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

## TL;DR

This paper proposes a robust portfolio optimization model minimizing MCVaR using ellipsoidal support and RKHS-based uncertainty, demonstrating superior performance in volatile and bear markets through extensive empirical testing.

## Contribution

It introduces a novel robust MCVaR portfolio optimization framework that does not assume return distributions and employs RKHS for uncertainty modeling, with a simplified SOCP formulation.

## Key findings

- Outperforms nominal, market, and equal-weight portfolios in expected returns and risk metrics.
- Shows particular robustness and risk protection in bear markets.
- Effective in volatile market conditions across different market phases.

## 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.