Changes in cross-correlations as an indicator for systemic risk

Efficient Multi-Change Point Analysis to Decode Economic Crisis Information from the S&P500 Mean Market Correlation

Identifying macroeconomic events that are responsible for dramatic changes of economy is of particular relevance to understanding the overall economic dynamics. We introduce an open-source available efficient Python implementation of a Bayesian multi-trend change point analysis, which solves significant memory and computing time limitations to extract crisis information from a correlation metric. Therefore, we focus on the recently investigated S&P500 mean market correlation in a period of roughly 20 years that includes the dot-com bubble, the global financial crisis, and the Euro crisis. The analysis is performed two-fold: first, in retrospect on the whole dataset and second, in an online adaptive manner in pre-crisis segments. The online sensitivity horizon is roughly determined to be 80 up to 100 trading days after a crisis onset. A detailed comparison to global economic events supports the interpretation of the mean market correlation as an informative macroeconomic measure by a rather good agreement of change point distributions and major crisis events. Furthermore, the results hint at the importance of the U.S. housing bubble as a trigger of the global financial crisis, provide new evidence for the general reasoning of locally (meta)stable economic states, and could work as a comparative impact rating of specific economic events.

Assessing systemic risk in financial markets using dynamic topic networks

Systemic risk in financial markets refers to the breakdown of a financial system due to global events, catastrophes, or extreme incidents, leading to huge financial instability and losses. This study proposes a dynamic topic network (DTN) approach that combines topic modelling and network analysis to assess systemic risk in financial markets. We make use of Latent Dirichlet Allocation (LDA) to semantically analyse news articles, and the extracted topics then serve as input to construct topic similarity networks over time. Our results indicate how connected the topics are so that we can correlate any abnormal behaviours with volatility in the financial markets. With the 2015-2016 stock market selloff and COVID-19 as use cases, our results also suggest that the proposed DTN approach can provide an indication of (a) abnormal movement in the Dow Jones Industrial Average and (b) when the market would gradually begin to recover from such an event. From a practical risk management point of view, this analysis can be carried out on a daily basis when new data come in so that we can make use of the calculated metrics to predict real-time systemic risk in financial markets.

Evolving Network Analysis of S&P500 Components: COVID-19 Influence of Cross-Correlation Network Structure

The economy is a system of complex interactions. The COVID-19 pandemic strongly influenced economies, particularly through introduced restrictions, which formed a completely new economic environment. The present work focuses on the changes induced by the COVID-19 epidemic on the correlation network structure. The analysis is performed on a representative set of USA companies-the S&P500 components. Four different network structures are constructed (strong, weak, typically, and significantly connected networks), and the rank entropy, cycle entropy, averaged clustering coefficient, and transitivity evolution are established and discussed. Based on the mentioned structural parameters, four different stages have been distinguished during the COVID-19-induced crisis. The proposed network properties and their applicability to a crisis-distinguishing problem are discussed. Moreover, the optimal time window problem is analysed.

Do economic shocks spread randomly?: A topological study of the global contagion network

The spread of economic shocks in an increasingly interconnected global economy has been subject to several studies recently. These studies mostly focus on the synchronization of business cycles among economies and search for the relationship between trade linkages and shock contagion. In contrast to previous studies in the field, this paper focuses on the topological properties of the shock contagion network as measured by pairwise Granger causality between economic output of countries. This topological approach can bring new insights into the dynamics of contagion and the relationship between trade and cycle synchronization while also allows to test the patterns of shock contagion against randomness. Results show that connectedness decreases over the previous decades until the first decade of the 21st century, showing less frequent shock transmission which shades previous results in the field which typically associate increasing trade and globalization with more frequent or unchanged contagion. We find significant non-random topology with respect to transitivity and path lengths, the skewness of the degree distribution and the stability of connections. Estimations show that there is a systematically existing (persistent) contagion path in 16% of all possible connections. However, we do not find significant geographical or development-wise patterns behind the modularity of the contagion network and no significant association is found between economic openness and exposure to shock transmission in either direction.

