highest portfolio and the lowest portfolio and Column " _t_ -stat" reports associated _t_ -statistics computed using Newey-West (1987) heteroskedastic-robust standard errors with 12 lags. The relative usual downside beta on average generates a significant spread of 0.18% and a spread significant at 5% within the first, second and fourth quintile sorted by the relative ES-implied beta. Panel B demonstrates that the relative ES-implied beta generates a significant spread at 1% within all quintiles sorted by the relative usual downside beta, suggesting that the predictive power of the relative ES-implied beta over returns prevails within all stocks regardless of their levels of relative usual downside beta. The results are similar for value-weighted returns and thus are not reported.

I then study the relation between the predictive power of relative downside betas and coskewness, since the literature documents a strong association between the predictive power of the relative usual downside beta and coskewness and Panel B in Table 1 shows a high correlation between the two. To find whether the predictive power of relative downside betas is affected by coskewness, I first sort stocks into quintile portfolios based on coskewness in the previous 12 months and then on the relative downside beta in the previous 12 months. Panel A and Panel B in Table 9 report equal-weighted returns of the 25 portfolios sorted by the relative usual downside beta and the relative ES-implied beta after controlling for coskewness, respectively. The relative usual downside beta only generates a significant spread within the first and second coskewness-sort quintiles, implying that the predictive power of the relative usual downside beta is limited to low coskewness stocks. In contrast, the relative ES-implied downside beta generates a highly significant spread around 0.5% within all coskewness-sort quintiles as Panel B in Table 9 shows. Therefore, while the relative usual downside beta only has significant predictive power over returns of stocks with low coskewness, the predictive power of the relative ES-implied downside beta over future returns is prevalent within stocks with any level of coskewness.

I further study the relation between the relative ES-implied downside beta and size, cokurtosis and volatility. Size and cokurtosis demonstrate a mild correlation with the relative ES-implied beta in Panel B of Table 1. As another measure of risk, volatility is also likely to explain the predictive power of the relative ES-implied beta over returns. Panel A in Table 10 reports equalweighted returns of portfolios sorted by size first and then the relative ES-implied downside beta. On average, the relative ES-implied downside beta generates a significant spread of 0.2% between the highest and lowest portfolios after controlling for size. The overall decreasing spread from low size-sort quintile to high size-sort quintile suggests that the predicitve power of the relative ES-implied beta may be stronger for small-cap stocks than for large-cap stocks.

Panel B in Table 10 reports equal-weighted returns of portfolios sorted by cokurtosis first and then the relative ES-implied downside beta. On average, the relative ES-implied beta generates a significant spread of 0.45%. Within each cokurtosis-sort quintile, the relative ES-implied beta also generates a spread significant at 5% except in the highest cokurtosis quintile, where the spread 15