Question 1

In this question, all financial assets are described by the CAPM. Suppose the

market portfolio M has (stochastic) return rM and variance sM. Consider two

portfolios A and B, with (stochastic) returns rA and rB respectively. Let rF denote the

risk free rate.

a) Let RA = E[rA] rF denote the excess return of portfolio A, and similarly for portfolio

B. Show that in the CAPM equilibrium the ratio of the excess returns RA / RB is equal

to the ratio of their covariances with the market portfolio, cov(rA,rM) / cov(rB,rM).

Interpret in terms of a risk/return trade-off. (Hint: rearrange the terms in the betaexpected

return condition that characterizes the CAPM equilibrium.)

(9 marks)

b) Suppose there is a recession and the market expected return E[rM] falls by a

factor of two, E[rM]= E[rM]/2.

Assume the risk free rate rF and A and B remain constant and denote the new

equilibrium expected return of portfolio A by E[rA].

What is E[rA]/E[rA] equal to?

Show that portfolio A falls more than the market (that is E[rA]/E[rA]<1>1,

and falls less than the market (that is E[rA]/E[rA]>1/2) if A <1.

Interpret in terms of sensitivity to the market. (8 marks)

c) Suppose that E[rA] = 5%, E[rB] = 15%. If the risk free rate is rF=3%, compute the

ratio A/B, that is, how more sensitive to the market is portfolio B than portfolio A.

If rF increases and approaches rA=5%, what happens to the ratio A/B? Interpret.