Finding the direction of lowest resilience in multivariate complex systems

The dynamics of complex systems, such as ecosystems, financial markets and the human brain, emerge from the interactions of numerous components. We often lack the knowledge to build reliable models for the behaviour of such network systems. This makes it difficult to predict potential instabilities. We show that one could use the natural fluctuations in multivariate time series to reveal network regions with particularly slow dynamics. The multidimensional slowness points to the direction of minimal resilience, in the sense that simultaneous perturbations on this set of nodes will take longest to recover. We compare an autocorrelation-based method with a variance-based method for different time-series lengths, data resolution and different noise regimes. We show that the autocorrelation-based method is less robust for short time series or time series with a low resolution but more robust for varying noise levels. This novel approach may help to identify unstable regions of multivariate systems or to distinguish safe from unsafe perturbations.

Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis

This paper discusses the effects of introducing nonlinear interactions and noise-filtering to the covariance matrix used in Markowitz’s portfolio allocation model, evaluating the technique’s performances for daily data from seven financial markets between January 2000 and August 2018. We estimated the covariance matrix by applying Kernel functions, and applied filtering following the theoretical distribution of the eigenvalues based on the Random Matrix Theory. The results were compared with the traditional linear Pearson estimator and robust estimation methods for covariance matrices. The results showed that noise-filtering yielded portfolios with significantly larger risk-adjusted profitability than its non-filtered counterpart for almost half of the tested cases. Moreover, we analyzed the improvements and setbacks of the nonlinear approaches over linear ones, discussing in which circumstances the additional complexity of nonlinear features seemed to predominantly add more noise or predictive performance.

How News May Affect Markets' Complex Structure: The Case of Cambridge Analytica

The claim of Cambridge Analytica, a political consulting firm, that it was possible to influence voting behavior by using data mined from the social platform Facebook created a sudden fear in its users of being manipulated; consequently, even the market price of the social platform was shocked.We propose a case study analyzing the effect of this data scandal not only on Facebook stock price, but also on the whole stock market. To such a scope, we consider 15-minutes prices and returns of the set of the NASDAQ-100 components before and after the Cambridge Analytica case. We analyze correlations and Mutual Information among components finding that assets become more correlated and their Mutual Information grows higher. We also observe that correlation and Mutual Information are mutually increasing and seem to follow a master curve. Hence, the market appears more fragile after the Cambridge Analytica event. In fact, as it is well-known in finance, an increase in the average value of correlations augments the systemic risk (i.e., all the market can collapse as a whole) and decreases the possibility of allocating a safe investment portfolio.

Stabilizing effect of volatility in financial markets

In financial markets, greater volatility is usually considered to be synonymous with greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To investigate this surprising feature, here we propose using the mean first hitting time, i.e., the average time a stock return takes to undergo for the first time a large negative (crashes) or positive variation (rallies), as an indicator of price stability, and relate this to a standard measure of volatility. In an empirical analysis of daily returns for 1071 stocks traded in the New York Stock Exchange, we find that this measure of stability displays nonmonotonic behavior, with a maximum, as a function of volatility. Also, we show that the statistical properties of the empirical data can be reproduced by a nonlinear Heston model. This analysis implies that, contrary to conventional wisdom, not only high, but also low volatility values can be associated with higher instability in financial markets. This proposed measure of stability can be extremely useful in risk control.

Measuring critical transitions in financial markets

Tipping points in complex systems are structural transitions from one state to another. In financial markets these critical points are connected to systemic risks, which have led to financial crisis in the past. Due to this, researchers are studying tipping points with different methods. This paper introduces a new method which bridges the gap between real-world portfolio management and statistical facts in financial markets in order to give more insight into the mechanics of financial markets.

Systemic risk and hierarchical transitions of financial networks

In this paper, the change in topological hierarchy, which is measured by the minimum spanning tree constructed from the cross-correlations between the stock indices from the S & P 500 for 1998-2012 in a one year moving time window, was used to analyze a financial crisis. The hierarchy increased in all minor crises in the observation time window except for the sharp crisis of 2007-2008 when the global financial crisis occurred. The sudden increase in hierarchy just before the global financial crisis can be used for the early detection of an upcoming crisis. Clearly, the higher the hierarchy, the higher the threats to financial stability. The scaling relations were developed to observe the changes in hierarchy with the network topology. These scaling relations can also identify and quantify the financial crisis periods, and appear to contain the predictive power of an upcoming crisis.

