Risk Bounds for Factor Models

31 Pages Posted: 3 Mar 2015 Last revised: 9 Feb 2017

Carole Bernard

Grenoble Ecole de Management

Ludger Rüschendorf

University of Freiburg

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: April 4, 2016

Abstract

Recent literature has investigated the risk aggregation of a portfolio X=(Xi) under the sole assumption that the marginal distributions of the risks Xi are specified but not their dependence structure. There exists a range of possible values for any risk measure of S=X1 X2 ... Xn and the dependence uncertainty spread, as measured by the difference between the upper bound and the lower bound on these values, is typically very wide. Obtaining bounds that are more practically useful requires additional information on dependence. Here, we study a partially specified factor model in which each risk Xi has a known joint distribution with the common risk factor Z, but we dispense with the conditional independence assumption that is typically made in fully specified factor models. We derive easy-to-compute bounds on risk measures such as Value-at-Risk (VaR) and law-invariant convex risk measures (e.g., Tail Value-at-Risk (TVaR)) and demonstrate their asymptotic sharpness. We show that the dependence uncertainty spread is typically reduced substantially and that, contrary to the case in which only marginal information is used, it is not necessarily larger for VaR than for TVaR.

Keywords: factor models, risk aggregation, dependence uncertainty, Value-at-Risk

Suggested Citation

Bernard, Carole and Rüschendorf, Ludger and Vanduffel, Steven and Wang, Ruodu, Risk Bounds for Factor Models (April 4, 2016). Finance and Stochastics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2572508 or http://dx.doi.org/10.2139/ssrn.2572508

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Steven Vanduffel (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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