Quantifying the behavior of stock correlations under market stress

Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios

Quantifying trading behavior in financial markets using Google Trends

Crises in financial markets affect humans worldwide. Detailed market data on trading decisions reflect some of the complex human behavior that has led to these crises. We suggest that massive new data sources resulting from human interaction with the Internet may offer a new perspective on the behavior of market participants in periods of large market movements. By analyzing changes in Google query volumes for search terms related to finance, we find patterns that may be interpreted as “early warning signs” of stock market moves. Our results illustrate the potential that combining extensive behavioral data sets offers for a better understanding of collective human behavior

On a kinetic model for a simple market economy

In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis

Sector Neutral Portfolios: Long Memory Motifs Persistence in Market Structure Dynamics

We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We observe long-memory processes in these structures in the form of power law decays in the number of persistent motifs. The decays then transition to a plateau regime with a power-law decay with smaller exponent. We demonstrate that identifying persistent motifs allows for forecasting and applications to portfolio diversification. Balanced portfolios are often constructed from the analysis of historic correlations, however not all past correlations are persistently reflected into the future. Sector neutrality has also been a central theme in portfolio diversification and systemic risk. We present an unsupervised technique to identify persistently correlated sets of stocks. These are empirically found to identify sectors driven by strong fundamentals. Applications of these findings are tested in two distinct ways on four different markets, resulting in significant reduction in portfolio volatility. A persistence-based measure for portfolio allocation is proposed and shown to outperform volatility weighting when tested out of sample

Ageing memory and glassiness of a driven vortex system

Many systems in nature, glasses, interfaces and fractures being some examples, cannot equilibrate with their environment, which gives rise to novel and surprising behaviour such as memory effects, ageing and nonlinear dynamics. Unlike their equilibrated counterparts, the dynamics of out-of- equilibrium systems is generally too complex to be captured by simple macroscopic laws. Here we investigate a system that straddles the boundary between glass and crystal: a Bragg glass formed by vortices in a superconductor. We find that the response to an applied force evolves according to a stretched exponential, with the exponent reflecting the deviation from equilibrium. After the force is removed, the system ages with time and its subsequent response time scales linearly with its age (simple ageing), meaning that older systems are slower than younger ones. We show that simple ageing can occur naturally in the presence of sufficient quenched disorder. Moreover, the hierarchical distribution of timescales, arising when chunks of loose vortices cannot move before trapped ones become dislodged, leads to a stretched-exponential response.Comment: 16 pages, 5 figure

Optimal leverage from non-ergodicity

In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loosely or too tightly constraining investors' risk preferences, from their respective perspectives. The conflict can be understood on the basis that the multiplicative models used in both approaches are non-ergodic which leads to ensemble-average returns differing from time-average returns in single realizations. The classic treatments, from the very beginning of probability theory, use ensemble-averages, whereas the Kelly-result is obtained by considering time-averages. Maximizing the time-average growth rates for an investment defines an optimal leverage, whereas growth rates derived from ensemble-average returns depend linearly on leverage. The latter measure can thus incentivize investors to maximize leverage, which is detrimental to time-average growth and overall market stability. The Sharpe ratio is insensitive to leverage. Its relation to optimal leverage is discussed. A better understanding of the significance of time-irreversibility and non-ergodicity and the resulting bounds on leverage may help policy makers in reshaping financial risk controls.Comment: 17 pages, 3 figures. Updated figures and extended discussion of ergodicit

Minding impacting events in a model of stochastic variance

We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold and another one when the local standard deviation outnumbers it. In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterised by large values of the Hurst exponent is greater than 0.8, which are ubiquitous features in complex systems.Comment: 18 pages, 5 figures, 1 table. To published in PLoS on

Is the Equivalence Principle violated by Generalized Uncertainty Principles and Holography in a brane-world?

It has been recently debated whether a class of generalized uncertainty principles that include gravitational sources of error are compatible with the holographic principle in models with extra spatial dimensions. We had in fact shown elsewhere that the holographic scaling is lost when more than four space-time dimensions are present. However, we shall show here that the validity of the holographic counting can be maintained also in models with extra spatial dimensions, but at the intriguing price that the equivalence principle for a point-like source be violated and the inertial mass differ from the gravitational mass in a specific non-trivial way.Comment: 5 pages, latex fil

Prediction of photoperiodic regulators from quantitative gene circuit models

Photoperiod sensors allow physiological adaptation to the changing seasons. The external coincidence hypothesis postulates that a light-responsive regulator is modulated by a circadian rhythm. Sufficient data are available to test this quantitatively in plants, though not yet in animals. In Arabidopsis, the clock-regulated genes CONSTANS (CO) and FLAVIN, KELCH, F-BOX (FKF1) and their lightsensitive proteins are thought to form an external coincidence sensor. We use 40 timeseries of molecular data to model the integration of light and timing information by CO, its target gene FLOWERING LOCUS T (FT), and the circadian clock. Among other predictions, the models show that FKF1 activates FT. We demonstrate experimentally that this effect is independent of the known activation of CO by FKF1, thus we locate a major, novel controller of photoperiodism. External coincidence is part of a complex photoperiod sensor: modelling makes this complexity explicit and may thus contribute to crop improvement

Thermodynamic signature of growing amorphous order in glass-forming liquids

Although several theories relate the steep slowdown of glass formers to increasing spatial correlations of some sort, standard static correlation functions show no evidence for this. We present results that reveal for the first time a qualitative thermodynamic difference between the high temperature and deeply supercooled equilibrium glass-forming liquid: the influence of boundary conditions propagates into the bulk over larger and larger lengthscales upon cooling, and, as this static correlation length grows, the influence decays nonexponentially. Increasingly long-range susceptibility to boundary conditions is expected within the random firt-order theory (RFOT) of the glass transition, but a quantitative account of our numerical results requires a generalization of RFOT where the surface tension between states fluctuates