Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.

Security strategies and equilibria in multiobjetives matrix games

Multiobjective matrix games have been traditionally analyzed from two different points of view: equiibrium concepts and security strategies. This paper is based upon the idea that both players try to reach equilibrium points playing pairs of security strategies, as it happens in scalar matrix games. We show conditions guaranteeing the existence of equilibria in security strategies, named security equilibria

Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

Semiclassical evaluation of average nuclear one- and two-body matrix elements

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results, and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elements it is shown how the Thomas-Fermi approach can be projected on good parity and also on good angular momentum. For the two-body case, the pairing matrix elements are considered explicitly.

A test of Jessor's problem behavior theory in a Eurasian and a Western European developmental context.

PURPOSE: The current study tested the applicability of Jessor's problem behavior theory (PBT) in national probability samples from Georgia and Switzerland. Comparisons focused on (1) the applicability of the problem behavior syndrome (PBS) in both developmental contexts, and (2) on the applicability of employing a set of theory-driven risk and protective factors in the prediction of problem behaviors. METHODS: School-based questionnaire data were collected from n = 18,239 adolescents in Georgia (n = 9499) and Switzerland (n = 8740) following the same protocol. Participants rated five measures of problem behaviors (alcohol and drug use, problems because of alcohol and drug use, and deviance), three risk factors (future uncertainty, depression, and stress), and three protective factors (family, peer, and school attachment). Final study samples included n = 9043 Georgian youth (mean age = 15.57; 58.8% females) and n = 8348 Swiss youth (mean age = 17.95; 48.5% females). Data analyses were completed using structural equation modeling, path analyses, and post hoc z-tests for comparisons of regression coefficients. RESULTS: Findings indicated that the PBS replicated in both samples, and that theory-driven risk and protective factors accounted for 13% and 10% in Georgian and Swiss samples, respectively in the PBS, net the effects by demographic variables. Follow-up z-tests provided evidence of some differences in the magnitude, but not direction, in five of six individual paths by country. CONCLUSION: PBT and the PBS find empirical support in these Eurasian and Western European samples; thus, Jessor's theory holds value and promise in understanding the etiology of adolescent problem behaviors outside of the United States.

An analytical approach to sorting in periodic and random potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.

Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

The mean-field theory of a spin glass with a specific form of nearest- and next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edgesthat is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

Continuous-time random-walk model for financial distributions

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollardeutsche mark future exchange, finding good agreement between theory and the observed data.

Random mixtures with orientational order, and the anisotropic resistivity tensor of high Tc superconductors

By generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa2Cu3O7¿x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper¿oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude. The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two¿dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite frequency resistivity does not vanish along the c axis, a result which would simply the existence of states at the Fermi surface, even in the superconducting state

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Structural disorder in two-dimensional random magnets: Very thin films of rare earths and transition metals

The low-temperature isothermal magnetization curves, M(H), of SmCo4 and Fe3Tb thin films are studied according to the two-dimensional correlated spin-glass model of Chudnovsky. We have calculated the magnetization law in approach to saturation and shown that the M(H) data fit well the theory at high and low fields. In our fit procedure we have used three different correlation functions. The Gaussian decay correlation function fits well the experimental data for both samples.