CFA Level IPortfolio ManagementMedium
An analyst constructs a two-asset portfolio with 60% invested in Stock X (standard deviation = 20%) and 40% invested in Stock Y (standard deviation = 30%). The correlation between the two stocks is 0.30. What is the portfolio's standard deviation?
- A19.35%
- B24.00%
- C26.00%
- D18.35%
Show answer & explanationAnswer & explanation
Correct answer: A. 19.35%
Portfolio variance = w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2 = (0.6²×0.20²)+(0.4²×0.30²)+(2×0.6×0.4×0.3×0.20×0.30) = 0.0144+0.0144+0.00864 = 0.03744. Standard deviation = √0.03744 ≈ 19.35%.
Why the other options are wrong
- B. Represents a simple weighted average of the two standard deviations, ignoring diversification benefits.
- C. Overstates risk by assuming perfect positive correlation (ρ=1).
- D. Slightly understates the covariance term contribution.
Two-Asset Portfolio Standard Deviation
The risk of a portfolio combining two assets depends on each asset's variance, weights, and the correlation between them.
- Formula: σp² = w1²σ1² + w2²σ2² + 2w1w2ρ1,2σ1σ2
- Lower correlation reduces portfolio risk through diversification
- When ρ = 1, portfolio std dev equals the weighted average of individual std devs
Memory trick: Weights, variances, and correlation blend to shrink risk