FRM Part II · FRM Exam Part II · Factors
A multi-factor equity fund combines a value sleeve and a momentum sleeve, each with 10% annualized volatility, in equal weights. The correlation between the two sleeves is -0.50. What is the annualized volatility of the combined portfolio?
The combined volatility is 5.00%. Portfolio variance equals 0.0025 from the two sleeve variances plus a covariance term of negative 0.0025 given the -0.50 correlation, and its square root is 5%. Ignoring the negative correlation would overstate risk.
- A5.00%Correct
- B7.07%
- C10.00%
- D8.66%
Explanation
Variance = 0.5^2(0.01)+0.5^2(0.01)+2(0.5)(0.5)(-0.5)(0.01) = 0.0025+0.0025-0.0025 = 0.0025. Square root = 5.00%. The 7.07% option uses zero correlation, 10% ignores diversification, and 8.66% uses +0.5 correlation.
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