Question

Question 20 5 pts An investor having a risk aversion coefficient (A) equal to 1.5 is considering three portfolios of varying risk and return 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 lowest utility to the investor The investor would have the same preference (ie, utility) for the high and medium risk portfolios The investor would have the same preference (i.e. utility) for the high and low risk portfolios. All three portfolios provide the same utility to the investor since they all have the same Sharpe ratio and lle on the Capital Allocation Line CAD The investor would have the same preference de utility for the low and medium rik portfolios

Answer 1

Correct: The investor would have the same preference (i.e utility) for the high and low risk portfolios.

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

ДА B C D E Risk Aversion Coefficient Return | Sharpe Ratio 0.30 Portfolio Low Risk Medium Risk High Risk 7% 10% 13% Volatility 10% 20% 30% Utility 6.25% 7.00% 6.25% 0.30 0.30

Cell reference -

A B C D E Risk Aversion Coefficient 1.5 Nm toro Portfolio Low Risk Medium Risk High Risk Return Volatility Sharpe Ratio 0.07 0.1 0.3 0.1 0.2 0.3 0.13 0.3 0.3 Utility =C6-0.5*$C$2*D642 =C7-0.5*$C$2*D742 =C8-0.5*$C$2*D8^2 9 11

Please note: Investor utility can be computed with following utility function:

U = E(R) – 0.5* A* 02

where,

U = Utility

E(R) = Expected Return

A = Risk Aversion Coefficient

$\large \sigma =$ Volatility

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.