Question

Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 25%. T-bills offer a risk free return rate of What is the maximum level of risk aversion for which the risky portfolio is still preferred to Tbilis? (Do not round Intermediate calculations. Round your answer to 2 decimal places) Som

Answer 1

Utility Formula: U = E(r) – 0,5 x A x σ²

where, E(r) = Expected Return ;=12%

σ² = Standard Deviation;= 25%

A = Risk Aversion Coefficient

Since standard deviation of T-bills is 0.

Utility for T-bills:-

Utility = 0.07 - 0.5A(0)²

= 0.07 - 0

= 0.07

Utility for portfolio:-

Utility = 0.12 - 0.5A(0.25)²

= 0.12 - 0.03125A

Setting the utility values of T-bills & portfolio equal and calculating A:

0.07 = 0.12 - 0.03125A

0.03125A = 0.05

A = 1.6

So, risk aversion(A) more than 1.6 means an investor would derive less utility from the risky portfolio and vice-versa.

Therefore, risk aversion (A) must be less than 1.6 for the risky portfolio to be preferred to T-bills.

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