Question

Consider stocks of two companies A and B, the table below gives their expected returns and standard deviation Expected return for Stock A 10% Expected return for Stock B 25% Standard deviation for Stock A 12% Standard deviation for Stock B 30% Plot the risk and expected return of portfolio of these two stocks for the following correlation coefficient : -1.0,-0.5,0.0,0.5,1.0

Answer 1

In the absence of additional information in the question, it is assumed that the portfolio will consist of 50% of Stock A and 50% of Stock B. For this portfolio, we shall calculate the risk and expected return at each correlation coefficient.

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