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FRM Part II · FRM Exam Part II · Factors

A portfolio manager regresses a fund's monthly excess returns on the market, size and value factors. The regression gives an R-squared of 0.85 and a total return variance of 400 (in %-squared units). How much of the fund's variance is attributable to idiosyncratic (non-factor) risk?

Idiosyncratic variance is the unexplained share of total variance: (1 - 0.85) x 400 = 60. The figure of 340 is the factor-explained variance, so it is the wrong component to report as residual risk.

  1. A60Correct
  2. B85
  3. C340
  4. D15

Explanation

Idiosyncratic variance equals (1 - R-squared) times total variance: 0.15 x 400 = 60. Option 340 is the factor-explained variance (0.85 x 400), a mix-up of which part is residual. Option 85 and 15 are raw percentages, not variances.

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