Capital Asset Pricing Model - Research Paper Example

Capital Asset Pricing Model Table of Contents Introduction 3 Assumptions of CAPM 4 Efficient Frontier with Riskless Lending and Borrowing 5 EfficientPortfolio with Introduction of Lending 6 Efficient Frontier with Borrowing and Lending 9 Merits of the Capital Asset Pricing Model (CAPM) 10 Demerits of CAPM 11 Assigning Values to the CAPM 11 Use in Investment Appraisal 11 Controversy to the SML 11 Historical Evidence 12 Empirical Approach towards the CAPM 13 Advantages of Fama-French over CAPM 14 Shortfalls of Fama-French Model 15 Arbitrage Pricing Approach to CAPM 16 APT vs. CAPM (Portfolios) 16 APT vs. CAPM (Individual securities) 17 Comparative Analysis of CAPM and APT 17 Relative Merits of CAPM 18 Conclusion 19 References 20 Bibliography 22 Introduction This research paper aims to be a fundamental work on the concept of Capital Asset Pricing Model (CAPM) which is a portfolio theory that describes the way investors should build efficient portfolios and select optimal portfolios. The paper deals with various merits and shortcomings of the model and incorporates different empirical approaches towards the model by explaining certain other models like the Fama and French model and the arbitrage pricing model. The Fama and French Model and the Arbitrage Pricing model pose as a challenge towards the CAPM as these theories describes various shortcomings of it. The objective of the research work is to illustrate the CAPM and find out its loopholes. The CAPM is a model which investors use to take decisions related to portfolio selection. It would be convenient to start with a brief description of the model including its assumptions, derivations and also limitations. After this brief discussion the paper would focus on the above mentioned models that ornately mention the areas where CAPM fails to comply with its expectations. The CAPM generally finds out the correlation between the average expected return and risk of portfolios and individual securities in the capital markets, if everyone behaved in the way the portfolio theory suggested. Assumptions of CAPM The merits of the CAPM cannot be discussed unless the basic assumptions of the model are known. The assumptions are listed below: 1) Investors take decisions by assessing the risks and returns associated with the assets. 2) Investors can purchase or sale assets in a huge number of divisible units. 3) It is the investors who determine the prices of assets by their actions. 4) There is ignorance to the transaction costs. 5) There is no personal income tax and thus the investors are not bothered about the form that returns are received (dividends or capital gains). 6) The investors lend or borrow funds at a rate which is equal to the rate for risk-free securities (government bonds). 7) The investors are supposed to hold assets for identical periods and also they expect identical returns on the assets (Burton, 1998). Efficient Frontier with Riskless Lending and Borrowing The portfolio theory states that investor’s portfolio (combination of assets) consists of risky assets. The investor faces an efficient frontier which contains the combination of efficient portfolios of risky assets. Now it is assumed that there also exists a riskless asset for investment which is generally the government bonds that provide certain returns on them. The investor is allowed to invest some portions of his funds in the riskless asset which is assumed to be equivalent to lending at a rate that is equal to the rate of return of the riskless asset. Let it be named as Rf. Also it can be assumed that the investors can borrow at the same rate of riskless asset for the purpose of investing in the portfolio of risky assets. The essence of such assumptions is that the investors would now be using own funds as well as borrowed funds for investment (Kaduff, n.d.). The efficient frontier of risky portfolios is generally a concave curve. When an investor uses riskless lending and borrowing in his investment activities, the concave shape transforms into a straight line. Y C Rp O’ B Rf O A X Portfolio Risk- SDp Efficient Portfolio with Introduction of Lending In the above figure, the concave figure ABC is the efficient frontier line of risky portfolios. B is the optimal portfolio (the optimal portfolio can be obtained by Markowitz Model) with Rp=15 % and SDp=8 %. There is a riskless asset available for investment with rate of return Rf=7 %. The risk or standard deviation of this would be zero. Thus it is plotted on the Y axis. The investor can decide on the portion of investment he wants to make on B, the optimal portfolio. The return and risk of the combined portfolio O’ may be calculated using the following formulae: Return Rc=wRm+(1-W)Rf Where Rc is the expected return on the combined portfolio w is the proportion of funds invested in risky portfolio (1-w) is the proportion of funds invested in the riskless asset Rm is the expected return on risky portfolio Rf is the rate of return on riskless asset. Risk SDc=wSDm+(1-w)SDf Where SDc is the standard deviation of the combined portfolio SDm is the standard deviation of risky portfolio SDf is the