FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology
A portfolio holds two assets with weights of 50% each. Both have annual volatility of 10%. The correlation between them is 0.5. What is the portfolio volatility?
Portfolio volatility is about 8.66%. Variance equals 0.0025 plus 0.0025 plus a covariance term of 0.0025, giving 0.0075, whose square root is 8.66%. Diversification benefit arises because correlation of 0.5 is below one, so volatility is under 10%.
- A10.00%
- B8.66%Correct
- C7.50%
- D5.00%
Explanation
Variance = 0.25(0.01) + 0.25(0.01) + 2(0.5)(0.5)(0.1)(0.1)(0.5) = 0.0025 + 0.0025 + 0.00125 = 0.00625. Wait, recompute: cross term = 2 x 0.5 x 0.5 x 0.01 x 0.5 = 0.0025. Total = 0.0075; square root = 8.66%. A 10% answer would assume correlation of 1.
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