Long Tails are the bane of many investors. As I derive a lot of investment insights from quantitative investing, I have to accept the precarious position of comparing investment strategies using mean and variances while obviously being aware that markets do not act “normally”.

Unlike the normal distribution, long tails are modelled differently.

One example is the size of cities.

Cities have a tendency to arrange themselves in power-law distributions which is governed by Zipf Law. The rank of a city multiplied by its size is a constant. New York has a population of 8.6M. Second in rank is Los Angeles has a population of 4M. 2 x 4M approximates the population of New York. The third largest city is Chicago has a population of 2.7M which is about a third of that of New York.

One model that explains why things somehow arrange themselves neatly into Power Laws is the preferential attachment model.