Question

An investor has the utility function

U=E[r]−A2σ2.

A portfolio has an expected rate of return of 18.5% and a standard deviation of 0.15. The risk-free rate is 6%. Which value of A (risk aversion) makes this investor indifferent between the risky portfolio and the risk-free asset?

Round your answer to 2 decimal places.

Answer 1

Expected Return of Risky portfolio = 18.5%

Standard deviation of Risky portfolio = 0.15

Risk free rate = 6%

Utility of Risky Portfolio = E(r) - 1/2 A * σ^2

= 18.5% - 1/2 * A * (0.15)^2

= 0.185 - 0.01125 * A

Utility of Risk Free Asset = E(r) - 1/2 A * σ^2

= 6% - 1/2 * A * 0^2

= 0.06

Utility of Risky Portfolio = Utility of Risk free asset

0.185 - 0.01125*A = 0.06

0.01125*A = 0.125

A = 11.111111

Therefore, Value of A is 11.11