We provide an entropy approach for measuring the asymmetric comovement between the return on a single asset and the market return. This approach yields a model-free test for stock return asymmetry, generalizing the correlation-based test proposed by Hong, Tu, and Zhou (2007). Based on this test, we find that asymmetry is much more pervasive than previously thought. Moreover, our approach also provides an entropy-based measure of downside asymmetric comovement. In the cross section of stock returns, we find an asymmetry premium: Higher downside asymmetric comovement with the market indicates higher expected returns.

In this article, we propose two asymmetry measures for stock returns. Unlike the popular skewness measure, our measures are based on the distribution function of the data rather than just the third central moment. We present empirical evidence that the greater upside asymmetries calculated using our new measures imply lower average returns in the cross section of stocks. In contrast, when using the skewness measure, the relationship between asymmetry and returns is inconclusive.