The Model Thinker #5 : Power Law Distributions: Long Tails

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. This model assumes that entities like cities grow at rates relative to their proportional size.

One effect of long tails is that the social influence creates greater inequality. A better book or catchier song may be slightly better than the book that is in second place, but it garners rewards much higher level than what it deserves.

In a world of long tails, we have to be prepared for large events to happen with much greater probability. Earthquakes satisfy a power law.

This is one reason why many investors do not sleep well at night.

When the market goes south, correlations increase to one so large losses will also be felt by portfolios with plenty of diversification.

Here's an experiment the reader can try with cryptocurrencies. One hypothesis of mine last year  is that the market capitalisation of crypto-coins should also follow Zipf Law and perhaps some sort of long-short trading technique can be used to trade cryptocurrencies.

Sadly, I lost interest in this asset class after it tumbled in 2018.