standard deviation of riskless asset The second expression on the right side of the above equation would be zero. By taking different proportions of investment on the risky portfolio and riskless assets, the returns and risks can be calculated. All the points obtained will lie on a straight line from Rf to B. Now let the borrowed funds by investors be considered for investing in the risky portfolio. The amount considered would be larger than own funds. Thus, three situations can be envisaged. If w=1 then the investor has fully committed his funds to the risky portfolio. If w1, it means the investor is taking loan at a rate equal to the rate of risk-free asset and investing a sum larger than his own money in the risky portfolio. The return and risk of such a levered portfolio would be Return Rl=wRm-(w-1)Rf Where, Rl is the return on the levered portfolio Rf is the risk-free borrowing or lending rate. The first term signifies the earnings by investing own money as well as the borrowed money in the risky portfolio. The second term is the cost of borrowing and hence it is deducted in order to find the net return. Risk SDl=wSDm If different proportions are taken and the returns and risks are calculated, it would be seen that the figures are larger than those of the risky portfolio because a levered portfolio would give increased return with increased risk. If plotted on the graph they would lie in a straight line to the right of the optimal portfolio. Y Rp B C Rf O A X Efficient Frontier with Borrowing and Lending The straight line which is created by the action of the investors by investing on the market portfolio as well as the riskless asset; is known as the capital market line (CML) and the relationship between the return and risk of any efficient portfolio on the CML can be expressed as follows: Re=Rf+{(Rm-Rf)/SDm}SDe Where, ‘e’ represents the efficient portfolio. The CAPM explains the risk-return relationship between all portfolios, whether it is efficient or not. For establishing such relationship, the systematic risk of a security or a portfolio has to be considered. β is taken as the systematic risk whose value is considered as 1, signifying that the security moves in the same rate and direction as the market. From this concept the Security Market Line (SML) arrives which is a straight line joining Rf and M (market portfolio having beta coefficient 1 and expected return Rm). Now the relationship between expected return and beta of a security or portfolio will be given as: Ri=Rf+βi(Rm-Rf) (Kevin, 2008). Merits of the Capital Asset Pricing Model (CAPM) The most visible merit of CAPM is its simplicity. It is constructed based on the portfolio theory that makes it easy to understand. CAPM distinguishes between systematic and unsystematic risk and ultimately depicts a simple pricing model. CAPM discovers one of the most important findings of finance: the expected return of all assets and also portfolio of assets in the economy. CAPM provides framework for assessing prices of securities so as to find out whether it is correctly priced, overpriced or underpriced by the use of SML (Security Market Line). CAPM has many advantages over various methods that are used to calculate required return: CAPM, considering only systematic risk, reflects a very practical picture of the market because investors generally have diversified portfolio through which they can eliminate unsystematic risk. CAPM can be extensively used to determine the movement of stocks with respect to the movement of market. For example, the S&P 500 has provided average annual return to investors of around 8.10 %. This type of conclusion can be arrived by the help of CAPM. Demerits of CAPM Assigning Values to the CAPM For using CAPM, it is required to assign values to the risk-free rate of return or the return on short term government bonds. But it is very difficult to assign on that basis as the yield on government bonds keep on changing on a daily basis. Thus to assume economic circumstances and than set the values is somewhat difficult. CAPM faces many problems when used in taking investment decisions because in CAPM a particular time specific decision is taken. But investment decision should include multi-period situation conditions. Use in Investment Appraisal It becomes difficult to calculate discount rate of a project. Say for example, it is tough to calculate proxy beta as it is very rare that a proxy company undertake a single business activity. Another reason for this difficulty is that a proxy company’s capital structure may not be readily available which is actively required in taking up the decisions (PDF Cast, 2008). Controversy to the SML In the long run, it has been seen that average returns are related to the beta, that is, systematic risk. The high beta portfolios give higher returns and falls above the SML and vice-versa. Thus, a line drawn with a few portfolios would look flatter than the SML considering the movement of the average returns in the long run. Historical Evidence The performance of CAPM over the last 30 years have not confronted to the aspects depicted in the model. It has been found that the relation between actual