An investor is indifferent between investing 30% and 120% in a risky portfolio w

Question

An investor is indifferent between investing 30% and 120% in a risky portfolio with E(r)=12% and standard deviation of 25%  and a risk free T-bill yielding 3%. What is the investors risk aversion?

Assume that you manage a fund with an expected rate of return of 9% and a standard deviation of 21%. The T-bill rate is 3%. Suppose your client would like to split her investment between your fund and T-bills so that she earns 12%. How much standard deviation does she need to take? (Provide your answer in percent rounded to two digits, omitting the % sign.)

Explanation / Answer

U=E(r)-0.5*A*variance
Utility should be equal to be indifferent:
30%*12%+70%*3%-0.5*A*(30%*25%)^2=120%*12%-20%*3%-0.5*A*(120%*25%)^2
=>A=1.92

E(r)=12%
=y*9%+(1-y)*3%=12%
=>y=1.5

Hence, standaard deviation=1.5*21%=31.5%

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