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

A hedge fund runs a betting-against-beta (BAB) strategy. The long leg has portfolio beta 0.6 and the short leg has beta 1.5. To make the strategy market neutral, the fund scales each leg by its beta. It invests 1 unit of capital in the long leg (before scaling). What is the correct position size in the short leg, and the resulting net market beta?

The short leg should be 0.40 units per unit of long position, because 0.6 divided by 1.5 equals 0.40. Net beta is then 0.6 minus 0.40 times 1.5, which is zero, making the strategy market neutral. Using equal dollar amounts would leave a net beta of -0.9.

  1. AShort 0.40 units of the short-leg portfolio; net beta zeroCorrect
  2. BShort 2.50 units of the short-leg portfolio; net beta zero
  3. CShort 0.40 units of the short-leg portfolio; net beta 0.20
  4. DShort 1.00 unit of the short-leg portfolio; net beta -0.90

Explanation

BAB levers the long leg by 1/0.6 and delevers the short leg by 1/1.5. Per unit of long capital, the short size is 0.6/1.5 = 0.40. Net beta = 1×0.6 - 0.40×1.5 = 0. Option 2 inverts the ratio, and option 4 leaves the legs unscaled, giving net beta 0.6-1.5 = -0.9.

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