Question

Suppose Wesley​ Publishing's stock has a volatility of 55 %​, while Addison​ Printing's stock has a volatility of 30 %. If the correlation between these stocks is 15 %​, what is the volatility of the following portfolios of Addison and​ Wesley:

a. 100 % Addison

b. 75 % Addison and 25 % Wesley

c. 50 % Addison and 50 % Wesley

a. The volatility of a portfolio of 100 % Addison stock is nothing​%. ​ (Round to two decimal​ places.)

b. The volatility of a portfolio of 75 % Addison and 25 % Wesley is nothing​%. ​ (Round to two decimal​ places.)

c. The volatility of a portfolio of 50 % Addison and 50 % Wesley is nothing​%. ​ (Round to two decimal​ places.)

Answer 1

Standard deviation (volatility) 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 (Addison)

w₂ = weight of Asset 2 (Wesley)

σ₁ = standard deviation of Asset 1. This is 30%, or 0.30.

σ₂ = standard deviation of Asset 2. This is 55%, or 0.55.

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. Correlation = 15%, or 0.15.

a]

Standard deviation σ_p = ((1.00² * 0.30²) + (0.00² * 0.55²) + (2 * 1.00 * 0.00 * 0.15 * 0.30 * 0.55))^1/2

Standard deviation σ_p = 30.00%

b]

Standard deviation σ_p = ((0.75² * 0.30²) + (0.25² * 0.55²​​​​​​​) + (2 * 0.75 * 0.25 * 0.15 * 0.30 * 0.55))^1/2

Standard deviation σ_p = 28.07%

c]

Standard deviation σ_p = ((0.50² * 0.30²) + (0.50² * 0.55²​​​​​​​) + (2 * 0.50 * 0.50 * 0.15 * 0.30 * 0.55))^1/2

Standard deviation σ_p = 33.24%