What is the Best Risk Measure in Practice? A Comparison of Standard Measures

Emmer, Susanne; Tasche, Dirk; Kratz, Marie

doi:10.2139/ssrn.2370378

Cited by 91 publications

(110 citation statements)

References 55 publications

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“…If one splits the specification of a stochastic model in a dependence function (copula) and the marginal distributions, show that expected shortfall is continuous with respect to the Lévy distance whenever the model uncertainty only concerns the dependence function. It has also been shown in Stahl et al (2012) and Emmer, Kratz, and Tasche (2013) that expected shortfall is continuous with respect to the Wasserstein distance.…”

Section: Robustnessmentioning

confidence: 88%

Model Uncertainty and Scenario Aggregation

Cambou

Filipović

2015

Mathematical Finance

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This paper provides a coherent method for scenario aggregation addressing model uncertainty. It is based on divergence minimization from a reference probability measure subject to scenario constraints. An example from regulatory practice motivates the definition of five fundamental criteria that serve as a basis for our method. Standard risk measures, such as value-at-risk and expected shortfall, are shown to be robust with respect to minimum divergence scenario aggregation. Various examples illustrate the tractability of our method. KEY WORDS: model uncertainty, scenario aggregation, expected shortfall, value-at-risk, statistical divergence, Swiss Solvency Test. INTRODUCTIONThe last decades have seen strong developments in the statistical measurement of risk. The quantitative methods used by banks and insurance companies for risk management serve many purposes such as enterprise risk management, pricing, capital allocation, or reporting to regulators. The latter have required regulated institutions to implement and document internal models that should be used to report their amount of required capital which is bearing the risk and to show that they would remain solvent in case of extreme scenarios. Although the risk modeling methodology of an institution is reported and subject to approval from the regulators or internal model validation, uncertainty on the validity of the model remains inherent and should therefore be challenged. The risk of inappropriate modeling can usually be raised at many levels. For example, in a factor model, one could question a specific choice of risk factors, the marginal distribution of these risk factors, or the dependence structure between them (see, e.g., Embrechts, Puccetti, and Rüschendorf 2013; Embrechts, Wang, and Wang 2014 for the last aspect).We thank Matthias Aellig, David Babbel, Alexis Bailly, Rama Cont, Freddy Delbaen, Kabir Dutta, Paul Embrechts, Jan Friedrich, Hansjörg Furrer, Jean-Francois Guérin, Andreas Haier, Stefan Jaschke, Thorsten Pfeiffer, Alexander Schied, Michael Schmutz, Ruodu Wang, three anonymous referees, the editor (Jerome Detemple), and participants at the In many examples of risk management processes, the model will be used to estimate risk measures that greatly depend on the tail of the loss distribution and one should therefore check that this part of distribution is appropriately modeled.This paper provides a coherent method for incorporating external views on scenarios into an internal model. This scenario aggregation method aims at supporting regulatory purposes, such as stress testing, and serves as a device to address internal model uncertainty.A clear distinction has been made in the literature, in the footsteps 1 of Knight (1921), between the notions of risk and uncertainty. The former relates to the unknowns with respect to future events for which probabilities are known with certainty, while the latter notion happens whenever these probabilities are unknown. Although the wording model risk is broadly used in both the academic and industry li...

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Section: Robustnessmentioning

confidence: 88%

Model Uncertainty and Scenario Aggregation

Cambou

Filipović

2015

Mathematical Finance

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“…Conversely, there is no consensus on how to backtest ES. Emmer, Kratz, and Tasche (2015) propose a framework to backtest ES based on a representation in terms of the integrated VaR:…”

Section: Var and Es Forecasting Using Dynamic Intensity Modelsmentioning

confidence: 99%

Multivariate dynamic intensity peaks‐over‐threshold models

Hautsch

Herrera

2019

J of Applied Econometrics

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Summary We propose a multivariate dynamic intensity peaks‐over‐threshold model to capture extremes in multivariate return processes. The random occurrence of extremes is modeled by a multivariate dynamic intensity model, while temporal clustering of their size is captured by an autoregressive multiplicative error model. Applying the model to daily returns of three major stock indexes yields strong empirical support for a temporal clustering of both the occurrence and the size of extremes. Backtesting value‐at‐risk and expected shortfall forecasts shows that the consideration of clustering effects and of feedback between the magnitudes and the intensity of extremes results in better forecasts of risk.

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“…Nevertheless, well known risk functionals violate at least one of the mentioned properties: the variance (which has neither of these properties), the standard deviation (which is not comonotone additive), the Value-at-Risk (which is not subadditive) and expectiles (which are in general not comonotone additive), see Emmer et al [15]. The questions arises what happens if one of the latter risk functionals is chosen in the portfolio selection problem (11) under complete dependence uncertainty.…”

Section: Proposition 1 If the Risk Functional R Is Subadditive Comonmentioning

confidence: 99%

“…That is we want to solve problem (14). The following heuristic allows us to rapidly compute a lower bound C L and an upper bound C U as given in (15), which translates into bounds for problem (14):…”

Section: Appendixmentioning

confidence: 99%

A Review on Ambiguity in Stochastic Portfolio Optimization

Pflug

Pohl

2017

Set-Valued Var. Anal

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In mean-risk portfolio optimization, it is typically assumed that the assets follow a known distribution P 0 , which is estimated from observed data. Aiming at an investment strategy which is robust against possible misspecification of P 0 , the portfolio selection problem is solved with respect to the worst-case distribution within a Wasserstein-neighborhood of P 0 . We review tractable formulations of the portfolio selection problem under model ambiguity, as it is called in the literature. For instance, it is known that high model ambiguity leads to equally-weighted portfolio diversification. However, it often happens that the marginal distributions of the assets can be estimated with high accuracy, whereas the dependence structure between the assets remains ambiguous. This leads to the problem of portfolio selection under dependence uncertainty. We show that in this case portfolio concentration becomes optimal as the uncertainty with respect to the estimated dependence structure increases. Hence, distributionally robust portfolio optimization can have two very distinct implications: Diversification on the one hand and concentration on the other hand.

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What is the Best Risk Measure in Practice? A Comparison of Standard Measures

Cited by 91 publications

References 55 publications

Model Uncertainty and Scenario Aggregation

Model Uncertainty and Scenario Aggregation

Multivariate dynamic intensity peaks‐over‐threshold models

A Review on Ambiguity in Stochastic Portfolio Optimization

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