Value-at-Risk vs. Expected Shortfall: Beware of the Aggregation Currency!

8 Pages Posted: 22 May 2014

See all articles by Peter Antal

Peter Antal

Swiss Reinsurance Company

Pablo Koch-Medina

University of Zurich - Department of Banking and Finance; Swiss Finance Institute

Date Written: May 21, 2014

Abstract

This note highlights the impact of changing the aggregation currency when testing for capital adequacy. This is exemplified using the two most prominent capital adequacy tests used in the financial industry: Value-at-Risk and Expected Shortfall. The test consists in establishing whether the Value-at-Risk or, respectively, the Expected Shortfall of the capital position is negative or not. We show that the sign of the Expected Shortfall of a capital position -- and, hence, the corresponding capital adequacy test -- critically depends on the aggregation currency. This is in contrast to Value-at-Risk, whose sign is independent of the chosen aggregation currency. This implies that due caution is needed when using Expected Shortfall to measure capital adequacy in a multi-currency environment.

Keywords: risk measures, Value-at-Risk, expected shortfall, exchange rates, capital adequacy

JEL Classification: C60, G11, G22

Suggested Citation

Antal, Peter and Koch-Medina, Pablo, Value-at-Risk vs. Expected Shortfall: Beware of the Aggregation Currency! (May 21, 2014). Available at SSRN: https://ssrn.com/abstract=2439575 or http://dx.doi.org/10.2139/ssrn.2439575

Peter Antal

Swiss Reinsurance Company ( email )

Mythenquai 50/60
P.O. Box
CH-8022 Zurich
Switzerland

Pablo Koch-Medina (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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