Question

An investor’s utility function for expected return and risk is U = E(r) − 4σ2. Which of the following would this investor prefer to invest in:

• A risk-free security offering a return of 8 percent per year
• A risky portfolio with expected return of 14 percent per year and standard deviation of 25 percent
  per year

Select one:

a. Risk-free security

b. Risky portfolio

Answer 1

Risk free Security

E(r) = 8%

standard deviation for a risk free security is 0 i.e., σ = 0

Therefore, investors utility from risk-free security is

U_risk-free = E(r)-4*σ² = 8% - 0 =8%

Risky portfolio

E(r) = 14%, σ = 25%

U_{risky portfolio} = E(r)-4*σ² = 14% - (4*0.25²) = 14% - 0.25 = -11%

Utility is maximum for Risk-free security, so investor should prefer Risk-free security