What Is the Best Risk Measure in Practice? A Comparison of Standard Measures
AbstractExpected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straight-forward than, e.g., backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit commonly accepted desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and Expectiles with regard to whether or not they enjoy these properties, with particular emphasis on Expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. In particular, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications, especially as we provide an alternative way for backtesting of ES.
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Date of creation: Dec 2013
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Backtesting; Capital Allocation; Coherence; Diversification; Elicitability; Expected Shortfall; Expectile; Forecasts; Probability Integral Transform (PIT); Risk Measure; Risk Management; Robustness; Value-at-Risk;
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- Johanna F. Ziegel, 2013. "Coherence and elicitability," Papers 1303.1690, arXiv.org, revised Mar 2014.
- Francis X. Diebold & Robert S. Mariano, 1994.
"Comparing Predictive Accuracy,"
NBER Technical Working Papers
0169, National Bureau of Economic Research, Inc.
- Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
- Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
- Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
- Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
- Michel Dacorogna & Höskuldur Ari Hauksson & Thomas Domenig & Ulrich Müller & Gennady Samorodnitsky, 2001.
"Multivariate extremes, aggregation and risk estimation,"
CeNDEF Workshop Papers, January 2001
P2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- H. A. Hauksson & M. Dacorogna & T. Domenig & U. Mller & G. Samorodnitsky, 2001. "Multivariate extremes, aggregation and risk estimation," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 79-95.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
- Tasche, Dirk, 2002.
"Expected shortfall and beyond,"
Journal of Banking & Finance,
Elsevier, vol. 26(7), pages 1519-1533, July.
- Clements,Michael & Hendry,David, 1998.
"Forecasting Economic Time Series,"
Cambridge University Press, number 9780521632423, April.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Marc Busse & Michel Dacorogna & Marie Kratz, 2013.
"The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio,"
- Marc Busse & Michel Dacorogna & Marie Kratz, 2014. "The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio," Risks, MDPI, Open Access Journal, vol. 2(3), pages 260-276, July.
- Marc Busse & Michel Dacorogna & Marie Kratz, 2013. "The impact of systemic risk on the diversification benefits of a risk portfolio," Papers 1312.0506, arXiv.org.
- Busse, Marc & Dacorogna, Michel & Kratz, Marie, 2013. "The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio," ESSEC Working Papers WP1321, ESSEC Research Center, ESSEC Business School.
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