Nowadays it is widely accepted to estimate minimum variance hedge ratio regressions in first differences. There are both statistical and economic reasons for a first difference approach. However, no study has ever analyzed whether the first difference approach is also consistent with the theory of minimum variance hedging. In this paper we show, on the basis of a simulation study, that the first difference model with intercept does not provide hedge ratio estimates that are in line with the theory of minimum variance hedging. Only a linear regression model in levels provides theoretically consistent results.