The situation
A portfolio holds equal weights in two assets with 20% annual volatility. Compare correlations of 0 and 0.5.
Your task
How does the correlation change portfolio volatility?
Reveal step-by-step solution
Set up the problem
Each weighted variance term is 0.5² × 0.20² = 0.01.
Work through the numbers
At zero correlation, variance is 0.02 and volatility is 14.14%. At 0.5 correlation, covariance contribution is 0.01, giving volatility √0.03 ≈ 17.32%.
Interpret the result
Both combinations diversify some risk, with less benefit at higher correlation. Stress a common drawdown as well.
What to remember
Compute variance with the covariance term and take the square root once.