Practical statistical convenience, not empirical fit, drove finance’s retention of the normal distribution

Evidence

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.” The “costs of rejecting normality for securities returns in favor of [Levy] non-normal distributions are substantial,” Fama wrote. Although “most of the models of the theory of finance” could be reconstructed on the basis of Levy distributions, the “exposition” of those models became more complicated and “statistical tools for handling data from [Levy] non-normal … distributions are primitive relative to the tools that are available to handle data from normal distributions.” — Donald MacKenzie, An Engine, Not a Camera, 510

Categorization

• XREF: Connects to the broader history of normal-vs-heavy-tailed distributions in finance; resonates with Taleb’s critique of Gaussian assumptions and the ‘dismal’ science of model choice on grounds of tractability. — connects to: The bell-curve shape of Gaussian distributions is what banks’ risk models assume; The randomness of price changes was a foundational open problem in finance — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 463; Mainstream statistics training in the 1970s ignored Levy distributions — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 481 (+2 more)
• DEFINE: Clarifies the Levy stable distribution concept and alpha as the tail-thickness parameter, with alpha=2 being the normal distribution.

Broader Connections

• Stock price changes are modeled with thin-tailed lognormal distributions, not fat-tailed ones #exemplifies (0.85) — Donald MacKenzie, An Engine, Not a Camera, 138