  Systemic risk arises as a multi-layer network phenomenon. Layers represent
direct financial exposures of various types, including interbank liabilities,
derivative- or foreign exchange exposures. Another network 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
portfolio holdings of financial agents we quantify systemic risk of overlapping
portfolios. We present an optimization procedure, where we minimize the
systemic risk in a given financial market by optimally rearranging overlapping
portfolio networks, under the constraints that the expected returns and risks
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 by using data from the European Banking Authority
stress test of 2016. We show that systemic-risk-efficient allocations are
accessible by the optimization. In the case of sovereign exposure, systemic
risk can be reduced by more than a factor of two, with- out 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 reduced dramatically in the optimized
network.
