Analysis of Kelly-optimal portfolios

Abstract

We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings. We show that when mean returns and volatilities of the assets are small and there is no risk-free asset, the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. Since in the investigated case the Kelly approach forbids short positions and borrowing, often only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is studied analytically in various model scenarios.

15 pages, 7 figures; extended list of references and some minor modifications

References in corpus (3)

• Dynamical Optimization Theory of a Diversified Portfolio
• How to quantify the influence of correlations on investment diversification
• Diversification and limited information in the Kelly game

Cited by in corpus (5)

• Diversification and limited information in the Kelly game
• Best Portfolio Management Strategies For Synthetic and Real Assets
• Model-Free Reinforcement Learning for Financial Portfolios: A Brief Survey
• Generalized framework for applying the Kelly criterion to stock markets
• Transaction fees and optimal rebalancing in the growth-optimal portfolio