Systemic risk is a multi-layer network phenomenon. Layers represent various types of direct financial exposure of various types, including interbank liabilities and derivative- or foreign exchange exposures. An important layer of systemic risk emerges through common asset holdings of financial institutions. Strongly overlapping portfolios lead to similar exposures that are caused by price movements of the underlying financial assets. Based on the knowledge of individual portfolio holdings of financial agents, we quantify the systemic risk of overlapping portfolios. We then present an optimization procedure whereby we minimize the systemic risk in a given financial market by optimally rearranging overlapping portfolio networks. The optimization is performed under the constraints that the expected returns and risk of the individual portfolios are unchanged. We explicitly demonstrate the power of the method on the overlapping portfolio network of sovereign exposure between major European banks, using data from the European Banking Authority stress test of 2016. Systemic risk can be reduced by more than a factor of two, without any detrimental effects for the individual banks. These results are confirmed by a simple simulation of fire sales in the government bond market. In particular, we show that the contagion probability is dramatically reduced in the optimized network. We comment on the efficiency of the network optimization approach in comparison to equity-injection-based ways to reduce systemic risk. To obtain the same risk levels that are obtained in the network optimization, it would be necessary to increase the actual available capital by two thirds. This shows the immense potential of network-based systemic risk management.

Financial markets create endogenous systemic risk, the risk that a substantial fraction of the system ceases to function and collapses. Systemic risk can propagate through different mechanisms and channels of contagion. One important form of financial contagion arises from indirect interconnections between financial institutions mediated by financial markets. This indirect interconnection occurs when financial institutions invest in common assets and is referred to as overlapping portfolios. In this work we quantify systemic risk from indirect interconnections between financial institutions. Complete information of security holdings of major Mexican financial intermediaries and the ability to uniquely identify securities in their portfolios, allows us to represent the Mexican financial system as a bipartite network of securities and financial institutions. This makes it possible to quantify systemic risk arising from overlapping portfolios. We show that focusing only on direct interbank exposures underestimates total systemic risk levels by up to 50% under the assumptions of the model. By representing the financial system as a multi-layer network of direct interbank exposures (default contagion) and indirect external exposures (overlapping portfolios) we estimate the mutual influence of different channels of contagion. The method presented here is the first quantification of systemic risk on national scales that includes overlapping portfolios.

We use a simple agent based model of value investors in financial markets to test three credit regulation policies. The first is the unregulated case, which only imposes limits on maximum leverage. The second is Basle II and the third is a hypothetical alternative in which banks perfectly hedge all of their leverage-induced risk with options. When compared to the unregulated case both Basle II and the perfect hedge policy reduce the risk of default when leverage is low but increase it when leverage is high. This is because both regulation policies increase the amount of synchronized buying and selling needed to achieve deleveraging, which can destabilize the market. None of these policies are optimal for everyone: risk neutral investors prefer the unregulated case with low maximum leverage, banks prefer the perfect hedge policy, and fund managers prefer the unregulated case with high maximum leverage. No one prefers Basle II.

The inability to see and quantify systemic financial risk comes at an immense social cost. Systemic risk in the financial system arises to a large extent as a consequence of the interconnectedness of its institutions, which are linked through networks of different types of financial contracts, such as credit, derivatives, foreign exchange, and securities. The interplay of the various exposure networks can be represented as layers in a financial multi-layer network. In this work we quantify the daily contributions to systemic risk from four layers of the Mexican banking system from 2007 to 2013. We show that focusing on a single layer underestimates the total systemic risk by up to 90%. By assigning systemic risk levels to individual banks we study the systemic risk profile of the Mexican banking system on all market layers. This profile can be used to quantify systemic risk on a national level in terms of nation-wide expected systemic losses. We show that market-based systemic risk indicators systematically underestimate expected systemic losses. We find that expected systemic losses are up to a factor of four higher now than before the financial crisis of 2007–2008. We find that systemic risk contributions of individual transactions can be up to a factor of one thousand higher than the corresponding credit risk, which creates huge risks for the public. We find an intriguing non-linear effect whereby the sum of systemic risk of all layers underestimates the total risk. The method presented here is the first objective data-driven quantification of systemic risk on national scales that reveal its true levels.