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

TL;DR

This paper develops an analytical model to explore how expectation feedbacks and overlapping portfolios influence financial system stability, revealing that myopic risk estimation can lead to chaos and systemic instability.

Contribution

It introduces a novel analytical framework modeling adaptive risk expectations and their impact on systemic stability, extending previous models with endogenous asset prices and feedback effects.

Findings

Risk expectations are central to systemic stability.

Myopic risk estimation can cause leverage cycles and chaos.

Market frictions influence stability under adaptive expectations.

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.