An Empirical Comparison of Quantile-Based Risk Measures for Portfolio Construction under Practical Constraints

Khalil Nozohouri ¹ ( Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran / Department of Listing, Tehran Stock Exchange, Tehran, Iran )
Hossein Ghanbari ² ( PhD Candidate in Industrial Engineering, Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran )
emran mohammadi ³ ( School of Industrial Engineering, Iran University of Science and Technology,iran )

Submited date : 2024-03-04 Accepted date : 2025-06-19

Keywords: Portfolio optimization, Quantile-based risk measures, Value at Risk, Conditional Value at Risk, Conditional Drawdown at Risk, Practical constraints,

Abstract :

Portfolio optimization plays a vital role in investment decision-making, striving to maximize returns while effectively managing and minimizing risk. In this process, selecting an appropriate risk measure is essential for achieving optimal outcomes. Among the various categories of risk measures, quantile-based risk measures have garnered significant attention for their effectiveness in capturing downside risk. Both investors and researchers are keenly interested in identifying which quantile-based risk measure delivers superior performance. However, despite this interest, there remains a lack of comprehensive studies comparing these measures. Therefore, this paper compares the performance of three widely recognized and practical quantile-based risk measures: Value at Risk (VaR), Conditional Value at Risk (CVaR), and Conditional Drawdown at Risk (CDaR). Evaluating the performance of different risk measures allows investors to make informed decisions and effectively manage their portfolios. The paper also incorporates practical constraints into the models to enhance their applicability in real-world investment scenarios. To facilitate the comparison, an empirical case study utilizing financial statements from the Tehran Stock Exchange (TSE) database is employed. The computational results obtained from our analysis indicate that the CVaR model yields superior outcomes compared to other risk measures considered in this study. By selecting CVaR as the preferred risk measure, investors can make more informed and well-grounded decisions in managing their portfolios. The findings contribute to a deeper understanding of these risk measures and their practical applicability in making informed investment decisions. This knowledge empowers investors to make well-informed choices and optimize their risk management strategies.

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