The Security Market Line (SML) The relevant risk measure for an individual risky asset is its covariance with the market portfolio (Covi,m) This is shown as the risk measure The return for the market portfolio should be consistent with its own risk, which is the covariance of the market with itself - or its variance:

Graph of Security Market Line (SML) Exhibit 8.5 Graph of Security Market Line (SML) SML RFR

The Security Market Line (SML) The equation for the risk-return line is We then define as beta

Graph of SML with Normalized Systematic Risk Exhibit 8.6 Graph of SML with Normalized Systematic Risk SML Negative Beta RFR

How is market risk measured for individual securities? Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio. It is measured by a stock’s beta coefficient, which measures the stock’s volatility relative to the market. 34

Definition of Risk When Investors Hold the Market Portfolio Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (b)of the security. Beta measures the responsiveness of a security to movements in the market portfolio.

How are betas calculated? Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis. The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b. Analysts typically use four or five years’ of monthly returns to establish the regression line. Some use 52 weeks of weekly returns. 35

Estimating b with regression Characteristic Line Security Returns Slope = bi Return on market % Ri = a i + biRm + ei

Use the historical stock returns to calculate the beta for XYZ. Year Market XYZ 1 25.7% 40.0% 2 8.0% -15.0% 3 -11.0% 4 15.0% 35.0% 5 32.5% 10.0% 6 13.7% 30.0% 7 42.0% 8 -10.0% 9 -10.8% -25.0% 10 -13.1% 25.0% 35

Calculating Beta for KWE XYZ = 0.83R M + 0.03 2 = 0.36 -40% -20% 0% 20% 40%

How is beta interpreted? If b = 1.0, stock has average risk. If b > 1.0, stock is riskier than average. If b < 1.0, stock is less risky than average. Most stocks have betas in the range of 0.5 to 1.5. Example of CAPM with 3 Stocks? 39

Determining the Expected Rate of Return for a Risky Asset Assume: RFR = 6% (0.06) RM = 12% (0.12) Implied market risk premium = 6% (0.06) E(RA) = 0.06 + 0.70 (0.12-0.06) = 0.102 = 10.2% E(RB) = 0.06 + 1.00 (0.12-0.06) = 0.120 = 12.0% E(RC) = 0.06 + 1.15 (0.12-0.06) = 0.129 = 12.9% E(RD) = 0.06 + 1.40 (0.12-0.06) = 0.144 = 14.4% E(RE) = 0.06 + -0.30 (0.12-0.06) = 0.042 = 4.2%

Determining the Expected Rate of Return for a Risky Asset In equilibrium, all assets and all portfolios of assets should plot on the SML Any security with an estimated return that plots above the SML is underpriced Any security with an estimated return that plots below the SML is overpriced

Price, Dividend, and Rate of Return Estimates

Comparison of Required Rate of Return to Estimated Rate of Return

Plot of Estimated Returns on SML Graph .22 .20 .18 .16 .14 .12 Rm .10 .08 .06 .04 .02 C SML A E B D -.40 -.20 .20 .40 .60 .80 1.20 1.40 1.60 1.80

The Effect of the Market Proxy The market portfolio of all risky assets must be represented in computing an asset’s characteristic line Standard & Poor’s 500 Composite Index is most often used Large proportion of the total market value of U.S. stocks Value weighted series

Weaknesses of Using S&P 500 as the Market Proxy Includes only U.S. stocks The theoretical market portfolio should include U.S. and non-U.S. stocks and bonds, real estate, coins, stamps, art, antiques, and any other marketable risky asset from around the world