FRM Part II · FRM Exam Part II · Portfolio Construction
An investor combines a value factor portfolio and a momentum factor portfolio. Each has an annual volatility of 10% and an expected excess return of 4%. The correlation between them is -0.5. If the investor allocates 50% to each, what is the volatility of the combined portfolio?
The combined volatility is 5.0%. With equal 50% weights, 10% volatilities and a -0.5 correlation, portfolio variance is 25 (in percent squared), whose square root is 5%. Ignoring the negative correlation would wrongly give a higher figure.
- A5.0%Correct
- B7.1%
- C10.0%
- D2.5%
Explanation
Variance = 0.25(100) + 0.25(100) + 2(0.5)(0.5)(-0.5)(100) = 25 + 25 - 25 = 25, so volatility = 5.0%. Using 7.1% would assume zero correlation (variance 50). Using 10% ignores diversification.
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