Measuring the systemic risk in indirect financial networks

ABSTRACT

In this study, we present a novel measurement approach for systemic risk by considering an indirect network structure. In a departure from previous studies, this measurement method captures spillovers arising from deleveraging and price impact in financial systems and calculates the amplification of losses during the contagion process. We show the relationship between a bank's vulnerability and its network connections. Applying the model to Chinese banks, we evaluate the fire-sale loss of each bank and quantify the impact of each asset in different simulated stress scenarios. Using both theoretical and empirical evidence, we show the ability of network centrality to explain systemic risk contribution: a bank with more network connections is systemically more important. We also present an optimal strategy to mitigate and govern systemic risk. Our result implies that the systemic importance of a bank is based not only on its size but also on the kinds of assets it holds; it provides useful systemic risk monitoring tools complementary to those currently used by supervisors.

KEYWORDS:

• Systemic risk
• indirect financial network
• fire sale
• deleveraging
• contagion

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Alternatively, some other channels may be adopted by banks to reduce the leverage, such as equity issuance and conversion of hybrid debt. One of them may be using equity issues, such as equity issuance, conversion of hybrid debt. Raising new equity may dilute the value of the shares of the existing shareholders and may signal that managers believe that the stock is overvalued, thereby leading to negative stock price reactions Myers and Majluf 1984. In addition, the issuance possibilities for banks are limited when they are in distress Wehinger 2012. Another channel involves increasing the use of stable funding sources (e.g. retail deposits and long-term wholesale funding). However, during a short time span, these measures are typically comparatively costly and/or difficult to implement, especially in periods of distress Bolton and Freixas 2006; Krishnamurthy 2010. Under such circumstances, the easy option for banks to alleviate pressures on their balance sheets might be to reduce assets European Central Bank 2012.

2 For example, Coval and Stafford 2007 show the price discount of stock by mutual funds; Pulvino 1998 uses a novel dataset to investigate liquidity-induced sales in the U.S. aircraft industry; Andersen and Nielsen 2017 show that the forced sales of real estate turn into fire sales. Bank loans would also be discounted when in fire-sale. Such discount gets worsen during crisis Krishnamurthy 2010. Duffie 2013 provides a summary of empirical results regarding the price impact of large sales in assets markets.

3 Similar to Greenwood, Landier, and Thesmar 2015, we assume a same price impact for each kind of asset. Assessing the price impact is quite difficult and a persistent challenge for empirical researchers. Coval and Stafford 2007. Greenwood, Landier, and Thesmar 2015 and Duarte and Eisenbach 2018 assume that the price impact is ${10}^{-13}$, so that €10 billion of trading imbalances lead to a price change of 10 basis points. The discount parameter essentially reflects the liquidity of assets or markets. Given that the development of market, the sample in Greenwood, Landier, and Thesmar 2015 and Duarte and Eisenbach 2018 is the European and U.S bond markets, respectively, in which the liquidity is much higher than in the Chinese market, and the discount may be much less. According to many influential studies, such as Coval and Stafford 2007; Dinc, Erel, and Liao 2017; Aguiar and Gopinath 2005, the price impact of fire sale usually varies from about 1% to 10%, therefore, we choose 0.01 for each $l_k$. Using various $l(l\in \{{10}^{-13},{10}^{-12},\dots ,{10}^{-5},{10}^{-4},{10}^{-3},0.01,0.02,0.03\dots ,0.1\})$, we show, in Appendix 1, that l only has an influence on the magnitude of the systemic impact, and that its influence on the ranking of systemically important financial institutions (SIFIs) is negligible.

4 In some regressions, scores of $R^2$ and adj.$R^2$ are small and have big difference. For example, in Table 6, the $R^2$ for SES is 0.010 and the $adj.R^2$ for that is -0.035. This is not only because of the limitation of the sample size but also due to the low explanatory power of the insignificant systemic risk indicator. As is shown in Tables 6–8, the difference between $R^2$ and adj.$R^2$ gets large when the systemic risk indicator is not significant. According to Gupta et al. 2019, Hollstein et al. 2019, Brooks et al. 2019 and Hoepner et al. 2021, those insignificant systemic risk indicators can only explain the profitability poorly, then the $R^2$ for the regression is small. Furthermore, when computing the adj.$R^2$, the insignificant indicator can hardly increase the goodness-of-fit, then the difference between $R^2$ and adj.$R^2$ gets large.

Additional information

Funding

This study is a product of the project “Dynamics and systemic risks of financial complex systems”. We appreciate the financial support by National Natural Science Foundation of China [grant numbers 71873146, 72131001].

Notes on contributors

Jie Cao

Jie Cao is a Ph.D. student at the School of Business, Central South University. He was a visiting scholar at Boston University in 2018. His research focuses primarily on systemic risk and financial risk management. He has published articles in peer-reviewed journals such as the Journal of Risk, Neural Networks.

Fenghua Wen

Fenghua Wen is a Professor at the School of Business, Central South University. His research focuses primarily on financial risk management, systemic risk, energy finance, and econometrics. He has published articles in peer-reviewed journals such as the International Review of Financial Analysis, Journal of Risk, International Review of Economics & Finance, Energy Economics.

H. Eugene Stanley

H. Eugene Stanley is currently an American Physicist, and a University Professor and a William Fairfield Warren Distinguished Professor with Boston University, USA. He has made fundamental contributions to complex systems, statistical physics, and is one of the founding fathers of eco-physics. His current research interests include eco-physics, complexity science, and statistical physics. He was elected to the U.S. National Academy of Sciences, in 2004.