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FRM Part II · FRM Exam Part II · Alpha (and the Low-Risk Anomaly)

A fund has a beta of 1.4 and an alpha of 0 relative to the market. The market's excess return has volatility of 15%. The fund's residual volatility is 10%. What is the fund's total volatility and the share of its variance explained by the market?

Systematic variance is 1.4 squared times 15 squared, which is 441. Adding residual variance of 100 gives 541, so total volatility is about 23.2%. The market explains 441 divided by 541, roughly 82% of variance. Variances add, volatilities do not.

  1. ATotal 21.0%; market explains about 82%
  2. BTotal 23.2%; market explains about 82%Correct
  3. CTotal 25.0%; market explains about 100%
  4. DTotal 23.2%; market explains about 18%

Explanation

Systematic variance = 1.4^2 x 15^2 = 1.96 x 225 = 441. Residual variance = 100. Total = 541, volatility = 23.26%, about 23.2%. R-squared = 441/541 = 81.5%, about 82%. Adding volatilities (21 + 10 = 31) or ignoring residual risk is wrong.

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