Question

An investor having a risk aversion coefficient (A) equal to 1.5 is considering three portfolios of varying ris as shown in the table below. Assuming a risk-free rate equal to 4%, which statement below is CORRECT? Investment Table Portfolio Return Volatility Sharpe Ratio Low Risk 7% 10% 0.30 Medium Risk 10% 20% 0.30 High Risk 13% 30% 0.30 Utility of High Risk Portfolio = 6.25% Of the three portfolios, the Medium Risk portfolio provides the highest utility to the investor. Of the three portfolios, the Low Risk portfolio provides the highest utility to the investor. The investor would have the same preference (i.e. utility) for the high and low risk portfolios Of the three portfolios, the High Risk portfolio provides the highest utility to the investor. All three portfolios provide the same utility to the investor since they all have the same Sharpe ratio and lie on the Capital Allocation Line (CAL)

Answer 1

Using Utility theory,

Utility E(R 0.5 A* o

where,

E(R) is the expected return on the portfolio

A is the risk aversion coefficient - higher the value more risk-averse the investor is

$\sigma^{2}$ is the variance (volatility) of the portfolio

Calculating the utility,

for low risk portfolio,    = 6.25%

U0.07 0.5 1.50.12=0.0625

for medium risk portfolio,    = 7.00%

UI 0.1 0.5 1.5 0.22 - 0.07

for high risk portfolio,   = 6.25%

U 0.13 0.5 1.5 0.32 0.0625

Correct Answers are:

Of the three portfolios, the Medium Risk portfolio provides the highest utility to the investor.

The investors would have same utility for the high and low-risk portfolios.