Consider a portfolio that offers an expected rate of return of 11% 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?

The  level of risk aversion must be less than 2.27 for the risky portfolio to be preferred to bills.

Explanation:

Let U presents utility level. Therefore, we can specify U as follows:

U = E(r) - (0.5 * A * SD^2) (1)

Where, risky portfolio, we have:

E(r) = expected rate of return = 11%, or 0.11

SD = Standard deviation = 21%, or 0.21

A = Level of risk aversion = ?

Substituting the values into equation (1), we have:

U of risky portfolio = 0.11 - (0.5 * A * 0.21^2)

U of risky portfolio = 0.11 - (A * 0.02205)

Since the T-bills offer a risk-free 6% rate of return, it therefore implies that:

U of T-bill = 6%, 0.06

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

U of risky portfolio > U of T-bill (2)

Substituting the values for the expression above and solve for A, we have:

0.11 - (A * 0.02205) > 0.06

-(A * 0.02205) > 0.06 - 0.11

-(A * 0.02205) > - 0.05

Divide through by -1 and change the inequality sign, we have:

A * 0.02205 < 0.05

A < 0.05 / 0.02205

A < 2.27

Therefore, the  level of risk aversion must be less than 2.27 for the risky portfolio to be preferred to bills.

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