Question

12. An investor invests 40% of his wealth in a risky asset with an expected rate of return of 15% and a variance of 0.04 and 60% in a treasury bill that pays 6%. Her portfolio's expected rate of return is and her portfolio return's standard deviation is 1) 8.0%, 12% 2) 9.6%, 8% 3) 11.4%, 10% 4) 13%, 12% moto of 4% One year

Answer 1

Weight of the risky asset in the portfolio = w₁ = 40%, Expected return on the risky asset = R₁ = 15%, Varaince of the risky-asset = σ₁² = 0.04

Weight of the treasury bill in the portfolio = w₂ = 60%, Return on treasury bill = R₂ = 6%, Variance of the treasury bill = σ₂² = 0 [Treasury bills are risk-free and therefore variance is zero]

Expected return of the portfolio is given by the formula:

Expected portfolio return = E[R_P] = w₁*R₁ + w₂*R₂ = 40%*15% + 60%*6% = 9.6%

Varaince of the portfolio is calculated using the formula:

Portfolio variance = σ_P² = w₁²*σ₁² = (40%)²*0.04 = 0.0064

Standard deviation is the square-root of the variance

Standard deviation of the portfolio = σ_P = (0.0064)^1/2 = 0.08 = 8%

Expected return of the portfolio = 9.6%

Standard deviation of the portfolio = 8%

Answer -> 9.6%, 8% (Option 2)