Hedge funds are fundamentally exposed to equity volatility, skewness, and kurtosis risks based on the systematic pattern and significant spread in alphas from the existing models that do not control for the higher-moment risks. The spread and pattern in alphas do not disappear with bootstrap simulation, Bayesian analysis to account for potential estimation error, adjustment for backfilling bias, and the inclusion of additional systematic factors. Significant cross-sectional variation in higher-moment exposures is observed across fund styles with equity-oriented styles displaying more extreme exposures. Investable higher-moment factors explain the time series behavior of returns of a large number of Managed Futures, Event Driven, and Long/Short Equity hedge funds. Average exposure sensitivities for higher-moment factors are statistically significant in an estimation that accounts for style fixed effects and fund random effects.