Question

Refer to the table below: 3 Doors, Inc. 20% 35 Down Co. 11% Expected return, E(R) Standard deviation, 0 Correlation 23 0.44 Using the information provided on the two stocks in the table above, find the expected return and standard deviation on the minimum variance portfolio. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Expected return Standard deviation

Answer 1

Minimum Variance Portfolio is found by this formula :

W_min(S) = [²_B - Cov(B,S)] / [²_S + ²_B - 2Cov(B,S)]

W_min(B) = 1 - W_min(S)

where W_min(S) = weight of Asset 1

W_min(B) = Asset 2

_B = standard deviation of Asset 2

_S = standard deviation of Asset 1

Cov(B,S) = covariance between Asset 1 and Asset 2

Cov(B,S) =   * _B * _S

= correlation between Asset 1 and Asset 2

W_min(S) = [²_B - Cov(B,S)] / [²_S + ²_B - 2Cov(B,S)]

W_min(S) = [0.23² - (0.44 * 0.35 * 0.23)] / [0.35² + 0.23² - (2 * 0.44 * 0.35 * 0.23)]

W_min(S) = 0.1672

W_min(B) = 1 - W_min(S)

W_min(B) = 1 - 0.1672 = 0.8328

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 = (0.1672 * 0.20) + (0.8328 * 0.11) = 12.50%

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 = ((0.1672² * 0.35²) + (0.8328² * 0.23²) + (2 * 0.1672 * 0.8328 * 0.44 * 0.35 * 0.23))^1/2

Standard deviation = 22.36%