Expected Shortfall: A Natural Coherent Alternative to Value at Risk
Abstract
We discuss the coherence properties of expected shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the ‘average of the 100% worst losses’ in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representations of ES which turn out to be more appropriate for certain purposes
(J.E.L.: G20, C13, C14).
Citing Literature
Number of times cited according to CrossRef: 219
- Vira Zrazhevska, Grigoriy Zrazhevsky, Generalized Approach for Estimatingand Forecasting of Dynamical VaRand CVaR Based on Metalog Distribution, Lecture Notes in Computational Intelligence and Decision Making, 10.1007/978-3-030-54215-3_15, (232-245), (2021).
- Young C. Joo, Sung Y. Park, Tail Risk Measures and Portfolio Selection, Behavioral Predictive Modeling in Economics, 10.1007/978-3-030-49728-6_7, (117-139), (2021).
- Mohammed Berkhouch, Ghizlane Lakhnati, A Review of Standard Spectral Risk Measures, Recent Applications of Financial Risk Modelling and Portfolio Management, 10.4018/978-1-7998-5083-0.ch018, (363-381), (2021).
- An Chen, Mitja Stadje, Fangyuan Zhang, On the Equivalence Between Value-at-Risk and Expected Shortfall in Non-Concave Optimization, SSRN Electronic Journal, 10.2139/ssrn.3533948, (2020).
- Athanasios Kokoris, Fragiskos Archontakis, Christos Grose, Market risk assessment, The Journal of Risk Finance, 10.1108/JRF-05-2019-0078, ahead-of-print, ahead-of-print, (2020).
- David Allen, Colin Lizieri, Stephen Satchell, A comparison of non-Gaussian VaR estimation and portfolio construction techniques, Journal of Empirical Finance, 10.1016/j.jempfin.2020.07.001, 58, (356-368), (2020).
- Julia S. Mehlitz, Benjamin R. Auer, A Monte Carlo evaluation of non-parametric estimators of expected shortfall, The Journal of Risk Finance, 10.1108/JRF-07-2019-0122, ahead-of-print, ahead-of-print, (2020).
- Farrukh Javed, Stepan Mazur, Edward Ngailo, Higher order moments of the estimated tangency portfolio weights, Journal of Applied Statistics, 10.1080/02664763.2020.1736523, (1-19), (2020).
- Gregor Dorfleitner, On the use of the terminal-value approach in risk-value models, Annals of Operations Research, 10.1007/s10479-020-03644-2, (2020).
- Keith K.F. Law, W.K. Li, Philip L.H. Yu, An alternative nonparametric tail risk measure, Quantitative Finance, 10.1080/14697688.2020.1787491, (1-12), (2020).
- Yuan Zhang, Huifu Xu, Wei Wang, Preference robust models in multivariate utility-based shortfall risk minimization, Optimization Methods and Software, 10.1080/10556788.2020.1827255, (1-41), (2020).
- Zsolt Bihary, Péter Csóka, Dávid Zoltán Szabó, Spectral risk measure of holding stocks in the long run, Annals of Operations Research, 10.1007/s10479-020-03678-6, (2020).
- Christoph Weskamp, Achim Koberstein, Frank Schwartz, Leena Suhl, Stefan Voß, A two-stage stochastic programming approach for identifying optimal postponement strategies in supply chains with uncertain demand, Omega, 10.1016/j.omega.2018.02.008, 83, (123-138), (2019).
- Alberto Burchi, Duccio Martelli, Paola Musile Tanzi, Sustainable and Responsible Investments: Same Sea, Different Fishes?, Socially Responsible Investments, 10.1007/978-3-030-05014-6, (101-124), (2019).
- İ. İlkay Boduroğlu, Portfolio Optimization via a Surrogate Risk Measure: Conditional Desirability Value at Risk (CDVaR), Learning and Intelligent Optimization, 10.1007/978-3-030-05348-2_23, (257-270), (2019).
- J.S.K. Chan, K.H. Ng, R. Ragell, Bayesian return forecasts using realised range and asymmetric CARR model with various distribution assumptions, International Review of Economics & Finance, 10.1016/j.iref.2019.01.003, (2019).
