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When panic makes you blind: A chaotic route to systemic risk

Piero Mazzarisi, Fabrizio Lillo and Stefano Marmi

Journal of Economic Dynamics and Control, 2019, vol. 100, issue C, 176-199

Abstract: We present an analytical model to study the role of expectation feedbacks and overlapping portfolios on systemic stability of financial systems. Building on Corsi et al. (2016), we model a set of financial institutions having Value-at-Risk capital requirements and investing in a portfolio of risky assets, whose prices evolve stochastically in time and are endogenously driven by the trading decisions of financial institutions. Assuming that they use adaptive expectations of risk, we show that the evolution of the system is described by a slow-fast random dynamical system, which can be studied analytically in some regimes. The model shows how the risk expectations play a central role in determining the systemic stability of the financial system and how wrong risk expectations may create panic-induced reduction or over-optimistic expansion of balance sheets. Specifically, when investors are myopic in estimating the risk, the fixed point equilibrium of the system breaks into leverage cycles and financial variables display a bifurcation cascade eventually leading to chaos. We discuss the role of financial policy and the effects of some market frictions, as the cost of diversification and financial transaction taxes, in determining the stability of the system in the presence of adaptive expectations of risk.

Keywords: Systemic risk; Backward-looking expectations; Leverage cycles; Financial innovations; Autoregressive dynamics; Random dynamical systems (search for similar items in EconPapers)
JEL-codes: G01 G20 G11 G17 (search for similar items in EconPapers)
Date: 2019
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