FRM Part II · FRM Exam Part II · Factor Theory
Two factor portfolios each have expected excess return of 4% and volatility of 8%. Their correlation is 0.25. A manager combines them 50/50 without leverage. What is the approximate Sharpe ratio of the combination (risk-free rate already netted out)?
The combined Sharpe ratio is about 0.62 to 0.63. Portfolio variance is 40 in percent squared, giving volatility near 6.32%, while expected excess return stays at 4%. Dividing gives roughly 0.63, up from 0.50 for each factor alone because of imperfect correlation.
- A0.50
- B0.56
- C0.62Correct
- D0.71
Explanation
Expected excess return = 4%. Variance = 0.25×64 + 0.25×64 + 2×0.25×0.25×64 = 16+16+8 = 40, so volatility = 6.32%. Sharpe = 4/6.32 = 0.63, approximately 0.62 to 0.63 given rounding. Individual Sharpe is 0.50, so 0.50 ignores diversification; 0.71 would apply at zero correlation.
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