Ludwig-Maximilians-Universität, Department of Physics, Schellingstraße 4, 80799 Munich and risklab GmbH, Seidlstraße 24, 80335, Munich.
Deutsches Zentrum für Luft- und Raumfahrt, Institut für Materialphysik im Weltraum, Münchner Strasse 20, 82234 Weßling.
Phys Rev E. 2017 Dec;96(6-1):062315. doi: 10.1103/PhysRevE.96.062315. Epub 2017 Dec 26.
Pearson correlation and mutual information-based complex networks of the day-to-day returns of U.S. S&P500 stocks between 1985 and 2015 have been constructed 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.
已构建了 1985 年至 2015 年间美国标准普尔 500 股票的日常收益的基于 Pearson 相关系数和互信息的复杂网络，以研究股票之间的相互依赖性及其性质。我们表明，这两个网络都检测到了定性差异，尤其是在（最近）动荡的市场时期，这表明在不断变化的经济环境中，不同公司的股票之间的互联关系波动强烈。使用替代数据得出了衡量非线性相关性强度的度量标准，并在金融市场危机期间得出了有趣的观察结果。与在危机期间相关性主要减少到线性相关的预期相反，我们表明（至少在 2008 年危机期间）非线性效应显著增加。事实证明，网络中的中心性概念可能可以用作异常市场行为的某种预警指标，我们用 2008 年次贷危机的例子证明了这一点。最后，我们应用了 Markowitz 均值方差投资组合优化，并将非线性相关性的度量纳入投资敞口。这与完全投资组合相比，表现出显著的优势。
