Black and Scholes could see how a zero-beta portfolio would have to be constructed. If the stock price x changed by the small amount Ax, the warrant or option price w would alter by Ax multiplied by aw/ax, the partial derivative of w with respect to x and thus the rate at which the warrant or option price changes as the stock price changes. (This partial derivative-" delta," as it was to become known to the option traders discussed in chapter 6 would vary with time and with stock-price changes, but would be calculable if w could be expressed as a differentiable function of x and of the other parameters of the problem.) So the necessary hedge was to short-sell a quantity aw/ax of stock for every warrant held. That was in a sense the same conclusion Thorp and Kassouf had arrived at: aw/ax is their hedging ratio, expressed in their case as the slope of the empirically derived curves of warrant price plotted against stock price as in figure 5.1.

Donald MacKenzie, An Engine, Not a Camera, loc. 579