The Capital Asset Pricing Model - Essay Example

? The Capital Asset Pricing Model An Elaborate Analysis Corporate Finance Assignment 30 March, The Capital Asset Pricing Model (CAPM) is a land mark in the field of corporate finance. The capital for any company refers to the money invested in the company necessary for the activities and the existence of the company. Every firm has a given capital requirement which it has to meet based on the financial regulations of the country in which the firm is operating. Every firm has to bear the cost for generating the capital for its business. The firm’s capital is divided into two parts: debt and equity. Thus each firm has to bear the cost of debt and cost of equity. These costs are calculated through various financial models designed to give an accurate analysis of the costs the firms have to bear. There are three models used by analysts and firms to calculate their cost of capital; the Capital Asset Pricing Model (CAPM), the Dividend Valuation Model and the Arbitrage Pricing Theory. The focus of this report is the CAPM model and a comparison between this model and the Dividend Valuation Model. “The capital asset pricing model attributable to Sharpe (1964) is a cornerstone of modern financial theory and originates from the analysis of the cost of capital.” (Chouodary 2004) this market model encompasses the concept of risk and comes under the domain of risk premium market models. This model takes into account the risks borne by the investor for investing in the securities. When an investor puts his money in any security he faces many risks ranging from liquidity to inflation etc. The underlying principle of the capital asset pricing model is that investors want to be compensated for bearing the risk in the form of extra return. This extra return is over and above the risk free rate as risk free securities have no risk due to their guaranteed nature. All government securities are risk free as the government will pay back all its investors and there is no default involved in this case. Thus, before actually giving you the CAPM equation one needs to understand the logic of risk and return i.e. the concepts that make up the component of the CAPM equation. Risk and return valuations are the most important part of investment decisions. The risk and return go proportionately with each other i.e. greater the risk greater will be the return. Deriving from the basics an expected return is the mean of the probability distribution of possible future returns. ‘The expected return on an investment is the average return from the investment and is calculated as the probability weighted sum of all potential returns.’(Rao, 1989) The concept of risk and return arises due to the uncertainty of future outcomes. The underlying factor here is that the actual return received may be different from the expected return, thus generating risk for the investors. All financial assets produce cash flows and the riskiness of these assets is derived from the riskiness of these cash flows. An asset considered in isolation carries stand-alone risk and is considered to be less risky as compared to when it is held in a portfolio. In a portfolio, assets with different expected return are grouped together. The risk of the portfolio is divided into two parts: diversifiable risk and market risk. The diversifiable risk is the one that can be eliminated and therefore this type of risk is not accounted for in the risk computation. The risk that the investors are really interested in calculating is the market risk (the non-diversifiable risk) i.e. the relevant risk which arises from the broad market movements. The measures of the risk are variance and standard deviation. The variance of a stock can be calculated using the below formula provided the required rate of return is given: N Var(R) = ?2 = ? pi(Ri – E[R])2 i=1 Where: N = the number of states pi = the probability of state i Ri = the return on the stock in state i E[R] = the expected return on the stock The positive square root of variance is standards deviation which indicates how much above or below the actual rate can move from the expected rate of return. SD(R) = ? = ?2 = (?2)1/2 = (?2)0.5 These calculations project risk computation on a standalone basis. However, most investors and firms hold a combination of asset known as the portfolio. Holding assets in a portfolio diversifies their standalone risk leaving the investor with the relevant risk only which is non-diversifiable. ‘The expected return on a portfolio is simply the weighted average of the expected returns on the individual assets in the portfolio with the weights being the fraction of the total portfolio invested in each asset.’ (Eugene, 1994) N E[Rp] = ? wiE[Ri] i=1 Where: E[Rp] = the expected return on the portfolio N = the number of stocks in the portfolio wi = the proportion of the portfolio invested in stock i E[Ri] = the expected return on stock i Unlike the return, the risk of portfolio is not the weighted average of the standard deviations of the assets that form the portfolio. The portfolio risk is generally lower than that of the individual stocks and it is this underlying factor that is the main rationale behind portfolio formation. By forming a portfolio investors diversify the standalone risk thus resulting in a better risk and return bargain. The reason behind the decrease in the risk of the portfolio can be attributed to the direction of the movements of the returns of the individual securities. And the measure of such relationship is called the covariance and so-relation coefficient. Covariance is the variance of stock along with the movement of the return of these stocks: N Cov(RA,RB) = ?A,B = ? pi(RAi - E[RA])(RBi - E[RB]) i=1 Where: ?A,B = the covariance between the returns on stocks A and B N = the number of states pi = the probability of state i RAi = the return on stock A in state i E[RA] = the expected return on stock A RBi = the return on stock B in state i E[RB] = the expected return on stock B The covariance gives us a number, this number along with the sign explains riskiness of the portfolio. As it is difficult to interpret the number of covariance, another formula that standardizes the covariance is the correlation coefficient: ?A,B Cov(RA,RB) Corr(RA,RB) = ?A,B = ?A?B = SD(RA)SD(RB) Where: ?A,B =the correlation coefficient between the returns on stocks A and B ?A,B =the covariance between the returns on stocks A and B, ?A=the standard deviation on stock A, and ?B =the standard deviation on stock B This correlation coefficient ranges between -1 to +1. The figure -1 indicates that the stocks in the portfolio are negatively correlated and the portfolio formation has diversified nearly all the standalone risk. A figure of +1 indicates positive correlation between the assets in the portfolio and signifies no diversification took place and the portfolio’s risk is same as that of the stocks. The risk analysis of a portfolio now boils down of the relationship of the stocks in the portfolio with the market risk. The tendency of the stocks to move up and down with the market is known as the beta coefficient. It measures the stock’s volatility with respect to the market. A beta of 1 means the stock is as volatile as the market, a figure less than one shows the stock is less volatile in the same proportion and a figure of greater than 1 shows the stock is more volatile as compared to the market in the same proportion. Having talked about beta, the relationship between the risk and return for a portfolio is expressed through the Capital Asset Pricing Model (CAPM). The CAPM takes into account the risk-free rate of return and calculates the required rate of return for the portfolio over and above this the risk-less profit taking into account the beta of individual stock. The equation used for CAPM is as follows: Ki = Krf + ?i(Km - Krf) Where: Ki = the required return for the individual security Krf = the risk-free rate of return ?i = the beta of the individual security Km = the expected return on the market portfolio (Km - Krf) is called the market risk premium According to this equation the differential of market risk and risk free rate of return times the tendency of the movement of the stock with respect to the market is the additional return that the investors will expect over and above the risk free rate for bearing additional risk of the stock. Thus this model measures market risk, additionally beta can also be found through this equation and the beta of portfolio can be calculated using the weighted average of betas of the stocks in the portfolio.[All formulae above are from Eugene (Eugene, 1994)] “The CAPM postulates that the opportunity cost of equity is equal to the return on risk free securities plus the company’s systematic risk (beta) multiplied by the market price of risk (market risk premium).” (Gross 2006) The detailed discussion of the capital asset pricing model explains the underlying concepts and the rationale for coming up with such model. However one needs to assess the limitation of this model as well. Empirical evidence shows that the model lacks practicality and has drawbacks. The first and most noticeable drawback of this model is the time line assumption of this model. “ …the single period time horizon of the model. This means that investors are only concerned with the wealth of their portfolio produces at the end of the current period.” (Kuschner 2008) In real life thou the investors are concerned with their lifetime view of their investments. Another drawback of this model is the nature of data used to compute return is futuristic like the expected return and beta. But the historical data is used to calculate the values of these variables. Also as we know that beta is associated with systematic risk with an assumption that all the unsystematic risk has been diversified away, this however is not possible in most cases. “ CAPM assumes only systematic risk need to be captured as unsystematic risk has been diversified away. This may not be the case in entities controlled by