Capital Asset Pricing and Arbitrage Pricing Theory

CHAPTER 7 7.1 THE CAPITAL ASSET PRICING MODEL Capital Asset Pricing and Arbitrage Pricing Theory Capital Asset Pricing Model (CAPM) Equilibrium model that underlies all modern financial theory Derived using principles of diversification with simplified assumptions Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development Assumptions (cont.) Information is costless and available to all investors Investors are rational meanmean-variance optimizers Homogeneous expectations Assumptions Individual investors are price takers SingleSingle-period investment horizon Investments are limited to traded financial assets No taxes nor transaction costs Resulting Equilibrium Conditions All investors will hold the same portfolio for risky assets – market portfolio Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value 7-1 Resulting Equilibrium Conditions (cont.) Risk premium on the market depends on the average risk aversion of all market participants Risk premium on an individual security is a function of its covariance with the market The Risk Premium of the Market Portfolio M rf E(rM) - rf = = = Market portfolio Risk free rate Market risk premium E(rM) - rf = Market price of risk = = Slope of the CAPM σM Expected Returns On Individual Securities: an Example Using the Dell example: E (rM ) − rf 1 = Figure 7.1 The Efficient Frontier and the Capital Market Line Expected Returns On Individual Securities The risk premium on individual securities is a function of the individual security’ security’s contribution to the risk of the market portfolio Individual security’ security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio Figure 7.2 The Security Market Line and Positive Alpha Stock E (rD ) − rf βD Rearranging gives us the CAPM’ CAPM’s expected returnreturn-beta relationship E ( rD ) = rf + β D  E ( rM ) − rf  7-2 SML Relationships Sample Calculations for SML E(rm) - rf = .08 rf = .03 β = [COV(ri,rm)] / σm2 E(rm) – rf = market risk premium βx = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% SML = rf + β[E(rm) - rf] βy = .6 e(ry) = .03 + .6(.08) = .078 or 7.8% Graph of Sample Calculations E(r) SML Rx=13% Rm=11% Ry=7.8% 3% .08 .6 1.0 1.25 ß yy ß m ß xx m 7.2 THE CAPM AND INDEX MODELS ß Estimating the Index Model Using historical data on TT-bills, S&P 500 and individual securities Regress risk premiums for individual stocks against the risk premiums for the S&P 500 Slope is the beta for the individual stock Table 7.1 Monthly Return Statistics for T-bills, S&P 500 and General Motors 7-3 Figure 7.3 Cumulative Returns for T-bills, S&P 500 and GM Stock Figure 7.4 Characteristic Line for GM Table 7.2 Security Characteristic Line for GM: Summary Output GM Regression: What We Can Learn GM is a cyclical stock Required Return: rf + β ( rM − rf ) = 2.75 + 1.24 x5.5 = 9.57% Next compute betas of other firms in the industry Predicting Betas The beta from the regression equation is an estimate based on past history Betas exhibit a statistical property THE CAPM AND THE REAL WORLD – Regression toward the mean 7-4 CAPM and the Real World The CAPM was first published by Sharpe in the Journal of Finance in 1964 Many tests of the theory have since followed including Roll’ Roll’s critique in 1977 and the Fama and French study in 1992 Multifactor Models Limitations for CAPM Market Portfolio is not directly observable Research shows that other factors affect returns Table 7.3 Summary Statistics for Rates of Return Series 7.4 MULTIFACTOR MODELS AND THE CAPM Fama French Three-Factor Model Returns are related to factors other than market returns Size Book value relative to market value Three factor model better describes returns Table 7.4 Regression Statistics for the Single-index and FF Three-factor Model 7-5 Arbitrage Pricing Theory 7.5 FACTOR MODELS AND THE ARBITRAGE PRICING THEORY Figure 7.5 Security Line Characteristics Arbitrage - arises if an investor can construct a zero beta investment portfolio with a return greater than the riskrisk-free rate If two portfolios are mispriced, the investor could buy the lowlow-priced portfolio and sell the highhigh-priced portfolio In efficient markets, profitable arbitrage opportunities will quickly disappear APT and CAPM Compared APT applies to well diversified portfolios and not necessarily to individual stocks With APT it is possible for some individual stocks to be mispriced - not lie on the SML APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio APT can be extended to multifactor models 7-6