- Denys Yemshanov, Robert G. Haight, Frank H. Koch, Robert C. Venette, Tom Swystun, Ronald E. Fournier, Mireille Marcotte, Yongguang Chen, Jean J. Turgeon, Optimizing surveillance strategies for early detection of invasive alien species, Ecological Economics, 10.1016/j.ecolecon.2019.04.030, 162, (87-99), (2019).
- Li Yang, Longfeng Zhao, Chao Wang, Portfolio optimization based on empirical mode decomposition, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2019.121813, (121813), (2019).
- Domenico Quagliarella, Value-at-Risk and Conditional Value-at-Risk in Optimization Under Uncertainty, Uncertainty Management for Robust Industrial Design in Aeronautics, 10.1007/978-3-319-77767-2_34, (541-565), (2019).
- Domenico Quagliarella, Emiliano Iuliano, UQ Sensitivity Analysis and Robust Design Optimization of a Supersonic Natural Laminar Flow Wing-Body, Uncertainty Management for Robust Industrial Design in Aeronautics, 10.1007/978-3-319-77767-2_37, (601-628), (2019).
- Angelo Corelli, Angelo Corelli, Beyond Normality and Correlation, Understanding Financial Risk Management, Second Edition, 10.1108/9781789737912, (123-151), (2019).
- Ramin Giahi, Cameron A. MacKenzie, Chao Hu, Design Optimization for Resilience for Risk-Averse Firms, Computers & Industrial Engineering, 10.1016/j.cie.2019.106122, (106122), (2019).
- Alexander Wasserburger, Alexander Schirrer, Christoph Hametner, undefined, 2019 IEEE Vehicle Power and Propulsion Conference (VPPC), 10.1109/VPPC46532.2019.8952431, (1-6), (2019).
- Nathan Lassance, Information-Theoretic Approaches to Portfolio Selection, SSRN Electronic Journal, 10.2139/ssrn.3500947, (2019).
- Raffaella Calabrese, Silvia Angela Osmetti, Luca Zanin, A joint scoring model for peer‐to‐peer and traditional lending: a bivariate model with copula dependence, Journal of the Royal Statistical Society: Series A (Statistics in Society), 10.1111/rssa.12523, 182, 4, (1163-1188), (2019).
- Peterson Owusu Junior, Imhotep Alagidede, Risks in emerging markets equities: Time-varying versus spatial risk analysis, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2019.123474, (2019).
- Christian Urom, Julien Chevallier, Bangzhu Zhu, A dynamic conditional regime-switching GARCH CAPM for energy and financial markets, Energy Economics, 10.1016/j.eneco.2019.104577, (104577), (2019).
- Giovanni Bonaccolto, Critical Decisions for Asset Allocation via Penalized Quantile Regression, SSRN Electronic Journal, 10.2139/ssrn.3436894, (2019).
- Jerry Anunrojwong, Krishnamurthy Iyer, David Lingenbrink, Persuading Risk-Conscious Agents: A Geometric Approach, SSRN Electronic Journal, 10.2139/ssrn.3386273, (2019).
- Holger Fink, Sebastian Geissel, Julia Herbinger, Frank Thomas Seifried, Portfolio Optimization with Optimal Expected Utility Risk Measures, SSRN Electronic Journal, 10.2139/ssrn.3412529, (2019).
- Robert Erhardt, Jesse Bell, Brian Blanton, Frank Nutter, Megan Robinson, Richard Smith, Stronger Climate Resilience with Insurance, Bulletin of the American Meteorological Society, 10.1175/BAMS-D-19-0073.1, 100, 8, (1549-1552), (2019).
- Simon A. Broda, Juan Arismendi Zambrano, Partial Moments for Quadratic Forms in Non-Gaussian Random Vectors: A Parametric Approach, SSRN Electronic Journal, 10.2139/ssrn.3369208, (2019).
