# Risk bounds for factor models

Carole Bernard (), Ludger Rüschendorf (), Steven Vanduffel () and Ruodu Wang ()
Carole Bernard: Grenoble Ecole de Management
Ludger Rüschendorf: University of Freiburg
Ruodu Wang: University of Waterloo

Finance and Stochastics, 2017, vol. 21, issue 3, 631-659

Abstract: Abstract Recent literature has investigated the risk aggregation of a portfolio X = ( X i ) 1 ≤ i ≤ n $X=(X_{i})_{1\leq i\leq n}$ under the sole assumption that the marginal distributions of the risks X i $X_{i}$ are specified, but not their dependence structure. There exists a range of possible values for any risk measure of S = ∑ i = 1 n X i $S=\sum_{i=1}^{n}X_{i}$ , and the dependence uncertainty spread, as measured by the difference between the upper 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 X i $X_{i}$ has a known joint distribution with the common risk factor Z $Z$ , 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 $\mathrm{VaR}$ ) and law-invariant convex risk measures (e.g. Tail Value-at-Risk ( TVaR $\mathrm{TVaR}$ )) 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 $\mathrm{VaR}$ than for TVaR $\mathrm{TVaR}$ .

Keywords: Factor models; Risk aggregation; Dependence uncertainty; Value-at-Risk; 97K50; 60E05; 60E15; 62P05 (search for similar items in EconPapers)
JEL-codes: C02 C10 G11 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8) Track citations by RSS feed

Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2