diversification: Nonlinear Function
Created: May 15, 2021
Modified: May 15, 2021

diversification

This page is from my personal notes, and has not been specifically reviewed for public consumption. It might be incomplete, wrong, outdated, or stupid. Caveat lector.

Perhaps the only free lunch in finance.

Given N investments all with the same expected value and level of risk (variance), whose performance is independent of each other, then spreading your portfolio evenly between them achieves the same expected value with risk / (N)\sqrt(N).

There's a risk-reward tradeoff, where risk is inherently undesirable, and the market is willing to accept a lower expected value in order to reduce risk. Bonds have, historically, a lower expected value than the stock market, but they are more stable, and there is a lot of demand for that.

At any given level of risk, then, diversification allows you to get higher expected value, because you can achieve that risk by averaging many high-expectation investments that are individually risky but uncorrelated. Of course, it's key that they are actually uncorrelated.