Why the head should know how the tail is behaving

The next issue of Science News has a good article on predicting financial risk. It covers how traditional models of estimating risk are missing a lot by discounting rare, freak events in their calculations. Gaussian distribution models fail to account for the outliers (the long tail of a probability distribution) that can drastically alter market behaviour. Although a normal distribution model does account for a lot of economic activity, it ignores the rare large freak events, so it doesn’t fully capture reality. Which is where power law models come in.

“Long tails are a mathematical clue that a different kind of behavior may be at play, one that physicists have long been fascinated by. When data follow what is called a power law distribution, the outlandish data points that generate the tail aren’t aberrant freaks; they fit right in.”

Gaussian distribution and power law regimes will predict fairly similar outcomes for unlikely but possible events, such as an event with a one-in-a-hundred likelihood of occurring. But for highly unlikely events, such as a one-in-ten-thousand event, the two models deliver hugely different predictions. The differences can’t be ignored. The article points out that most economists think that current models are too simplistic, but the challenge remains how to reconcile freak occurrences with traditional models based on stability.