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.