Pricing Model - Coursework Example

The Relevance of Portfolio Theory and the Capital Asset Pricing Model (CAPM) Today’s investors and fund managers are reasonably well-informed individuals who employ several quantitative methods in making decisions. Their decisions are arrived at after careful and deliberate consideration of two major elements: what the investor aims to earn, and how much risk will he expose himself to in order to earn it. Some of the more important academic theories developed that shaped today’s general knowledge about investments shall be discussed in the following pages. Modern Portfolio Theory Modern portfolio theory states that there exists a positive relationship between the risk and the expected return of a financial asset (Reilly & Brown, 2006). Thus, in order to attain a higher level of expected return, an investor should be willing to assume a higher level of risk; conversely an investor who assumes a greater risk will expect to be compensated for it with a proportionately higher return (Wan, 2005). The originator of the modern portfolio theory is Harry M. Markowitz, who stumbled upon the idea of portfolio risk and returns while he was searching for a topic for his masteral dissertation. Markowitz pondered the possibility of applying mathematical methods to explain the behaviour of stock prices under conditions of uncertainty. During his research, he came across John Burr Williams’s Theory of Investment Value. This theory equated the value of a stock with the present value of its future cash dividends. The problem with this theory is that it does not explain investors’ combination of several stocks to create a portfolio, unlike the purchase of just a single stock which Williams’ theory tended to suggest (Markowitz, 1991). Essentially, the modern portfolio theory states that investors diversify in order to try to maximize their returns while minimizing their risk; it is the risk consideration that William’s theory failed to address. Mathematically, risk is represented by the variance of the returns, that is, the degree to which returns would tend to vary. Also, the level of covariances between assets in the portfolio determines the level of risk of the portfolio. This interplay between risk and return became the cornerstone principle behind the modern portfolio theory. The Capital Asset Pricing Model A model that is popular among most finance professionals, and is based on the modern portfolio theory that has seen wide acceptance by both academics and practitioners is the Sharpe-Lintner Capital Asset Pricing Model. Essentially, this model establishes a relationship between the risk and the return of an asset, and the premium it commands over the risk free rate of return. Before one can understand CAPM, however, one must understand the concept of betas. A beta is a coefficient that embodies the risk of the stock. It determines the premium of expected rate of return over the risk free rate, given the fluctuation in the market rate of return. Beta is computed by regressing the rate of return of the market over a period of time with the rate of return of the overall market portfolio. The linear regression equation is given by: Where: x = independent variable (return of the market) y = dependent variable (stock return) X = value for x Y = value for y m = slope of the regression equation, equivalent to beta b = y-intercept of the regression equation N = number of elements An example of the computation of beta is given in Table A shown at the end of this paper. The beta derived therein is equivalent to the slope of the regression which is -0.74. The beta coefficient is the indicator for risk, and shall be used to derive the expected rate of return on the stock in the Capital Asset Pricing Model. Mathematically, the CAPM is denoted by the following formula: Where kj = expected rate of return of the stock Rf = risk-free rate of return βj = beta of the stock km = expected rate of return of the market The following example illustrates the use of CAPM to determine expected return: Alex wanted to invest his money in the stock in our example, with a beta of -0.74. At the time he made his investment, the rate of return of the stock index (representing the market portfolio) was -3%. The negative return indicates that the market was downtrending, which is expected in this time of economic recession. The rate of return of government securities (representing the risk-free rate of return) was 8%. The rate of return that Alex could expect out of this stock would then be: kj = 8% + (-0.74) (5% - 8%) = 10.22% Notice how, during a downtrending market when the so-called index stocks and blue chips (the beta-positive stocks) would be returning losses, a stock such as this would even be gaining. This shows an important use of beta, that of managing risks by combining beta-positive and beta-negative stocks in order to minimize possible losses. The relation between beta and expected returns are graphically shown in what is called the security market line (SML). The figure below is a depiction of the SML. Source: Wang, 2003 The CAPM is a theoretical model and like all theoretical models depends on some important assumptions. Wang (2003) lists these assumptions as follows: 1. All the investors agree on the distribution of asset returns. 