Question

Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 21%. T-bills offer a risk-free 6% 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

When we specify utility by U = E(r) - 0.5Aσ2, the utility level for T-bills is:

The utility level for the risky portfolio is:

U = 0.12 - 0.5 × A × (0.21)2 = 0.12 - 0.02205× A

In order for the risky portfolio to be preferred to bills, the following must hold:

0.12 - 0.02205A > 0.06⇒ A < 0.06/0.02205= 2.72

A must be less than 2.72 for the risky portfolio to be preferred to bills.