Nonlinear correlations in financial markets: A complex network based analysis

It is common practice in finance to quantify correlations among financial time series in terms of their linear Pearson correlation coefficient. Knowing that financial time series show intermittent behavior being reminiscent of turbulence and leading to the well-known fat tails in the probability distribution as well as nonlinearities that also significantly show up as deviations from randomness in the distribution of Fourier phases, it is justified to assume that also nonlinear correlations among financial time series may be present. Therefore, 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. By deriving a measure for the strength of nonlinear correlations using surrogate data we show that a significant amount of information is lost when only relying on linear correlations measures.Our studies revealed that in contrast to the expectation that dependencies reduce mainly to linear correlations during crises, at least in the 2008 crisis nonlinear effects are significantly increasing. More specifically, we find that there are different types of financial crises in terms of nonlinear effects. Our results indicate that during the 2008 crisis nonlinear effects were significantly stronger than in preceding crises like the bursting of the Dot-com bubble. Furthermore, we found that major political events seem to have no significant mid- and long-term impact on market correlation structure in contrast to financial crises. In addition, 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 also demonstrate with the example of the 2008 subprime mortgage crisis. Finally we developed a practical application in the field of portfolio optimization. We showed that scaling the investment exposure based on the strength of nonlinear correlations leads to an outperformance compared to a fully invested portfolio with static exposure. Furthermore, we obtained first interesting results on the relationship of linear and nonlinear correlations with causality measure