Linear and nonlinear market correlations: characterizing financial crises and portfolio optimization

TL;DR

This paper analyzes the complex dependencies among US stocks over 30 years using correlation and mutual information networks, revealing nonlinear effects during crises and proposing network centrality as an early warning indicator, with implications for portfolio optimization.

Contribution

It introduces a method to measure nonlinear dependencies in financial markets and demonstrates their significance during crises, enhancing portfolio optimization strategies.

Findings

Nonlinear dependencies increase significantly during the 2008 crisis.

Network centrality can serve as an early warning indicator.

Incorporating nonlinear measures improves portfolio performance.

Abstract

Pearson correlation and mutual information based complex networks of the day-to-day returns of US S&P500 stocks between 1985 and 2015 have been constructed in order to investigate the mutual dependencies of the stocks and their nature. We show that both networks detect qualitative differences especially during (recent) turbulent market periods thus indicating strongly fluctuating interconnections between the stocks of different companies in changing economic environments. A measure for the strength of nonlinear dependencies is derived using surrogate data and leads to interesting observations during periods of financial market crises. In contrast to the expectation that dependencies reduce mainly to linear correlations during crises we show that (at least in the 2008 crisis) nonlinear effects are significantly increasing. It turns out that the concept of centrality within a network could potentially be used as some kind of an early warning indicator for abnormal market behavior as we demonstrate with the example of the 2008 subprime mortgage crisis. Finally, we apply a Markowitz mean variance portfolio optimization and integrate the measure of nonlinear dependencies to scale the investment exposure. This leads to significant outperformance as compared to a fully invested portfolio.