Someone who believes that the collection of all stocks satisfies a single-factor

Question

Someone who believes that the collection of all stocks satisfies a single-factor model with the market portfolio serving as the factor gives you information on three stocks which make up a portfolio. In addiction, you know that the market portfolio has an expected rate of return of 12% and a standard deviation of 18% The risk-free rate is 5%.

a. What is the portfolio's expected rate of return?

b. Assuming the factor model is accurate, what is the stadard deviation of the rate of return?

For stock A: Beta = 1.1, standard deviation of random error term = 7% and the weight in portfolio = 20%

For stock B: Beta= .80, standard deviation of random error term = 2.3% and the weight in portfoilio = 50%

For stock C: Beta = 1.0, standard deviation of random error term= 1.0% and the weight in portfolio = 30%

I will only give out full points to whomever answers both parts a and b!!

Explanation / Answer

a. Expected return for Stock A = 5%+1.1*(12%-5%) = 12.7%

Expected return for Stock B = 5%+0.8*(12%-5%) = 10.6%

Expected return for Stock C = 5%+1*(12%-5%) = 12%

portfolio's expected rate of return = (WA)*rA+ (WB)*rB + (WC)*rC = 20%*12.7% + 50%*10.6% + 30%*12% = 11.44%

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