Hedge funds display a strong non-linear payoff structure because of the use of highly dynamic trading strategies. This article examines the relevance of using higher-order comoment equity risk premiums implied in the united states and the emerging markets for capturing these return non-linearities. We provide evidence that the higher-order comoment equity risk premiums help in explaining the returns of the different hedge fund strategies from the hedge fund research classification. We perform a dynamic analysis where moment risk exposures are examined separately in up and down markets. We show that hedge fund styles tend to vary their exposures to moment risks according to the market regimes.