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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.)
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]<1/2) if ?A >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.
Paper#9210901 | Written in 27-Jul-2016Price : $19