Finance

Finance Homework 3 Question 1 The Betas of four stocks in a perfect capital market are as follows: ??A = -1 ??B = 0 ??C = 1 ??D = 2 Assume that the market is in equilibrium, that the returns on the risk-free asset is 6% and that the expected return on the “market portfolio” is 14%. Calculate the expected returns on shares A, B, C and D. Question 2 Assume a perfect capital market in which investors are constrained to holding portfolios that consist only of a single risky asset, that borrowing or lending at a riskless interest rate is possible, and that in equilibrium the following relationship between two risky securities i and j holds: Security i Security j Exp. ret. (%) 26 18 Standard Dev. (%) 15 9 (a) What is the riskless rate of interest in this market? (Hint: in equilibrium under the above conditions both securities must lie on the same market line). (b) If the investor wishes to hold a portfolio with a standard deviation of only 6%, what should be his investment strategy? (c) What would his investment strategy be if he wanted to reach an expected return of 24%? Question 3 Assume a perfect capital market in which investors are constrained to holding portfolios that consist of a single risky asset and the riskless asset. In equilibrium the following relationship between two risky securities i and j holds: Security i Security j Exp. ret. (%) 18 25 Standard Dev. (%) 8 12 (a) What is the rate of interest in this market? (b) Assume that the investor is confronted with two mutually exclusive alternatives: A portfolio of $900 worth of stock i: A portfolio of $600 worth of stock j plus $300 worth of the riskless asset. Which of the two alternatives is preferable? Question 4 There are three stocks in the market and the CAPM holds. The parameters of the stocks are as follows: A B C ri 15% 20% 30% ??I 1/2 1 ? What should be ??3 such that the CAPM holds? What is the mean rate of return on the market portfolio? What is the risk-free interest rate? Question 5 The following describes the mean return and betas of DuPont, Dow Chemical and Union Carbide: DuPont DowChemical UnionCarbide ri 4.6% 10% 30% ??I .86 .74 .71 Determine the arbitrage portfolio with zero investment and a zero beta. Is there room for arbitrage profit?