Question

USE THE INFORMATION BELOW FOR THE FOLLOWING Question Asset 1 Asset 2 E(R)=12 E(R2) = 16 Eſstandard dev 1) = .04 Efstandard dev 2) = .06 Question: Calculate the expected return and expected standard deviation of a two- stock portfolio when I 1260 and w1 - 75. 13 and.0024 12 and 0585 O.13 and .0455 13 and.6758 .12 and.5585

Answer 1

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

where R_p = expected return

w₁ = weight of Asset 1. This is 0.75

R₁ = expected return of Asset 1. This is 0.12.

w₂ = weight of Asset 2. This is (1 - 0.75) = 0.25.

R₂ = expected return of Asset 2. This is 0.16.

Expected return = (0.75 * 0.12) + (0.25 * 0.16)  

Expected return = 0.13

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

where σ_p = expected standard deviation of the portfolio

w₁ = weight of Asset 1. This is 0.75.

w₂ = weight of Asset 2. This is 0.25.

σ₁ = expected standard deviation of Asset 1. This is 0.04.

σ₂² = expected standard deviation of Asset 2. This is 0.06.

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

Expected standard deviation σ_p = ((0.75² * 0.04²) + (0.25² * 0.06²) + (2 * 0.75 * 0.25 * 0.60 * 0.04 * 0.06)^1/2

Expected standard deviation σ_p = 0.0455