© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Chapter 6: Risk, Return, and the Capital Asset Pricing Model Corporate Finance, 3e Graham, Smart, and Megginson

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Systematic Risk and Asset Pricing Investors can only expect compensation for systematic risk:  Contribution of an asset’s risk to a diversified portfolio  Measured by beta The capital asset pricing model (CAPM) relates an asset’s return to its systematic risk.  Assumes that rational, risk-averse investors select efficient portfolios

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Additional Example: Risk-Free Borrowing and Lending Return: 6% Risk-free asset Y Buying asset Y = Lending money at 6% interest How would a portfolio with $100 (50%) in asset X and $100 (50%) in asset Y perform? Portfolio return and volatility are exactly halfway between those of the risky asset and the risk-free asset. Three possible returns: -10%; 10%; 30% Risky asset X Expected return 10% Standard deviation 16.3% $100 Asset X $100 Asset Y Three possible returns: -2%; 8%; 18% Expected return 8% Standard deviation 8.16%

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Risk-Free Borrowing and Lending What if we sell short asset Y instead of buying it? Borrow $100 at 6% Must repay $106 Invest $300 in X: Original $200 investment plus $100 in borrowed funds When X Pays –10%When X Pays 10%When X Pays 30%

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Risk-Free Borrowing And Lending The more we invest in X, the higher the expected return. This relationship is linear. The expected return is higher, but so is the volatility.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Finding the Optimal Risky Portfolio  If investors can borrow and lend at the risk-free rate, then from the entire feasible set of risky portfolios, one portfolio will emerge that maximizes the return investors can expect for a given standard deviation.  To determine the composition of the optimal portfolio, you need to know the expected return and standard deviation for every risky asset, as well as the covariance between every pair of assets.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. The Market Portfolio Only one risky portfolio is efficient. Equilibrium requires this to be the market portfolio. Suppose investors agree on which portfolio is efficient. Market portfolio: Value weighted portfolio of all available risky assets The line connecting R f to the market portfolio is called the Capital Market Line

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. The Capital Market Line  The line connecting R f to the market portfolio is called the Capital Market Line (CML).  The CML quantifies the relationship between the expected return and standard deviation for combinations of the risk-free asset and the market portfolio:

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Capital Asset Pricing Model (CAPM) Only beta changes from one security to the next. For that reason, analysts classify the CAPM as a single-factor model, meaning that just one variable explains differences in returns across securities.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. The Security Market Line  Plots the relationship between expected return and betas  In equilibrium, all assets lie on this line  If stock lies above the line…  Expected return is too high.  Investors bid up price until expected return falls.  If stock lies below the line…  Expected return is too low.  Investors sell stock, driving down price until expected return rises.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Beta  The numerator is the covariance of the stock with the market.  The denominator is the market’s variance. A stock’s systematic risk is captured by beta.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Beta and Expected Return The market risk premium is the reward for bearing market risk: R m  R f Beta measures a stock’s exposure to market risk. E(R i ) = R f +  [E(R m ) – R f ] Return for bearing no market risk Stock’s exposure to market risk Reward for bearing market risk

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Calculating Expected Returns E(R i ) = R f +  [E(R m ) – R f ] Assume Risk-free rate = 2% Expected return on the market = 8% If stock’s beta is…Then expected return is… 02% 0.55% 18% 214% When  = 0, the return equals the risk-free rate. When  = 1, the return equals the expected market return.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. Criticisms of the CAPM  Model is based on expected returns, which are unobservable.  CAPM is a one-period model and does not account for changing expectations.  Because even Treasury bonds are not free of all types of risk, R f is not known precisely.  Market indices (such as the S&P 500) are an imperfect proxy for the true market portfolio.  The relationship between stock returns and estimated betas is flatter than predicted and not stable over time.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. The Fama-French Model  In the Fama-French model, asset returns are affected by three factors:  The market risk premium  A “size effect” measured by the return on a portfolio of small stocks, minus the return on a portfolio of large stocks  A “value effect” measured by the return on a portfolio of stocks with high book-to-market ratios, minus the return on a portfolio of stocks with low book-to-market ratios Betas represent sensitivities to each source of risk. Terms in parentheses are the rewards for bearing each type of risk.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. The Current State of Asset Pricing Theory  Investors demand compensation for taking risk because they are risk averse.  There is widespread agreement that systematic risk drives returns.  You can measure systematic risk in several different ways depending on the asset pricing model you choose.  The CAPM is still widely used in practice in both corporate finance and investment-oriented professions.