Untangling complex networks: Risk minimization in financial markets through accessible spin glass ground states

Recurrent international financial crises inflict significant damage to societies and stress the need for mechanisms or strategies to control risk and tamper market uncertainties. Unfortunately, the complex network of market interactions often confounds rational approaches to optimize financial risks. Here we show that investors can overcome this complexity and globally minimize risk in portfolio models for any given expected return, provided the margin requirement remains below a critical, empirically measurable value. In practice, for markets with centrally regulated margin requirements, a rational stabilization strategy would be keeping margins small enough. This result follows from ground states of the random field spin glass Ising model that can be calculated exactly through convex optimization when relative spin coupling is limited by the norm of the network’s Laplacian matrix. In that regime, this novel approach is robust to noise in empirical data and may be also broadly relevant to complex networks with frustrated interactions that are studied throughout scientific fields.     

Random matrix theory filters in portfolio optimisation: A stability and risk assessment

Random matrix theory (RMT) filters, applied to covariance matrices of financial returns, have recently been shown to offer improvements to the optimisation of stock portfolios. This paper studies the effect of three RMT filters on the realised portfolio risk, and on the stability of the filtered covariance matrix, using bootstrap analysis and out-of-sample testing.We propose an extension to an existing RMT filter, (based on Krzanowski stability), which is observed to reduce risk and increase stability, when compared to other RMT filters tested. We also study a scheme for filtering the covariance matrix directly, as opposed to the standard method of filtering correlation, where the latter is found to lower the realised risk, on average, by up to 6.7%.We consider both equally and exponentially weighted covariance matrices in our analysis, and observe that the overall best method out-of-sample was that of the exponentially weighted covariance, with our Krzanowski stability-based filter applied to the correlation matrix. We also find that the optimal out-of-sample decay factors, for both filtered and unfiltered forecasts, were higher than those suggested by Riskmetrics [J.P. Morgan, Reuters, Riskmetrics technical document, Technical Report, 1996. http://www.riskmetrics.com/techdoc.html], with those for the latter approaching a value of α=1.In conclusion, RMT filtering reduced the realised risk, on average, and in the majority of cases when tested out-of-sample, but increased the realised risk on a marked number of individual days–in some cases more than doubling it.     

Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets

Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients, which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are overconfident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.     

Towards a $$Z\prime $$ Gauge Boson in Noncommutative Geometry

We study all possible U(1)-extensions of the standard model within the framework of noncommutative geometry with the algebra . Comparison to experimental data about the mass of a hypothetical gauge boson leads to the necessity of introducing at least one new family of heavy fermions.     

Memory effect and multifractality of cross-correlations in financial markets

We introduce an instantaneous and an average instantaneous cross-correlation function to detect the temporal cross-correlations between individual stocks based on the daily data of the United States and the Chinese stock markets. The memory effect of the instantaneous cross-correlations is investigated by applying the detrended fluctuation analysis (DFA), where the DFA exponents can be partly explained by the correlation function from the common sense. Long-range memory is observed for the average instantaneous cross-correlations, and persists up to a month magnitude of timescale for the United States stock market and half a month magnitude of timescale for the Chinese stock market. In addition, multifractal nature is investigated by a multifractal detrended fluctuation analysis.     

Rényi’s information transfer between financial time series

In this paper, we quantify the statistical coherence between financial time series by means of the Rényi entropy. With the help of Campbell’s coding theorem, we show that the Rényi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others. This accentuation is controlled with Rényi’s parameter q$q$. To tackle the issue of the information flow between time series, we formulate the concept of Rényi’s transfer entropy as a measure of information that is transferred only between certain parts of underlying distributions. This is particularly pertinent in financial time series, where the knowledge of marginal events such as spikes or sudden jumps is of a crucial importance. We apply the Rényian information flow to stock market time series from 11 world stock indices as sampled at a daily rate in the time period 02.01.1990–31.12.2009. Corresponding heat maps and net information flows are represented graphically. A detailed discussion of the transfer entropy between the DAX and S&P500 indices based on minute tick data gathered in the period 02.04.2008–11.09.2009 is also provided. Our analysis shows that the bivariate information flow between world markets is strongly asymmetric with a distinct information surplus flowing from the Asia–Pacific region to both European and US markets. An important yet less dramatic excess of information also flows from Europe to the US. This is particularly clearly seen from a careful analysis of Rényi information flow between the DAX and S&P500 indices.     

