On Cost-Sensitive Distributionally Robust Log-Optimal Portfolio

ArXiv ID: 2410.23536 “View on arXiv”

Authors: Unknown

Abstract

This paper addresses a novel \emph{“cost-sensitive”} distributionally robust log-optimal portfolio problem, where the investor faces \emph{“ambiguous”} return distributions, and a general convex transaction cost model is incorporated. The uncertainty in the return distribution is quantified using the \emph{“Wasserstein”} metric, which captures distributional ambiguity. We establish conditions that ensure robustly survivable trades for all distributions in the Wasserstein ball under convex transaction costs. By leveraging duality theory, we approximate the infinite-dimensional distributionally robust optimization problem with a finite convex program, enabling computational tractability for mid-sized portfolios. Empirical studies using S&P 500 data validate our theoretical framework: without transaction costs, the optimal portfolio converges to an equal-weighted allocation, while with transaction costs, the portfolio shifts slightly towards the risk-free asset, reflecting the trade-off between cost considerations and optimal allocation.

Keywords: Distributionally Robust Optimization, Wasserstein Metric, Log-Optimal Portfolio, Transaction Costs, Duality Theory

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper involves advanced mathematics such as Wasserstein metrics, duality theory, and infinite-dimensional optimization transformed into convex programs, indicating high mathematical complexity. However, the empirical validation is based on a single dataset (S&P 500) with a simple illustration (equal-weighted vs. risk-free shift) rather than comprehensive backtesting or implementation details, suggesting limited empirical rigor.

  flowchart TD
    A["Research Goal: Cost-Sensitive<br>Distributionally Robust<br>Log-Optimal Portfolio"] --> B["Methodology: Wasserstein Metric<br>for Ambiguity Set &<br>Duality Theory"]
    B --> C["Data: S&P 500 Historical Returns"]
    C --> D["Computational Process:<br>Finite Convex Program"]
    D --> E{"Transaction Costs?"}
    E -- No --> F["Outcome: Converges to<br>Equal-Weighted Allocation"]
    E -- Yes --> G["Outcome: Shifts to<br>Risk-Free Asset"]