Semi-coskewnesses and the cross-section of excepted stock returns: Evidence from China

We propose an alternative nonlinear semi-risk measure, by decomposing the traditional coskewness into four components associated with the signed excess market and asset returns, that captures the asymmetries in nonlinear markets. We find that the two semi-coskewnesses attributable to (positive) negative excess market returns predict significantly (lower) higher future returns based on high-frequency data from China’s A-share market. After conducting a wide range of implementations, the risk premium for negative coskewness stands out as the most significant, followed by the premium for mixed negative coskewness. In contrast, the results for positive and mixed positive coskewnesses are not always significantly negative. More importantly from an economically meaningful perspective, for a downside risk premium of 25.40% per annum, a 2-standard-deviation increase in negative semi-coskewness gives rise to an increase of approximately 13.71% in annual expected return.

Methods
We calculate daily realized semi-coskewnesses using 5-minute intraday returns and aggregate them to obtain weekly frequency based on all the listed stocks of China’s A-share stock market. We also extract market capitalization, turnover rate, and book-to-market ratio for each stock from the CRSP database and the RESSET Financial Research database respectively. Lastly, we use daily returns to compute weekly returns, realized (co)moments, realized semi-risk factors, and lagged returns as well as maximum/minimum returns over the previous month.