Coupled effects of market impact and asymmetric sensitivity in financial markets

By incorporating market impact and asymmetric sensitivity into the evolutionary minority game, we study the coevolutionary dynamics of stock prices and investment strategies in financial markets. Both the stock price movement and the investors’ global behavior are found to be closely related to the phase region they fall into. Within the region where the market impact is small, investors’ asymmetric response to gains and losses leads to the occurrence of herd behavior, when all the investors are prone to behave similarly in an extreme way and large price fluctuations occur. A linear relation between the standard deviation of stock price changes and the mean value of strategies is found. With full market impact, the investors tend to self-segregate into opposing groups and the introduction of asymmetric sensitivity leads to the disappearance of dominant strategies. Compared with the situations in the stock market with little market impact, the stock price fluctuations are suppressed and an efficient market occurs. Theoretical analyses indicate that the mechanism of phase transition from clustering to self-segregation in the present model is similar to that in the majority–minority game and the occurrence and disappearance of efficient markets are related to the competition between the trend-following and the trend-aversion forces. The clustering of the strategies in the present model results from the majority-wins effect and the wealth-driven mechanism makes the market become predictable.     

An agent-based model of stock markets incorporating momentum investors

It has been widely accepted that there exist investors who adopt momentum strategies in real stock markets. Understanding the momentum behavior is of both academic and practical importance. For this purpose, we propose and study a simple agent-based model of trading incorporating momentum investors and random investors. The random investors trade randomly all the time. The momentum investors could be idle, buying or selling, and they decide on their action by implementing an action threshold that assesses the most recent price movement. The model is able to reproduce some of the stylized facts observed in real markets, including the fat-tails in returns, weak long-term correlation and scaling behavior in the kurtosis of returns. An analytic treatment of the model relates the model parameters to several quantities that can be extracted from real data sets. To illustrate how the model can be applied, we show that real market data can be used to constrain the model parameters, which in turn provide information on the behavior of momentum investors in different markets.     

A generalized spin model of financial markets

We reformulate the Cont-Bouchaud model of financial markets in terms of classical “super-spins” where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this simplified model by switching on interactions among the super-spins to model the tendency of agencies getting influenced by the opinion of other managers. We also introduce a fictitious temperature (to model other random influences), and time-dependent local fields to model a slowly changing optimistic or pessimistic bias of traders. We point out close similarities between the price variations in our model with N super-spins and total displacements in an N-step Levy flight. We demonstrate the phenomena of natural and artificially created bubbles and subsequent crashes as well as the occurrence of “fat tails” in the distributions of stock price variations. Received 13 October 1998     

Transition from coherence to bistability in a model of financial markets

We present a model describing the competition between information transmission and decision making in financial markets. The solution of this simple model is recalled, and possible variations discussed. It is shown numerically that despite its simplicity, it can mimic a size effect comparable to a crash localized in time. Two extensions of this model are presented that allow to simulate the demand process. One of these extensions has a coherent stable equilibrium and is self-organized, while the other has a bistable equilibrium, with a spontaneous segregation of the population of agents. A new model is introduced to generate a transition between those two equilibriums. We show that the coherent state is dominant up to an equal mixing of the two extensions. We focus our attention on the microscopic structure of the investment rate, which is the main parameter of the original model. A constant investment rate seems to be a very good approximation. Received 7 August 2000 and Received in final form 10 September 2000     

New Gaugings and Non‐Geometry

We discuss the possible realisation in string/M theory of the recently discovered family of four‐dimensional maximal gauged supergravities, and of an analogous family of seven‐dimensional half‐maximal gauged supergravities. We first prove a no‐go theorem that neither class of gaugings can be realised via a compactification that is locally described by ten‐ or eleven‐dimensional supergravity. In the language of Double Field Theory and its M theory analogue, this implies that the section condition must be violated. Introducing the minimal number of additional coordinates possible, we then show that the standard S ³ and S ⁷ compactifications of ten‐ and eleven‐dimensional supergravity admit a new class of section‐violating generalised frames with a generalised Lie derivative algebra that reproduces the embedding tensor of the and gaugings respectively. The physical meaning, if any, of these constructions is unclear. They highlight a number of the issues that arise when attempting to apply the formalism of Double Field Theory to non‐toroidal backgrounds. Using a naive brane charge quantisation to determine the periodicities of the additional coordinates restricts the gaugings to an infinite discrete set and excludes all the gaugings other than the standard one.     

