The CAPM Class 11 Financial Management, 15.414MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Today The CAPM • Measuring risk • Systematic vs. diversifiable risk • The trade-off between risk and return Reading • Brealey and Myers, Chapter 8.2 – 8.5MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Review Diversification Diversification reduces risk, as long as stocks aren’t perfectly correlated with each other. Portfolio variance depends primarily on the covariances among stocks, not the individual variances. Risk common to all firms cannot be diversified away. Investors should try to hold portfolios that maximize expected return for a given level of risk. The tangency portfolio is the best portfolio. 3MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Diversification 12% 10% 8% 6% 4% 2% 0% Std dev of portfolio If correlation = 1.0 If correlation = 0.4 If correlation = 0.0 1 112131415161718191 Number of stocks 4MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Optimal portfolios Mean 2.4% 1.8% 1.2% 0.6% 0.0% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% Tangency portfolio Riskfree asset GM IBM Motorola Efficient frontier Std dev 5MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 The CAPM Capital Asset Pricing Model Stock prices are affected by firm-specific and marketwide risks. Investors care only about risk that is non-diversifiable. A stock’s non-diversifiable risk is measured by beta, the slope when the stock is regressed on the market: Ri = α + β RM + ε Expected, or required, returns are a linear function of betas: E[Ri] = rf + βi E[RM – rf] Market risk premium For example, a stock with β = 2 is twice as risky as the market, so investors require twice the risk premium. 6MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 CAPM: Security Market Line 0% 5% 10% 15% 20% 25% Stock's expected return Slope = E[RM] – rf β = 1.5 β = 0.5 β = 0 Market portfolio (β = 1) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Stock's beta 7MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Beta Regression slope How sensitive is the stock to overall market movements? How much does the stock go up or down when other stocks go up or down? Ri = α + β RM + ε ε = firm-specific return (‘diversifiable,’ ‘idiosyncratic,’ or ‘unsystematic’ risk) β = sensitivity to market returns (‘systematic,’ ‘non-diversifiable,’ or ‘macroeconomic’ risk) R2 = explained variance (fraction of variance explained by market returns) 8MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Regressions in Excel 9MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Gillette vs. Total U.S. market return -20% -15% -10% -5% 0% 5% 10% 15% 20% -20% -15% -10% -5% 15% Monthly returns β = 0.81 R2 = 0.19 0% 5% 10% 20% 10MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 NASDAQ vs. Total U.S. market return -20% -15% -10% -5% 0% 5% 10% 15% 20% -20% -15% -10% -5% 10% 15% 20% Monthly returns β = 1.57 R2 = 0.77 0% 5% 11MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Betas, 1960 – 2001 Size-sorted portfolios 1960 – 1979 Decile β R21980 – 2001 Decile β R2 Smallest 1.58 0.60 Smallest 1.27 0.49 2 1.45 0.76 2 1.25 0.72 3 1.45 0.81 3 1.26 0.75 4 1.36 0.84 4 1.22 0.79 5 1.32 0.86 5 1.18 0.80 6 1.27 0.90 6 1.13 0.85 7 1.22 0.92 7 1.09 0.89 8 1.16 0.95 8 1.04 0.91 9 1.05 0.96 9 1.02 0.95 Largest 0.92 0.97 Largest 0.96 0.97 12MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 CAPM Key insight For a diversified investor, beta measures a stock’s contri-bution to portfolio risk. Beta, not variance, is the appropriate measure of risk. The required return on a stock equals: E[Ri] = rf + βi E[RM – rf] 13MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Security Market Line 0% 5% 10% 15% 20% 25% Stock's expected return Slope = E[RM] – rf β = 1.5 β = 0.5 β = 0 Market portfolio (β = 1) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Stock's beta 14MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Example 1 Using monthly returns from 1990 – 2001, you estimate that Microsoft has a beta of 1.49 (std err = 0.18) and Gillette has a beta of 0.81 (std err = 0.14). If these estimates are a reliable guide for their risks going forward, what rate of return is required for an investment in each stock? E[Ri] = rf + βi E[RM – rf] Tbill rate = 1.0%; market risk premium is around 4 – 6%. Expected returns Gillette: E[RGS] = 0.01 + (0.81 × 0.06) = 5.86% Microsoft: E[RMSFT] = 0.01 + (1.49 × 0.06) = 9.94% 15MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Example 2 Over the past 40 years, the smallest decile of firms had an average monthly return of 1.33% and a beta of 1.40. The largest decile of firms had an average return of 0.90% and a beta of 0.94. Over the same time period, the riskfree rate averaged 0.43% and the market risk premium was 0.49%. Are the average returns consistent with the CAPM? E[Ri] = rf + βi E[RM – rf] Tbill rate = 0.43%; market risk premium is 0.49%. How far are average returns from the CAPM security market line? 16MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Size portfolios, 1960 – 2001 Average returns vs. CAPM Avg CAPM Decile return β rf + βi E[RM – rf] Difference Smallest 1.33 1.40 1.15 0.19 2 1.06 1.33 1.11 -0.06 3 1.13 1.34 1.12 0.01 4 1.14 1.28 1.09 0.05 5 1.14 1.24 1.07 0.07 6 1.10 1.19 1.04 0.06 7 1.04 1.14 1.02 0.02 8 1.10 1.09 0.99 0.11 9 1.00 1.03 0.97 0.03 Largest 0.90 0.94 0.93 -0.03 Difference = Avg. return – CAPM prediction 17MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Size portfolios, 1960 – 2001 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 Return 0.70 0.90 1.10 1.30 1.50 1.70 Beta 18MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Example 3 You are choosing between two mutual funds. Over the past 10 years, BlindLuck Value Fund had an average return of 12.8% and a β of 0.9. EasyMoney Growth Fund had a return of 17.9% and a β of 1.3. The market’s average return over the same period was 14% and the Tbill rate was 5%. Which fund is better? CAPM Portfolio Avg return β rf + βi E[RM – rf] Dif Market 14.0% 1.0 BlindLuck 12.8 0.9 13.1 -0.30 EasyMoney 17.9 1.3 16.7 1.20 [‘Dif’ is referred to as the fund’s ‘alpha’] 19MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 Example 3 Market 0% 6% 12% 18% 24% Avg return Easy Money Blind Luck 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Beta 20MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 11 CAPM Applications Measures and quantifies