Lucky Factors

99 Pages Posted: 22 Nov 2014 Last revised: 8 Apr 2021

See all articles by Campbell R. Harvey

Campbell R. Harvey

Duke University - Fuqua School of Business; National Bureau of Economic Research (NBER)

Yan Liu

Purdue University

Date Written: April 8, 2021


Identifying the factors that drive the cross-section of expected returns is challenging for at least three reasons. First, the choice of testing approach (time-series versus cross-sectional) will deliver different sets of factors. Second, varying test portfolio sorts changes the importance of candidate factors. Finally, given the hundreds of factors that have been proposed, test multiplicity must be dealt with. We propose a new method that makes measured progress in addressing these key challenges. We apply our method in a panel regression setting and shed some light on the puzzling empirical result that the market factor drives the bulk of the variance of stock returns, but is often knocked out in cross-sectional tests. In our setup, the market factor is not eliminated. Further, we bypass arbitrary portfolio sorts and instead execute our tests on individual stocks | with no loss in power. Finally, our bootstrap implementation, which allows us to impose the null hypothesis of no cross-sectional explanatory power, naturally controls for the multiple testing problem.

The on-line appendix appears in this version of the paper.

Forthcoming, Journal of Financial Economics

Note: This paper was formerly circulated under the title "How Many Factors?"

Keywords: Factors, Variable selection, Bootstrap, Data mining, Orthogonalization, Multiple testing, Predictive regressions, Fama-MacBeth, GRS, Performance evaluation, Return prediction

JEL Classification: G12, G14, C12, C21, C22, C31, C32

Suggested Citation

Harvey, Campbell R. and Liu, Yan, Lucky Factors (April 8, 2021). Available at SSRN: or

Campbell R. Harvey (Contact Author)

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States
919-660-7768 (Phone)


National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Yan Liu

Purdue University ( email )

West Lafayette, IN 47907-1310
United States


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