We study portfolio compression, a procedure that removes cycles of liabilities in a financial network. We analyze the incentives for banks to engage in compression and its systemic effects in terms of all banks' equities. We show that, contrary to conventional wisdom, portfolio compression may be socially and individually detrimental and banks' incentives may be misaligned with social welfare. We then present sufficient conditions under which banks involved in the compression have an incentive to agree to it or under which the compression is even a Pareto improvement for all banks. Our results contribute to a better understanding of the implications of recent regulatory policy.

We consider the problem of clearing a system of interconnected banks that have been exposed to a shock on their assets. Eisenberg and Noe (2001) showed that when banks can only enter into simple debt contracts with each other, then a clearing vector of payments can be computed in polynomial time. In this paper, we show that the situation changes radically when banks can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank. We prove that computing an approximate solution to the clearing problem with sufficiently small constant error is PPAD-complete. To do this, we demonstrate how financial networks with debt and CDSs can encode arithmetic operations such as addition and multiplication. Our results have practical impact for network stress tests and reveal computational complexity as a new concern regarding the stability of the financial system.

We consider the problem of clearing a system of interconnected banks that have been exposed to a shock on their assets. Due to this shock, some of the banks may go into bankruptcy and default on their obligations towards other banks. Clearing means computing the payments to be made from each bank to each other bank in accordance with bankruptcy law. The design of good clearing mechanisms is challenging because of the complex and often cyclic interdependencies in realistic financial networks. Eisenberg and Noe (2001) showed that when banks can only enter into debt contracts with each other, then there always exists a unique Pareto efficient clearing payment vector and it can be computed in polynomial time. Rogers and Veraart (2013) extended this result to a setting where defaulting banks can only recover part of their assets.