Question

Question A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return|Standard Deviation Stock fund (S) 15% 32% Bond fund (B) 23 9 The correlation between the fund returns is .15. Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of 0% to 100% in increments of 20%. What expected return and standard deviation does your graph show for the minimum-variance portfolio?

Poforlio and fund management

Answer 1

Expected return of two-asset portfolio R_p = w₁R₁ + w₂R_2,

where R_p = expected return

w₁ = weight of Asset 1

R₁ = expected return of Asset 1

w₂ = weight of Asset 2

R₂ = expected return of Asset 2

Expected variance for a two-asset portfolio σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2

where σ_p² = variance of the portfolio

w₁ = weight of Asset 1

w₂ = weight of Asset 2

σ₁² = variance of Asset 1

σ₂² = variance of Asset 2

Cov_1,2 = covariance of returns between Asset 1 and Asset 2

Cov_1,2 = ρ_1,2 * σ₁ * σ_2, where ρ_1,2 = correlation of returns between Asset 1 and Asset 2

f((B102)*($c$2^2))+((C10^2)*($c$3^2))+(2*B10*C10*$B$4*$C$2*$C$3))^0.5 E10 H A C D E G Expected Standard Deviation Return 1 2 Stock Fund 15% 32% 3 Bond Fund 23% 9% Correlation 0.15 5 6 Stock Fund Bond Fund Expected Standard Weight Deviation Weight Return 7 Portfolio 0% 100% 9.00% 23% 8 1 20% 80% 10.20% 20% 2 20% 40% 60% 11.40% 10 3 60% 40% 12.60% 23% 11 4 80% 20% 13.80% 27% 12 5 32% 100% 0% 15.00% 13 6 14

35.00% 30.00% 25.00% 20.00% Expected Return 15.00% Standard Deviation 10.00% 5.00% 0.00% 5. 2. 6 1 3 4.

The minimum-variance portfolio is portfolio 3. Although portfolio 2 has the same standard deviation as portfolio 3, the latter has a higher expected return

For the minimum-variance portfolio 3, expected return is 11.40% and standard deviation is 20%