FRM Part II · FRM Exam Part II · Factors
Using a three-factor model, a fund's monthly excess return is modeled as: alpha + 1.10×MKT + 0.40×SMB − 0.25×HML. Over a month the factor returns are MKT = 2.0%, SMB = 1.0%, HML = 3.0%. The fund's realized excess return is 2.30%. What is the fund's estimated alpha for the month?
The alpha is 0.45%. Factor-explained return is 1.10×2.0% plus 0.40×1.0% minus 0.25×3.0%, which equals 1.85%. Subtracting this from the realized excess return of 2.30% leaves 0.45% as the unexplained return, or alpha, for the month.
- A0.45%Correct
- B−0.15%
- C0.00%
- D0.30%
Explanation
Factor-explained return = 1.10×2.0 + 0.40×1.0 − 0.25×3.0 = 2.20 + 0.40 − 0.75 = 1.85%. Alpha = 2.30 − 1.85 = 0.45%. Ignoring the negative sign on HML gives 2.20+0.40+0.75=3.35 and alpha of −1.05%; omitting HML gives −0.30%.
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