Alpha Combination And Neutralization

Alpha combination and neutralization

Three numbers in a standard alpha research note are routinely wrong, and none of them raise. The IC t-stat, because the observations are not independent. The word "neutral", because the exposure came from the wrong window. And the winsorization step, because it was placed after a rank and clips nothing.

Everything marked ✅ Measured comes from scripts/alpha_combine.py — numpy + pandas + scipy, seed 20260909, 200 names x 1,200 days x 8 sectors, 7 s. The panel's alphas have their skill planted in known components of the return, so neutralization can be checked rather than asserted.

1. Conventions this skill uses, so the numbers can be checked

✅ Measured — the script's vectorized rank IC agrees with scipy.stats.spearmanr row by row to 1.39e−17. Do not take a hand-rolled IC on trust; ten rows against scipy costs nothing.

2. IC is not the number that decides anything

✅ Measured, five alphas, daily rebalance, 10 bps one-way:

🔑 idio_fast and sector_bet are ranked opposite ways by IC and by net Sharpe. IC is a per-period correlation; it has no idea how often the book has to be rebuilt to harvest it. An IC table with no turnover column beside it cannot be acted on.

⚠️ Note the control: pure_noise has an IC of 0.0027 (indistinguishable from zero) and a net Sharpe of −6.27. Costs alone turn a zero-edge signal into a large negative. Always run a noise alpha through the same pipeline — it calibrates what "no edge" looks like on your own plots.

3. 🚨 The IC t-stat, and why "overlapping returns" is the wrong diagnosis

The usual rule — overlapping forward returns inflate the t-stat, so use Newey-West with h−1 lags — is half right, and the wrong half is load-bearing.

✅ Measured, same panel, the same alpha at four horizons:

idio_slow — a persistent alpha

idio_fast — a near-i.i.d. alpha

🔑 Read the AC(1) column first. Overlap by itself inflates nothing. What breaks the i.i.d. standard error is autocorrelation in the IC series, and that needs a persistent alpha as well as an overlapping return. For the fast alpha, daily sampling against a 63-day return really does carry ~63× the observations: its naive t = 2.7 is roughly honest and sampling every 63rd day throws the evidence away (t = 0.4). For the slow alpha at the same horizon, 16.0 should be about 3.6.

🚨 And lags = h − 1 is a rule about the overlap, not about the alpha. At h = 1 it prescribes zero lags, so idio_slow's daily IC keeps t = 27.6 — while its IC autocorrelation is 0.41. ✅ Measured: with 21 lags the same series gives t = 10.8. A daily, non-overlapping IC can still need a HAC correction, and the standard recipe will not give it one.

What to do: choose the lag from the IC series' own autocorrelation, not from the return horizon. max(h − 1, first lag where the IC autocorrelation is insignificant) is a defensible floor. Report AC(1) next to every IC t-stat so a reader can see which regime you are in.

⚠️ ../../../fin-core/skills/factor-and-timeseries-research/SKILL.md §1.5 states the HAC rule for Fama-MacBeth; this section is the measurement of when it bites and when it does not.

4. Neutralization: what it removes, and how to check it

neutralize() is one cross-sectional OLS per period — regress the alpha on sector dummies and/or beta, keep the residual. The residual has exactly zero cross-sectional correlation with every column of the design, by construction.

✅ Measured — rank IC, raw and residual:

🔑 This table is the acceptance test, and it is the one people skip. Neutralization must remove the exposure you named and nothing else. sector_bet goes to zero under eight dummies, exactly as designed; the idiosyncratic alphas do not move. 🚨 If your "idiosyncratic" alpha also dies, it was never idiosyncratic — you had a sector bet with a stock-level story attached.

⚠️ low_beta is the instructive row: it keeps most of its IC either way. Neutralization is not primarily an IC intervention — which is §5.

5. 🚨 Neutralizing with a beta the market has already told you

Beta-neutral is a promise about the book's realized exposure. ✅ Measured on low_beta, a persistent tilt against high-beta names, with betas that genuinely drift (AR(1), ~138-day half-life):

🔑 The IC column barely moves and tells you nothing. The realized-beta column is the whole story. And because a single panel proves nothing, the script re-runs it on three:

✅ Measured — |realized book beta| across panel sizes:

🚨 Invariant — the leak. A hedge fitted on a window reaching 63 days past t removes about 85% of the book's beta on every panel, where every causal hedge removes about half. That gap is not a seed artefact, and it is bought entirely with a hedge ratio you could not have had. Same shape as the volatility look-ahead in ../trend-following-models/SKILL.md §3: the leak is in the hedge, not the signal, so every causality check aimed at the signal passes.

