We propose an innovative theoretical model to determine the optimal hedge ratio (OHR) with futures contracts as the minimizer of a quantile risk measure. This class of measures is very large and allows to recover the minimum-VaR and the minimum-expected shortfall hedge ratios as special cases. The copula representation of quantiles yields an accurate and flexible estimation of the dependence structure between the spot and the futures position. Employing data for the main UK and US indices, and EUR/USD and EUR/GBP exchange rates, we investigate the hedging effectiveness of our model compared to that of existing approaches. We document that our model improves upon the hedging performance of minimum-VaR and minimum-expected shortfall hedge ratios, provided that the copula shows an acceptable fit to the data. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:658–675, 2014