Sep

11

Gappy (Giuseppe Paleologo) posted this on X, and it prompted me to wonder if a power law would apply to the skill differences and win rates of tennis players viz their rankings. Need to find some easily accessible data for that. And of course, how PLs apply to the distribution of returns with the S&P 500 in a given time period. But could it be predictive?

Power Laws in Economics and Finance
Xavier Gabaix, Stern School, NYU

A power law (PL) is the form taken by a large number of surprising empirical regularities in economics and finance. This review surveys well-documented empirical PLs regarding income and wealth, the size of cities and firms, stock market returns, trading volume, international trade, and executive pay. It reviews detail-independent theoretical motivations that make sharp predictions concerning the existence and coefficients of PLs, without requiring delicate tuning of model parameters. These theoretical mechanisms include random growth, optimization, and the economics of superstars, coupled with extreme value theory. Some empirical regularities currently lack an appropriate explanation. This article highlights these open areas for future research.

Asindu Drileba writes:

One of the funniest commodities traded in Uganda (my country) is Vanilla. The price fell from, $156 per kilo, to $1.14 per kilo. A -99% drop during the 2020 covid lock down.

Vanilla cultivation is special in that it can't be farmed mechanically.

- It only flowers once a year
- The flower is only open for 24 hours in one year
- It can only be hand pollinated
- If you miss those 24 hours in one year, your done, wait for the next season.

So a lot of the cultivation is by small "artisanal" farmers.

Madagascar produces close to 80% of the world's vanilla. All other countries produce the rest. So its a power law distribution. The smallest hiccup in Madagascar can cause the vanilla price to skyrocket or drop.

I think power laws outside prices (like supply chains of vanilla) can be used to predict what asset, commodity or instrument will be volatile (large moves both up & down). I think these underlying setups in assets are what echo as power law distributions into prices.


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