The optimal hedge ratio (OHR) has important implications for investors in order to hedge against the price risk. Several different approaches have been suggested in the literature in order to estimate the OHR, among others, constant parameter and time-varying approaches. One pertinent issue in this regard that has not been investigated, to our best knowledge, is whether the OHR has an asymmetric character or not. This issue is addressed in the current paper by mathematically proving that the OHR is asymmetric. In addition, we provide a method to deal with this asymmetry in the estimation of the underlying OHR. This method is applied to the US equity market using weekly spot and future share prices during the period January 5, 2006 to September 29, 2009. We find empirical support for an asymmetric OHR.