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

ArXiv ID: 2503.07498 “View on arXiv”

Authors: Unknown

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.

Keywords: Utility Theory, Exponential Utility, Logarithmic Utility, Half-Kelly Criterion, Generalized Mean-Variance, Multi-Asset (Portfolio Optimization)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is heavily theoretical, using advanced mathematical frameworks like Bayesian posterior predictive distributions, compound distributions, and deriving closed-form solutions for various utility functions. However, it lacks any implementation details, backtesting results, or empirical data validation, focusing solely on theoretical derivations.

  flowchart TD
    A["Research Goal: Optimal Portfolio Allocation via Utility Theory"] --> B["Methodology: Apply Utility Functions & Compound Distributions"]
    B --> C{"Input: Asset Returns & Uncertainties"}
    C --> D["Process: Exponential Utility for Diversification"]
    C --> E["Process: Logarithmic Utility for Leverage"]
    D --> F["Outcome: Maximizing Expected Utility"]
    E --> F
    F --> G["Finding: Natural explanation of Half-Kelly Criterion"]
    F --> H["Outcome: Generalized Mean-Variance Extension"]