Module 1 Chapter 3 CAPM MODEL PDF

# LESSON 16: CAPITAL ASSET PRICING MODEL ## INTRODUCTION A fundamental question in finance is how the risk of an investment should affect its expected return. The Capital Asset Pricing Model (CAPM) provided the first coherent framework for answering this question. The CAPM was developed in the ear...

# LESSON 16: CAPITAL ASSET PRICING MODEL ## INTRODUCTION A fundamental question in finance is how the risk of an investment should affect its expected return. The Capital Asset Pricing Model (CAPM) provided the first coherent framework for answering this question. The CAPM was developed in the early 1960s by William Sharpe (1964), Jack Treynor (1962), John Lintner (1965a,b) and Jan Mossin (1966). The CAPM is based on the idea that not all risks should affect asset prices. In particular, a risk that can be diversified away when held along with other investments in a portfolio is, in a very real way, not a risk at all. The CAPM gives us insights about what kind of risk is related to return. This paper lays out the key ideas of the Capital Asset Pricing Model, places its development in a historical context, and discusses its applications and enduring importance to the field of finance. ## OBJECTIVES After reading this lesson the student should be able to understand Capital Asset Pricing Model. ## CONTENT - 16.1 Capital Asset Pricing Model - 16.2 Assumptions Of CAPM - 16.3 Lending And Borrowing - 16.4 Risk Return Trade Off - 16.5 Security Market Line - 16.6 Evaluation Of Securities - 16.7 Empirical Tests Of The CAPM - 16.8 Present Validity Of CAPM - 16.9 Arbitrage Pricing Theory ## 16.1 CAPITAL ASSET PRICING MODEL The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM assumes a particular form of utility functions (in which only first and second moments matter, that is risk is measured by variance, for example a quadratic utility) or alternatively asset returns whose probability distributions are completely described by the first two moments (for example, the normal distribution) and zero transaction costs (necessary for diversification to get rid of all idiosyncratic risk). Under these conditions, CAPM shows that the cost of equity capital is determined only by beta.[1][2] Despite it failing numerous empirical tests, [3] and the existence of more modern approaches to asset pricing and portfolio selection (such as arbitrage pricing theory and Merton's portfolio problem), the CAPM still remains popular due to its simplicity and utility in a variety of situations. The CAPM was introduced by Jack Treynor (1961, 1962), [4] William F. Sharpe (1964), John Lintner (1965a,b) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe, Markowitz and Merton Miller jointly received the 1990 Nobel Memorial Prize in Economics for this contribution to the field of financial economics. Fischer Black (1972) developed another version of CAPM, called Black CAPM or zerobeta CAPM, that does not assume the existence of a riskless asset. This version was more robust against empirical testing and was influential in the widespread adoption of the CAPM. ## 16.2 ASSUMPTIONS OF CAPM All investors: 1. Aim to maximize economic utilities (Asset quantities are given and fixed). 2. Are rational and risk-averse. 3. Are broadly diversified across a range of investments. 4. Are price takers, i.e., they cannot influence prices. 5. Can lend and borrow unlimited amounts under the risk free rate of interest. 6. Trade without transaction or taxation costs. 7. Deal with securities that are all highly divisible into small parcels (All assets are perfectly divisible and liquid). 8. Have homogeneous expectations. 9. Assume all information is available at the same time to all investors. ## 16.3 LENDING AND BORROWING Here, it is assumed that the investor could borrow or lend any amount money at riskless rate of interest. When this opportunity is given to the investors, they can mix risk free assets with the risky assets in a portfolio to obtain a desired rate of risk-return combination. - R_p = Portfolio return - X_f = the proportion of funds invested in risk free assets - 1 - X_f = the proportion of funds invested in risky assets - R_f = Risk free rate of return - R_m = Return on risky assets The expected return on the combination of risky and risk free combination is Rp = RX_f + R_m(1-X_f) This formula can be used to calculate the expected returns for different situations, like mixing ri assets with risky assets, investing only in the risky asset and mixing the borrowing with risky assets. ## 16.4 RISK - RETURN TRADE OFF | Portfolio Return | Risk-free Return | Premium | Portfolio Risk | Factor of Proportionality (Rp - Rf)/σ_p | |---|---|---|---|---| | 16.25 | 12.5 | 3.75 | 7.5 | 0.5 | | 20.0 | 12.5 | 7.5 | 15.0 | 0.5 | | 23.75 | 12.5 | 11.25 | 22.5 | 0.5 | The risk-return proportionality ratio is a constant 0.5, indicating that one unit of risk premium is accompanied by 0.5 unit of risk. ## 16.6 SECURITY MARKET LINE The risk-return relationship of an efficient portfolio is measured by the capital market line. But, it does not show the risk-return trade off for other portfolios and individual securities. Inefficient portfolios lie below the capital market line and the risk-return relationship cannot be established with the help of the capital market line. Standard deviation includes the systematic and unsystematic risk. Unsystematic risk can be diversified and it is not related to the market. If the unsystematic risk is eliminated, then the matter of concern is systematic risk alone. This systematic risk could be measured by beta. The beta analysis is useful for individual securities arid portfolios whether efficient or inefficient. When an additional security is added to the market portfolio, an additional risk is also added to it. The variance of a portfolio is equal to the weighted sum of the co-variances of the individual securities in the portfolio. If we add an additional security to the market portfolio, its marginal contribution to the variance of the market is the covariance between the security's return and market portfolio's return. If the security i am included, the covariance between the security and the market measures the risk. Covariance can be standardized by dividing it by standard deviation of market portfolio cov_im/σ_m. This shows the systematic risk of the security. Then, the expected return of the security i is given by the equation: R_i = R_f + (R_m-R_f/σ_m) Cov_im/σ_m This equation can be rewritten as follows: R_i = R_f + β_i (R_m-R_f) This equation of the SML is same as the beta of the market (single index) model. In equilibrium, all efficient and inefficient portfolios lie along the security market line. The SML line helps to determine the expected return for a given security beta. In other words, when betas are given, we can generate expected returns for the given securities. This is explained in fig. If we assume the expected market risk premium to be 8% and the risk free rate of return tube 7%, we can calculate expected return for A, B, C and D securities using the formula: E(R_i) = R_f + β_i[E(R_m)-R_f] If beta for β = 1 E(R_i) = 7 + 1 (8) = 15% ## 16.6 EVALUATION OF SECURITIES Relative attractiveness of the security can be found out with the help of security market line. Stocks with high risk factor are expected to yield more return and vice-versa. But the investor would be interested in knowing whether the security is offering return more or less proportional to its risk. ### Evaluation of Securities with SML The figure provides an explanation for the evaluation. There are nine points in the diagram. A, B and C lie on the security market line, R, S and T above the SML and U, V and W below the SML. ARU have the same beta level of, 0.9. Likewise beta values of SBV = 1.00 and TCW = 1.10. The stocks above the SML yield higher returns for the same level of risk. They are underpriced compared to their beta value. With the simple rate of return formula, we can prove that they are undervalued. P₁ is the present price P₀ - the purchase price and Div - Dividend. When the purchase price is low i.e. when the denominator value is low, the expected return could be high. Applying the same principle the stocks U, V and W can be classified as overvalued securities and are expected to yield lower returns than stocks of comparable risk. The denominator value may be high i.e. the purchase price may be high. The prices of these scripts may fall and lower the denominator. There by, they may increase the returns on securities. The securities A, B and C are on the line. Therefore considered to be appropriately valued. They offer returns in proportion to their risk. They have average 4oclc performance, since they are neither undervalued nor overvalued. ## Market Imperfection and SML Information regarding the share price and market condition may not immediately available to all investors. Imperfect information may affect the valuation of securities. In a market with perfect information, all securities should lie on SML. Market imperfections would lead to a band of SML rather than a single line. Market imperfections affect the width of the SML to a band. If imperfections are more, the width also would be larger. SML in imperfect market is given in figure. ## 16.7 EMPIRICAL TESTS OF THE CAPM In the CAPM, beta is used to estimate the systematic of the security and reflects the future volatility of the stock in relation to the market. Future volatility of the stock is estimated only through historical data. Historical data are used to plot the regression line or the characteristic line and calculate beta. If historical betas are stable over a period of time, they would be good proxy for their ex-ante or expected risk. Robert A. Levy, Marshall B. Blume and others have studied the question of beta stability in depth. I calculated betas for both Individual securities and portfolios. His study results have provided the following conclusions: 1. The betas of individual stocks are unstable; hence the past betas for the individual securities are not good estimators of future risk. 2. The betas of portfolios of ten or more randomly selected stocks are reasonably stable, hence the portfolio betas are good estimators of future portfolio volatility. This is because of the errors in the estimates of individual securities' betas tend to offset one another in a portfolio. Various researchers have attempted to find out the validity of the model by calculating beta and realized rate of return. They attempted to test (1) whether the intercept is equal to i.e. risk free rate of interest or the interest rate offered for treasury bills (2) whether the line is linear and pass through the beta = 1 being the required rate of retürn of the market. In general, the studies have showed the following results. 1. The studies generally showed a significant positive relationship between the expected return and systematic risk. But the slope of the relationship is usually less than that of predicted by the CAPM. 2. The risk and return relationship appears to be linear. Empirical studies give no evidence of significant curvature in the risk/return relationship. 3. The attempts of the researchers to assess the relative importance of the market and company risk have yielded definite results. The CAPM theory implies that unsystematic risk is not relevant, but unsystematic and systematic risks are positively related to security returns. Higher returns are needed to compensate both the risks. Most of the observed relationship reflects statistical problems rather than the true nature of capital market. 4. According to Richard Roll, the ambiguity of the market portfolio leaves the CAPM untestable. The practice of using indices as proxies is loaded with problems. Different indices yield different betas for the same security. 