An Analytic Solution for Asset Allocation with a Multivariate Laplace Distribution

ArXiv ID: 2411.08967 “View on arXiv”

Authors: Unknown

Abstract

In this short note the theory for multivariate asset allocation with elliptically symmetric distributions of returns, as developed in the author’s prior work, is specialized to the case of returns drawn from a multivariate Laplace distribution. This analysis delivers a result closely, but not perfectly, consistent with the conjecture presented in the author’s article Thinking Differently About Asset Allocation. The principal differences are due to the introduction of a term in the dimensionality of the problem, which was omitted from the conjectured solution, and a rescaling of the variance due to varying parameterizations of the univariate Laplace distribution.

Keywords: Multivariate Asset Allocation, Elliptical Distributions, Multivariate Laplace Distribution, Mean-Variance Optimization, Portfolio Theory, Equities

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats
• Why: The paper is heavily analytical, deriving a closed-form solution using advanced mathematics like Bessel functions and Mahalanobis distances for a specific distribution (multivariate Laplace). However, it lacks any empirical backtesting, real-world data, or implementation details, focusing purely on theoretical derivation.

  flowchart TD
    A["Research Goal:<br>Analytic Asset Allocation<br>for Multivariate Laplace"] --> B{"Methodology"}
    B --> C["Use Elliptical Distribution Theory<br>from Prior Work"]
    C --> D["Specialize to<br>Multivariate Laplace Distribution"]
    D --> E["Computational Process:<br>Derive Analytic Solution<br>for Mean-Variance Optimization"]
    E --> F{"Outcomes/Findings"}
    F --> G["Consistent with Conjecture<br>in 'Thinking Differently...'"]
    F --> H["Key Deviations Found:<br>1. Rescaling of Variance<br>2. Term in Dimensionality"]
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    style B fill:#ccf,stroke:#333,stroke-width:2px
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