⚠️ Not invariant — and this is the useful part. Whether ONE full-sample beta beats a noisy trailing one flips with the panel (better at 60 names, worse at 80 and 200). A constant cannot track drift; a short window is noisy; which loses is an empirical question about your data. 🔑 So you cannot reason your way to the right estimator. And the gross-Sharpe column is not reliably signed either — on an 80x700 panel the peeking hedge lowers Sharpe — so "the Sharpe went up" is not how you detect this.

Check it directly: regress the book's realized P&L on the factor and report the coefficient. realized_beta() is four lines. A neutralization you did not measure is a comment, not a constraint.

6. 🚨 Winsorizing after ranking clips exactly nothing

✅ Measured — idio_fast with one 60x outlier injected every 37 days (excess kurtosis 2824.5):

🚨 0.00%. A rank maps every row onto [−0.5, 0.5], whose cross-sectional standard deviation is 0.289, so a 3-sd clip sits at ±0.87 — wider than the data can ever be. The line runs, raises nothing, and a reviewer reads it as outlier protection.

⚠️ Two things this does not say.

1. Ranking is fine — it scores best in the table. The objection is to the dead winsorize line after it, not to the rank.
2. winsorize → z-score and z-score → winsorize print identical rows — and that is a fact about the metrics, not the frames. ✅ Measured: the two frames differ by up to 10.175 (z-scoring a clipped row rescales by the clipped sd), but each is an affine image of the other, so after to_weights they agree to 2.78e−17 and every scale-free statistic downstream is identical. 🔑 Order starts to matter the moment a step is not affine — which is exactly what a rank is. "Winsorize first" is folklore in the affine case and load-bearing in the rank case.

🔑 The number to be alarmed by is the first row: one name takes 44% of a 200-name book because one input cell was 60× too large. That is what winsorization is for, and it is what a rank gives you for free at the price of discarding magnitude.

7. Combining, and paying for it

✅ Measured — four alphas (idio_fast, idio_slow, low_beta, pure_noise), 10 bps:

🔑 The best gross book is not the best net book. IC-weighted rank wins gross; cost-aware wins net, at 40% of the turnover. cost_aware_weights() scales each alpha's IC by its own net Sharpe / gross Sharpe traded alone — it charges an alpha for the turnover it brings, and zeroes one that cannot pay for itself.

⚠️ Equal weighting is worse than either here, but it is not always: IC weights are estimated on the same data they are scored on, and that is a fitted parameter like any other. Log it in ../../../fin-core/skills/backtest-validation/scripts/trial_ledger.py.

Smoothing the combined signal (EWMA halflife, days) is the cheapest turnover control there is:

⚠️ On this panel at 10 bps the net optimum sits at the low end of the grid, not in the middle — the IC-weighted combination is already fairly slow. Where the optimum sits is a function of the cost, not a property of the strategy, so it moves when the cost assumption moves. Sweep it as a curve: ../../../fin-core/skills/backtest-validation/scripts/cost_curve.py.

8. Use alphalens for the tear sheet, not for the lag

Do not re-implement quantile tear sheets, IC decay plots or turnover-by-quantile — alphalens- reloaded has them. 🚨 But its forward-return convention is a trap this library has already verified in source: see ../../../fin-libraries/skills/lib-alphalens/SKILL.md and ../../../fin-core/skills/factor-and-timeseries-research/SKILL.md §1.1. Lag your factor before you pass it in. The functions here are for the parts alphalens does not do — neutralization, combination weights, and the HAC-corrected t-stat.

9. Scripts and where this sits

scripts/alpha_combine.py — the panel, IC/ICIR/HAC t-stats, neutralize, realized_beta, cs_zscore/cs_rank/winsorize, to_weights/turnover/net_of_cost, the combination weightings, and every table above. numpy + pandas + scipy, seed 20260909, 7 s.

• Computing the raw signal causally in the first place — ../../../fin-core/skills/signal-construction/SKILL.md and its ../../../fin-core/skills/signal-construction/scripts/assert_causal.py.
• One time-series signal per instrument, rather than a cross-section — ../trend-following-models/SKILL.md.
• Factor libraries, Fama-MacBeth, alpha mining and the trial count that implies — ../../../fin-core/skills/factor-and-timeseries-research/SKILL.md.
• Turning the combined signal into weights under real constraints, and risk decomposition — ../../../fin-core/skills/portfolio-and-risk/SKILL.md.
• How much of the book to hold — ../position-sizing-kelly/SKILL.md.
• Getting the turnover done at the assumed cost — ../execution-algorithms/SKILL.md and ../../../fin-core/skills/execution-cost-analysis/SKILL.md.
• Whether the surviving combination is a discovery: trials, SPA and the cost curve — ../../../fin-core/skills/backtest-validation/SKILL.md and ../../../fin-core/skills/research-integrity-guards/SKILL.md.
• The tear sheet — ../../../fin-libraries/skills/lib-alphalens/SKILL.md.