Wednesday, November 17, 2010

Return Distributions: Power Law > Gaussian

Power Law distributions explain fat-tail distributions much more accurately than Normal. I am aware that most academics are drilled about how Gaussian curves fit EVERYTHING in real life. That is nonsense. The existence of alternative distributions in math/stat textbooks that track empirical real life tell a very different story. Basically, extreme (potentially profitable) events occur MUCH MORE frequently than what Gaussian assumes.

According to someone who models stock returns with a normal distribution (this probably includes 99% of academic finance grads), the 1 day big market drops in 1929, 1987, 1998, 2008, Enron, GM, etc. are supposed to happen at most once every 10^30, or nonillion years. So it's numerically convenient, and obviously wrong, yet they embrace it as if it's the one and only truth.

The brilliant options trader, writer of The Black Swan, and once a professor at MIT, Taleb mentioned in Haug's Derivative Models on Models that the state of academic finance is intellectually insulting. Having met some folks from local business schools, I must agree.

It would seem more out of political reasons for this persistent blind faith of normal distributions in modern finance. As an overwhelming majority of current financial practices rely on Gaussian moments such as standard deviations, which we now know is completely meaningless in financial time series, an official recognition of this error would mean job loss for university staff, so-called analysts, and embarrassment for a number of people who came up with useless concepts such as "modern portfolio theory", "CAPM", "Black-Scholes Option Pricing", "VaR", and etc.

Is it intentional deception or incompetence? I'd say a bit of both.

0 Reflections: