Asymmetries in Stock Returns: Statistical Tests and Economic Evaluation

Abstract

In this paper, we provide a model-free test for asymmetric correlations which suggest stocks tend to have greater correlations with the market when the market goes down than when it goes up. We also provide such tests for asymmetric betas and covariances. In addition, we evaluate the economic significance of asymmetric correlations by answering the question that what is the utility gain for an investor who switches from a belief of symmetric stock returns into a belief of asymmetric returns. Applying our methodology to three portfolios grouped by size, Fama and French's size and book-to-market, and industry, we find that asymmetries show up in sample estimates for all the portfolios, but they are statistically ignificant primarily for small size portfolios. Nevertheless, asymmetries are of substantial economic importance for an investor who switches her symmetry belief into an asymmetric one, irrespective of the portfolios.