ABSTRACTThis paper examines the importance of forecasting higher moments for optimal hedge ratio estimation. To this end, autoregressive conditional density (ARCD) models are employed which allow for time variation in variance, skewness and kurtosis. The performance of ARCD models is evaluated against that of GARCH and of other conventional hedge ratio estimation methodologies based on exponentially weighted moving averages, ordinary least squares and error correction, respectively. An empirical application using spot and futures data on the DJI, FTSE and DAX equity indices compares the in‐sample and out‐of‐sample hedging effectiveness of each approach in terms of risk minimization. The results show that the ARCD approach has the best performance, thus suggesting that forecasting higher moments is of practical importance for futures hedging. Copyright © 2012 John Wiley & Sons, Ltd.