An Empirical Investigation of the Long Memory Effect on the Relation of Downside Risk and Stock Returns

This chapter resolves an inconclusive issue in the empirical literature about the relationship between downside risk and stock returns for Asian markets. This study demonstrates that the mixed signs on the risk coefficient stem from the fact that the excess stock return series is assumed to be stationary with a short memory, which is inconsistent with the downside risk series featuring a long memory process. After we appropriately model the long memory property of downside risk and apply a fractional difference to downside risk, the evidence consistently supports a significant and positive risk–return relation. This holds true for downside risk not only in the domestic market but also across markets. The evidence suggests that the risk premium is higher if the risk originates in a dominant market, such as the US. These findings are robust even when we consider the leverage effect, value-at-risk feedback, and the long memory effect in the conditional variance.