Is Diversification a Fantasy in Cryptoland?

Isotropic Correlation Seems to Fit the Bill

Photo by Traxer on Unsplash

I’ve recently been writing a lot about the “effective” degrees of freedom in equity markets, and how there seems to be:

1. insufficient independence to “normalize” large portfolio returns;
2. weak support in recent data for linear factor models; and,
3. a surprisingly good fit in reality for what I’d previously viewed as a toy model: fully isotropic returns.

By “isotropic returns” I mean that all pairwise correlations of returns are equal — that there is no preferred direction in the multidimensional space of asset returns.

This is a empirically supported by two facts: firstly, that the returns of “large” portfolios like the S&P 500 or the Russell 3000 are simply not normal in any way — in gross defiance of the Central Limit Theorem, which should be kicking in even for the Dow with it’s motley collection of thirty stocks. (Thirty being the sample size they tell you to use in statistics class to decide if the Normal distribution is likely to be an “ok” approximation to your data.”