The martingale hypothesis for futures prices is investigated using a nonparametric approach where it is assumed that the expected futures returns depend (nonparametrically) on a linear combination of predictors. We first collapse the predictors into a single-index variable where the weights are identified up to scale, using the average derivative estimator proposed by T. Stoker (1986). We then use the Nadaraya–Watson kernel estimator to calculate (and visually depict) the relationship between the estimated index and the expected futures returns. We discuss implications of this finding for a noninfinitely risk-averse hedger. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1040–1065, 2008