average return and beta which is explained in the equation of CML has been weaker (Massachusetts Institute of Technology, 2010). Empirical Approach towards the CAPM Generally the Fama- French Model has been broadly used as an alternative measure to the CAPM. The table below shows the comparison of the two. CAPM Fama-French Market behavior assumptions Efficient : Risk-Return Efficient: Risk-Return Risk factors Market returns Market Returns Size Book to market ratio Analytical Approach Portfolio theory Empirical regularities The Fama-French model assumes that returns are like a reward towards bearing the risk associated with a portfolio and that the markets are efficient. This assumption resembles the one in CAPM. The most important assumption of Fama-French model which can also be regarded as the main modification to the CAPM lies in its definition of the risk factor due to which the returns on stocks are affected. While CAPM assumes that only one factor is associated with the risk, that is, the market return, Fama-French model assumes that along with market returns, there are other two factors also that influence the risk factor. They are the market capitalization and the ratio of book-to-market. This means that small firms become more exposable towards the market risk than the large firms. Book-to-ratio means indications towards the financial distress. A high ratio can determine financial distress. Also two of the approaches differ in another aspect: their bases of assumptions. CAPM bases its assumptions on the theory of portfolio while in Fama-French model the assumptions are on the basis of empirical regularities. This means Fama-French model takes the practical side of the theories into account. Many firms in the recent times have advocated the use of Fama-French model to be more practical and more logical than the CAPM. For example in an LPG enquiry, the Fama-French model was used to check CAPM (Oxera, n.d.). Advantages of Fama-French over CAPM Fama-French approach states that the systematic risk can explain only 70% of returns. According to this approach, although CAPM can predict returns on stocks but cannot predict returns on all equity portfolio. The approach also explains that return can be calculated from size and value, that is, market capitalisation and book/market ratio. Thus it provides a less complicated framework unlike CAPM. Higher market cap of an investor’s portfolio generates more expected return. Fama-French model views size and value more than estimated beta. In this model, it is presumed that investors are rewarded more for risk factors but the risk factors in this scenario are the size and value and not the estimated beta. For example, if an investor wants to invest in a portfolio of stocks of companies listed on the exchange and a risk-free asset like the Gilts fund, it would be enough to measure its market cap and book/market ratio for taking decision. Considering Fama-French model, there is negligible requirement to calculate beta for those assets. Shortfalls of Fama-French Model Many academic researchers have been seemed unconvinced by the assumption of Fama-french model that states investors earn a risk premium for holding portfolios of firms having small book/market ratio. Some raised the point of survivorship bias which means that in applying this model, only the firms which have survived in the market are considered and the failed firms are ignored. Another group of researchers found that concept of risk premium is somewhat irrational. A few evidences were also found which showed that actual returns have come lower than the expected assumed by the Fama-French model. Controversial issues even suggested that the assumptions are based on characteristics and not covariance of returns. It was called a characteristic based model. It was mentioned that there is relationship between expected return and characteristic variables like liquidity and there is no link with covariance of returns. All these controversial measures against Fama-French led to the conclusion that there is no premium of return that is associated with the three-factor model (Malin & Veeraraghavan, 2004). Arbitrage Pricing Approach to CAPM The Arbitrage Pricing theory is simply based on the size of the portfolio and has been obtained on the basis of the law of large numbers. In the CAPM, a particular efficient portfolio with risk and return is considered and used to formulate the systematic risk of it. The unsystematic risk has been totally ignored on the assumption that they can be removed simply by choosing another portfolio, i.e., by diversification. But in Arbitrage Pricing theory (APT) a number of factors are used to formulate the systematic risk. The key point in these theories is that both of them take into consideration two different types of risks. The CAPM neglects the unsystematic risk and APT that sees the market with large number of assets; focusing on the decree of huge numbers, ignores essential risk (Khan & Sun, 1997). APT vs. CAPM (Portfolios) The APT does not have to strictly follow the assumptions of CAPM. Unlike CAPM it does not base its assumption on the market portfolio. The APT can be based on