- G.-J. Siouris, D. Skilogianni, A. Karagrigoriou, Post Model Correction in Risk Analysis and Management, International Journal of Mathematical, Engineering and Management Sciences, 10.33889/IJMEMS.2019.4.3-044, 4, 3, (542-566), (2019).
- Denys Yemshanov, Robert G Haight, Ning Liu, Cuicui Chen, Chris J K MacQuarrie, Krista Ryall, Robert Venette, Frank H Koch, Acceptance sampling for cost-effective surveillance of emerald ash borer in urban environments, Forestry: An International Journal of Forest Research, 10.1093/forestry/cpz028, (2019).
- Deepak Jadhav, T.V. Ramanathan, Portfolio optimization based on modified expected shortfall, Studies in Economics and Finance, 10.1108/SEF-05-2018-0160, (2019).
- Prayut Jain, Shashi Jain, Can Machine Learning-Based Portfolios Outperform Traditional Risk-Based Portfolios? The Need to Account for Covariance Misspecification, Risks, 10.3390/risks7030074, 7, 3, (74), (2019).
- Denys Yemshanov, Robert G. Haight, Cuicui Chen, Ning Liu, Christian J. K. MacQuarrie, Frank H. Koch, Robert Venette, Krista Ryall, Managing biological invasions in urban environments with the acceptance sampling approach, PLOS ONE, 10.1371/journal.pone.0220687, 14, 8, (e0220687), (2019).
- Kirsten L. MacDonald, Robert J. Bianchi, Michael E. Drew, Equity risk versus retirement adequacy: asset allocation solutions for KiwiSaver, Accounting & Finance, 10.1111/acfi.12481, 0, 0, (2019).
- A. Wasserburger, C. Hametner, N. Didcock, Risk-averse real driving emissions optimization considering stochastic influences, Engineering Optimization, 10.1080/0305215X.2019.1569646, (1-17), (2019).
- Mauro Bernardi, Roy Cerqueti, Arsen Palestini, Allocation of risk capital in a cost cooperative game induced by a modified expected shortfall, Journal of the Operational Research Society, 10.1080/01605682.2019.1686958, (1-14), (2019).
- Simona Hašková, Petr Fiala, A fuzzy approach for the estimation of foreign investment risk based on values of rating indices, Risk Management, 10.1057/s41283-019-00051-1, (2019).
- Mauro Bernardi, Roy Cerqueti, Arsen Palestini, The Skew Normal multivariate risk measurement framework, Computational Management Science, 10.1007/s10287-019-00350-8, (2019).
- Barbara Dömötör, Kata Váradi, Stock market stress from the central counterparty’s perspective, Studies in Economics and Finance, 10.1108/SEF-03-2016-0063, (2019).
- Simon A. Broda, Jochen Krause, Marc S. Paolella, Approximating expected shortfall for heavy-tailed distributions, Econometrics and Statistics, 10.1016/j.ecosta.2017.07.003, 8, (184-203), (2018).
- Gah-Yi Ban, Noureddine El Karoui, Andrew E. B. Lim, Machine Learning and Portfolio Optimization, Management Science, 10.1287/mnsc.2016.2644, 64, 3, (1136-1154), (2018).
- Jae Wook Song, Bonggyun Ko, Woojin Chang, Analyzing systemic risk using non-linear marginal expected shortfall and its minimum spanning tree, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2017.08.076, 491, (289-304), (2018).
- Mathieu Sauvageau, Mustafa Kumral, Cash-Flow at Risk valuation of mining project using Monte-Carlo simulations with stochastic processes calibrated on historical data, The Engineering Economist, 10.1080/0013791X.2017.1413150, (0), (2018).
- Yu Chen, Zhicheng Wang, Zhengjun Zhang, Mark to market value at risk, Journal of Econometrics, 10.1016/j.jeconom.2018.09.017, (2018).
- Duc Hong Vo, Thach Ngoc Pham, Trung Thanh Vu Pham, Loc Minh Truong, Thang Cong Nguyen, Risk, return and portfolio optimization for various industries in the ASEAN region, Borsa Istanbul Review, 10.1016/j.bir.2018.09.003, (2018).
- Anton Kajtazi, Andrea Moro, The Role of Bitcoin in Well Diversified Portfolios: A Comparative Global Study, SSRN Electronic Journal, 10.2139/ssrn.3261266, (2018).
- Anton Kajtazi, Andrea Moro, Bitcoin and Portfolio Diversification: Evidence from Portfolios of U.S., European and Chinese Assets, SSRN Electronic Journal, 10.2139/ssrn.3095172, (2018).
- Zhibin Pan, Tao Pang, Yang Zhao, A Simple and Robust Approach for Expected Shortfall Estimation, SSRN Electronic Journal, 10.2139/ssrn.3341748, (2018).
- Longfeng Zhao, Gang-Jin Wang, Mingang Wang, Weiqi Bao, Wei Li, H. Eugene Stanley, Stock market as temporal network, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2018.05.039, 506, (1104-1112), (2018).
- Federico Bassetti, Maria Elena De Giuli, Enrica Nicolino, Claudia Tarantola, Multivariate dependence analysis via tree copula models: An application to one-year forward energy contracts, European Journal of Operational Research, 10.1016/j.ejor.2018.02.037, 269, 3, (1107-1121), (2018).
- Martin Eling, Kwangmin Jung, Copula approaches for modeling cross-sectional dependence of data breach losses, Insurance: Mathematics and Economics, 10.1016/j.insmatheco.2018.07.003, 82, (167-180), (2018).
- Xiu Xu, Andrija Mihoci, Wolfgang Karl Härdle, lCARE - localizing conditional autoregressive expectiles, Journal of Empirical Finance, 10.1016/j.jempfin.2018.06.006, 48, (198-220), (2018).
- Zsolt Bihary, Péter Csóka, Gábor Kondor, A részvénytartás spektrális kockázata hosszú távon, Közgazdasági Szemle, 10.18414/KSZ.2018.7-8.687, 65, 7-8, (687-700), (2018).
- Wenjun Zhu, Ken Seng Tan, Lysa Porth, Chou-Wen Wang, SPATIAL DEPENDENCE AND AGGREGATION IN WEATHER RISK HEDGING: A LÉVY SUBORDINATED HIERARCHICAL ARCHIMEDEAN COPULAS (LSHAC) APPROACH, ASTIN Bulletin, 10.1017/asb.2018.6, 48, 02, (779-815), (2018).
- References, Fundamental Statistical Inference, undefined, (537-560), (2018).
- Silvana Pesenti, Pietro Millossovich, Andreas Tsanakas, Cascade Sensitivity Measures, SSRN Electronic Journal, 10.2139/ssrn.3270839, (2018).
- Matteo Spada, Florentina Paraschiv, Peter Burgherr, A comparison of risk measures for accidents in the energy sector and their implications on decision-making strategies, Energy, 10.1016/j.energy.2018.04.110, 154, (277-288), (2018).
- Dmitry Chebotarev, Haircuts and Rates: A Theory of Repo, SSRN Electronic Journal, 10.2139/ssrn.3308073, (2018).
- Tom Burdorf, Gary van Vuuren, An evaluation and comparison of Value at Risk and Expected Shortfall, Investment Management and Financial Innovations, 10.21511/imfi.15(4).2018.02, 15, 4, (17-34), (2018).
- Nick Costanzino, Michael Curran, A Simple Traffic Light Approach to Backtesting Expected Shortfall, Risks, 10.3390/risks6010002, 6, 1, (2), (2018).
- Charles-Olivier Amédée-Manesme, Fabrice Barthélémy, Didier Maillard, Computation of the corrected Cornish–Fisher expansion using the response surface methodology: application to VaR and CVaR, Annals of Operations Research, 10.1007/s10479-018-2792-4, (2018).
- Longfeng Zhao, Wei Li, Andrea Fenu, Boris Podobnik, Yougui Wang, H Eugene Stanley, The q -dependent detrended cross-correlation analysis of stock market , Journal of Statistical Mechanics: Theory and Experiment, 10.1088/1742-5468/aa9db0, 2018, 2, (023402), (2018).
- Yuhan Liu, Dan A. Ralescu, Chen Xiao, Waichon Lio, Tail value-at-risk in uncertain random environment, Soft Computing, 10.1007/s00500-018-3492-3, (2018).
- Alfred Larm Teye, Jan de Haan, Marja G. Elsinga, Risks and interrelationships of subdistrict house prices: the case of Amsterdam, Journal of Housing and the Built Environment, 10.1007/s10901-017-9568-z, 33, 2, (209-226), (2017).
- Fabio Caccioli, Imre Kondor, Gábor Papp, Portfolio optimization under Expected Shortfall: contour maps of estimation error, Quantitative Finance, 10.1080/14697688.2017.1390245, 18, 8, (1295-1313), (2017).
- Giovanni Bonaccolto, Massimiliano Caporin, Sandra Paterlini, Asset allocation strategies based on penalized quantile regression, Computational Management Science, 10.1007/s10287-017-0288-3, 15, 1, (1-32), (2017).
- Pan Liu, Dmitry Vedenov, Gabriel J. Power, Is hedging the crack spread no longer all it's cracked up to be?, Energy Economics, 10.1016/j.eneco.2017.01.020, 63, (31-40), (2017).
- Christel Baier, Joachim Klein, Sascha Klüppelholz, Sascha Wunderlich, Maximizing the Conditional Expected Reward for Reaching the Goal, Tools and Algorithms for the Construction and Analysis of Systems, 10.1007/978-3-662-54580-5_16, (269-285), (2017).
- Mauro Bernardi, Antonello Maruotti, Lea Petrella, Multiple risk measures for multivariate dynamic heavy–tailed models, Journal of Empirical Finance, 10.1016/j.jempfin.2017.04.005, 43, (1-32), (2017).
- Leon Li, Testing and comparing the performance of dynamic variance and correlation models in value-at-risk estimation, The North American Journal of Economics and Finance, 10.1016/j.najef.2017.02.006, 40, (116-135), (2017).
- Peter Reichling, Gordon Schulze, Peter Reichling, Gordon Schulze, Downside-Effizienz, Downside-orientiertes Portfoliomanagement, 10.1007/978-3-658-16664-9, (121-175), (2017).
- Jean-Paul Laurent, The Knowns and the Known Unknowns of Capital Requirements for Market Risks, Financial Regulation in the EU, 10.1007/978-3-319-44287-7, (277-307), (2017).
- Filippo Fratini, An Actuarial Mathematics Approach to Option Pricing, SSRN Electronic Journal, 10.2139/ssrn.3010358, (2017).
- Gregor Dorfleitner, On the Use of the Terminal-Value Approach in Risk-Value Models, SSRN Electronic Journal, 10.2139/ssrn.2905827, (2017).
- Anton Kajtazi, Andrea Moro, Bitcoin, Portfolio Diversification and Chinese Financial Markets, SSRN Electronic Journal, 10.2139/ssrn.3062064, (2017).
- Takashi Kato, Asymptotic Analysis for Spectral Risk Measures Parameterized by Confidence Level, SSRN Electronic Journal, 10.2139/ssrn.3074504, (2017).
- Domenico Quagliarella, Emiliano Iuliano, Robust Design of a Supersonic Natural Laminar Flow Wing-Body, IEEE Computational Intelligence Magazine, 10.1109/MCI.2017.2742718, 12, 4, (14-27), (2017).
- Casian BUTACI, Simona DZITAC, Ioan DZITAC, Gabriela BOLOGA, PRUDENT DECISIONS TO ESTIMATE THE RISK OF LOSS IN INSURANCE, Technological and Economic Development of Economy, 10.3846/20294913.2017.1285365, 23, 2, (428-440), (2017).
- Denys Yemshanov, Robert G. Haight, Frank H. Koch, Robert Venette, Kala Studens, Ronald E. Fournier, Tom Swystun, Jean J. Turgeon, A safety rule approach to surveillance and eradication of biological invasions, PLOS ONE, 10.1371/journal.pone.0181482, 12, 7, (e0181482), (2017).
