Optimal Kelly Portfolio under Risk Constraints

Abstract

The Kelly strategy is renowned for its theoretically optimal long-term growth, however, its practical application in financial markets is constrained by several limitations, including high-risk exposure and the absence of clearly defined profit-loss ratios. These challenges make it difficult to widely adopt the Kelly strategy, especially in market characterized by high volatility. To address these issues, this paper integrates contraction estimation and ridge regression techniques into the Kelly framework. By quantifying portfolio unit risk and incorporating it as a penalty term in the optimization model, we refine the asset allocation process. Additionally, machine learning methods are employed to enhance portfolio construction, where clustering is used for asset selection, and neural networks are applied to predict return performance. Empirical analysis using data from the A-share stock market demonstrates that the proposed approach not only preserves the high return potential of the Kelly strategy, but also effectively mitigates the risks associated with market volatility, delivering superior performance in medium-term to long-term investments.