Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 24%. 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?

The maximum level of risk aversion for which the risky portfolio is still preferred to T-bills must be LESS THAN 3.09

Explanation:

Denote utility as U; r as rate of return; A as risk aversion and σ as standard deviation.

Then take U = E(r) - 0.5Aσ² as Equ. (1)

this makes the utility level for T-bills to be 0.07

To get the utility level for the risky portfolio,

Substitute data into Equ. (1),

U = 12% - 0.5 × A × (24% - 6%)²

U = 0.12 - 0.0162 × A

U = 0.12 - 0.0162A

For the risky portfolio to be preferred to bills, these conditions must be fulfilled:

(1). 0.12 - 0.0162A MUST BE GREATER THAN 0.07

(2). The risk aversion, A, MUST BE LESS THAN 0.05/0.0162 = 3.09

Therefore, the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills must be LESS THAN 3.09

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