Limitations of the Capital Asset Pricing Model - Essay Example

Explain the limitations of the Capital Asset Pricing Model and the extent to which the multi-factors approach has overcome these limitations” Contents Introduction 3 Discussion 4 Composition of Efficient portfolio 6 Mean Variance of the market portfolio under CAPM 8 Arbitrage Pricing Theory 8 Application of Multifactor approach over CAPM 10 Conclusion 11 Assumptions behind the derivation of CAPM 12 Predictions of CAPM 13 Is CAPM empirically testable? 13 Introduction Capital pricing model is mainly used or applied to establish the relationship between the risk and the expected rate of return in order to evaluate the price of high risk securities. It can be established with the following formula (Berk and DeMarzo, 2007). Ra = Rf + Ba (Rm – Rf) Where, Ba = Beta of the security Rf = Risk free return Rm = Market return that is expected. The investors prefer CAPM model as it provides compensation related to the time value of money and the risk related factor. Here Beta represents that the shares with high beta value will increase the return. The efficient frontier is mainly used in CAPM model as it helps in estimating the risk and return ratio at a given point of time for all portfolios. Under the efficient frontier the portfolio generally has minimum risk and it measures the variance of returns therefore it is known as the minimum variance portfolio with the minimum rate of return and the maximum return portfolio which includes maximum risk. The portfolio that stands below the efficient frontier mainly provides less return for the same level of risk (Nonaka, 2001). CAPM explains the extent to which the asset is priced in terms of the risk. The APT is considered as another equilibrium pricing model. The CAPM mainly faces criticism which is not testable. Therefore APT is considered as alternative to testable. The combination of the different factors is estimated for finding out the return on the asset that is risky which affects the return on the assets. Discussion The various possible portfolios are represented on the various indifference curves that generally do not yield high return for the same level of risk. These portfolios generally stand below the efficient frontier. The optimal portfolio can be defined as the portfolio on the efficient frontier that yields the best combination of the risk and return for the specific investors which will provide maximum possible satisfaction for the investors (Markowitz, 2008) Figure 1: Risk indifference curve Apart from the advantages there are various limitations in respect of applying the CAPM model such as: CAPM model is mainly based on the various assumptions that differ from reality. This creates a problem in explaining accurately the Capital asset pricing model related to the investment attitude of the investor and the beta may not be able to determine the risk of investment. It is very difficult to calculate the project related discount rate. CAPM model is very difficult and critical to validate. It is sometimes difficult to establish correlation between the expected return and beta. Beta measures and estimates the future risk of the securities therefore it is expected that beta must remain stable and constant. But under CAPM model beta does not remain stable therefore it creates problem for the investors in estimating the data. The main limitation of CAPM model is that only single time period horizon is taken into consideration for the investment appraisal which odds out the investment appraisal under multi period investment appraisal. And it is impossible that all the investors have common and specific expectations that all the investors will react rationally on the basis of the standard deviation and expected rate of return. CAPM model is mainly based on the optimal portfolio that is not relevant in terms of the incomplete market. Market portfolio is not considered when different proxies are used for finding out the sources of risk that are considered important for the investors. Therefore it is required to consider the pricing problems and the selection of the portfolio related to various multifactor models (Asthana, 2013). E (RP) = Y1 = Y0 ƩW1 + Y1 Ʃ W1 B1 + Y2 [(Ʃ W1 ᵠm ƩWJ ) / ᵠm ]. The above equation represents that Y1, Y2; Y3 varies frequently due to the assumptions related to the residual value of the return of stock. Multi factor pricing model mainly refers to as the return that is expected from the different assets which can be explained with the help of the specified and particular factors in case of a linear model. The return under the various factor models is calculated as Rt = A + B1f1t + B2 F2t + Et Asset pricing theory mainly offers guidance in selection of the factors. The multifactor theory suggests and explains that the asset is expected to bring a very high return on average if the asset performs poorly in uneven situations. Under multifactor pricing model various factors are taken into consideration such as the expected and the unexpected inflation, the spread between the low and high grade bonds, the spread between the short and long interest rates, the aggregate consumption, industrial production and the price or the cost of the oil. The yield spread and the yield are provided importance in the treasury and the corporate bond market in case of the multi factor pricing model (Brown, 2003). The Bayesian model is also taken into consideration which interprets the bayes factor. It assumes and takes into consideration all related probabilities. It can be derived as: M1: R = X1 B1 + E, I = 1… 2k Composition of Efficient portfolio The modern portfolio mainly reduces or decreases the risk of the portfolio by identifying and balancing the assets that is based on the various statistical techniques that define the extent of diversification by determining the expected rate of return, the standard deviation is applied for assessing the individual securities and finding or developing the correlation between the assets by calculating and determining the actual coefficients. This differs from that of the traditional approach as the modern portfolio mainly applies the various quantitative