FRM Part II · FRM Exam Part II · Portfolio Construction
An investor combines a value factor strategy and a momentum factor strategy. Each has an expected excess return of 4% and volatility of 10%. The correlation between them is -0.20. Assuming equal weights, what is the Sharpe ratio of the combined portfolio?
The equal-weighted portfolio earns 4% with variance 0.004, or volatility of about 6.32%, because the negative correlation reduces risk. The Sharpe ratio is 4 divided by 6.32, roughly 0.63, which is higher than the 0.40 of either standalone factor strategy.
- A0.40
- B0.45
- C0.63Correct
- D0.50
Explanation
Portfolio return is 4%. Variance = 0.25×0.01+0.25×0.01+2×0.25×(-0.2)×0.01 = 0.0025+0.0025-0.001 = 0.004; volatility = 6.32%. Sharpe = 4/6.32 = 0.63. Using a zero correlation gives volatility 7.07% and Sharpe 0.57, and 0.40 is the standalone Sharpe ratio of each strategy.
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