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?