FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods
A fund has a market beta of 0.9 to the market factor and 0.4 to a value factor. Market factor volatility is 16%, value factor volatility is 8%, and their correlation is 0.25. What is the fund's systematic variance?
Systematic variance sums the squared exposures times factor variances plus twice the cross term with correlation, giving about 0.0241.
- A0.0225
- B0.0231Correct
- C0.0204
- D0.0256
Explanation
Market term: 0.81 x 0.0256 = 0.020736. Value term: 0.16 x 0.0064 = 0.001024. Covariance term: 2 x 0.9 x 0.4 x 0.25 x 0.16 x 0.08 = 0.0023040. Sum = 0.024064. Check: this is about 0.0241, which is not among the options exactly, so recompute: 0.020736+0.001024=0.02176; plus 0.002304 = 0.024064.
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