Tackling estimation risk in Kelly investing using options

2025-08-26

AI Summary

The Kelly criterion maximizes the long-term growth rate of wealth but suffers from poor robustness due to its high sensitivity to estimation errors in probability and payoff parameters, often leading to substantial performance degradation. Method: To address this limitation, we propose a Kelly-type investment strategy integrating European options within a binomial model framework. By incorporating options as explicit risk-hedging instruments into the Kelly optimization—formulated as expected logarithmic utility maximization—we construct a growth-optimal portfolio inherently robust to parameter uncertainty. Contribution/Results: Theoretical analysis and numerical experiments demonstrate that the proposed strategy maintains stable wealth growth under parameter misspecification, significantly enhancing portfolio robustness and long-horizon performance in uncertain environments. This extends the practical applicability of the Kelly framework to realistic financial settings where precise parameter estimation is infeasible.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The Kelly criterion provides a general framework for optimizing the growth rate of an investment portfolio over time by maximizing the expected logarithmic utility of wealth. However, the optimality condition of the Kelly criterion is highly sensitive to accurate estimates of the probabilities and investment payoffs. Estimation risk can lead to greatly suboptimal portfolios. In a simple binomial model, we show that the introduction of a European option in the Kelly framework can be used to construct a class of growth optimal portfolios that are robust to estimation risk.

Problem

• Addressing estimation risk in Kelly portfolio optimization
• Using options to create robust growth-optimal portfolios
• Mitigating sensitivity to probability and payoff estimation errors

Innovation

• Using options to reduce Kelly estimation risk
• European options create robust growth portfolios
• Options mitigate binomial model sensitivity