Question

Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 22%. T-bills offer a risk-free 5% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Utility for T-bills is:

U =E(r) – 0.5Aσ²= 0.05 - 0.5A(0)²= 0.05

Utility for the risky portfolio: U =E(r) – 0.5Aσ2= 0.12 - 0.5A(0.22)² = 0.12 - 0.0242A

Set the Utility values equal and solve for A:

0.12 – 0.0242A = 0.05

A = 0.07/0.0242 = 2.89

For A = 2.89, the investor would be indifferent between the risky portfolio with E(r) = 12% and σ = 22% and the risk-free rate of 5%.

Therefore the risk-aversion parameter (A) must be less than 2.89 for the risky portfolio to be preferred to T-Bills.