The McAlhany Investment Fund has total capital of $500 million invested in 5 sto
ID: 2667125 • Letter: T
Question
The McAlhany Investment Fund has total capital of $500 million invested in 5 stocks: Stock
Investment Beta
A $160,000,000 0.50
B 120,000,000 2.0
C 80,000,000 4.0
D 80,000,000 1.0
E 60,000,000 3.0
The current risk-free rate is 8 percent, whereas market returns have the following
estimated probability distribution for the next period:
Probability Market return
0.1 10%
0.2 12
0.4 13
0.2 16
0.1 17
a. Compute the expected return for the market.
b. Compute the beta coefficient for the investment fund.
c. What is the estimated equation for the Security Market Line?
d. Compute the fund’s required rate of return for the next period
Explanation / Answer
According to the given information, Risk-free rate (Rf) = 8% We need to find the beta co-efficient of the fund that is the portfolio beta.Also we have to calculate the Expected market return using the probabilities and the market returns. a) Computing the expected rate of return for the market: E(Rm) = (0.1 * 0.10) + (0.2 * 0.12) + (0.4 * 0.13) + (0.2 * 0.16) + (0.1 * 0.17) = 0.01 + 0.024 + 0.052 + 0.032 + 0.017 = 0.135 or 13.5% Therefore, the expected market return is 13.5% b) Computing the beta co-efficient for the investment fund: To compute the beta, we need to find the weights of each stock in the investment fund. Weight of stock-A = $160 / $500 = 0.32 or 32% Weight of stock-B = $120 / $500 = 0.24 or 24% Weight of stock-C = $80 / $500 = 0.16 or 16% Weight of stock-D = $80 / $500 = 0.16 or 16% Weight of stock-E = $60 / $500 = 0.12 or 12% The formula for calculating the portfolio beta is p = (Wa * a) + (Wb * b) + (Wc * c) + (Wd * d) + (We * e) = (0.32 * 0.50) + (0.24 * 2.0) + (0.16 * 4.0) + (0.16 * 1.0) + (0.12 * 3.0) = 0.16 + 0.48 + 0.64 + 0.16 + 0.36 = 1.8 Therefore, the beta co-efficient of the investment fund is 1.8 c) The estimated equation of the SML is Re = Rf + [E(Rm) - Rf] where Re is the require rate of return Rf is the risk-free rate of return is the beta co-efficient E(Rm) is the expected market return [E(Rm) - Rf] is the market risk premium d) Computing the required rate of return using the SML equation. Re = 0.08 + 1.8 [ 0.135 - 0.08] = 0.08 + 1.8 [ 0.055] = 0.08 + 0.099 = 0.179 or 17.9% Therefore, the required rate of return for the investment fund is 17.9%Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.