Kelly-Optimal Cryptocurrency Portfolios with Multiple Assets
A Case Study using Bitcoin, Ethereum, Cardano, and more.
Introduction
The Kelly criterion is a well-known strategy for sizing bets to maximize long-run expected log wealth. It is widely applied to sports betting and casino gambling. Most sources provide coverage only for the single-asset case, however. We discuss the Kelly criterion for balancing a portfolio with multiple assets — taking into account yield rates and incorporation of risky and non-risky assets — and apply the strategy to a basket of popular cryptocurrencies.
Background
The central object of study in classical Markowitz portfolio theory is the so-called efficient frontier. Points on the frontier (corresponding to portfolio allocations) are optimal in the sense that return cannot be increased without also increasing volatility, and volatility cannot be decreased without decreasing return. The point with optimal Sharpe ratio lies on this frontier. It turns out that the Kelly criterion, also lies on this frontier — albeit at a different location from the max Sharpe. It is known that the Kelly formula favors allocations with higher volatility and higher expected return rates compared to Sharpe-optimal points, so as to maximize expected log growth.
