FRM Part II · FRM Exam Part II · Factors
An investor combines two uncorrelated factor strategies, each with an expected excess return of 4% and volatility of 8%, in equal weights. What is the Sharpe ratio of the combined portfolio?
Combining two uncorrelated strategies equally keeps the 4% return but cuts volatility to about 5.66%, so the Sharpe ratio is about 0.71, up from 0.50 for each. Diversification reduces volatility by the square root of two, not by half.
- A0.50
- B0.71Correct
- C1.00
- D0.35
Explanation
Expected return = 4%. Volatility = sqrt(0.5^2x64 + 0.5^2x64) = sqrt(32) = 5.657%. Sharpe = 4/5.657 = 0.707. Each strategy alone has 0.50; option 1.00 wrongly assumes volatility halves.
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