Kelly's Criterion in Portfolio Optimization: A Decoupled Problem

TL;DR

This paper integrates Kelly's Criterion into portfolio optimization by combining risk and return into a single objective, solved with evolutionary algorithms, and verified through Monte Carlo simulations.

Contribution

It introduces a novel model that incorporates Kelly's Criterion into standard portfolio optimization, using differential evolution and Monte Carlo verification.

Findings

Evolutionary algorithms effectively solve Kelly-based portfolio optimization.

The model successfully balances risk and return in portfolio selection.

Monte Carlo methods confirm the accuracy of the optimization results.

Abstract

Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.