Question

your portfolio has 20% invested in stock a and 80% invested in stock b. stock a has an expected return of 10% and a volatility of 15%. stock b has an expected return of 12% and volatility of 25%. the correlation between stock a and b is 0.3. what is the variance of your portfolio return?

Answer 1

Your portfolio of investment is: 20% stock A and 80% stock B. The portfolio variance of return is 0.0445

Portfolio variance is a risk assessment that describes how the aggregate actual returns of a portfolio's assets fluctuate over time.

Formula for the portfolio variance is:

Portfolio variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov₁₂

Where:

w = weight of each asset

σ = standard deviation or volatility of each asset

Cov₁₂ = covariance between two assets.

Cov₁₂ = σ₁σ₂ x Corr₁₂

Parameters given in the problem:

w₁ = 20%

w₂ = 80%

σ₁ = 15%

σ₂ = 25%

Corr₁₂  = 0.3

Compute the covariance:

Cov₁₂ =  15% x 25% x 0.3 = 0.01125

Hence,

Portfolio variance = 0.2² x 0.15² + 0.8² x 0.25² + 2 x 0.2 x 0.8 x 0.01125

                             = 0.0445

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