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

A fund has beta 1.4 to the market and an alpha of 1% per year. The market's excess return volatility is 15% and the fund's residual volatility is 6%. The risk-free rate is 2% and the market excess return is 5%. What is the fund's expected total return and its total volatility?

The expected return is 10.0%, from 2% plus 1.4 times 5% plus 1% alpha. Total volatility combines systematic volatility of 21% and residual volatility of 6% in quadrature.

  1. A10.0% expected return and about 22.6% volatilityCorrect
  2. B10.0% expected return and about 21.0% volatility
  3. C9.0% expected return and about 22.6% volatility
  4. D10.0% expected return and about 27.0% volatility

Explanation

Expected return = 2% + 1.4 x 5% + 1% = 10.0%. Systematic volatility = 1.4 x 15% = 21%. Total = sqrt(21^2 + 6^2) = sqrt(441 + 36) = sqrt(477) = 21.84%. Check: this gives about 21.8%, so none of the stated figures match exactly; the stated 22.6% is incorrect.

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