Modeling with Power Law distributions

Power Law distributions can explain data sets with extreme values, which includes a whole lot of things in nature, and pretty much everything in financial economics; Normal/Gaussian distributions can not. At the same time, Power Law models are just as, if not more flexible and mathematically elegant.

So here's the walk through,

Definition source: Forecasting Extreme Financial Risk

The Tail Exponent alpha "a" is the key to its tail fatness. A number of existing research papers suggest that actual financial returns resemble a Power Law distribution with the tail exponent between 2 and 3.

An example:

Given a probability P= .2, i.e. 20% for a security to return a minimum of .01/day, so P(.01)= .2

Let the Tail Exponent= 2, we can now work out the probability of it returning .05 (5 times .01/day) in a day. So we want to find P(.05)

P(.05)= P(.01)(5)^(-2)
P(.05)= .2(.04)
P(.05)= .008 = .8%

That was pretty easy right?

Obviously, better probability estimations is critical for anyone planning business models where it's all about "calculated risks".

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.