Optimal portfolio allocation with uncertain covariance matrix

ArXiv ID: 2311.07478 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we explore the portfolio allocation problem involving an uncertain covariance matrix. We calculate the expected value of the Constant Absolute Risk Aversion (CARA) utility function, marginalized over a distribution of covariance matrices. We show that marginalization introduces a logarithmic dependence on risk, as opposed to the linear dependence assumed in the mean-variance approach. Additionally, it leads to a decrease in the allocation level for higher uncertainties. Our proposed method extends the mean-variance approach by considering the uncertainty associated with future covariance matrices and expected returns, which is important for practical applications.

Keywords: portfolio allocation, covariance matrix uncertainty, CARA utility, mean-variance approach, marginalization, Portfolio Management (Multi-Asset)

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, featuring advanced probability theory, moment-generating functions, and analytical derivations of optimal weights under uncertainty, but it lacks concrete backtesting, code, or empirical datasets, focusing instead on mathematical models and conceptual frameworks.

  flowchart TD
    A["Research Goal: Optimal Portfolio Allocation with Uncertain Covariance Matrix"] --> B["Methodology: Expected CARA Utility & Marginalization"]
    B --> C["Inputs: Historical Data & Prior Distribution of Covariance"]
    C --> D["Computational Process: Integrate over Covariance Uncertainty"]
    D --> E{"Key Finding: Logarithmic Dependence on Risk"}
    D --> F{"Key Finding: Reduced Allocation under High Uncertainty"}
    E --> G["Outcome: Extended Mean-Variance Framework for Uncertain Inputs"]
    F --> G