approaches for decreasing or reducing the risk. The prime objective or the importance of the modern portfolio is that the efficient portfolio mainly yields or provides greater return for particular risk. The profit or the gain of the company can be increased by identifying the optimal portfolio that provides greater return for the investor on the basis of the tolerance for the risk (Edwards, 2007). Figure 2: Risk indifference curves The diagram in the figure 3 represents that the risk indifference curves are mainly allotted for finding out the investment opportunity that is established or developed for the achievement of the attainable portfolio. The portfolio beta in case of the systematic risk is equivalent to the summation of the beta of the weighted average for identifying the value each security above and over the value of its portfolio. Portfolio Beta = Ʃ Dollar amount of assets k / Dollar amount of portfolio * Beta for asset k. The interpretation of the portfolio is same as that of the stocks. The investors mainly realize that there is volatility in the stock market for investing money by the investors. The volatility is mainly considered as the means of dispersion of the mean or the average rate of return on the security. The best and the appropriate way for measuring the volatility are by the application of standard deviation by identifying the price of the stock that is mainly grouped around the moving average. Mean Variance of the market portfolio under CAPM E[Rh] – Rf / E [Rm] – Rf = Cov[ x1, Rh] / Cov[ x1, Rm] E[Rh] – Rf / E [Rm] – Rf = Cov[ Rm, Rh] / Var [Rm] Bh = Cov[ Rm, Rh] / Var [Rm] Arbitrage Pricing Theory The arbitrage pricing theory is mainly used as the alternative of the CAPM model since the APT is more flexible as compared to that of the CAPM. The APT mainly applies the expected return of the risky assets and the risk related premium of the various macro economic factors (Koch, 2009). The APT model is mainly used to ascertain the profit by taking the benefit of the various mispriced securities. It is mainly represented by: Rj = aj + bj1 F1 + bj2 F2 +… + bjn Fn + ϵj Where, Aj = Asset that is constant Fk = Systematic factor Bjk = The sensitivity that is related to the jth asset in relation to the k factor ϵj = The risky asset with zero mean. It establishes the linear function of the sensitiveness of the asset in relation to the expected return of the asset. It mainly calculates the expected rate of return from the undervalued and the overvalued securities in the inefficient market without undertaking any type of incremental risk and the additional zero investments (Gruber, 1991). The opportunity of the arbitrage can be explained by: Assets (i) Ei BI 1 .07 0.5 2 .10 1.4 3 .09 1.0 Ei = 0.05 + 0.04 bi1 EP = 0.5 E1 + 0.5 E2 = 0.5 (0.07 + 0.10) = 0.085 Bp1 = 0.5 b11 + 0.5 b21 = 0.5 (0.5 + 1.4) = 0.95 Therefore the payoff portfolio can be established as: R3t - Rpt = (E3 + b31F1t) – ( EP + bp1 F1t ) = (0.09 + 1. F1t) – (0.085 + 1. F1t ) = 0.005 This represents the arbitrage profit and the return derived from the random component F1t is protected away. Consumption of Capital Asset pricing model can be defined as the model that estimates the risk of any security in order to establish co variance between the market portfolio rate of return and the rate of return on security. The asset pricing model when it is applied in macro economics it is termed as the consumption based asset pricing model. The beta related to consumption measures the services derived from the investment, the investor’s ability or the capacity to consume goods and the return that is derived from the market index. The utility under CCAPM is calculated as: U = u (co) + Bu(c1) Application of Multifactor approach over CAPM The application of the multifactor approach mainly includes the strategies related to the neutral factors, optimization of the portfolio, hedging and management of the risk, estimation and measurement of the risk, exposures related to tailoring of the risk, evaluation of the performances and arbitrage and trading. The multifactor model mainly allows the different stocks to be sensitive for different types of shocks across the market. It works with different portfolio. CAPM model mainly establishes the relationship related to individual securities and multi factor approach deals with many securities and the factors under which the portfolio is constructed (Brunel, 2006). Figure 3: Security versus well diversified portfolio The Fama and the French factor mainly consider the three factor model. The testing and the estimation of the multifactor asset pricing model are applied on the portfolio of the assets as compared to the individual assets. The return is expected to stable in terms of the mean and covariance. The individual are more volatile therefore the estimation becomes difficult. CAPM considers only the single factor whereas various factors are required to identify the market risk of the security. CAPM is not testable due to its composition of portfolio under the market. CAPM cannot be used for identifying the deviation of the portfolio from the security line therefore it is inadequate to determine the market portfolio. APT includes the choice for various factors. APT is considered and regarded as the improved and developed version over the CAPM. Conclusion In addition to the advantages CAPM model has limitations but based on the limitations the CAPM model cannot be rejected or ignored because it is very difficult to observe the portfolio of the market in the absence of the CAPM model. In reality the market portfolio does not have existence there are various sources of risk which are considered very significant for the investors. Both CAPM and APT is exposed to vulnerability In case of CAPM it is very difficult to identify the degree of deviation and gap from the security market line It is very difficult to consider it as a bench mark because it is subjected to inadequacy in the portfolio. And in case of APT there is no fixed standard for the selection of the appropriate factors. But the APT is regarded as the development of the CAPM. CAPM can be used or applied in the determination of the