- Lisa R. Goldberg, Ola Mahmoud, Drawdown: from practice to theory and back again, Mathematics and Financial Economics, 10.1007/s11579-016-0181-9, 11, 3, (275-297), (2016).
- Taras Bodnar, Taras Zabolotskyy, How risky is the optimal portfolio which maximizes the Sharpe ratio?, AStA Advances in Statistical Analysis, 10.1007/s10182-016-0270-3, 101, 1, (1-28), (2016).
- Zhen Yan, Junjian Zhang, Adjusted empirical likelihood for value at risk and expected shortfall, Communications in Statistics - Theory and Methods, 10.1080/03610926.2014.1002933, 46, 5, (2580-2591), (2016).
- Susanne Wruck, Iris F.A. Vis, Jaap Boter, Risk control for staff planning in e-commerce warehouses, International Journal of Production Research, 10.1080/00207543.2016.1207816, 55, 21, (6453-6469), (2016).
- Marcus Kriele, Jochen Wolf, Marcus Kriele, Jochen Wolf, Abhängigkeiten, Wertorientiertes Risikomanagement von Versicherungsunternehmen, 10.1007/978-3-662-50257-0, (83-114), (2016).
- Maria Rosa Nieto, Esther Ruiz, Frontiers in VaR forecasting and backtesting, International Journal of Forecasting, 10.1016/j.ijforecast.2015.08.003, 32, 2, (475-501), (2016).
- Arlie O. Petters, Xiaoying Dong, Arlie O. Petters, Xiaoying Dong, Capital Market Theory and Portfolio Risk Measures, An Introduction to Mathematical Finance with Applications, 10.1007/978-1-4939-3783-7_4, (151-208), (2016).
- Anindya Chakrabarty, Rameshwar Dubey, Anupam De, An innovative approach to mitigating horizon mismatch, International Journal of Innovation Science, 10.1108/IJIS-06-2016-011, 8, 2, (161-180), (2016).
- Massimiliano Amarante, A representation of risk measures, Decisions in Economics and Finance, 10.1007/s10203-016-0170-8, 39, 1, (95-103), (2016).
- Enrico G. De Giorgi, Ola Mahmoud, Diversification preferences in the theory of choice, Decisions in Economics and Finance, 10.1007/s10203-016-0182-4, 39, 2, (143-174), (2016).
- Oliver Janke, Qinghua Li, Portfolio optimization under shortfall risk constraint, Optimization, 10.1080/02331934.2016.1173693, 65, 9, (1733-1755), (2016).
- Paweł Fiedor, Artur Hołda, Information-theoretic approach to quantifying currency risk, The Journal of Risk Finance, 10.1108/JRF-03-2015-0029, 17, 1, (93-109), (2016).
- Manuel Kleinknecht, Wing Lon Ng, Reducing Basel III Capital Requirements with Dynamic Conditional Correlation and Monte Carlo Simulation, SSRN Electronic Journal, 10.2139/ssrn.2717051, (2016).
- Jonathan B. Dressler, Loren W. Tauer, Estimating Expected and Unexpected Losses for Agricultural Mortgage Portfolios, American Journal of Agricultural Economics, 10.1093/ajae/aaw049, 98, 5, (1470-1485), (2016).
- Istvan Varga-Haszonits, Fabio Caccioli, Imre Kondor, Replica approach to mean-variance portfolio optimization, Journal of Statistical Mechanics: Theory and Experiment, 10.1088/1742-5468/aa4f9c, 2016, 12, (123404), (2016).
- Peter Miu, Bogie Ozdemir, Evren Cubukgil, Michael Giesinger, Determining Hurdle Rate and Capital Allocation in Credit Portfolio Management, Journal of Financial Services Research, 10.1007/s10693-015-0221-2, 50, 2, (243-273), (2015).
- P. Date, R. Bustreo, Value-at-Risk for fixed-income portfolios: a Kalman filtering approach, IMA Journal of Management Mathematics, 10.1093/imaman/dpv016, 27, 4, (557-573), (2015).
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