Evaluating Utility-Based and Coherent Risk Measures in Financial Risk Management

Risk is an inherent part of our daily personal and professional life, and it can be found in every aspect of it. Particularly in finance and economics, managing and understanding risk is very important, yet defining and measuring it is a challenge due to its subjective nature. Effective risk management requires different tools and methodologies, many of which originated from Markowitz’s work in 1952. This paper examines risk measures, emphasizing the concept of coherence introduced by Artzner et al. (1999). A coherent risk measure satisfies monotonicity, positive homogeneity, sub-additivity, and translation invariance. Key measures, including variance, skewness, Value at Risk (VaR), and Conditional Tail Expectation (CTE) will be analyzed in this paper. While widely used, variance and skewness lack coherence. VaR, popular in finance, also fails to meet coherence standards. In contrast, CTE emerges as a coherent and reliable metric, addressing VaR’s shortcomings by focusing on extreme scenarios.