Random Matrix Theory and Fund of Funds Portfolio Optimisation

The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a Fund of Hedge Funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The Inverse Participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.Comment: 17 Page

Are Financial Crashes Predictable?

We critically review recent claims that financial crashes can be predicted using the idea of log-periodic oscillations or by other methods inspired by the physics of critical phenomena. In particular, the October 1997 `correction' does not appear to be the accumulation point of a geometric series of local minima.Comment: LaTeX, 5 pages + 1 postscript figur

A model for correlations in stock markets

We propose a group model for correlations in stock markets. In the group model the markets are composed of several groups, within which the stock price fluctuations are correlated. The spectral properties of empirical correlation matrices reported in [Phys. Rev. Lett. {\bf 83}, 1467 (1999); Phys. Rev. Lett. {\bf 83}, 1471 (1999.)] are well understood from the model. It provides the connection between the spectral properties of the empirical correlation matrix and the structure of correlations in stock markets.Comment: two pages including one EPS file for a figur

Efectos en la percepción del clima motivacional generado por los entrenadores y compañeros sobre la diversión y el compromiso : diferencias en función de género

En el presente trabajo se describe la percepción del clima motivacional generado por el entrenador y por los compañeros en una muestra de deportistas jóvenes y se analizan las diferencias en función del género así como el efecto de los climas motivacionales en la diversión y el compromiso. 121 deportistas cadetes (39 chicas y 82 chicos) completaron las versiones españolas de los instrumentos de clima motivacional promovido por el entrenador, clima motivacional promovido por los compañeros y compromiso deportivo. Los resultados muestran que las chicas perciben climas motivacionales de implicación a la tarea significativamente más altos y de implicación al ego significativamente más bajos que los chicos tanto en el caso del generado por el entrenador como en el caso de los generados por los compañeros. Las deportistas se divierten significativamente más y están igualmente comprometidas con la práctica deportiva que los chicos. El principal predictor del compromiso es la generación de un clima de implicación a la tarea por parte de entrenadores y compañeros. En consecuencia cabría recomendar que los programas de intervención hagan especial hincapié en la generación de climas motivacionales de implicación a la tareaThis study describes the perception of the motivational climate created by coaches and teammates in a sample of young athletes; gender differences and the effect of motivational climates on enjoyment and commitment were analysed. 121 athletes with a mean age of 14.39 years (Mage= 14.39; SD= .96, 39 girls and 82 boys) completed the Spanish versions of the motivational climate instruments promoted by the coach, motivational climate promoted by teammates and commitment to sport. The results showed that girls perceived a significantly higher motivational climate related to task involvement and a significantly lower ego involvement than boys both in the case of the climate created by the coach as well as the climate created by teammates. Female athletes enjoyed themselves significantly more and were also significantly more committed to sports than boys. The main predictor of commitment was the creation of a climate of task involvement by coaches and teammates. As a result, it would be advisable for intervention programmes to lay particularly emphasis on creating motivational climates related to task involvemen

Asymmetric correlation matrices: an analysis of financial data

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.Comment: Revised version; 11 pages, 13 figure

Statistical pairwise interaction model of stock market

Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or others are agent-based models with rules designed in order to recover some empirical behaviours. Here we show that the pairwise model is actually a statistically consistent model with observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach based only on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviours, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.Comment: 11 pages, 8 figure

Variety and Volatility in Financial Markets

We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days subsequent to these extreme events. We analyze each ensemble return distribution by extracting its first two central moments. We observe that these moments are fluctuating in time and are stochastic processes themselves. We characterize the statistical properties of ensemble return distribution central moments by investigating their probability density functions and temporal correlation properties. In general, time-averaged and portfolio-averaged price returns have different statistical properties. We infer from these differences information about the relative strength of correlation between stocks and between different trading days. Lastly, we compare our empirical results with those predicted by the single-index model and we conclude that this simple model is unable to explain the statistical properties of the second moment of the ensemble return distribution.Comment: 10 pages, 11 figure

Noise Dressing of Financial Correlation Matrices

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the present study is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). In particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.Comment: Latex (Revtex) 3 pp + 2 postscript figures (in-text

Seizure characterisation using frequency-dependent multivariate dynamics

The characterisation of epileptic seizures assists in the design of targeted pharmaceutical seizure prevention techniques and pre-surgical evaluations. In this paper, we expand on recent use of multivariate techniques to study the crosscorrelation dynamics between electroencephalographic (EEG) channels. The Maximum Overlap Discrete Wavelet Transform (MODWT) is applied in order to separate the EEG channels into their underlying frequencies. The dynamics of the cross-correlation matrix between channels, at each frequency, are then analysed in terms of the eigenspectrum. By examination of the eigenspectrum, we show that it is possible to identify frequency dependent changes in the correlation structure between channels which may be indicative of seizure activity. The technique is applied to EEG epileptiform data and the results indicate that the correlation dynamics vary over time and frequency, with larger correlations between channels at high frequencies. Additionally, a redistribution of wavelet energy is found, with increased fractional energy demonstrating the relative importance of high frequencies during seizures. Dynamical changes also occur in both correlation and energy at lower frequencies during seizures, suggesting that monitoring frequency dependent correlation structure can characterise changes in EEG signals during these. Future work will involve the study of other large eigenvalues and inter-frequency correlations to determine additional seizure characteristics

Cross-correlation dynamics in financial time series

The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined. A basic one-factor model is proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a market plus sectors model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found for empirical data