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FRM Part II · FRM Exam Part II · Factor Theory

A portfolio has exposures of 0.8 to Factor A and 0.5 to Factor B. Factor premiums over the period were A: 4% and B: -2%. The portfolio's total return in excess of the risk-free rate was 3.0%. What was the portfolio's residual (alpha) return?

The residual return is 0.8%. Factor contributions are 0.8 times 4%, or 3.2%, plus 0.5 times negative 2%, or negative 1.0%, totalling 2.2%. Subtracting this from the 3.0% excess return leaves 0.8% unexplained by the factors.

  1. A0.8%Correct
  2. B0.2%
  3. C0.8% lower, at -0.8%
  4. D0.2% lower, at -0.2%

Explanation

Factor return = 0.8 x 4% + 0.5 x (-2%) = 3.2% - 1.0% = 2.2%. Residual = 3.0% - 2.2% = 0.8%. Ignoring the negative sign of B's premium gives 4.2% factor return and -1.2%, and subtracting the other way gives -0.8%.

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