FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
Two assets have return volatilities of 10% and 20% and a correlation of 0.5. A portfolio holds 50% in each asset. What is the portfolio return volatility?
The portfolio volatility is about 13.23%. Portfolio variance equals 0.0025 plus 0.01 plus 0.005, which is 0.0175, and its square root is 13.23%. Simply averaging the two volatilities gives 15%, which wrongly assumes perfect correlation.
- A12.50%
- B13.23%Correct
- C15.00%
- D17.50%
Explanation
Variance = 0.25*0.01 + 0.25*0.04 + 2*0.5*0.5*0.5*0.1*0.2 = 0.0025 + 0.01 + 0.005 = 0.0175. Square root = 13.23%. The 15% option is the simple average of volatilities, which ignores diversification (it holds only with correlation of 1).
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