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?
