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FRM Part II · FRM Exam Part II · Factor Theory

A fund's returns are regressed on the market, size (SMB), value (HML) and momentum (UMD) factors using monthly data. The estimated monthly alpha is 0.10%. Betas are: market 1.10, SMB 0.30, HML -0.20, UMD 0.50. Monthly factor premiums are: market excess return 0.60%, SMB 0.20%, HML 0.30%, UMD 0.50%. The fund's average monthly excess return was 1.05%. Assuming the model fits exactly on average, which is the best interpretation?

Factor-explained return is 0.66 + 0.06 - 0.06 + 0.25 = 0.91% per month. Matching the 1.05% average would need alpha of 0.14%, not the reported 0.10%, so the data are not consistent with an exact fit.

  1. AThe model implies factor-explained return of 0.91%, so alpha of 0.14% would be required to match the 1.05% average, not 0.10%, indicating the data are inconsistent with exact fitCorrect
  2. BThe factor-explained return is 1.05%, leaving alpha of zero
  3. CThe factor-explained return is 0.99%, leaving alpha of 0.06%
  4. DThe factor-explained return is 1.15%, so the fund has negative alpha of 0.10%

Explanation

Factor return = 1.10×0.60 + 0.30×0.20 + (-0.20)×0.30 + 0.50×0.50 = 0.66 + 0.06 - 0.06 + 0.25 = 0.91%. Residual = 1.05 - 0.91 = 0.14%, which differs from the reported 0.10%, so exact fit does not hold. The other options use wrong arithmetic or ignore the negative HML contribution.

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