Question

You are creating a portfolio of two stocks. The first one has a standard deviation of 28% and the second one has a standard deviation of 40%. The correlation coefficient between the returns of the two is 0.3. You will invest 50% of the portfolio in the first stock and the rest in the second stock. What will be the standard deviation of this portfolio's returns? Answer in percent, rounded to two decimal places (e.g., 4.32%=4.32).

Answer 1

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

σ₁ = standard deviation of Asset 1

σ₂ = standard deviation 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 = ((0.50² * 0.28²) + (0.50² * 0.40²) + (2 * 0.50 * 0.50 * 0.3 * 0.28 * 0.40))^1/2

standard deviation of portfolio = 27.64%