2. Investors have the same fixed investment horizon. 3. Investors all hold efficient frontier portfolios. 4. There is a risk-free asset in zero net supply 5. The demand for assets equals the supply 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. Arbitrage Pricing Theory Some experts have commented on the shortcomings of the CAPM. They reason that not all risks could be accommodated by one coefficient because of the different kinds of risks. Furthermore, they argue that there is no such thing as a “market portfolio” which theoretically should include all possible investments at all times (Block & Hirt, 2006). Because of this, several multifactor models came about, indicating that an asset may react to the changes in different indicators Where bjm = factor loading or the sensitivity of asset to the factor n RPm = risk premium of the factor The following are the assumptions of the Arbitrage Pricing Theory (APT) (Ellul, 2005) 1. Security returns can be described by a multi-factor model 2. There are sufficient securities so that firm-specific risk can be diversified away 3. Well-functioning security markets do not allow for persistent arbitrage opportunities 4. Investors want to hold infinite positions in an arbitrage opportunity 5. This should create pressures on prices to go up where they are too low and fall where they are too high 6. In equilibrium, the market should satisfy the no-arbitrage condition. 7. There is a fundamental difference between risk-return dominance denoted by CAPM, and arbitrage arguments (APT) Briefly illustrating the use of APT, supposing that investor Bob wanted to put his money on an asset that responds to a change in GDP by the factor of 0.5; to a change in the foreign exchange rate by the factor of 0.4; and to a change in interest rates by the factor of -0.3. If GDP rose by 10%, the foreign exchange rate by 6%, and interest rates by 4%, and the risk-free rate was 8%, the resulting return that Bob may expect on this investment would be: kj = 8% + (0.5 x 10%) + (0.4 x 6%) + (-0.3 x 4%) kj = 8% + 5% + 2.4% - 1.2% kj = 14.2% Comparing the APT to the CAPM, it is at once seen that the APT requires more variables, coefficients, and a more complex computation especially if the model specifies more than three factors. But some investors and fund managers, as well as many academicians, prefer the multifactor models because they are more sensitive to changes in the macroeconomy, and studies have shown that there is a greater accuracy to this model, because it agrees more closely to the empirical data (Reilly & Brown, 2006). Critical comments about the APT and the CAPM A paper written by Ekern (2006) praised the important conceptual foundations laid down by the CAPM in relation to the net present value discounted model. However, these are not enough, as the basic CAPM relies on a quantification of the relevant risk of an asset as derived from its covariance with the market return, represented by beta (Ekern, 2006, p. 1). There exists a “conceptual fallacy” in the form of a systematic mispricing between CAPM and NPV compared to benchmarks of the theoretical model. Simply stated, the CAPM systematically fails to capture the risk factor that leads to a consistently reliable computation of asset value. Fama and French (1992, as cited in Adrian & Franzoni, 2008) had presented convincing proof that the simplified unconditional CAPM does not account for several risk factors, such as the returns of size and book-to-market (B/M) sorted portfolios. Since that time, academic studies on asset pricing have presented several alternatives, which parts ways with the original CAPM in several aspects. There are those that maintain the single-factor structure, but have evolved into conditional versions, on the theory that CAPM may hold for a certain time t but not for an indefinite period, as the unconditional CAPM specifies. And, as already noted, there are those theories that explored the multi-factor version of the CAPM, such as the APT. One example of conditional CAPM is that proposed by Hens, Laitenberger, & Loffler (2002), where they explored the possibility of multiple equilibria in the absence of a riskless asset. There is a theory explored by Malevergne and Sornette concerning the self-consistency of the market portfolio and the risk factors employed in CAPM. Self-consistency, they explain, implies a correlation among the return disturbances that are indicated