[Paper Review] Systemic-risk-efficient asset allocation: Minimization of systemic risk as a network optimization problem

Anton Pichler, Sebastian Poledna+1 more|arXiv (Cornell University)|Jan 31, 2018

Banking stability, regulation, efficiency20 references3 citations

TL;DR

This paper proposes a network optimization framework to minimize systemic risk in financial systems by reorganizing overlapping portfolios without altering individual banks' expected returns or risk levels. Using quadratic programming, it reduces systemic risk by over 50% in European sovereign bond exposures, significantly enhancing resilience to fire sales and contagion.

ABSTRACT

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.

Motivation & Objective

• To address systemic risk arising from overlapping portfolios in financial networks, which amplifies contagion during market stress.
• To develop a systematic method for identifying systemic-risk-efficient portfolio allocations that preserve individual risk-return profiles.
• To provide a benchmark for regulatory monitoring and incentive design by quantifying the optimal network topology for financial stability.
• To demonstrate the feasibility and impact of network optimization in real-world financial data, such as European bank sovereign exposures.
• To explore how regulatory frameworks could be reformed to internalize systemic risk through optimized capital requirements or risk-based taxes.

Proposed method

• Formulates systemic-risk-efficient asset allocation as a quadratically constrained quadratic programming (QCQP) problem to minimize systemic risk while preserving individual portfolio expected returns and risk levels.
• Models financial systems as multi-layer networks, with one layer representing overlapping portfolios of common assets (e.g., government bonds) that amplify systemic risk through fire-sale externalities.
• Employs the DebtRank measure to quantify systemic impact of individual institutions and assess network-wide contagion propagation under stress.
• Uses real data from the 2016 European Banking Authority stress test to reconstruct the sovereign bond holding network among major European banks.
• Applies optimization to redistribute portfolio holdings such that systemic risk is minimized under fixed mean and variance constraints per portfolio.
• Validates results via agent-based simulations of fire sales, comparing leverage ratios and default probabilities in original vs. optimized networks.

Experimental results

Research questions

• RQ1 Can systemic risk arising from overlapping portfolios be systematically reduced through optimal network reconfiguration without altering individual bank risk-return objectives?
• RQ2 To what extent can network optimization reduce the probability of financial contagion and fire-sale cascades in sovereign bond markets?
• RQ3 How does the optimized network topology compare to the original in terms of resilience under stress scenarios such as fire sales?
• RQ4 What role do portfolio overlaps play in amplifying systemic risk, and can this be quantitatively mitigated via structural changes?
• RQ5 Can the optimized network serve as a regulatory benchmark for monitoring systemic risk and evaluating incentive schemes like systemic risk taxes?

Key findings

• Systemic risk in the European sovereign bond market can be reduced by more than 50% through optimal reallocation of overlapping portfolios without changing individual banks’ expected returns or risk levels.
• The optimized network exhibits significantly lower default probabilities and more stable leverage ratios during simulated fire sales compared to the original network.
• Even under extreme stress, the optimized network maintains equity and capital levels close to initial values, while the original network shows sharp increases in leverage and distress.
• The optimization is robust across different levels of market impact (ε = 0.01, 0.025, 0.05), indicating consistent performance under varying assumptions.
• The method provides a practical benchmark for regulatory monitoring, enabling detection of market divergence from systemic-risk-efficient configurations.
• The approach is extendable to other asset classes and financial institutions, though computational complexity increases with scale, suggesting segmentation or selective inclusion as viable strategies.