Validating cross-sectional dependence assumptions in a factor model

Assessing market efficiency and investment performance often relies on a simultaneous test for zero intercepts in a factor model, and such a test is asymptotically valid under some cross-sectional dependence (CSD) assumptions such as sparsity or sufficiently weak CSD. Because these assumptions are imposed from theoretical needs, a direct validation is almost infeasible. This paper introduces a novel approach to indirectly validating the CSD assumptions by adapting existing tests to factor model residuals. Theoretically, the adapted tests can be shown to exhibit a normal limit under the same conditions as the original tests. Empirically, the adapted tests indicate that some prominent factor models fail to capture CSD, confounding the intended interpretation of the original tests. While CSD is always a problematic feature in returns, we identify various stock characteristics as promising for constructing factors explaining CSD.