Question

Stock A: E (R) = 9%, STD DEVIATION =36%

Stock B : E (R) = 15%, STD DEVIATION =62%

1. Calculate the expected return of a portfolio that is composed of 35% of a stock A and 65% of stock B

2. calculate the std deviation of this portfolio when the correlation coefficient between the returns is 0.5

3. calculate the std deviation of this portfolio same weights in each stock when the correlation coefficient is now -0.5

4. how did the changes in the correlation between the returns on A and B affect the std deviation of the portfolio?

Answer 1

1]

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 = (0.35 * 0.09) + (0.65 * 0.15) = 12.90%

2]

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

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 = ((0.35)²(0.36)² + (0.65)²(0.62)² + (2)(0.35)(0.65)(0.5)(0.36)(0.62))^1/2

standard deviation = 48%

3]

standard deviation = ((0.35)²(0.36)² + (0.65)²(0.62)² + (2)(0.35)(0.65)(-0.5)(0.36)(0.62))^1/2

standard deviation = 36%

4]

The change in correlation from a positive to negative correlation reduced the standard deviation of the portfolio