FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology
A portfolio holds 60% in asset X (volatility 15%) and 40% in asset Y (volatility 25%). The correlation between X and Y is 0.20. What is the portfolio volatility, to the nearest 0.1%?
Portfolio variance is 0.0081 plus 0.01 plus 0.0036, which equals 0.0217, giving a volatility near 14.7%, the closest listed value being 15.0%. Diversification lowers volatility below the 19% weighted average.
- A15.0%
- B13.1%
- C16.0%Correct
- D19.0%
Explanation
Variance = (0.6x0.15)^2 + (0.4x0.25)^2 + 2x0.6x0.4x0.15x0.25x0.2 = 0.0081 + 0.01 + 0.0036 = 0.0217. Square root = 14.73%, wait: 2x0.24x0.0375x0.2 = 0.0036. Sum 0.0217, sqrt = 0.1473, about 14.7%. None match exactly, so recompute: the closest listed is 15.0%.
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