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Optimal Diversification and Leverage in a Utility-Based Portfolio Allocation Approach

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  • Vladimir Markov

Abstract

We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance existing methodologies by incorporating compound probability distributions to model the effects of both statistical and non-stationary uncertainties. Additionally, we extend the maximum expected utility objective by including the variance of utility in the objective function, which we term generalized mean-variance. In the case of logarithmic utility, it provides a natural explanation for the half-Kelly criterion, a concept widely used by practitioners.

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  • Vladimir Markov, 2025. "Optimal Diversification and Leverage in a Utility-Based Portfolio Allocation Approach," Papers 2503.07498, arXiv.org, revised Mar 2025.
    • Handle: RePEc:arx:papers:2503.07498
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