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

A betting-against-beta (BAB) factor is built by going long leveraged low-beta stocks and short de-leveraged high-beta stocks. The long leg has beta 0.8 and the short leg has beta 1.25. How are the legs scaled so the factor is market neutral, and what is the result?

Each leg is divided by its own beta: the long leg is levered by 1.25 and the short leg scaled by 0.8. Both then have beta of one, and the net market beta is zero, which makes the factor market neutral.

  1. ALong leg scaled by 1/0.8 = 1.25 and short leg by 1/1.25 = 0.8, so each leg has beta of 1 and net beta is zeroCorrect
  2. BLong leg scaled by 0.8 and short leg by 1.25, giving net beta of zero
  3. CBoth legs held at unit dollar weight, so net beta is zero
  4. DLong leg scaled by 1.25 and short leg by 1.25, giving net beta of 0.45

Explanation

Dividing each leg by its beta gives 0.8×1.25 = 1 on the long and 1.25×0.8 = 1 on the short. Net beta is 1 − 1 = 0. Equal dollar weights would leave net beta of 0.8 − 1.25 = −0.45. Multiplying by beta instead of dividing moves betas further apart.

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