Expected shortfall and beyond

By Dirk Tasche. 2002

420 citations recorded by the source corpus.

Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is defined as a fixed level quantile of the random variable under consideration, is the most popular risk measure. Unfortunately, it fails to reward diversification, as it is not "subadditive". In the search for a suitable alternative to value-at-risk, "Expected Shortfall" (or "conditional value-at-risk" or "tail value-at-risk") has been characterized as the smallest "coherent" and "law invariant" risk measure to dominate value-at-risk. We discuss these and some other properties of Expected Shortfall as well as its generalization to a class of coherent risk measures which can incorporate higher moment effects. Moreover, we suggest a general method on how to attribute Expected Shortfall "risk contributions" to portfolio components. Key words: Expected Shortfall; Value-at-Risk; Spectral Risk Measure; coherence; risk contribution.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/5e67b18b5bbecabbeac590a2ef31ff13d9380ba3

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Citations in the corpus

Higher moment coherent risk measures (2007, background): “In the context of axiomatically defined risk measures, an interesting example of spectral risk measure that corresponds to ‘pessimistic manipulation' of X and is sensitive to higher moments was considered by Tasche (2002 ).”
Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions (2014, background): “Second, random loss variables with light-tailed distributions or heavy-tailed distributions may have the same VaR (Tasche, 2002).”
Extremes on the discounted aggregate claims in a time dependent risk model (2010, background): “For a discussion regarding the advantage of this risk measure over VaR we refer the reader to Tasche ( 2002 ).”
MEASUREMENT OF RISK, SOLVENCY REQUIREMENTS AND ALLOCATION OF CAPITAL WITHIN FINANCIAL CONGLOMERATES (2002, background): “See Tasche (2001, 2002) and Acerbi and Tasche (2002) who refer to it as expected shortfall.”
AN AXIOMATIC APPROACH TO CAPITAL ALLOCATION (2005, positive): “Furthermore, ESα is coherent (Acerbi and Tasche 2002) and satisfies the monotonicity condition in Delbaen (2000).”
Multinomial VaR Backtests: A simple implicit approach to backtesting expected shortfall (2016, methodology): “Expected shortfall at level α is the conditional expected loss given exceedance of VaR at that level and is a coherent risk measure (Acerbi & Tasche, 2002; Tasche, 2002).”
Multivariate Tweedie distributions and some related capital-at-risk analyses (2010, positive): “It should also be emphasized that TCE is a coherent risk measure (cf. Artzner et al., 1999; Acerbi and Tasche, 2002; Tasche, 2002), it is a particular member of the distorted risk functionals (cf.”
Two-sided coherent risk measures and their application in realistic portfolio optimization (2008, background): “The only four papers, which mentioned the application of higher moments in the coherent risk measure construction, are Delbaen (2002), Fischer (2001, 2003) and Tasche (2002).”
Hedging and Value at Risk: A Semi-Parametric Approach (2009, background): “An alternative measure of risk that addresses this shortcoming is Conditional Value at Risk (CVaR) or Expected Shortfall (see, for example, Tasche, 2002).”
Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle (2007, background): “(3.5b) 5With respect to other classes of risk measures see, e.g., Fischer (2003) for a discussion of derivatives of one-sided moment measures and Tasche (2002) for a suggestion of how to apply (3.7a) to spectral risk measures.”
A wavelet-based assessment of market risk: The emerging markets case (2012, background): “Since has several limitations (see, for example, Tasche (2002)), an alternative measure has been proposed , the expected shortfall (also called conditional VaR).”
Optimality of general reinsurance contracts under CTE risk measure (2011, methodology): “…(1999) while others have used names such as the Tail Conditional Expectation (see Artzner et al., 1999), Conditional Value-at-Risk (CVaR) (see Rockafellar and Uryasev, 2002), Tail Value-at-Risk (TVaR) (see Dhaene et al., 2006) and Expected Shortfall (ES) (see Tasche, 2002 and McNeil et al., 2005).”
Hidden Markov Models In Finance (2007, methodology): “g Hamilton [17], and Diebold and Rudebusch [10]).”
Portfolio diversification and value at risk under thick-tailedness (2009, background): “§Several recent papers (see among others, Acerbi and Tasche 2002 , Tasche 2002 ) recommend to use the expected shortfall as a coherent alternative to the value at risk (see Artzner et al.”
Robustness and sensitivity analysis of risk measurement procedures (2010, positive): “These properties are studied in detail for some well known examples of risk measures: Value-at-Risk, Expected Shortfall/ CVaR [1, 16, 17] and the class of spectral risk measures introduced by Acerbi [2].”