Shortfall Deviation Risk: An Alternative for Risk Measurement

29 Pages Posted: 19 Dec 2014 Last revised: 11 May 2016

See all articles by Marcelo Righi

Marcelo Righi

Universidade Federal do Rio Grande do Sul (UFRGS)

Paulo Sergio Ceretta

Universidade Federal de Santa Maria

Multiple version iconThere are 2 versions of this paper

Date Written: May 10, 2016

Abstract

We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce, contemplating two fundamental pillars of the risk concept – the probability of adverse events and the variability of an expectation – and considers extreme results. We demonstrate that SD is a generalized deviation measure, whereas SDR is a coherent risk measure. We achieve the dual representation of SDR, and we discuss issues such as its representation by a weighted ES, acceptance sets, convexity, continuity and the relationship with stochastic dominance. Illustrations with real and simulated data allow us to conclude that SDR offers greater protection in risk measurement compared with VaR and ES, especially in times of significant turbulence in riskier scenarios.

Keywords: Shortfall deviation risk, risk management, risk measures, coherent risk measures, generalized deviation measures.

JEL Classification: C60, G10

Suggested Citation

Righi, Marcelo and Ceretta, Paulo Sergio, Shortfall Deviation Risk: An Alternative for Risk Measurement (May 10, 2016). Available at SSRN: https://ssrn.com/abstract=2539775 or http://dx.doi.org/10.2139/ssrn.2539775

Marcelo Righi (Contact Author)

Universidade Federal do Rio Grande do Sul (UFRGS) ( email )

Washington Luis, 855
Porto Alegre, Rio Grande do Sul 90010-460
Brazil

Paulo Sergio Ceretta

Universidade Federal de Santa Maria ( email )

Santa Maria
Brazil

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