by the use of the factors. Self-consistency are theorized to lead to renormalized betas observable with standard ordinary least squares (OLS) regression. They have arrived at the conclusion, among other things, that in the multi-period approach, the conditions imposed by the study for self-consistency force the betas to be time-dependent with specific constraints. Fama and French are among the earliest to criticize the shortcomings of CAPM and developed their own theory that supports a three-factor (FF3) model, which is similar to the APT discussed earlier. Simpson and Ramchander (2008) have tested the three factor theory based on the impact of surprises in 23 different types of macroeconomic announcements on stock returns, and compared their results with the impact of these same 23 surprises based on the CAPM. The study came to conclude that the FF3 model outperforms the CAPM as a predictor model, in that the former is capable of capturing information that is related to personal consumption, retail sales, CPI, PPI, factor orders, leading indicators, construction spending, housing stats, and new home sales. Simply stated, FF3 is confirmed to be more sensitive and reliable than CAPM. There are some theorists who come to the defense of the CAPM and its validity as an estimation tool. MacKinlay (1995) developed a framework that showed that, ex-ante, CAPM deviations attributable to missing risk factors are difficult to empirically prove, while deviations that are caused by non-risk based sources are easily traced. The results tend to suggest that the multifactor pricing models, which are supposed to be improvements that address the shortcomings of the CAPM, do not entirely settle the matter of CAPM deviations. A more recent testament of the usefulness of the CAPM is presented by the study of Omran (2007) which sought to find evidence of the workings of CAPM in the Egyptian stock market. The study offers proof that confirms the validity of modern portfolio theory and capital asset pricing models to Egypt’s emerging stock market. Market risk, measured by the beta and preference for skewness, is an important indicator in the returns dynamics in that equity market. Portfolios based on consumer staples and financial companies with low betas had outperformed portfolios containing construction, materials, hotels, and weaving companies with large betas. Conclusion Overall, the MPT, CAPM and APT have found useful application in the field of investments and portfolio management. Portfolio theories’ holistic approach to risk and return have brought a conceptual shift from single-stock choices to comprehensive management of risk and return. The debate about which model is better than the other will continue, however, while analysts and fund managers continue to rely on these theories for their investment decisions. Table A: Computation of Beta of a Stock REFERENCES Adrian, T & Fanzoni, F 2008 Learning about Beta: Time-Varying Factor Loadings, Expected Returns, and the Conditional CAPM. Staff Report No. 193, Federal Reserve Bank of New York Staff Reports. Bernstein, P L & Damodaran, A 1998 Investment Management. John Wiley & Sons, Inc. Block, S B & Hirt, G A 2006 Foundations of Financial Management, eleventh edition. McGraw-Hill Irwin. Downes, J & Goodman, J E 1995 Dictionary of Finance and Investment Terms. 4th Edition. Barron’s Educational Series, Inc. Ekern, S 2006 A Dozen Consistent CAPM-Related Valuation Models – So Why Use the Incorrect One? Conference Paper presented at the European Financial Management Association, 2006 Annual Meeting in Madrid (Spain) Ellul, A 2005 Asset Pricing Models: Factor Models. Lecture presentation, Kelley School of Business, Indiana University. Hens, T; Laitenberger, J; & Loffler, A 2002 Two remarks on the uniqueness of equilibria in the CAPM. Journal of Mathematical Economics, vol. 37, pp. 123-132 MacKinlay, A C 1995 Multifactor models do not explain deviations from the CAPM. Journal of Financial Economics, vol. 38, pp. 3-28. Malevergne, Y & Sornette, D 2007 Self-consistent asset pricing models. Physica A, vol. 382, pp. 149-171. Markowitz, H M 1991 Autobiography. The Nobel Foundation. Retrieved 4 February 2010 from http://nobelprize.org/nobel_prizes/economics/laureates/1990/markowitz-autobio.html. Omran, M F 2007 An analysis of the capital asset pricing model in the Egyptian stock market. The Quarterly Review of Economics and Finance, vol. 46, pp. 801-812 Reilly, F K & Brown, K C 2006 Investment Analysis and Portfolio Management, 8th ed. Thomson South-Western Simpson, M W & Ramchander, S 2008 An inquiry into the economic fundamentals of the Fama and French equity factors. Journal of Empirical Finance, vol. 15, pp. 801-815 Wan, S-P 2005. Chapter 5: Modern Portfolio Theory. Investments. Retrieved 5 February 2010 from http://www.ifa.com/Media/Images/PDF%20files/MPTTextbook.pdf Read More