# Portfolio Optimization with Robust Covariance and Conditional Value-at-Risk Constraints

arXiv: https://arxiv.org/abs/2406.00610 · HTML: https://mlsanity.com/paper/2406.00610/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 12 references that are in the map.
- First posted on arXiv 2 Jun 2024.

## Built on by (most cited first, 9 of 9)

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- [A Novel approach to portfolio construction](https://mlsanity.com/paper/2602.03325/) (2026)

## Abstract (arXiv)

The measure of portfolio risk is an important input of the Markowitz framework. In this study, we explored various methods to obtain a robust covariance estimators that are less susceptible to financial data noise. We evaluated the performance of large-cap portfolio using various forms of Ledoit Shrinkage Covariance and Robust Gerber Covariance matrix during the period of 2012 to 2022. Out-of-sample performance indicates that robust covariance estimators can outperform the market capitalization-weighted benchmark portfolio, particularly during bull markets. The Gerber covariance with Mean-Absolute-Deviation (MAD) emerged as the top performer. However, robust estimators do not manage tail risk well under extreme market conditions, for example, Covid-19 period. When we aim to control for tail risk, we should add constraint on Conditional Value-at-Risk (CVaR) to make more conservative decision on risk exposure. Additionally, we incorporated unsupervised clustering algorithm K-means to the optimization algorithm (i.e. Nested Clustering Optimization, NCO). It not only helps mitigate numerical instability of the optimization algorithm, but also contributes to lower drawdown as well.