Dynamics of Stock Market Correlations

We present a novel approach to the study the dynamics of stock market correlations. This is achieved through an innovative visualization tool that allows an investigation of the structure and dynamics of the market, through the study of correlations. This is based on the Stock Market Holography (SMH) method recently introduced. This qualitative measure is complemented by the use of the eigenvalue entropy measure, to quantify how the information in the market changes in time. Using this innovative approach, we analyzed data from the New York Stock Exchange (NYSE), and the Tel Aviv Stock Exchange (TASE), for daily trading data for the time period of 2000–2009. This paper covers these new concepts for the study of financial markets in terms of structure and information as reflected by the changes in correlations over time.Correlation, Stock Market Holography, eigenvalue entropy, sliding window

Index Cohesive Force Analysis Reveals That the US Market Became Prone to Systemic Collapses Since 2002

BACKGROUND: The 2007-2009 financial crisis, and its fallout, has strongly emphasized the need to define new ways and measures to study and assess the stock market dynamics. METHODOLOGY/PRINCIPAL FINDINGS: The S&P500 dynamics during 4/1999-4/2010 is investigated in terms of the index cohesive force (ICF--the balance between the stock correlations and the partial correlations after subtraction of the index contribution), and the Eigenvalue entropy of the stock correlation matrices. We found a rapid market transition at the end of 2001 from a flexible state of low ICF into a stiff (nonflexible) state of high ICF that is prone to market systemic collapses. The stiff state is also marked by strong effect of the market index on the stock-stock correlations as well as bursts of high stock correlations reminiscence of epileptic brain activity. CONCLUSIONS/SIGNIFICANCE: The market dynamical states, stability and transition between economic states was studies using new quantitative measures. Doing so shed new light on the origin and nature of the current crisis. The new approach is likely to be applicable to other classes of complex systems from gene networks to the human brain

A Fokker-Planck model for wealth inequality dynamics

Studying the mechanisms that govern the dynamics of the wealth distribution is essential for understanding the recent trend of growing wealth inequality. A particularly important explanation is Piketty's argument, giving credit to the seminal events of the first half of the 20th century for the relatively egalitarian second half of this century. Piketty suggested that these dramatic events were merely a perturbation imposed on the economy affecting the wealth structure, while in general, wealth inequality tends to increase regularly. We present a simple stochastic model for wealth and income based on coupled geometric Brownian motions and derive a Fokker-Planck equation from which the joint wealth-income distribution and its moments can be extracted. We then analyze the dynamics of these moments and hence of the inequality. Our analysis largely supports Piketty's argument regarding the irregularity of the 20th century, that wealth inequality inevitably tends to increase. We find, however, that even if wealth inequality will eventually go up, under plausible conditions, it can go down for periods of up to several decades

Analytical study of index-coupled herd behavior in financial markets

Herd behavior in financial markets had been investigated extensively in the past few decades. Scholars have argued that the behavioral tendency of traders and investors to follow the market trend, notably reflected in indices both on short and long time scales, is substantially affecting the overall market behavior. Research has also been devoted to revealing these behaviors and characterizing the market herd behavior. In this paper we present a simple herd behavior model for the dynamics of financial variables by introducing a simple coupling mechanism of stock returns to the index return, deriving analytic expressions for statistical properties of the returns. We found that several important phenomena in the stock market, namely the correlations between stock market returns and the exponential decay of short-term autocorrelations, are derived from our model. These phenomena have been given various explanations and theories, with herd market behavior being one of the leading. We conclude that the coupling mechanism, which essentially encapsulates the herd behavior, indeed creates correlation and autocorrelation. We also show that this introduces a time scale to the system, which is the characteristic time lag between a change in the index and its effect on the return of a stock

RMT Assessments of the Market Latent Information Embedded in the Stocks' Raw, Normalized, and Partial Correlations