individuals or families where the shareholders are unlikely to be fully diversified.” (Ogilvie2009) One more assumption which is faulty is the risk free security, there is no practically available risk less security in the real world. All securities carry risk, some securities like government which are supposed to be riskless carry little risk as well. This model also unrealistically assumes that all the expectations for all investors are homogenous, it over rules the risk taker or risk averse nature of investors and treats their expectations about risk and return at an equal level. According to the model the securities are valued correctly and the market is a perfect market with no inherent cost. The risk and return graph known as the security market line (SML) shows relationship between risk and return in a perfect market with investors holding efficient portfolios. CAPM assumes that all securities lie on the security market line which is again a drawback of this model . Due to the empirical weakness of the CAPM model Fama and French came up with their three factor model as opposed to the single factor (using beta) model CAPM. “The pure CAPM provides fundamental insights about risk and return. However, while providing an introduction to fundamental concepts of asset pricing and portfolio theory, CAPM’s empirical problems probably invades pure CAPM’s use in application.” (Pratt & Grabowski 2011) Comparing CAPM with the dividend valuation model also gives good insight about these two methods. The dividend valuation method, also know as the stock valuation method, calculates the value of the stock be discounting the dividends. The present value of the dividends is the price of the stock and if the share price in the stock market is less than the present value of dividends than the stock is undervalued. The analysis of these two models gives a picture that CAPM can be used for companies in any stage of the lifecycle. But the dividend valuation model is good for the companies who are giving out dividends and preferably constant dividends, for those who are not giving out any dividends cannot have their stock evaluated through this model. “Dividend valuation models are best suited for companies in the expansion or maturity life-cycle phase. Dividends of these companies are more predictable and usually make up larger percentage of the total return than capital gains.” (Hirt & Block 2009) The CAPM has a single equation for all stocks, however for the dividend valuation model different formulae are used for a zero growth stock, for a constant growth stock (Gordon’s Growth Model) etc. the dividend growth model ignores the capital gains, however this is not a cause of concern for the CAPM model. Both these models have issues in implementation for the CAPM model obtaining a completely riskless security is impossible and thus analysts have to use the historical data and the least risky security for computing values using CAPM. The dividend growth model requires the earning growth rate and the dividend streams which again is based on historical and cannot be accurately ascertained. “In implementing the model, the analysts must obtain an estimate of the growth rate(s) in earnings and dividends (and stock price) expected by investors.” (Moyer, R. et al. 2009) Thus the CAPM and discounted cash flow model both have limitations but both have been used by firms for the valuations of their stock. “ However, of the two, we can probably conclude that the CAPM is likely to provide the more reliable figure. The reason for reaching this conclusion is the fact that the dividend valuation model – in its practical application – really does have an almost have insurmountable problem with regard to identifying a reliable estimate of the future rate of growth of dividends.” (Lumbly & Jones 2003) References Brigham, E. F. & Gapenski, L.S.C (1994). Financial Management Theory and Practice. New York: Harcourt Brace College Publishers. Choudary, M. (2004) Corporate Bonds & Structured Financial Products, Burlington: Elsevier Butterworth Heinemann, p.192 Gross, S. (2006) Bank and Shareholder Value: An overview of bank valuation and empirical evidence on shareholder value for banks, Germany: Gabler Edition Wissenscraft, Hirt, G. and Block, S. (2009) Fundamentals of Investment Management, 8th ed. New Delhi: Tata McGraw Hill, p.176. Kurschner, M. (2008) Limitations of the Capital Asset Pricing Model (CAPM) - Criticisms and new developments, Scholarly Paper, p.6. Lumbly, S. and Jones, C. (2003) Corporate Finance - Theory & Practice, 7th ed. London: Thomson Learning. Moyer, R. et al. (2009) Contemporary Financial Management, 11th ed. Mason: South Western Cenagage Learning, Oligvie, J. (2009) Management Accounting Financial Strategy, Burlington: CIMA Publishing, p.191. Pratt, S. and Grabowski, R. (2011) Cost of Capital in Litigation - Applications and examples, New Jersey: John Wiley & Sons Inc., p.42. Rao, R. R. S., (1989). Fundamentals of Financial Management. London: Collier Machmillian Publishers. Read More