A Statistical Test for Detecting Dependency Breakdown in Financial Markets

Abstract

Correlations among stock returns during volatile markets differ substantially as compared to those from quieter markets. During times of financial crisis, it has been observed that the ‘traditional’ dependencies in global markets break down. However, such an upheaval in the dependency structure happens over a span of several months, with the breakdown coinciding with a major bankruptcy or a sovereign default. An important aspect of risk management is to effectively identify the duration of breakdown and create tailor-made models for these extreme events; nevertheless, there are few statistical methods to identify such significant breakdowns. The purpose of this paper is to propose a simple test to detect such structural changes in global markets. This test relies on the assumption that asset price follows a Geometric Brownian Motion. We test for a breakdown in dependence structure using eigenvalue decomposition of the correlation matrix. We derive the asymptotic distribution of the test statistic under the null hypothesis and apply the test to stock returns. We also compute the power of this proposed test and compare it with the power of other existing tests. Through extensive experimentation, we show that the proposed test is able to effectively detect the times of structural breakdown in global stock markets, despite the simplifying assumption of Geometric Brownian Motion of stock prices.