expected rate of return and establishing the linear function for evaluating the systematic risk. Roll in his argument stated that CAPM can never be tested. The basic problem is that the market portfolio has been explained theoretically and it does not include the assets that are required to be included. Therefore it is required to conduct the test in order to determine the validity of the model. Assumptions behind the derivation of CAPM CAPM was introduced as a model in 1964 by William Sharpe and his co researchers in the year 1964. The model is widely used by the investors in judging the riskiness of a particular stock. The reason behind the wide popularity of the model is its simplicity and its intuitive appeal. These two factors have contributed to the wide use of the model by investors. CAPM actually builds on an earlier work by Markowitz commonly known as efficient market hypothesis. So the assumptions of EMH are in essence the assumption of CAPM. The assumptions are Investors are in general risk averse There is unlimited fund available that can be borrowed at risk free rate The market is efficient that is all information is available to the investors at the same time. There are taxes, transaction costs or inflation that is involved. So the buyer can buy or sell a stock unlimited amount of time. A particular investment can be further split into as many parts as possible. Predictions of CAPM CAPM along with efficient market hypothesis assumes that investors in general are risk averse. So when the investors decide to choose between two different stocks the only thing that they care about is mean and variance of one period investment return. So, CAPM predicts that the investors choose mean variance portfolio. This means that investors choose those portfolios which 1. Minimize the variance of portfolio return when expected returns are given and 2. Maximize expected return provided variance is given (Fama & French, 1993). In short the investors’ looks for those stocks that give them highest return at lowest level of risk. Since investors in general are risk averse, so in order to take on additional risk the investors wants some compensation. So the formula for CAPM includes the risk free rate of return or Rf and due to the fact that investors take on additional risk a risk premium is added to this risk free rate of return as β (Rm-Rf). The investors are to be compensated in two ways. One is by time value of money that is given by the risk free rate of return, for the other part that is to compensate for the risk part β (Rm-Rf) is used. Is CAPM empirically testable? The main guiding element in the CAPM model is the β. This β is used to calculate riskiness of a stock. The β measures how the particular stock is performing in respect of the market portfolio. But to consider the market portfolio as is determined and ideally required by the model requires the consideration of all stocks in the market. There lies the fundamental problem of the model. If the model is ideally followed it should imply that we should consider all assets not just traded financial assets. However that is practically impossible. So, one has to narrow the scope of market portfolio. The fundamental problem that arises is which stocks or how many stocks should be considered in the portfolio without fundamentally going against the guiding criteria laid down by the model (Roll, 1977). The question that arises is should one limit the scope of the model to include only shares that are traded in the US stock market or should the model should encompass other financial instruments such as bonds and other assets? Should the choice country be limited to a particular country or should it be expanded to include many countries? So it is nearly impossible to empirically test the model due to this fundamental limitation. Another critique of the CAPM model stated that the smaller companies (measured in terms of market capitalization) perform much better that that is predicted by the CAPM model (Banz, 1981). This effect is actually known as the size effect. However there has been other group of researchers who have said that size related anomaly is not actually an anomaly (Berk, 1995). It is quite a natural occurrence and would have been considered an anomaly had this been not actually found. References Asthana, S., 2013. Financial reporting and capital markets/stock market returns. International Journal of Accounting, Auditing and Performance Evaluation. Vol. 8(1), pp.44-45. Banz, R. 1981. The relation between return and market values of common stock, journal of financial economics. 9(1). pp. 3-18 Berk, J. B. and DeMarzo, P. M., 2007., Corporate finance. London: Pearson Addison Wesley. Berk, J. B.1995. A critique of size related anomalies, review of financial studies. 8(2). pp. 275-286 Brown, K., 2003. Investment Analysis and Portfolio Management. Boston: Thompson Learning. Brunel, J.P., 2006. Integrated Wealth Management: The New Direction for Portfolio Managers. London: Euromoney Books. Edwards, R., 2007. Technical Analysis of Stock Trends. Ninth Edition. Florida: CRC Press. Fama, E. & French, K. 2004. The Capital Asset Pricing Model: Theory and Evidence, Journal of Economic Perspectives. 18(3). pp. 25-46. Focardi, S.M. and Fabozzi, F.J. 2004. The mathematics of financial modeling and investment management. NJ: John Wiley & Sons Gruber, M. J., 1991. Arbitrage Pricing Theory and Portfolio Management. Hong Kong: City Polytechnic of Hong Kong. Helfert, E., 2001. Techniques of Financial Analysis: A Practical Guide to Measuring Business Performance. New York: McGraw Hill. Koch, C., 2009. The Arbitrage Pricing Theory as an Approach to Capital Asset Valuation. Nordersted: Grin Verlag. Markowitz, H., 2008. Harry Markowitz: selected works. Singapore: World Scientific Pahl, N., 2009. Principles of the capital asset pricing model and the importance in firm valuation. Norderstedt: BoD – Books on Demand. Nonaka, I., 2001. Towards a new theory of financial management. International Review of Financial Analysis. Vol. 9 (3), pp.150-151. Roll, R. 1977. A critique of the asset pricing theory’s test, journal of financial economics, 4(2) pp. 129-176. Read More