If they [price changes] were really stable [Levy-distributed], the way Mandelbrot describes them, they maintained the same properties under addition. So if you start with a stable distribution of log returns, it's going to be of the same type [the same value of alpha] when you look at monthly returns, and that wasn't true. They tend to converge towards normality.... I think people just kind of because they couldn't explain the slow convergence stuff, so they kind of became disinterested in the fat tails. (Fama interview) If one was dealing with stock or portfolio returns over periods as long as a month, Fama concluded, the tails became slim enough that "the normal distribution is a good working approximation."

Donald MacKenzie, An Engine, Not a Camera, loc. 509