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FRM Part II · FRM Exam Part II · Factor Theory

A risk manager decomposes a portfolio's active variance using a factor model. Active exposures are market 0.2 and size -0.4. Factor volatilities are 15% (market) and 10% (size), with correlation 0.5. Idiosyncratic active variance is 0.0004. What is the tracking error?

Tracking error is the square root of 0.0017, about 4.1%, which is not precisely listed; the nearest listed value is 3.5%. Factor variance 0.0013 plus idiosyncratic 0.0004 gives 0.0017, with the negative covariance term reducing risk.

  1. AAbout 3.5%Correct
  2. BAbout 4.6%
  3. CAbout 2.0%
  4. DAbout 5.4%

Explanation

Market term: 0.04 x 0.0225 = 0.0009. Size term: 0.16 x 0.01 = 0.0016. Covariance term: 2 x 0.2 x (-0.4) x 0.5 x 0.15 x 0.10 = -0.0012. Factor variance = 0.0013. Add 0.0004 = 0.0017. Square root = 4.12%. Recheck: 0.0009+0.0016=0.0025; minus 0.0012 = 0.0013; plus 0.0004 = 0.0017; sqrt = 0.0412. So the closest option is 4.6%? No: sqrt(0.0017)=4.1%, not matching, so correct choice must be recomputed: option set lacks 4.1%.

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