Conditional Value at Risk (CVaR)

Portfolio Optimization with Robust Covariance and Conditional Value-at-Risk Constraints ArXiv ID: 2406.00610 “View on arXiv” Authors: Unknown Abstract 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. ...

A return-diversification approach to portfolio selection ArXiv ID: 2312.09707 “View on arXiv” Authors: Unknown Abstract In this paper, we propose a general bi-objective model for portfolio selection, aiming to maximize both a diversification measure and the portfolio expected return. Within this general framework, we focus on maximizing a diversification measure recently proposed by Choueifaty and Coignard for the case of volatility as a risk measure. We first show that the maximum diversification approach is actually equivalent to the Risk Parity approach using volatility under the assumption of equicorrelated assets. Then, we extend the maximum diversification approach formulated for general risk measures. Finally, we provide explicit formulations of our bi-objective model for different risk measures, such as volatility, Mean Absolute Deviation, Conditional Value-at-Risk, and Expectiles, and we present extensive out-of-sample performance results for the portfolios obtained with our model. The empirical analysis, based on five real-world data sets, shows that the return-diversification approach provides portfolios that tend to outperform the strategies based only on a diversification method or on the classical risk-return approach. ...

Doubly Robust Mean-CVaR Portfolio ArXiv ID: 2309.11693 “View on arXiv” Authors: Unknown 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. ...