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

The dependency structure of the financial multiplex network model: New evidence from the cross-correlation of idiosyncratic returns, volatility, and trading volume

This work describes the design of a novel financial multiplex network composed of three layers obtained by applying the MST-based cross-correlation network, using the data from 465 companies listed on the US market. The study employs a combined approach of complex multiplex networks, to examine the statistical properties of asset interdependence within the financial market. In addition, it performs an extensive analysis of both the similarities and the differences between this financial multiplex network, its individual layers, and the commonly studied stock return network. The results highlight the importance of the financial multiplex network, demonstrating that its network layers offer unique information within the multiplex dataset. Empirical analysis reveals dissimilarities between the financial multiplex network and the stock return monoplex network, indicating that the two networks provide distinct insights into the structure of the stock market. Furthermore, the financial multiplex network outperforms the singleplex network of stock returns because it has a structure that better determines the future Sharpe ratio. These findings add substantially to our understanding of the financial market system in which multiple types of relationship among financial assets play an important role.

Linear and nonlinear causality in financial markets

Identifying and quantifying co-dependence between financial instruments is a key challenge for researchers and practitioners in the financial industry. Linear measures such as the Pearson correlation are still widely used today, although their limited explanatory power is well known. In this paper, we present a much more general framework for assessing co-dependencies by identifying linear and nonlinear causalities in the complex system of financial markets. To do so, we use two different causal inference methods, transfer entropy and convergent cross-mapping, and employ Fourier transform surrogates to separate their linear and nonlinear contributions. We find that stock indices in Germany and the U.S. exhibit a significant degree of nonlinear causality and that correlation, while a very good proxy for linear causality, disregards nonlinear effects and hence underestimates causality itself. The presented framework enables the measurement of nonlinear causality, the correlation-causality fallacy, and motivates how causality can be used for inferring market signals, pair trading, and risk management of portfolios. Our results suggest that linear and nonlinear causality can be used as early warning indicators of abnormal market behavior, allowing for better trading strategies and risk management.

Enhancing portfolio management using artificial intelligence: literature review

Building an investment portfolio is a problem that numerous researchers have addressed for many years. The key goal has always been to balance risk and reward by optimally allocating assets such as stocks, bonds, and cash. In general, the portfolio management process is based on three steps: planning, execution, and feedback, each of which has its objectives and methods to be employed. Starting from Markowitz's mean-variance portfolio theory, different frameworks have been widely accepted, which considerably renewed how asset allocation is being solved. Recent advances in artificial intelligence provide methodological and technological capabilities to solve highly complex problems, and investment portfolio is no exception. For this reason, the paper reviews the current state-of-the-art approaches by answering the core question of how artificial intelligence is transforming portfolio management steps. Moreover, as the use of artificial intelligence in finance is challenged by transparency, fairness and explainability requirements, the case study of post-hoc explanations for asset allocation is demonstrated. Finally, we discuss recent regulatory developments in the European investment business and highlight specific aspects of this business where explainable artificial intelligence could advance transparency of the investment process.

Universal window size-dependent transition of correlations in complex systems

Correlation analysis serves as an easy-to-implement estimation approach for the quantification of the interaction or connectivity between different units. Often, pairwise correlations estimated by sliding windows are time-varying (on different window segments) and window size-dependent (on different window sizes). Still, how to choose an appropriate window size remains unclear. This paper offers a framework for studying this fundamental question by observing a critical transition from a chaotic-like state to a nonchaotic state. Specifically, given two time series and a fixed window size, we create a correlation-based series based on nonlinear correlation measurement and sliding windows as an approximation of the time-varying correlations between the original time series. We find that the varying correlations yield a state transition from a chaotic-like state to a nonchaotic state with increasing window size. This window size-dependent transition is analyzed as a universal phenomenon in both model and real-world systems (e.g., climate, financial, and neural systems). More importantly, the transition point provides a quantitative rule for the selection of window sizes. That is, the nonchaotic correlation better allows for many regression-based predictions.

Identifying causality drivers and deriving governing equations of nonlinear complex systems

Identifying and describing the dynamics of complex systems is a central challenge in various areas of science, such as physics, finance, or climatology. While machine learning algorithms are increasingly overtaking traditional approaches, their inner workings and, thus, the drivers of causality remain elusive. In this paper, we analyze the causal structure of chaotic systems using Fourier transform surrogates and three different inference techniques: While we confirm that Granger causality is exclusively able to detect linear causality, transfer entropy and convergent cross-mapping indicate that causality is determined to a significant extent by nonlinear properties. For the Lorenz and Halvorsen systems, we find that their contribution is independent of the strength of the nonlinear coupling. Furthermore, we show that a simple rationale and calibration algorithm are sufficient to extract the governing equations directly from the causal structure of the data. Finally, we illustrate the applicability of the framework to real-world dynamical systems using financial data before and after the COVID-19 outbreak. It turns out that the pandemic triggered a fundamental rupture in the world economy, which is reflected in the causal structure and the resulting equations.

Portfolio Optimization with a Mean-Entropy-Mutual Information Model

This paper describes a new model for portfolio optimization (PO), using entropy and mutual information instead of variance and covariance as measurements of risk. We also compare the performance in and out of sample of the original Markowitz model against the proposed model and against other state of the art shrinkage methods. It was found that ME (mean-entropy) models do not always outperform their MV (mean-variance) and robust counterparts, although presenting an edge in terms of portfolio diversity measures, especially for portfolio weight entropy. It further shows that when increasing return constraints on portfolio optimization, ME models were more stable overall, showing dampened responses in cumulative returns and Sharpe indexes in comparison to MV and robust methods, but concentrated their portfolios more rapidly as they were more evenly spread initially. Finally, the results suggest that it was also shown that, depending on the market, increasing return constraints may have positive or negative impacts on the out-of-sample performance.

Linear and Nonlinear Effects in Connectedness Structure: Comparison between European Stock Markets

The purpose of this research is to compare the risk transfer structure in Central and Eastern European and Western European stock markets during the 2007-2009 financial crisis and the COVID-19 pandemic. Similar to the global financial crisis (GFC), the spread of coronavirus (COVID-19) created a significant level of risk, causing investors to suffer losses in a very short period of time. We use a variety of methods, including nonstandard like mutual information and transfer entropy. The results that we obtained indicate that there are significant nonlinear correlations in the capital markets that can be practically applied for investment portfolio optimization. From an investor perspective, our findings suggest that in the wake of global crisis and pandemic outbreak, the benefits of diversification will be limited by the transfer of funds between developed and developing country markets. Our study provides an insight into the risk transfer theory in developed and emerging markets as well as a cutting-edge methodology designed for analyzing the connectedness of markets. We contribute to the studies which have examined the different stock markets' response to different turbulences. The study confirms that specific market effects can still play a significant role because of the interconnection of different sectors of the global economy.

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.