Herd Behaviors in the Stock and Foreign Exchange Markets

TL;DR

This paper investigates herd behaviors in Korean financial markets, revealing power-law distributions of returns, conditions for crashes, and a crossover to Gaussian distribution at specific time scales.

Contribution

It demonstrates that return distributions follow power-law behavior with specific exponents and identifies thresholds associated with market crashes and distribution crossover points.

Findings

Returns follow power-law distributions with exponents 2.2 and 2.4.

Market crashes occur when the herding parameter exceeds 2.33.

Normalized returns show a crossover to Gaussian distribution at a time step of 252.

Abstract

The herd behaviors of returns for the won-dollar exchange rate and the KOSPI are analyzed in Korean financial markets. It is shown that the probability distribution $P(R)$ of price returns $R$ for three values of the herding parameter tends to a power-law behavior $P(R) \simeq R^{-\beta}$ with the exponents $ \beta=2.2$(the won-dollar exchange rate) and 2.4(the KOSPI). The financial crashes are found to occur at $h >2.33$ when the relative increase in the probability distribution of exteremely high price returns is observed. Especially, the distribution of normalized returns shows a crossover to a Gaussian distribution for the time step $\Delta t=252$. Our results will be also compared to the other well-known analyses.