Extreme risk spillover network: application to financial institutions

Abstract

Using the CAViaR tool to estimate the value-at-risk (VaR) and the Granger causality risk test to quantify extreme risk spillovers, we propose an extreme risk spillover network for analysing the interconnectedness across financial institutions. We construct extreme risk spillover networks at 1% and 5% risk levels (which we denote 1% and 5% VaR networks) based on the daily returns of 84 publicly listed financial institutions from four sectors—banks, diversified financials, insurance and real estate—during the period 2006–2015. We find that extreme risk spillover networks have a time-lag effect. Both the static and dynamic networks show that on average the real estate and bank sectors are net senders of extreme risk spillovers and the insurance and diversified financials sectors are net recipients, which coheres with the evidence from the recent global financial crisis. The networks during the 2008–2009 financial crisis and the European sovereign debt crisis exhibited distinctive topological features that differed from those in tranquil periods. Our approach supplies new information on the interconnectedness across financial agents that will prove valuable not only to investors and hedge fund managers, but also to regulators and policy-makers.

Keywords:

• Extreme risk spillovers
• Financial network
• Financial institutions
• Financial crisis

AMS Subject Classifications:

• C51
• G01
• G20

Acknowledgements

We are grateful to the editor and two anonymous referees for their insightful comments and helpful suggestions.

Notes

No potential conflict of interest was reported by the authors.

1 For example, the topological constraint for the MST (PMFG) network is that the graph remains a tree (planar) when a new edge is added.

2 In the literature mean spillover is also known as return spillover.

3 We also consider two GARCH(1,1) models (i.e. AR(1)-GARCH(1,1)-Gaussian and AR(1)-GARCH(1,1)-Skewed-t) as alternative approaches to estimate time-varying VaRs, but the backtesting results for evaluating the accuracy of VaR estimates computed by the CAViaR model and the two GARCH(1,1) models show that the CAViaR model is a better choice than the two GARCH(1,1) models (see Appendix 1).

4 Two continuous networks represent two networks at two continuous time windows and . Suppose at the time window we have a network and at the next time window we have another network , these two networks and are designated two continuous networks.

5 The financial institutions are selected based on their inclusion in the financial sector of the S&P 500 index as of March 2016. Note that on 31 August 2016, stock exchange listed Equity REITs and other listed real estate companies from the financial sector were moved to a new real estate sector in the GICS.

6 To measure bank capital adequacy, for example, the Bank for International Settlements (BIS) uses the 1% VaR, and the JPMorgan Chase & Co. uses the 5% VaR.

7 Due to space limitations, we do not include the results of VaR for each financial institution estimated by the CAViaR models of Engle and Manganelli (2004) and the statistics of the Granger causality risk test of Hong et al. (2009) for each pair of financial institutions, but they are available upon request.

8 Note that our results based on extreme risk spillover networks are somewhat different from the systemic risk rankings provided by the volatility institute (V-Lab) of NYU Stern School of Business (see http://vlab.stern.nyu.edu/analysis/RISK.USFIN-MR.MES) that are based on the systemic risk measures (SRISK) proposed by Acharya, Engle et al. (2012); Acharya, Pedersen et al. (2017) and Brownlees and Engle (2017). According to the V-Lab, for example, the NTRS owning the largest out-degree in the 1% VaR network is only ranked 21 on 31 December 2015, but the high rankings of some banks (e.g. Bank of American, Citigroup and Goldman Sachs) in our network are consistent with the results obtained by the V-Lab. There are two possible reasons for the difference. (i) Our approach differs from the V-Lab measurements (e.g. SRISK) developed by Acharya, Engle et al. (2012); Acharya, Pedersen et al. (2017) and Brownlees and Engle (2017) that investigate an individual institution’s capital shortfall when the system is in distress, and our proposed network focuses on the extreme risk spillover interconnectedness across different financial institutions. (ii) The data samples differ. Our sample includes 22 real estate companies that can influence the interconnectedness across financial institutions and thus may lead to a different ranking. For example, some real estate companies (e.g. General Growth Properties and Essex Property Trust) have high out-degree rankings in the 1% VaR network.

9 In previous research, Wang et al. (2010) and Liu and Wan (2011), who, respectively, investigate cross-correlations between the Chinese A-Share and B-Share markets and between crude oil spot and futures markets using rolling windows, explain how to choose the window width. They indicate (i) that one can use a large window width (e.g. four trading years) to study the long-term market dynamics because the evolution of statistic properties is smooth and general tends can be detected and (ii) that to examine the effects of exogenous events (e.g. seasonal factors and financial crisis) on market short-term dynamics, a small window width (e.g. a 250-day trading year) is a better option. They also state that when the window width is too small the statistical measures evolve too rapidly, making local trends difficult to observe. Thus, we choose a small window width of 250 trading days and a step size of 20 trading days to study the dynamic interconnectedness across financial institutions. To test the robustness of our results, we also consider four cases of window width L and step size : (i) and , (ii) and , (iii) and and (iv) and . In (i) and (ii), we keep the same window width but change the step size. In (iii) and (iv), we keep the same the step size but change the window width. Because when we use these window widths and step sizes the dynamic ND and GE results for the time-varying extreme risk spillover networks are similar to those in figures 8 and 9, we hold that our results are robust. The detailed results are available upon request.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 71501066], [grant number 71373072], [grant number 71521061], [grant number 71201054]; the China Scholarship Council [grant number 201506135022]; the Specialized Research Fund for the Doctoral Program of Higher Education [grant number 20130161110031]. The Boston University work was supported by NSF [grant numbers CMMI 1125290, PHY 1505000 and CHE- 1213217] and DOE Contract [grant number DE-AC07-05Id14517].