Because it offers returns that are certain, the hedged portfolio can therefore earn only the riskless rate of interest, "not for the reason of [the capital] asset pricing model but ... to avoid arbitrage, or money machine": a way of generating certain profits with no net investment (Merton interview). For Merton, then, the "key to the Black-Scholes analysis" was an assumption Black and Scholes did not initially make: continuous trading, the capacity to adjust a portfolio at all times and instantaneously. "Only in the instantaneous limit are the warrant price and stock price perfectly correlated, which is what is required to form the `perfect' hedge." (Merton 1972a, p. 38) Black and Scholes were not initially convinced of the correctness of Merton's approach.

Donald MacKenzie, An Engine, Not a Camera, loc. 600