Question

sam is considering to take his retirement portfolio into internationaland local investments. He has the following information;Investment FundExpected return Standard deviationS&P 500 Fund12.4%20%International Fund14%30%Freddy who is risk adverse has three options: i) Invest only in S&P 500 ii) Investonly in the international fund or iii) Invest equally his money in above assets. Helpout Freddy to decide. Also you must know that correlation coefficient (ρ) betweenabove assets is -0.65

Investment Fund S&P 500 Fund International Fund Expected return Standard deviation 12.4% 14% 30% Freddy who is risk adverse has three options: i) Invest only in S&P 500 ii) Invest

Answer 1

To decide the best option, the option with the lowest coefficient of variation (CV) should be chosen.

CV = standard deviation / expected return.

i]

CV = 20% / 12.4% = 1.61

ii]

CV = 30% / 14% = 2.14

iii]

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 return = (0.50 * 12.4%) + (0.50 * 14%) = 13.20%.

Standard deviation for a two-asset portfolio σ_p = (w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2)^1/2

where σ_p = Standard deviation 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

Standard deviation = ((0.50)²(0.20)² + (0.50)²(0.30)² + (2)(0.50)(0.50)(-0.65)(0.124)(0.14))^1/2

Standard deviation = 16.39%

CV = 16.39% / 13.20% = 1.24.

Option (iii) - Invest equally in both assets. This is the best option because it has the lowest coefficient of variation.