We present here assessment of the latent market information embedded in the raw, affinity (normalized), and partial correlations. We compared the Zipf plot, spectrum, and distribution of the eigenvalues for each matrix with the results of the corresponding random matrix. The analysis was performed on stocks belonging to the New York and Tel Aviv Stock Exchange, for the time period of January 2000 to March 2009. Our results show that in comparison to the raw correlations, the affinity matrices highlight the dominant factors of the system, and the partial correlation matrices contain more information. We propose that significant stock market information, which cannot be captured by the raw correlations, is embedded in the affinity and partial correlations. Our results further demonstrate the differences between NY and TA markets

Bacterial linguistic communication and social intelligence

Bacteria have developed intricate communication capa-bilities (e.g. quorum-sensing, chemotactic signaling and plasmid exchange) to cooperatively self-organize into highly structured colonies with elevated environ-mental adaptability. We propose that bacteria use their intracellular flexibility, involving signal transduction networks and genomic plasticity, to collectively main-tain linguistic communication: self and shared interpre-tations of chemical cues, exchange of chemical messages (semantic) and dialogues (pragmatic). Mean-ing-based communication permits colonial identity, intentional behavior (e.g. pheromone-based courtship for mating), purposeful alteration of colony structure (e.g. formation of fruiting bodies), decision-making (e.g. to sporulate) and the recognition and identification o

A Quantitative Study of the Dynamics of Adaptive Mutation Appearance

We present two dynamical models for the appearance of adaptive mutations, which permit a quantitative comparison with experimental observations. The models quantify two alternative pictures: The hyper-mutating sub-population picture, andthe population-wide mutation picture. We #nd that both models are equally successful in reproducing the results of experiments in which a single mutation is required. They also enable us to estimate the values of key biological parameters, such as successful mutation rates. We then analyze the multiple mutations experiment of Rosche and Foster (Proc. Natl. Acad

The Dynamics of Wealth Inequality and the Effect of Income Distribution

<div><p>The rapid increase of wealth inequality in the past few decades is one of the most disturbing social and economic issues of our time. Studying its origin and underlying mechanisms is essential for policy aiming to control and even reverse this trend. In that context, controlling the distribution of income, using income tax or other macroeconomic policy instruments, is generally perceived as effective for regulating the wealth distribution. We provide a theoretical tool, based on the realistic modeling of wealth inequality dynamics, to describe the effects of personal savings and income distribution on wealth inequality. Our theoretical approach incorporates coupled equations, solved using iterated maps to model the dynamics of wealth and income inequality. Notably, using the appropriate historical parameter values we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. It is found that the effect of personal savings on wealth inequality is substantial, and its major decrease in the past 30 years can be associated with the current wealth inequality surge. In addition, the effect of increasing income tax, though naturally contributing to lowering income inequality, might contribute to a mild increase in wealth inequality and vice versa. Plausible changes in income tax are found to have an insignificant effect on wealth inequality, in practice. In addition, controlling the income inequality, by progressive taxation, for example, is found to have a very small effect on wealth inequality in the short run. The results imply, therefore, that controlling income inequality is an impractical tool for regulating wealth inequality.</p></div

Unraveling Hidden Order in the Dynamics of Developed and Emerging Markets

<div><p>The characterization of asset price returns is an important subject in modern finance. Traditionally, the dynamics of stock returns are assumed to lack any temporal order. Here we present an analysis of the autocovariance of stock market indices and unravel temporal order in several major stock markets. We also demonstrate a fundamental difference between developed and emerging markets in the past decade - emerging markets are marked by positive order in contrast to developed markets whose dynamics are marked by weakly negative order. In addition, the reaction to financial crises was found to be reversed among developed and emerging markets, presenting large positive/negative autocovariance spikes following the onset of these crises. Notably, the Chinese market shows neutral or no order while being regarded as an emerging market. These findings show that despite the coupling between international markets and global trading, major differences exist between different markets, and demonstrate that the autocovariance of markets is correlated with their stability, as well as with their state of development.</p></div