any diversified portfolio. But the conclusion is still similar to CAPM, for at least a well diversified portfolio. APT vs. CAPM (Individual securities) CAPM assumes the same risk-return relationship for both portfolios and individual securities. But APT states that it is true only for well-diversified portfolios (University of Maryland, n.d.). The APT is also an equilibrium model but here the equilibrium is achieved by arbitrage. In CAPM equilibrium is achieved by risk aversion and optimizing mean-variance. Due to its simple assumptions than CAPM, APT is more common and flexible (University of Delaware, n.d.). Comparative Analysis of CAPM and APT Both CAPM and APT are theories on asset pricing but the basic difference is that APT is an explanatory approach whereas CAPM is quite restrictive in nature as it is totally based on a few assumptions, beyond which it can go. APT assumes that each investor has his own set of betas and they hold unique portfolios. This is in contradiction to the assumptions of ‘market portfolio’. But CAPM can be considered as a special case of APT because it explains a security market line that represents a single-factor model. In this case the beta is related to the market changes. APT can be said to be the supply side because its beta represents relationship between asset and economic factors. On the other hand, CAPM is the demand side of the theory as it arises from the maximisation of the utility function of each investor. Relative Merits of CAPM CAPM takes market risk into account which is the most relevant risk to stockholders. Thus to determine the effect of a project on the stock price, the model gives right inference on its acceptance. Overall the CAPM looks fine with its relationship equation and it takes into account almost all the influencing aspects that help investors to take decisions. The relation that CAPM provides can be effectively used to measure the expected return on a security given the systematic risk. The model says that investors are rewarded with a risk-premium of market for holding risky assets. Conclusion It can be summarized from the above study that CAPM bears some notable merits but the empirical approaches to it that have been developed over the years add new dimensions to CAPM. Fama-French approach to CAPM is a modification to the CAPM model and it presents some logical evidences towards the findings of CAPM. The research paper has firstly described the CAPM in detail so that it becomes easy to evaluate its relative merits. In a section of this paper, comparison between the assets pricing models has been dealt with. The objective of this paper was to analyze different dimensions of the Capital Asset Pricing Model and its applicability in different sectors. References Burton, J., 1998. Revisiting the Capital Asset Pricing Model. Stanford University. [Online] Available at: www.stanford.edu/~wfsharpe/art/djam/djam.htm [Accessed November 10, 2010]. Kaduff, J. V., No Date. Shortfall-Probability-Optimized Portfolios in the Case of Riskless Borrowing and Lending. Abstract. [Online] Available at: www.actuaries.org/AFIR/colloquia/Cairns/Kaduff.pdf [Accessed November 10, 2010]. Khan, M. A. & Sun, Y., 1997. The Capital-Asset-Pricing Model and Arbitrage Pricing Theory: A Unification. Abstract. [Online] Available at: http://www.pnas.org/content/94/8/4229.full [Accessed November 10, 2010]. Massachusetts Institute of Technology, 2010. Capital Asset Pricing Model (CAPM). Road Map. [Online] Available at: http://web.mit.edu/15.407/file/Ch11.pdf [Accessed November 10, 2010]. Malin, M. & Veeraraghavan, M., 2004. On the Robustness of the Fama and French Multifactor Model: Evidence from France, Germany, and the United Kingdom. International Journal of Business and Economics. [Online] Available at: http://www.ijbe.org/table%20of%20content/pdf/vol3-2/vol3-2-05.pdf [Accessed November 13, 2010]. Oxera, No Date. Fama-French: A challenge to the CAPM? Agenda. [Online] Available at: http://www.oxera.com/cmsDocuments/Agenda_May%2006/Fama%20French.pdf [Accessed November 10, 2010]. PDF Cast, 2008. CAPM: Theory, Advantages, and Disadvantages. Students accountant. [Online] Available at: http://pdfcast.org/pdf/capm-theory-advantages-and-disadvantages [Accessed November 13, 2010]. University of Maryland, No Date. Arbitrage Pricing Theory and Multifactor Models of Risk and Return. Department of Economics. [Online] Available at: http://econweb.umd.edu/~trandafi/econ435/Chapter_11_6spp.pdf [Accessed November 10, 2010]. University of Delaware, No Date. Using the CAPM. Alfred Lerner College of Business & Economics. [Online] Available at: http://www.buec.udel.edu/harrisj/week7.pdf [Accessed November 10, 2010]. Bibliography Fabozzi, F. J. & Et. Al., 2006. Financial Modeling of the Equity Market. John Wiley & Sons, Inc. Fama, E. F. & French, K. R., 1996. Industry Cost of Equity. Journal of Financial Economics 43 (1997) Kurschner, M., 2008. Limitations of the Capital Asset Pricing Model (CAPM). GRIN Verlag, Petkova, R., 2006. Do the Fama–French Factors Proxy for Innovations in Predictive Variables? The Journal of Finance. Ross, S. A. & Et. Al., 2004. Corporate Finance. Tata McGraw-Hill. Read More