Assume the risk-free rate is 1% (rf = 1%), the expected return on the market portfolio is 5% (E[rM] = 5%) and the standard deviation of the return on the market portfolio is 15% (σM = 15%). (All numbers are annual.) Assume the CAPM holds

a. What are the portfolio weights (in the risk-free asset and the market portfolio) for efficient portfolios (portfolios on the efficient frontier/CML) with expected returns of

(i) 4%

(ii) 5%

(iii) 7%

b. What are the portfolio weights (in the risk-free asset and the market portfolio) for efficient portfolios (portfolios on the efficient frontier/CML) with standard deviations of

(i) 6%

(ii) 15%

(iii) 21%

c. For a moment (but just a moment) assume that the CAPM may not hold. A non-dividend paying stock has a current price of $50/share and an expected price in 1 year of

$53/share (based on your personal analysis of the company’s prospects).

(i) If the stock has a beta of 1 (β = 1.0), what is its alpha (α)?

(ii) What is the alpha (α) if the beta is 2 (β = 2.0)?