Robust MCVaR Portfolio Optimization with Ellipsoidal Support and Reproducing Kernel Hilbert Space-based Uncertainty

ArXiv ID: 2509.00447 “View on arXiv”

Authors: Rupendra Yadav, Aparna Mehra

Abstract

This study introduces a portfolio optimization framework to minimize mixed conditional value at risk (MCVaR), incorporating a chance constraint on expected returns and limiting the number of assets via cardinality constraints. A robust MCVaR model is presented, which presumes ellipsoidal support for random returns without assuming any distribution. The model utilizes an uncertainty set grounded in a reproducing kernel Hilbert space (RKHS) to manage the chance constraint, resulting in a simplified second-order cone programming (SOCP) formulation. The performance of the robust model is tested on datasets from six distinct financial markets. The outcomes of comprehensive experiments indicate that the robust model surpasses the nominal model, market portfolio, and equal-weight portfolio with higher expected returns, lower risk metrics, enhanced reward-risk ratios, and a better value of Jensen’s alpha in many cases. Furthermore, we aim to validate the robust models in different market phases (bullish, bearish, and neutral). The robust model shows a distinct advantage in bear markets, providing better risk protection against adverse conditions. In contrast, its performance in bullish and neutral phases is somewhat similar to that of the nominal model. The robust model appears effective in volatile markets, although further research is necessary to comprehend its performance across different market conditions.

Keywords: Portfolio Optimization, Conditional Value at Risk, Robust Optimization, SOCP, Reproducing Kernel Hilbert Space, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 9.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts such as Mixed CVaR, Reproducing Kernel Hilbert Space (RKHS), and Second-Order Cone Programming (SOCP) reformulations, indicating high mathematical density. It also demonstrates high empirical rigor with comprehensive backtesting across six distinct financial markets (including DJIA, S&P 100, and NIFTY 50), multiple market phases (bull/bear/neutral), and the use of 13 statistical performance metrics.

  flowchart TD
    A["Research Goal: Robust MCVaR Optimization"] --> B["Inputs: 6 Financial Markets Data"]
    B --> C["Formulation: Ellipsoidal Support & RKHS Uncertainty"]
    C --> D["Solution: SOCP Conversion"]
    D --> E["Comparison: Nominal, Market, Equal-Weight Portfolios"]
    E --> F["Results: Bear Markets & High Volatility"]