No Sparsity in Asset Pricing: Evidence from a Generic Statistical Test

Abstract

We present a novel test to determine sparsity in characteristic-based factor models. Applying the test to industry and pseudo-random portfolios, we reject the null hypothesis that fewer than ten factors are sufficient to explain returns, and show that at least forty factors are needed for the various sample periods examined. We find that dense models outperform sparse ones in both pricing and investing. Testing with tree-based portfolios also indicates no sparsity. Our results suggest that most existing factor models, which have fewer than six factors, are questionable, and that future research on such low-dimensional models is unlikely to be fruitful.

Keywords: JEL Classification: G12, C12 factor models, characteristic-based factors, sparsity, test

JEL Classification: G12, C12