Fortin, Alain-Philippe Gagliardini, Patrick Scaillet, Olivier 2023 This article studies new tests for the number of latent factors in a large cross-sectional factor model with small time dimension. These tests are based on the eigenvalues of variance–covariance matrices of (possibly weighted) asset returns and rely on either an assumption of spherical errors, or instrumental variables for factor betas. We establish the asymptotic distributional results using expansion theorems based on perturbation theory for symmetric matrices. Our framework accommodates semi-strong factors in the systematic components. We propose a novel statistical test for weak factors against strong or semi-strong factors. We provide an empirical application to U.S. equity data. Evidence for a different number of latent factors according to market downturns and market upturns is statistically ambiguous in the considered subperiods. In particular, our results contradict the common wisdom of a single-factor model in bear markets. application/pdf https://susi.usi.ch/global/documents/330210 https://n2t.net/ark:/12658/srd1330210 https://susi.usi.ch/documents/330210/files/Gagliardini_2023_OUP_J Financial Econometrics_Eigenvalue Tests.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1093/jjfinec/nbad024 info:eu-repo/semantics/altIdentifier/ark/12658/srd1330210 info:eu-repo/semantics/openAccess CC BY Journal of financial econometrics. - 2023, vol. 00, p. nbad024 Factor model Principal component analysis Panel data Large n and fixed T asymptotics Equity returns info:eu-repo/classification/udc/33 Eigenvalue tests for the number of latent factors in short panels http://purl.org/coar/resource_type/c_6501