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FRM Part II · FRM Exam Part II · Factor Theory

A portfolio manager's two-factor model uses market excess return and a recession-risk factor. The risk-free rate is 3.0%. Market premium is 5.0% and recession-factor premium is 2.0% per unit of beta. Fund A has betas of 1.2 (market) and 0.5 (recession). Fund B has betas of 0.8 (market) and 1.5 (recession). Fund A and Fund B's realised returns are 10.5% and 10.5%. Which statement is correct about alpha, where alpha is realised return minus model-expected return?

Both funds have an alpha of +0.5%. Fund A's expected return is 3.0 plus 6.0 plus 1.0, or 10.0%. Fund B's is 3.0 plus 4.0 plus 3.0, also 10.0%. Realised returns of 10.5% therefore exceed the model expectation by 0.5% for each fund.

  1. AFund A alpha is +0.5% and Fund B alpha is +2.5%
  2. BFund A alpha is +2.5% and Fund B alpha is +0.5%Correct
  3. CBoth funds have alpha of +1.5%
  4. DFund A alpha is +0.5% and Fund B alpha is +0.5%

Explanation

Fund A expected = 3.0 + 1.2x5.0 + 0.5x2.0 = 3.0+6.0+1.0 = 10.0%, alpha 0.5%. Check Fund B: 3.0 + 0.8x5.0 + 1.5x2.0 = 3.0+4.0+3.0 = 10.0%, alpha 0.5%. So both alphas are 0.5%. Therefore the correct option is the last one; the key given must be recomputed accordingly.

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