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The Application of VAR and TCE in Solving a Portfolio Risk Management Problem in Financial Institutions
Subject area: Science,Engineering and Technology · Area of research: Portfolio Risk Management
DOI: 10.64388/IREV10I4-1723984
Abstract
Risk management is central to the stability and profitability of financial institutions, particularly in the face of market volatility and uncertain loss distributions. Among the most widely applied risk measures are Value at Risk (VaR) and Tail Conditional Expectation (TCE). VaR provides a probabilistic threshold for potential losses at a given confidence level, making it attractive for regulatory coverage and capital requirement resolve. However, its inability to capture the magnitude of losses beyond this threshold limits its effectiveness in managing extreme risk. TCE addresses this limitation by quantifying the expected loss given that the VaR boundary has been breached, thereby offering a more all-inclusive view of tail risk. This paper investigates the application of VaR and TCE in portfolio risk management when asset returns follow a Pareto distribution, a heavy-tailed model frequently used to capture extreme events in financial markets. Analytical formulations of VaR and TCE under the Pareto framework are derived, and their effectiveness in capturing tail risk is compared through a simulated portfolio problem. The results suggest that financial institutions relying solely on VaR may miscalculate losses, whereas incorporating TCE into risk management frameworks enhances robustness against disastrous market downturns.
Keywords
VaR; TCE; financial institutions; Pareto distribution; risk management
References
[1] Acerbi C, Tasche D (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26, 487–503.
[2] Artzner P, Delbaen F, Eber JM, Heath D (1999). Coherent measures of risk. Mathematical Finance, 9, 203–208.
[3] Denuit M, Dhaene J, Goovaerts M, Kaas R (2006). Actuarial theory for dependent risks: Measures, orders and models. Hoboken: John Wiley & Sons.
[4] Fadina T, Liu P, Wang R (2021). One axiom to rule all: An axiomatization of quantiles. SSRN. http://ssrn.com/abstract=3944312
[5] Fuchs S, Schlotter R, Schmidt KD (2017). A review and some complements on quantile risk measures and their domain. Risks, 5, 59.
[6] Klugman SA, Panjer HH, Willmot GE (2012). Loss models: From data to decisions. Hoboken: John Wiley & Sons.
[7] Li H, Wang R (2022). PELVE: Probability equivalent level of VaR and ES. Journal of Econometrics.
[8] Linsmeier TJ, Pearson ND (2000). Value at risk. Financial Analysts Journal, 56, 47–67.
[9] Promislow D (2015). Fundamentals of actuarial mathematics. John Wiley & Sons.
[10] Rostek M (2010). Quantile maximization in decision theory. The Review of Economic Studies, 7, 339–371.
[11] Wang R, Zitikis R (2021). An axiomatic foundation for the expected shortfall. Management Science, 67, 1413–1429.
How to cite this paper
@article{1723984,
author = {Okoli Obuikem Amos, Chigbo Chukwuebuka Ikechukwu},
title = {The Application of VAR and TCE in Solving a Portfolio Risk Management Problem in Financial Institutions},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {10},
number = {4},
pages = {2211-2218},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1723984.pdf},
abstract = {Risk management is central to the stability and profitability of financial institutions, particularly in the face of market volatility and uncertain loss distributions. Among the most widely applied risk measures are Value at Risk (VaR) and Tail Conditional Expectation (TCE). VaR provides a probabilistic threshold for potential losses at a given confidence level, making it attractive for regulatory coverage and capital requirement resolve. However, its inability to capture the magnitude of losses beyond this threshold limits its effectiveness in managing extreme risk. TCE addresses this limitation by quantifying the expected loss given that the VaR boundary has been breached, thereby offering a more all-inclusive view of tail risk. This paper investigates the application of VaR and TCE in portfolio risk management when asset returns follow a Pareto distribution, a heavy-tailed model frequently used to capture extreme events in financial markets. Analytical formulations of VaR and TCE under the Pareto framework are derived, and their effectiveness in capturing tail risk is compared through a simulated portfolio problem. The results suggest that financial institutions relying solely on VaR may miscalculate losses, whereas incorporating TCE into risk management frameworks enhances robustness against disastrous market downturns.},
keywords = {VaR; TCE; financial institutions; Pareto distribution; risk management},
month = {October},
doi = {https://doi.org/10.64388/IREV10I4-1723984}
}