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

We provide a generic statistical test to discern whether there is sparsity in high-dimensional characteristic-based factor models. Applying the test with both industry and “pseudo” random portfolios as test assets, we find that the null hypothesis — suggesting fewer than ten factors are capable of explaining the cross-section of equity returns — is rejected. Moreover, a dense model representation outperforms sparse models in pricing the cross-section and as an investment strategy. Furthermore, we explore novel test assets constructed using tree-based models (P-Tree). Our conclusion still holds when a multitude of firm characteristics are used in the construction of P-Tree portfolios. Overall, there is no sparsity in asset pricing in the large space of characteristic-based factors.