Portfolio diversification, differentiation and the robustness of holdings networks

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Networks of portfolio holdings exemplify how interdependence both between the agents and their assets can be a source of systemic vulnerability. We study a real-world holdings network and compare it with various alternative scenarios from randomization and rebalancing of the original investments. Scenarios generation relies on algorithms that satisfy the global constraints imposed by the numbers of outstanding shares in the market. We consider fixed-diversification models and diversification-maximizing replicas too. We extensively analyze the interplay between portfolio diversification and differentiation, and how the outreach of exogenous shocks depends on these factors as well as on the type of shock and the size of the network with respect to the market. We find that real portfolios are poorly diversified but highly similar, that portfolio similarity correlates with systemic fragility and that rebalancing can come with an increased similarity depending on the initial network configuration. We show that a large diversification gain is achieved through rebalancing but, noteworthy, that makes the network vulnerable in front of unselective shocks. Also, while the network is riskier in the presence of targeted shocks, it is safer than its random counterparts when it is stressed by widespread price downturns.