Herding, Noise Traders, and Super-Exponential Financial Bubbles

Summary

This document presents an equilibrium model with a risky asset and a risk-free asset, populated by rational investors and noise traders. Rational investors choose allocations based on expected return and risk under constant relative risk aversion utility. Noise traders imitate one another and use momentum trading, while their propensity to herd changes randomly over time. The model is designed to explain how interactions between these groups can shape prices and returns.

The authors report that the framework reproduces fat-tailed returns and volatility clustering, and can generate temporary bubble growth faster than exponential with approximate log-periodic patterns. They relate its price dynamics to the dotcom bubble from 1995 to 2000 and find momentum strategies temporarily profitable, consistent with momentum reinforcing herding. These are model-based findings and a historical comparison; the excerpt does not provide estimation details, robustness checks, or evidence that the strategy remains profitable outside bubble conditions.

Key ideas

• Rational investors allocate between risky and risk-free assets according to expected utility.
• Noise traders imitate others and trade on momentum, with a time-varying tendency to herd.
• The model generates fat-tailed returns, volatility clustering, and temporary faster-than-exponential bubbles.
• The authors compare the model with the dotcom bubble from 1995 to 2000.
• Momentum strategies are reported as temporarily profitable and as potentially reinforcing herding.

Tags

# Super-exponential endogenous bubbles in an equilibrium model of rational and noise traders


# Super-exponential endogenous bubbles in an equilibrium model of rational and noise traders









We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility with respect to their allocation on the risky asset versus the risk-free asset. Noise traders are subjected to social imitation and follow momentum trading. Allowing for random time-varying herding propensity, we are able to reproduce several well-known stylized facts of financial markets such as a fat-tail distribution of returns and volatility clustering. In particular, we observe transient faster-than-exponential bubble growth with approximate log-periodic behavior and give analytical arguments why this follows from our framework. The model accounts well for the behavior of traders and for the price dynamics that developed during the dotcom bubble in 1995-2000. Momentum strategies are shown to be transiently profitable, supporting these strategies as enhancing herding behavior.

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