The “practitioner Black-Scholes delta” for hedging equity options is a delta calculated from the Black-Scholes-Merton model with the volatility parameter set equal to the implied volatility. As has been pointed out by a number of researchers, this delta does not minimize the variance of a trader’s position. This is because there is a negative correlation between equity price movements and implied volatility movements. The minimum variance delta takes account of both the impact of price changes and the impact of the expected change in implied volatility conditional on a price change. In this paper, we use ten years of data on options on stock indices and individual stocks to investigate the relationship between the Black-Scholes delta and the minimum variance delta. Our approach is different from earlier research in that it is empirically-based. It does not require a stochastic volatility model to be specified. Joint work with Allan White.