Question
Mikkelson Corporation's stock had a required return of 13.50% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Then an increase in investor risk aversion caused the market risk premium to rise by 2%. The risk-free rate and the firm's beta remain unchanged. What is the company's new required rate of return? (Hint: First calculate the beta, then find the required return.) ?Answer
a. 20.58%
b. 16.19%
c. 16.36%
d. 16.87%
e. 15.52%
Company A has a beta of 0.70, while Company B's beta is 1.30. The required return on the stock market is 11.00%, and the risk-free rate is 4.25%. What is the difference between A's and B's required rates of return? (Hint: First find the market risk premium, then find the required returns on the stocks.) ?Answer
a. 3.73%
b. 4.90%
c. 4.74%
d. 3.60%
e. 4.05%
? Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What is the standard deviation of the company’s expected stock return?
.
.Economic Conditions . Prob. . Return
Strong 30% 34.0%
Normal 40% 10.0%
Weak . 30% -16.0%
.
?Answer
a. 20.92%
b. 19.37%
c. 15.88%
d. 21.89%
e. 22.28%
? Assume that you are the portfolio manager of the SF Fund, a $3 million hedge fund that contains the following stocks. The required rate of return on the market is 11.00% and the risk-free rate is 5.00%. What rate of return should investors expect (and require) on this fund?
Amount . Beta
Stock A . $825,000 . 1.20
Stock B . $675,000 . 0.50
Stock C . $1,000,000 . 1.40
Stock D . $500,000 . 0.75
$3,000,000 .
.
. ?Answer
a. 12.21%
b. 10.64%
c. 9.30%
d. 11.21%
e. 10.87%
Explanation / Answer
a) According to CAPM: Re = Rf + [E(Rm) - Rf] * Beta Where Rf is the risk-free rate Re is the required rate of return E(Rm) - Rf is the market risk premium Calculating the beta value before increase in market risk premium. 0.1350 = 0.055 + 0.0475 * Beta 0.08 = 0.0475 * Beta Beta = 1.68 Calculating the new required rate of return: Re = 0.055 + 0.0675 * 1.684 = 0.1687 or 16.87% Therefore, the correct option is c) 16.87% b) Calculating the market risk premium: E(Rm) - Rf = 0.11 - 0.0425 = 0.0675 or 6.75% Calculating the required return for Company A: Re = 0.0425 + 0.0675 * 0.70 = 0.08975 or 8.975% Calculating the required return for Company B: Re = 0.0425 + 0.0675 * 1.30 = 0.13025 or 13.025% Difference in the required rate of return is (13.025 - 8.975 ) 4.05% Therefore, the correct option is e) 4.05% c) Calculating the Expected return : E(Rp) = 0.3 * 0.34 + 0.4 * 0.1 + 0.3 * (-0.16) = 0.102 + 0.04 - 0.048 = 0.094 or9.4% Squared deviation from expected return: 0.3 * (0.34 - 0.094)^2 + 0.4 * (0.1 - 0.094)^2 + 0.3 * (-0.16 - 0.094)^2 0.018 + 0.0000144 + 0.01935 = 0.03736 Portfolio variance = 0.03736 Portfolio standard deviation = 0.1937 or 19.37% Therefore, the correct option is b) 19.37% d) Calculating the weight of each stock: StockA: $825,000 / $3,000,000 = 0.275 or 27.5% StockB: $675,000 / $3,000,000 = 0.225 or 22.5% StockC: $1,000,000 / $3,000,000 = 0.33 or 33% StockD: $500,000 / $3,000,000 = 0.17 or 17% Calculating the portfolio beta: POrtfolio beta = 0.275 * 1.20 + 0.225 * 0.50 + 0.33 * 1.40 + 0.17 * 0.75 = 0.33 + 0.1125 + 0.462 + 0.1275 = 1.032 Calculating the portfolio expected return using CAPM: Rp = Rf + [E(Rm) - Rf] * Beta = 0.05 + [0.11 - 0.05] * 1.032 = 0.05 + 0.06192 = 0.11191 or 11.21% Therefore, the correct option is d) 11.21% Calculating the required return for Company B: Re = 0.0425 + 0.0675 * 1.30 = 0.13025 or 13.025% Difference in the required rate of return is (13.025 - 8.975 ) 4.05% Therefore, the correct option is e) 4.05% c) Calculating the Expected return : E(Rp) = 0.3 * 0.34 + 0.4 * 0.1 + 0.3 * (-0.16) = 0.102 + 0.04 - 0.048 = 0.094 or9.4% Squared deviation from expected return: 0.3 * (0.34 - 0.094)^2 + 0.4 * (0.1 - 0.094)^2 + 0.3 * (-0.16 - 0.094)^2 0.018 + 0.0000144 + 0.01935 = 0.03736 Portfolio variance = 0.03736 Portfolio standard deviation = 0.1937 or 19.37% Therefore, the correct option is b) 19.37% d) Calculating the weight of each stock: StockA: $825,000 / $3,000,000 = 0.275 or 27.5% StockB: $675,000 / $3,000,000 = 0.225 or 22.5% StockC: $1,000,000 / $3,000,000 = 0.33 or 33% StockD: $500,000 / $3,000,000 = 0.17 or 17% Calculating the portfolio beta: POrtfolio beta = 0.275 * 1.20 + 0.225 * 0.50 + 0.33 * 1.40 + 0.17 * 0.75 = 0.33 + 0.1125 + 0.462 + 0.1275 = 1.032 Calculating the portfolio expected return using CAPM: Rp = Rf + [E(Rm) - Rf] * Beta = 0.05 + [0.11 - 0.05] * 1.032 = 0.05 + 0.06192 = 0.11191 or 11.21% Therefore, the correct option is d) 11.21%