Constructing a signal: standardisation, neutralisation and combination

SIG · Chapter 212 min readAsked at Two Sigma, AQR, Citadel, Point72

Assumes The research pipeline: from hypothesis to live capital.

After this lesson you should be able to

  • Standardise a raw feature without leaking information.
  • Neutralise a signal against known factors and say what remains.
  • Combine several signals sensibly.

A raw feature is not a signal. Turning one into the other means putting it on a comparable scale across assets, removing the exposures you are not being paid for, and deciding how it combines with everything else you already trade — and each of those steps can destroy the signal if done carelessly.

Proposition 2.1

Standardise cross-sectionally

Convert the raw value to a z-score within each date, using only that date’s cross-section. That makes assets comparable, puts the signal on a scale you can size from, and — crucially — uses no information from any other date, so it cannot leak the future.

Holds when

  • Winsorise or rank first: a single extreme value otherwise dominates the whole cross-section’s scale.
  • Ranking is the most robust choice and discards magnitude, which is usually a reasonable price.
  • Never standardise using full-sample statistics — that is look-ahead with no trace in the code.

Derivation 2.2

Neutralisation

Remove the part of the signal explained by exposures you do not want.

  1. st=Xtβt+s~ts_t = X_t\beta_t + \tilde{s}_t

    Regress the signal cross-sectionally on the factor exposures at each date.

  2. s~t=st−Xtβ^t\tilde{s}_t = s_t - X_t\hat\beta_t

    Keep the residual — the part orthogonal to the factors.

a signal with zero exposure to sector, beta, size and anything else in X\text{a signal with zero exposure to sector, beta, size and anything else in } X

Why you give up return to neutralise. Neutralising almost always lowers the raw information coefficient, which looks like a loss and is usually a gain. The exposure you removed was paying you a factor premium you could have bought far more cheaply with an index — so you were not being paid for skill, and you were carrying a risk your risk model already charges you for. What remains is smaller and genuinely yours, and because it is uncorrelated with the factors it adds far more to a portfolio than its standalone IC suggests. This is the Frisch–Waugh–Lovell theorem doing portfolio work.

Example 2.3

A signal has an IC of 0.060.06 raw and 0.040.04 after neutralising against sector and beta. Which do you trade?

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Worked solution

  1. Formula
    the question is what the lost 0.02 was\text{the question is what the lost } 0.02 \text{ was}
  2. Substitute
    raw 0.06=factor exposure+residual alpha\text{raw } 0.06 = \text{factor exposure} + \text{residual alpha}
  3. Solve
    the neutralised 0.04 is uncorrelated with factors you already hold\text{the neutralised } 0.04 \text{ is uncorrelated with factors you already hold}
  4. the extra 0.02 is a beta and sector tilt, available from an index\text{the extra } 0.02 \text{ is a beta and sector tilt, available from an index}
  5. Answer
    the neutralised version\text{the neutralised version}

Sanity check. If a third of the raw IC had vanished instead of a third of it surviving — say 0.060.06 falling to 0.0050.005 — the correct conclusion would be different: the signal was a factor bet, and there is no alpha to trade.

Proposition 2.4

Decay and smoothing

A signal computed each day is noisy, and trading it in full each day generates turnover that costs more than the noise is worth. Smoothing — an exponentially weighted average over a horizon matched to the signal’s half-life — keeps most of the information and cuts the turnover sharply.

Holds when

  • Match the smoothing horizon to the IC decay curve, not to convenience.
  • Over-smoothing delays the signal and costs real alpha, so it is a trade rather than a free improvement.
  • A trading band — only rebalance when the target moves enough — is often better than smoothing the signal itself.

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Constructing a signal: standardisation, neutralisation and combination · QuantMax