Self-organizing Ising model of financial markets

We study a dynamical Ising-like model of agents' opinions (buy or sell) with learning, in which the coupling coefficients are re-assessed continuously in time according to how past external news (time-varying magnetic field) have explained realized market returns. By combining herding, the impact of external news and private information, we find that the stylized facts of financial markets are reproduced only when agents misattribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the Ising critical point.     

The timing of information transmission in financial markets

This article shows turbulent behavior in a series of financial indexes assuming that they follow a cascade process of the same type as do turbulent fluids. With such a model, the energy flux between the eddies that emerge in the fluid is analogous to the financial information flux over the course of time. The results obtained confirm the variability of variation of the indexes for the considered time scale (the turbulent intermittency typical for fluids), and they also confirm that when we descend along the cascade, that is to say, when we consider smaller time intervals, the rate at which the hypothetical eddies of information dissipate becomes greater than the rate at which the information is transmitted. This fact can explain the cyclical nature of crises: ultimately, financial events have a memory of the past. Besides, the NASDAQ singular behavior regarding the number of jumps, the degree of intermittency of the turbulence and the life time of the hypothetical eddies has been analysed.     

推广的EZ模型中的普适性行为

探讨了推广EZ模型的可能性,并给出了相应的模型中人群大小分布函数的形式解.研究表明金融市场中不同大小的人群数目的交易人的数目在重新标度后将具有最广泛的普适性行为 关键词： 金融物理 人群效应 主方程     

Hausdorff clustering of financial time series

A clustering procedure is introduced based on the Hausdorff distance as a similarity measure between clusters of elements. The method is applied to the financial time series of the Dow Jones industrial average (DJIA) index to find companies that share a similar behavior. Comparisons are made with other linkage algorithms.     

Delayed information flow effect in economy systems. An ACP model study

Applying any strategy requires some knowledge about the past state of the system. Unfortunately in the case of economy, collecting information is a difficult, expensive and time consuming process. Therefore, the information about the system is usually known only at the end of some well-defined intervals, e.g. through company, national bank inflation data and Gross Domestic Product (GDP) reports, etc. They describe a (market) situation in the past. The time delay is specific to the market branch. It can be very short (e.g. stock market offer is updated every minute or so and this information is quasi-immediately available) or long, like months in the case of agricultural markets, when the decisions are taken based on the results from the previous harvest.The analysis of the information flow delay can be based on the Ausloos-Clippe-P?kalski (ACP) model of spatial evolution of economic systems. The entities can move on a (square) lattice and when meeting take one of the two following decisions: merge or create a new entity. The decision is based on the system state, which is known with some time delay. The effect of system's feedback is hereby investigated. We consider the case of company distribution evolution in a heterogeneous field. The information flow time delay implies different final states, including cycles; it is like a control parameter in a logistic map.     

Towards the Standard Model in F‐theory

This article explores possible embeddings of the Standard Model gauge group and its matter representations into F‐theory. To this end we construct elliptic fibrations with gauge group as suitable restrictions of a ‐fibration with rank‐two Mordell‐Weil group. We analyse the five inequivalent toric enhancements to gauge group along two independent divisors W₃ and W₂ in the base. For each of the resulting smooth fibrations, the representation spectrum generically consists of a bifundamental , three types of representations and five types of representations (plus conjugates), in addition to charged singlet states. The precise spectrum of zero‐modes in these representations depends on the 3‐form background. We analyse the geometrically realised Yukawa couplings among all these states and find complete agreement with field theoretic expectations based on their U(1) charges. We classify possible identifications of the found representations with the Standard Model field content extended by right‐handed neutrinos and extra singlets. The linear combination of the two abelian gauge group factors orthogonal to hypercharge acts as a selection rule which, depending on the specific model, can forbid dangerous dimension‐four and ‐five proton decay operators.     

Towards a gravitation theory in Berwald-Finsler space

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated.