(Simple) ΔCoVaR bounds

ABSTRACT

We develop simple versions of upper bounds of the widely used systemic risk measure of ΔCoVaR that are straightforward to calculate, and may prove useful as (conservative) benchmarks in an applied context.

KEYWORDS:

• $\mathrm{\Delta }$CoVaR
• systemic risk
• risk measure
• probability bounds

JEL CLASSIFICATION:

• G01
• G21
• G28
• G32

Acknowledgments

We are grateful to C. Alexander, H. Alexandre, P. Armand, B. Düring, F. Fiordelisi, I. Hasan, C. Hurlin, J.P. Lardy, L. Lepetit, J.S. Oberoi, A. Tarazi, and W. Wagner for helpful comments on previous versions of this paper; the usual disclaimer applies.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ For some recent papers using this measure, see e.g. Anginer et al. (2018a); Anginer, Demirgüç-Kunt, and Mare (2018b); Bakkar, De Jonghe, and Tarazi (2019); Berger, Roman, and Sedunov (2020); Bostandzic and Weiss (2018); Brownlees et al. (2020); Brunnermeier, Rother, and Schnabel (2020), Chu et al. (2020).

² As derived in Barrieu and Scandolo (2015) and Mercadier and Strobel (2021), respectively; note that one-sided inequalities are most relevant in the sense of ‘how bad could losses be’.

³ See also Giesecke and Kim (2011), Chen, Iyengar, and Moallemi (2013) and Löffler and Raupach (2018) for alternative perspectives on systemic risk.

⁴ The proof of Equation 3(3) $\mathrm{\Delta }\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}{\mathrm{R}}_{\alpha t}\left(X_i\right)={\gamma }_{it}\cdot \left[\mathrm{V}\mathrm{a}{\mathrm{R}}_{\alpha t}\left(X_i\right)-\mathrm{V}\mathrm{a}{\mathrm{R}}_{0.5,t}\left(X_i\right)\right]$(3) is given in Benoit et al. (2013), Appendix B.

⁵ Mercadier and Strobel (2021, fn. 3) reports unimodality tests for stock returns, for a sample of 1748 firms in 44 countries covering the period 1991q1–2020q1; the hypothesis of unimodality was not rejected in 96% of all cases at the quarterly level using conditional, i.e. GARCH(1,1) filtered, firm returns, with analogous results obtained for unconditional firm returns.

⁶ See FSB (2020); they are Citigroup (C), HSBC Holdings (HSBA), JP Morgan Chase & Co (JPM), Bank of America (BAC), Bank of China (BCL), Barclays (BARC), BNP Paribas (BNP), Deutsche Bank (DBK), Industrial & Commercial Bank of China (ITL), Mitsubishi UFJ Financial Group (MITF), China Construction Bank (CON), Agricultural Bank of China (ABC), Bank of New York Mellon (BK), Credit Suisse Group (CSGN), Goldman Sachs Group (GS), Credit Agricole (CRDA), ING Groep (INGA), Mizuho Financial Group (MIZH), Morgan Stanley (MS), Royal Bank of Canada (RY), Banco Santander (SAN), Societe Generale (SGE), Standard Chartered (STAN), State Street (STT), Sumitomo Mitsui Financial Group (SMFI), Toronto-Dominion Bank (TD), UBS Group (UBSG), Unicredit (UCG), Wells Fargo & Co (WFC) (note that Groupe BPCE is not listed).

⁷ Calculations are carried out using MATLAB R2020a, drawing in part on code provided by Benoit et al. (2013) via www.runmycode.org.

⁸ Similar results are obtained for the other G-SIBs on the FSB (2020) list; these are available in the (online) technical appendix.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.