Asymmetric Correlation of Stock Returns: Statistical Tests and Economic Evaluation

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. 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 correlations into a belief of asymmetric correlations. Applying our methodology to three portfolios grouped by size, Fama and French’s size and book-to-market, and industry, we find that asymmetric correlations show up in sample estimates for all the portfolios, but they are statistically significant only for small size portfolios. Nevertheless, asymmetric correlations are of substantial economic importance, irrespective of the portfolios, for the investor who switches her symmetry belief into asymmetric correlations.