Network Versus Portfolio Structure in Financial Systems

Abstract

The question of how to stabilize financial systems has attracted considerable attention since the global financial crisis of 2007-2009. Recently, Beale et al. ("Individual versus systemic risk and the regulator's dilemma", Proc Natl Acad Sci USA 108: 12647-12652, 2011) demonstrated that higher portfolio diversity among banks would reduce systemic risk by decreasing the risk of simultaneous defaults at the expense of a higher likelihood of individual defaults. In practice, however, a bank default has an externality in that it undermines other banks' balance sheets. This paper explores how each of these different sources of risk, simultaneity risk and externality, contributes to systemic risk. The results show that the allocation of external assets that minimizes systemic risk varies with the topology of the financial network as long as asset returns have negative correlations. In the model, a well-known centrality measure, PageRank, reflects an appropriately defined "infectiveness" of a bank. An important result is that the most infective bank need not always be the safest bank. Under certain circumstances, the most infective node should act as a firewall to prevent large-scale collective defaults. The introduction of a counteractive portfolio structure will significantly reduce systemic risk.

Clearing Algorithms and Network Centrality

“…Puhr et al (2014) and Alter et al (2015) find that the Katz centrality and its close cousin (see Newman (2010)), the Eigenvector centrality, have the best explanatory power for contagion losses from a Eisenberg and Noe (2001)-type clearing model for the Austrian and the German banking system, respectively. Kobayashi (2013) and Gauthier et al (2013) obtain similar results in simulations. In this study I demonstrate that these results were indeed to be expected, as the solution of the clearing model converges to a generalized Katz centrality measure as a crisis tends to affect the entire financial system.…”

Efficient immunization strategies to prevent financial contagion

“…The first one is based on the costs that would result from bank failures. Following Beale et al 1 and Kobayashi 16 , we assume that social costs take the form C ( n ) = n χ , χ ∈ [1, ∞), where n is the number of failed banks. The expected cost is thus given as where N ( = 1000) is the total number of banks in the financial market and q (·) is the probability function.…”

“…We call the former type uniform immunization and the latter counteractive immunization (see Methods). Counteractive immunization does not change the riskiness of individual banks, but Kobayashi 16 showed that assigning negatively correlated assets to highly “infective” banks would reduce systemic risk.…”

“…As an objective measure of systemic risk, we employ the χ -th moment of the number of defaulted banks 1 16 . In addition, to see the effects of immunization on the connectivity of the financial network, we also show the likelihood that the giant strongly connected component (GSCC) disappears due to the removal of defaulted banks (see Methods).…”

A model of financial contagion with variable asset returns may be replaced with a simple threshold model of cascades

“…The failure of a single bank can spread through financial networks, generating default cascades. Over the past few years, many researchers in various fields of natural and social sciences, such as physicists, ecologists and economists, have been addressing the question of how to prevent financial contagion (e.g., Nier et al, 2007, Soramaki et al, 2007, Gai and Kapadia, 2010, Gai et al, 2011, Lenzu and Tedeschi, 2012, Kobayashi, 2013, Kobayashi and Hasui, 2014.…”