Nanyang Business School Forum on Risk Management and Insurance
Endogenous Risk-Exposure and Systemic Instability
Is financial system’s interconnectedness a leading factor for the 2008 global financial crisis? This question has sparked a wide range of interest from academics to policymakers. On one hand, a highly connected financial system has been argued to be robust to financial crises due to its co-insurance for each individual bank (Allen and Gale, 2000; Freixas et al., 2000). On the other hand, recent papers argued that the relationship between the banking system’s interconnectedness and the financial stability is not monotonic because the interlinkages also pose a propagation risk (Gai et al., 2011; Acemoglu et al., 2015).
The existing literature, analyzing either the financial network’s co-insurance or propagation mechanism, assumes that the initial shocks happened exogenously and with equal probability. However, banks’ exposure to those shocks is an endogenous choice variable. For example, a bank chooses between safe borrowers and subprime borrowers or chooses its exposure on asset-backed securities. Without a clear understanding of banks’ endogenous choices of risk exposure, the analysis of financial networks’ systemic stability remains, at best, incomplete. This paper fills this gap by studying how the interbank network influences banks’ ex-ante risk exposure incentives.
I present a theoretical framework to study banks’ equilibrium risk-exposure in financial networks. The paper shows that banks in densely connected networks rationally choose greater risk exposure because of a risk-taking externality. In financial networks, solvent banks need to reimburse failed banks a positive amount of private bailout due to the interbank connection. This private bailout reduces banks’ upside payoffs (the payoffs when they are solvent). On the other hand, banks’ downside payoffs are always zero due to the limited liability. To compensate for this asymmetric distortion from the private bailout, banks will desire riskier projects with greater upside payoffs. The risk-taking distortion is higher when each bank anticipates a higher likelihood of such private bailout, or in other words, when its counterparties take greater risks. Therefore, banks’ risk-taking is strategically complementary and there exists a risk-taking externality.
Moreover, banks in greater connected networks will be more affected by such risk-taking externality. I show that banks’ endogenous choices of risk exposure are higher if they are in highly connected complete networks than in loosely connected ring networks. In complete networks, each bank is connected to every other bank. I first confirm Allen and Gale (2000) that complete networks are better at co-insurance in the sense that more failed banks’ deposits are reimbursed by successful banks. However, due to precisely this co-insurance, each bank, if succeeds, will anticipate a greater amount of private bailout to failed banks’ depositors, hence creating a greater risk-taking externality. The losses that will be bettered co-insured, as in Allen and Gale (2000)’s complete networks, will be more likely to endogenously evolve in the first place. Similarly, the intuition also applies to networks with more counterparties: banks in financial networks with more counterparties (either complete or ring networks) will rationally choose to expose to greater risks.
I also show that every bank will rationally coordinate to expose to one single systemic risk if endogenizing banks’ decisions to correlate their risk exposure. In anticipation of the interbank transfers, a correlated portfolio will reduce the possibility of private bailouts. Hence it will increase each bank’s expected profit. As a result of the endogenous correlation, a financial crisis (or simultaneous failure of several banks) will be more likely to endogenously evolve in connected 5 banking systems. The model explains the empirical findings of the 2008 financial crisis by the Financial Crisis Inquiry Commission (2011): “Some financial institutions failed because of a common shock: they made similar failed bets on housing.”
I show that the deposit insurance is crucial for the risk-taking externalities. Deposit insurance eliminates depositors’ price disciplining ability, an invisible hand. Absent deposit insurance, depositors fully anticipate banks’ the network risk-taking externality and their choices of risk exposure. As a result, the deposit rates will endogenously adjust to equalize banks’ default probabilities regardless of the structure of financial networks. This result is a generalization of the Modigliani-Miller (MM) theorem in the sense that banks’ interbank debt structure is also irrelevant to their choices of risk exposure. On the other hand, with deposit insurance, depositors are “informative insensitive” to the structure of the banking network. In this case, there is no price disciplining from deposit rates. The network risk-taking externality exists.
The paper then proceeds by proposing several government regulations aiming to reduce the network risk-taking externalities. I first show that an individual bank’s equity buffer generates a positive externality on systemic stability. The equity buffer not only directly reduces a bank’s own risk-taking (Jensen and Meckling, 1976) but also reduces the risk-taking of every other bank in the financial system. The intuition is simple: if a bank’s project fails, its equity buffer first induces its own shareholders to absorb part of the shock. As a result, the loss that may be otherwise propagated to other banks will now be curbed at the origin. That implies every bank in the financial network will anticipate a smaller private bailout to failed banks, and will ex-ante choose to expose to fewer risks. From that, I propose a network-adjusted capital regulation: a higher tier-one capital ratio requirement for banks with stronger interbank connections or more counterparties.
The second policy the paper explores is government bailouts. Conventional wisdom states that a government bailout, or simply anticipation of it, is harmful to the systemic stability since it encourages excessive risk-taking. In this paper, I show that a government bailout instead reduces connected banks’ risk-taking because it decreases the network risk-taking distortion. In presence of the possibility of a government bailout, every bank will anticipate a smaller private bailout to its failed counterparties. Hence the network risk-taking distortion is reduced and so does every bank’s choices of risk exposure.
The complete paper is available at: