Paper: arXiv 2309.11693

Abstract

In this study, we address the challenge of portfolio optimization, a critical aspect of managing investment risks and maximizing returns. The mean-CVaR portfolio is considered a promising method due to today’s unstable financial market crises like the COVID-19 pandemic. It incorporates expected returns into the CVaR, which considers the expected value of losses exceeding a specified probability level. However, the instability associated with the input parameter changes and estimation errors can deteriorate portfolio performance. Therefore in this study, we propose a Doubly Robust mean-CVaR Portfolio refined approach to the mean-CVaR portfolio optimization. Our method can solve the instability problem to simultaneously optimize the multiple levels of CVaRs and define uncertainty sets for the mean parameter to perform robust optimization. Theoretically, the proposed method can be formulated as a second-order cone programming problem which is the same formulation as traditional mean-variance portfolio optimization. In addition, we derive an estimation error bound of the proposed method for the finite-sample case. Finally, experiments with benchmark and real market data show that our proposed method exhibits better performance compared to existing portfolio optimization strategies.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel doubly robust mean-CVaR formulation, deriving theoretical properties like error bounds and casting it as a second-order cone problem, showing high math complexity. It also validates the method using benchmark and real market data with performance comparisons, indicating significant empirical implementation and backtesting.

Research Flowchart

  flowchart TD
  A["Research Goal: Stabilize Mean-CVaR Portfolio Optimization"] --> B["Methodology: Doubly Robust Approach"]
  B --> C["Data/Inputs: Benchmark & Real Market Data"]
  C --> D["Computational Process: SOCP Formulation & Estimation Error Bound Derivation"]
  D --> E["Outcome: Improved Performance vs. Existing Strategies"]