Definition
The "factor zoo" is the proliferation of hundreds of candidate factors proposed to explain the cross-section of expected stock returns (Cochrane 2011; Harvey-Liu-Zhu 2016). The central problem is disciplining this list: how to judge whether a new factor adds genuine explanatory power beyond the high-dimensional set of factors already discovered. Feng-Giglio-Xiu (2020) give a valid statistical test by marrying double-selection LASSO with Fama-MacBeth two-pass regression (Feng-Giglio-Xiu 2020).
Key Ideas
- The proliferation problem. Decades of research produced ~150+ published factors, many likely redundant or the product of data snooping; a new candidate must be evaluated against all of them at once — a high-dimensional model-selection problem.
- Why naive LASSO fails. Running a single LASSO over the large factor set to pick controls and then testing the new factor gt (or just checking whether gt is selected) is unreliable: model-selection mistakes omit relevant controls and induce omitted-variable bias, invalidating inference.
- Double-selection. Following Belloni-Chernozhukov-Hansen (2014), select two sets of controls from the high-dimensional factors ht: those useful for (a) explaining the cross-section of expected returns and (b) predicting the new factor gt (mitigating omitted-variable bias). Including both sets as controls is essential for valid inference on gt's SDF loading / risk premium.
- Two-pass estimation. The selected controls enter a Fama-MacBeth-style cross-sectional regression, yielding an estimate and valid standard error for the marginal contribution (risk premium) of gt robust to selection mistakes.
- Empirical verdict. Applied to a library of ~150 factors, most recently-proposed factors are redundant relative to existing ones, but a few retain statistically significant explanatory power. (E.g. a factor can have a significant alpha vs. the Fama-French three-factor model yet fail once tested against the full zoo.)
Where Feng-Giglio-Xiu discipline the zoo by estimation (valid post-selection inference on a new factor's risk premium), Harvey-Liu-Zhu (2016) discipline it by significance testing. Their argument: factor discovery is a multiple-testing problem, so the conventional t>2.0 cutoff — comfortably cleared by the market beta's t=2.57 in Fama-MacBeth (1973) — is far too lax once hundreds of factors have been tried. Applying Bonferroni, Holm (family-wise error) and Benjamini-Hochberg-Yekutieli (false-discovery-rate) adjustments to the historical factor count, they derive time-varying hurdles and conclude a credible new factor should clear roughly t>3.0 today (a floor, since failed factors go unpublished). Their blunt corollary — most claimed findings in financial economics are likely false — is the finance analogue of Ioannidis (2005), and the cross-sectional twin of the same authors' Sharpe-ratio backtest haircut.
Why It Matters
- Inference discipline for a data-snooped literature. It replaces "my factor has a significant alpha vs. a small benchmark" with "my factor survives against hundreds of competitors, with valid post-selection inference" — a much higher bar.
- A template beyond finance. The double-selection recipe for valid inference on one variable amid many high-dimensional controls (see High-Dimensional Inference, Lasso) applies wherever a treatment/target effect must be isolated from many possible confounders.
- Sharpens the joint-hypothesis debate. It gives the EMH/asset-pricing field a principled way to prune the factor list rather than endlessly appending new ones.
Open Questions
- Sensitivity to the LASSO penalty/tuning and to the composition of the factor library.
- Weak-factor and errors-in-variables problems in two-pass risk-premium estimation under high dimension.
- Distinguishing risk factors from characteristics and from purely mispricing-driven spreads within the same framework.
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