see attachment for Q's[5]

from an investments course

PROBLEM SET 2 - Solution F2016 Show your work for all problems. 1. Bond portfolio, D, and stock portfolio, E, lie on the minimum variance frontier. Portfolio, P is the tangency portfolio for the best capital allocation line. We know: ER E 13% 12% D 8% 7% 2/3 P 11% a) If the correlation between E and D equals 15%, what are the weights of E and D that form portfolio P? b) What is the standard deviation of portfolio P? c) If the CAPM holds, what must be the risk-free rate, RF? 2. Your firm has made the following forecasts: ERD ERE ERM Probability = 30% 0.03 -0.06 0.04 Probability = 70% 0.09 0.30 0.12 a) What is the expected return for the market portfolio, M? b) If the risk-free bond is paying 4%, what are the betas of stock X and Y? 3. The forecast return for the market portfolio is 11% and the risk-free rate is 4%. a) What rate of return would be expected for a stock with beta = 0.25? b) Currently priced at $55, you forecast the stock's price to be $58.59 in two years. An annual dividend of $1 is expected at the end of each of the next two years. Given the stock's beta, is it currently over- or under-priced? 1 PROBLEM SET 2 - Solution F2016 4. The following have been estimated: ER Firm-Specific Total Big stock 11% 21% 30% 0.95 Small stock 16% 45% 1.5 RF 5% a) What are the total risks (i.e. ) of the Market portfolio and of Small stock? b) Suppose portfolio C has weights of 1/3, 1/2 and 1/6 in Big stock, Small stock and RF, respectively. Show calculations for C of: ER, non-systematic risk, systematic risk, and beta. 5. A bond with a face value of $1,000 pays semi-annual coupons, at a coupon rate of 5%. Originally issued at par, the bond now has 8 years until maturity. a) Today similar bonds are yielding 9%. What is the price this bond? b) Whichever bond you buy today, you plan to sell one year from now. You forecast that market rates will fall to from 9% to 7.6% shortly before you sell. What before- tax holding period return do you expect? c) Suppose your marginal tax rates are 32% for regular income and 16% for capital gains. What after-tax holding period return do you expect? 2