Calculating Portfolio Betas. You own a stock portfolio invested 15 percent in Stock Q, 25 percent in Stock R, 40 percent in Stock S, Stock T. The betas for these four stocks are .85, .91, 1.31, and 1.76, respectively. What is the portfolio beta? The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is:
11d92730123ada7b4bb9f30a172d8ab0071db287.xlsx Using CAPM A stock has a beta of 1.15, the expected return on the market is 10.9 percent, and the risk-free rate is 3.8 percent. The CAPM states the relationship between the risk of an asset and its expected return. The CAPM is Substituting the values we are given, we find: 3.80% + ( 10.9% - 3.80% ) ( 1.15 ) 7.100% 1.15 E(R i ) = R f + [E(R M ) – R f ] × b i E( R i ) = .038 + (.1090 – .038)(1.15) E( R i ) = .1197, or 11.97%
11d92730123ada7b4bb9f30a172d8ab0071db287.xlsx Page 8 PROBLEM 14 Using CAPM. A stock has an expected return of 13.6 percent, the risk-free rate is 3.7percent, and the market risk premium is 7.1 percent. What must the beta of this One important thing we need to realize is that we are given the market risk premium. The market risk premium is the expected return of the market minus the risk-free rate. We must be careful not to use this value as the expected return of the market. Using the CAPM, we find: 13.6% = 3.70% + 7.10% bi - -3.70% = 9.900% / 7.10% 1.394366 We are given the values for the CAPM except for the b of the stock. We need to substitute these values into the CAPM, and solve for the b of the stock. E( R i ) = R f + [E( R M ) – R f ] × b i .136 = .037 + .071 b i b i = 1.394
11d92730123ada7b4bb9f30a172d8ab0071db287.xlsx Using CAPM A stock has an expected return of 12.50 percent and a beta of 1.15, and the expected return on the market is 11.5 percent. What must the risk-free r Here, we need to find the risk-free rate, using the CAPM. Substituting the values given, and solving for the risk-free rate, we find: 11.5% 1.15 13.225% 12.500% -0.725% -0.15 4.83% E( R i ) = R f + [E( R M ) – R f ] × b i .1250 = R f + (.1150 – R f )(1.15) .1250 = R f + .13225 – 1.15 R f R f = .0483, or 4.83%
11d92730123ada7b4bb9f30a172d8ab0071db287.xlsx Reward-to-Risk Ratios. Stock Y has a beta of 1.25 and an expected return of 12.6 percent. Stock Z has a beta of .8 and an expected return of 9.9 percent. If th risk-free rate is 4.1 percent and the market risk premium is 7 percent, are these stocks correctly priced? 7.00% x 1.25 8.75% 4.10% 12.85% For Stock Z, we find: 7.00% x 0.8 5.60% 4.10% 9.70% Reward-to-risk ratio Y = (.126 – .041) / 1.25 Reward-to-risk ratio Y = .0680 Reward-to-risk ratio Z = (.099 – .041) / .80 Reward-to-risk ratio Z = .0725 There are two ways to correctly answer this question. We will work through both. First, we can use the CAPM.
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