Financial instability transition under heterogeneous investments and portfolio diversification

Paper: arXiv 2501.19260

Authors: Preben Forer, Barak Budnick, Pierpaolo Vivo, Sabrina Aufiero, Silvia Bartolucci, Fabio Caccioli

Abstract

We analyze the stability of financial investment networks, where financial institutions hold overlapping portfolios of assets. We consider the effect of portfolio diversification and heterogeneous investments using a random matrix dynamical model driven by portfolio rebalancing. While heterogeneity generally correlates with heightened volatility, increasing diversification may have a stabilizing or destabilizing effect depending on the connectivity level of the network. The stability/instability transition is dictated by the largest eigenvalue of the random matrix governing the time evolution of the endogenous components of the returns, for which different approximation schemes are proposed and tested against numerical diagonalization.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework using random matrix theory and the replica method to analyze systemic risk and dynamic portfolio rebalancing networks. However, it lacks empirical validation using real-world financial transaction or balance sheet data, relying entirely on numerical simulations and theoretical derivations.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze financial network stability under portfolio diversification & heterogeneous investments"] --> B["Inputs: Overlapping asset portfolios & portfolio rebalancing dynamics"]
    B --> C["Model Construction: Formulate random matrix dynamical model of endogenous returns"]
    C --> D["Analysis: Compute largest eigenvalue via approximation schemes vs. numerical diagonalization"]
    D --> E["Outcome 1: Heterogeneity generally correlates with heightened volatility"]
    D --> F["Outcome 2: Diversification stabilizes or destabilizes depending on network connectivity"]