Giglio, Liao & Xiu — Thousands of Alpha Tests (Review of Financial Studies 34(7), 2021)
T1 — peer-reviewed, Review of Financial Studies (top-tier finance journal), 2021, pp. 3456–3496. Stefano Giglio (Yale SOM/NBER/CEPR), Yuan Liao (Rutgers), Dacheng Xiu (Chicago Booth). Found for growth edge 1 on this spoke's own list ("a source that reports its N"), the half deflated-sharpe-ratio and pseudo-mathematics-financial-charlatanism left open: the theory of trial-count correction was in the corpus, and no example of a publication that actually states its N.
This paper states its N, and applies the correction with it
After filtering (minimum 36-month track record), the sample is 1,761 hedge funds over 290 months (TASS database; robustness checked against Evestment). That is not a background detail — the paper runs one alpha test per fund, so the trial count is the fund count, and it says so on the page that reports results: "the results of the multiple alpha tests for the 1,761 hedge funds in our sample." This is the exact object the edge asked for: a published analysis that names its own N rather than reporting a Sharpe or an alpha with the trial count left implicit or absent.
What the method does
A new multiple-hypothesis-testing framework for linear asset-pricing models, built to stay valid when the number of tests (funds) is large relative to the sample length — the finance-specific version of the "many hypotheses, few observations" problem deflated-sharpe-ratio names generically. It combines a matrix-completion step (handling funds with missing months — over 70% of fund-months are missing in this sample) with a wild-bootstrap procedure for finite-sample inference, and controls the false discovery rate across all 1,761 simultaneous tests rather than reading each fund's p-value in isolation.
The finding
Out of 1,761 funds, the procedure deems 19% to have positive alpha after the correction, with the selected funds averaging 70 basis points per month, statistically significant. Compared against naive per-fund significance testing (which would flag more funds as skilled by ignoring the multiple- comparisons inflation this spoke's pseudo-mathematics-financial-charlatanism page already derives), the corrected procedure is more conservative and — the paper's stated payoff — better at building portfolios that hold up out of sample: portfolios formed from the FDR-selected funds achieve "superior out-of-sample alpha even with significantly larger portfolios," which is the paper's answer to the standard objection that a stricter filter must mean fewer investable funds.
What it does to the edge
Growth edge 1 was two things bundled together: the theory of why N matters (closed 2026-08-08 by deflated-sharpe-ratio and pseudo-mathematics-financial-charlatanism) and a worked example of someone actually reporting N and correcting for it (open until now). This paper closes the second half directly, though it is worth stating precisely what kind of N it reports: fund count, i.e. how many existing strategies were tested against each other for skill — not the configuration count the original edge text asked about (how many parameter variations of one strategy were searched before publishing the winner, the strategy-optimization case). Both are the same statistical problem (selection among many trials inflates the apparent best), but they are different objects: one tests which of many managers is skilled, the other tests which of many parameter sets is real. The corpus now has a clean worked example of the first kind and still none of the second — the edge is closed for "does anyone report N," open for "does anyone report N for their own single strategy's search."
Related
deflated-sharpe-ratio · pseudo-mathematics-financial-charlatanism · strategy-optimization · backtest-overfitting · synthesis