5. If the CAPM were completely valid, i4 should apply to all financial assets including bonds. But, when bonds are introduced into the analysis, they do not fall on the security market line. ## 16.8 PRESENT VALIDITY OF CAPM The CAPM is greatly appealing at an intellectual level, logical and rational. The basic assumptions on which the model is built raise, some doubts in the minds of the investors. Yet, investment analysts have been more creative in adapting CAPM for their uses. 1. The CAPM focuses on the market risk, makes the investors to think about the riskiness of the assets in general. CAPM provides basic concepts which are truly of fundamental value. 2. The CAPM has been useful in the selection of securities and portfolios. Securities with higher returns are considered to be undervalued and attractive for buy. The below normal expected return yielding securities are considered to be overvalued and Suitable for sale. 3. In the CAPM, it has been assumed that investors consider only the market risk. Given the estimate of the risk free rate, the beta of the firm, stock and the required market rate of return, one can find out the expected returns for a firm's security. This expected return can be used as an estimate of the cost of retained earnings. 4. Even though CAPM has been regarded as a useful tool to financial analysts, it has its own critics too. They point out, when the model is ex-ante, the inputs also should be ex-ante, i.e. based on the expectations of the future. Empirical tests and analyses have used ex-post i.e. past data only. 5. The historical data regarding the market return, risk free rate of return and betas vary differently for different periods. The various methods used to estimate these inputs also affect the beta value. Since the inputs cannot be estimated precisely, the expected return found out through the CAPM model is also subjected to criticism 4 ## 16.9 ARBITRAGE PRICING THEORY In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly—the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line. The theory was proposed by the economist Stephen Ross in 1976. The APT formula is: E(r_j) = r_f + b_j1RP₁ + b_j2RP₂ + b_j3RP₃ + b_j4RP₄ + ... + b_jnRP_n where: - E(r_j) = the asset's expected rate of return - r_f = the risk-free rate - b_j = the sensitivity of the asset's return to the particular factor - RP = the risk premium associated with the particular factor The general idea behind APT is that two things can explain the expected return on a financial asset: 1) macroeconomic/security-specific influences and 2) the asset's sensitivity to those influences. This relationship takes the form of the linear regression formula above. There are an infinite number of security-specific influences for any given security including inflation, production measures, investor confidence, exchange `rates, market indices or changes in interest rates. It is up to the analyst to decide which influences are relevant to the asset being analyzed. Once the analyst derives the asset's expected rate of return from the APT model, he or she can determine what the "correct" price of the asset should be by plugging the rate into a discounted cash flow model. Note that APT can be applied to portfolios as well as individual securities. After all, a portfolio can have exposures and sensitivities to certain kinds of risk factors as well. The APT was a revolutionary model because it allows the user to adapt the model to the security being analyzed. And as with other pricing models, it helps the user decide whether a security is undervalued or overvalued and so he or she can profit from this information. APT is also very useful for building portfolios because it allows managers to test whether their portfolios are exposed to certain factors. APT may be more customizable than CAPM, but it is also more difficult to apply because determining which factors influence a stock or portfolio takes a considerable amount of research. It can be virtually impossible to detect every influential factor much less determine how sensitive the security is to a particular factor. But getting "close enough" is often good enough; in fact studies find that four or five factors will usually explain most of a security's return: surprises in inflation, GNP; investor confidence and shifts in the yield curve. ## REVISION POINTS In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. ## INTEXT QUESTIONS 1. What are the basic assumptions of CAPM? What are the advantage of adopting CAPM model in the portfolio management? 2. Explain the CAPM theory and its validity in the stock market? ## SUMMARY The capital asset pricing model (CAPM) is used to calculate the required rate of return for any risky asset. The general idea behind CAPM is that investors need to be compensated in two ways i.e., time value of money and risk. ## TERMINAL EXERCISE 1. **__** is used to calculate the required rate of return for any risky asset. **Ans:** The capital asset pricing model ## SUPPLEMENTARY MATERIALS - money.rediff.com - money control.com - amfiindia.com - nseindia - bseindia.com - rbi.org.in ## ASSIGNMENTS 1. State the reason for the treynor and sharpe giving conflicting performance ranking? 2. Disting between the securitity market line and capital market line? ## SUGGESTED READINGS 1. M. Ranganathan and R. Madhumathi: Investment Analysis and Portfolio Management, Pearson Education, New Delhi. 2. Punithavathy Pandian: Security Analysis and Portfolio Management, Vikas Publishing House Pvt. Ltd., New Delhi. 3. Prasanna Chandra: Investment Analysis and Portfolio Management, TMH, Delhi. ## LEARNING ACTIVITIES "When the borrowing and lending are different, the notion of market price of the risk is meaningless". Appraise the statement. ## KEY WORDS Risky assets, rate of return, capital asset price