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Set out what neutralization means and the various ways alphas are refined so as to be neutral.

FRM® Part II · Risk Management and Investment Management · Portfolio Construction · FRM2.IM.4.c

The idea

Neutralization means adjusting alphas so that the optimizer is not rewarded for taking exposures the manager did not intend to take. Benchmark neutral alphas give the benchmark a weighted average alpha of zero. Let β be the asset's beta and αB the benchmark's alpha. Each alpha is then reduced by the asset's beta times the benchmark's alpha, as below. Adjusted = α − β × αB. Cash neutral alphas for a long-short portfolio are shifted so that their weighted average is zero. Factor neutral alphas subtract, for each unwanted factor, the asset's exposure times the alpha of that factor's portfolio. With no other constraints, benchmark neutral alphas lead to a portfolio with zero active beta. Constraints can still reintroduce exposures, so check the result.

Formulas

Benchmark neutral alpha

adjusted α = α − β × αB

α
the asset's raw alpha
β
the asset's beta to the benchmark
αB
the benchmark's weighted average raw alpha

Makes the benchmark's weighted average alpha zero. Gives zero active beta only without other constraints, so check beta after a constrained optimisation.

Factor neutral alpha

adjusted α = α − x × αF

α
the asset's raw alpha
x
the asset's exposure to the unwanted factor
αF
the alpha of that factor's portfolio

Repeat for each unwanted factor. A raw alpha that was mostly a factor tilt can turn negative.

A practice question

From the question bank, with the reason each wrong option is wrong.

What does it mean for a set of alphas to be benchmark neutral?

  1. Every individual asset's alpha is zero.Why not: This removes all stock selection information; only the benchmark-weighted average must be zero.
  2. The equal-weighted average of alphas is zero, whatever the benchmark weights.Why not: Uses equal weights; benchmark neutrality uses the benchmark weights.
  3. The benchmark portfolio's weighted average alpha is zero. - correct
  4. Alphas are scaled so none exceeds the benchmark return.Why not: Compares alphas with the benchmark return, which has nothing to do with neutrality.

Benchmark neutral alphas satisfy sum of (benchmark weight x alpha) = 0. The optimizer then has no reason to make a bet on the benchmark itself.

A harder one

An asset has a raw alpha of 2.0% and a beta of 1.2 to the benchmark. The benchmark's weighted average alpha is 0.5%. The benchmark neutral alpha of the asset is:

  1. 1.50%Why not: Subtracts the benchmark alpha without multiplying by the asset's beta.
  2. 2.60%Why not: Adds beta x benchmark alpha instead of subtracting it.
  3. 1.58%Why not: Divides the benchmark alpha by beta instead of multiplying (2.0 - 0.5 / 1.2).
  4. 1.40% - correct

Adjusted alpha = raw alpha - beta x benchmark alpha = 2.0 - 1.2 x 0.5 = 1.40%. Because the benchmark's beta is one, its adjusted alpha becomes zero.

The hardest tier

A stock has a raw alpha of 1.0% and an exposure of 1.5 to the size factor. The alpha of the size factor portfolio is 0.8%. The size-neutral alpha of the stock is closest to:

  1. 0.20%Why not: Subtracts the factor portfolio alpha without scaling by the stock's exposure of 1.5.
  2. -0.20% - correct
  3. 2.20%Why not: Adds exposure x factor alpha instead of subtracting it.
  4. 0.47%Why not: Divides the factor alpha by the exposure (1.0 - 0.8 / 1.5) instead of multiplying.

Factor neutral alpha = raw alpha - exposure x factor alpha = 1.0 - 1.5 x 0.8 = -0.20%. The stock's alpha was mostly compensation for the size tilt.

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