Question

4. Using the popular Utility function U=E(r) - 0.5*A*Variance(r), what is the utility for an investor with risk-aversion index of 3, whose portfolio has an expected return of 7% and a standard deviation of 16%?

Report 2 decimals in your answer

6. South Park Company's stock has an expected Return of 6.56% while Quahog Company's stock has an expected return of 3.8%. What % of my wealth should I invest in Quahog Company's stock to have an expected return of 10.86%? Report you answer as a % with 2 decimals. If your answer is 3.56%, just enter/type "3.56"

Answer 1

Given:

Risk-Aversion Index = A = 3

Expected Return = E(R) = 7% = 0.07

Standard Deviation = (Variance)^1/2 = 16% = 0.16

To Find: Utility for an investor

Solution:

U = E(r) - 0.5 * A * Variance(r) = E(r) - 0.5 * A * (Standard Deviation)²

U = 7% - 0.5 * 3 * (16%)²

U = 0.0316 = 3.16%