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FRM Part II · FRM Exam Part II · Factors

A fund's returns are modeled with a Fama-French three-factor model. Market factor variance is 0.0400 (annual), SMB variance is 0.0100, HML variance is 0.0100, and factors are uncorrelated. Loadings are 1.0 (market), 0.5 (SMB), and 0.4 (HML). Residual variance is 0.0050. What is the fund's annual volatility?

Annual volatility is about 22.2%. Total variance is 0.04 from market, 0.0025 from SMB, 0.0016 from HML and 0.005 residual, summing to 0.0491; its square root is roughly 0.222.

  1. AApproximately 21.6%
  2. BApproximately 22.6%Correct
  3. CApproximately 47.5%
  4. DApproximately 20.0%

Explanation

Variance = 1.0²(0.04) + 0.5²(0.01) + 0.4²(0.01) + 0.005 = 0.04 + 0.0025 + 0.0016 + 0.005 = 0.0491. Square root = 0.2216, about 22.2%. Recomputing: sqrt(0.0491)=0.2216, so the nearest option is the one near 22%.

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