Interplay between past market correlation structure changes and future volatility outbursts

We report significant relations between past changes in the market correlation structure and future changes in the market volatility. This relation is made evident by using a measure of "correlation structure persistence" on correlation-based information filtering networks that quantifies the rate of change of the market dependence structure. We also measured changes in the correlation structure by means of a "metacorrelation" that measures a lagged correlation between correlation matrices computed over different time windows. Both methods show a deep interplay between past changes in correlation structure and future changes in volatility and we demonstrate they can anticipate market risk variations and this can be used to better forecast portfolio risk. Notably, these methods overcome the curse of dimensionality that limits the applicability of traditional econometric tools to portfolios made of a large number of assets. We report on forecasting performances and statistical significance of both methods for two different equity datasets. We also identify an optimal region of parameters in terms of True Positive and False Positive trade-off, through a ROC curve analysis. We find that this forecasting method is robust and it outperforms logistic regression predictors based on past volatility only. Moreover the temporal analysis indicates that methods based on correlation structural persistence are able to adapt to abrupt changes in the market, such as financial crises, more rapidly than methods based on past volatility.

Quantifying Systemic Risk by Solutions of the Mean-Variance Risk Model

The world is still recovering from the financial crisis peaking in September 2008. The triggering event was the bankruptcy of Lehman Brothers. To detect such turmoils, one can investigate the time-dependent behaviour of correlations between assets or indices. These cross-correlations have been connected to the systemic risks within markets by several studies in the aftermath of this crisis. We study 37 different US indices which cover almost all aspects of the US economy and show that monitoring an average investor’s behaviour can be used to quantify times of increased risk. In this paper the overall investing strategy is approximated by the ground-states of the mean-variance model along the efficient frontier bound to real world constraints. Changes in the behaviour of the average investor is utlilized as a early warning sign.

Exploring Market State and Stock Interactions on the Minute Timescale

A stock market is a non-stationary complex system. The stock interactions are important for understanding the state of the market. However, our knowledge on the stock interactions on the minute timescale is limited. Here we apply the random matrix theory and methods in complex networks to study the stock interactions and sector interactions. Further, we construct a new kind of cross-correlation matrix to investigate the correlation between the stock interactions at different minutes within one trading day. Based on 50 million minute-to-minute price data in the Shanghai stock market, we discover that the market states in the morning and afternoon are significantly different. The differences mainly exist in three aspects, i.e. the co-movement of stock prices, interactions of sectors and correlation between the stock interactions at different minutes. In the afternoon, the component stocks of sectors are more robust and the structure of sectors is firmer. Therefore, the market state in the afternoon is more stable. Furthermore, we reveal that the information of the sector interactions can indicate the financial crisis in the market, and the indicator based on the empirical data in the afternoon is more effective.

Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

Visibility Graph Based Time Series Analysis

Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.

Realized volatility and absolute return volatility: a comparison indicating market risk

Measuring volatility in financial markets is a primary challenge in the theory and practice of risk management and is essential when developing investment strategies. Although the vast literature on the topic describes many different models, two nonparametric measurements have emerged and received wide use over the past decade: realized volatility and absolute return volatility. The former is strongly favored in the financial sector and the latter by econophysicists. We examine the memory and clustering features of these two methods and find that both enable strong predictions. We compare the two in detail and find that although realized volatility has a better short-term effect that allows predictions of near-future market behavior, absolute return volatility is easier to calculate and, as a risk indicator, has approximately the same sensitivity as realized volatility. Our detailed empirical analysis yields valuable guidelines for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods.

Dynamic evolution of cross-correlations in the Chinese stock market

The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management.

Cohesiveness in financial news and its relation to market volatility

Motivated by recent financial crises, significant research efforts have been put into studying contagion effects and herding behaviour in financial markets. Much less has been said regarding the influence of financial news on financial markets. We propose a novel measure of collective behaviour based on financial news on the Web, the News Cohesiveness Index (NCI), and we demonstrate that the index can be used as a financial market volatility indicator. We evaluate the NCI using financial documents from large Web news sources on a daily basis from October 2011 to July 2013 and analyse the interplay between financial markets and finance-related news. We hypothesise that strong cohesion in financial news reflects movements in the financial markets. Our results indicate that cohesiveness in financial news is highly correlated with and driven by volatility in financial markets.