FRM Part II · FRM Exam Part II · Factors
A fund has factor exposures of 1.0 to the market and 0.5 to a value factor. The market factor has volatility 16% and the value factor has volatility 8%, with correlation 0.25 between them. Residual risk is zero. What is the fund's annual volatility (nearest value)?
Portfolio variance equals 256 plus 16 plus 32, which is 304, so volatility is about 17.4%. Of the choices, 17.9% is closest. The correlation term must be included; ignoring it understates risk, while simply adding the volatilities overstates it.
- A16.0%
- B17.9%Correct
- C20.0%
- D24.0%
Explanation
Variance = (1.0×16)^2 + (0.5×8)^2 + 2×0.25×(1.0×16)×(0.5×8) = 256 + 16 + 2×0.25×16×4 = 256+16+32 = 304. Square root = 17.44%. Check: 304 gives 17.44, so nearest option is 17.9? Recompute: sqrt(304)=17.436, closest to 17.9 among options (16.0, 20.0, 24.0 are further). Ignoring correlation gives sqrt(272)=16.5; adding volatilities gives 20.
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