FRM Part II · FRM Exam Part II · Factor Theory
A portfolio has two uncorrelated factor exposures. Factor A contributes a variance of 4.0 (%^2) and Factor B contributes 5.0 (%^2). Specific risk variance is 6.0 (%^2). What proportion of total portfolio variance is attributable to factor risk, and what is total volatility?
Total variance is 4 plus 5 plus 6, equal to 15. Factor variance of 9 is 60% of the total. Volatility is the square root of 15, approximately 3.87%. The other 40% is specific risk.
- A60% of variance; volatility 3.87%Correct
- B75% of variance; volatility 3.00%
- C60% of variance; volatility 3.87% squared
- D40% of variance; volatility 3.87%
Explanation
Total variance = 4 + 5 + 6 = 15. Factor share = 9/15 = 60%. Volatility = sqrt(15) = 3.87%. Option 4 uses the specific share instead.
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