602 research outputs found
Alternation of different fluctuation regimes in the stock market dynamics
Based on the tick-by-tick stock prices from the German and American stock
markets, we study the statistical properties of the distribution of the
individual stocks and the index returns in highly collective and noisy
intervals of trading, separately. We show that periods characterized by the
strong inter-stock couplings can be associated with the distributions of index
fluctuations which reveal more pronounced tails than in the case of weaker
couplings in the market. During periods of strong correlations in the German
market these distributions can even reveal an apparent L\'evy-stable component.Comment: 19 page
The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics
The nature of fluctuations in the Indian financial market is analyzed in this
paper. We have looked at the price returns of individual stocks, with
tick-by-tick data from the National Stock Exchange (NSE) and daily closing
price data from both NSE and the Bombay Stock Exchange (BSE), the two largest
exchanges in India. We find that the price returns in Indian markets follow a
fat-tailed cumulative distribution, consistent with a power law having exponent
, similar to that observed in developed markets. However, the
distributions of trading volume and the number of trades have a different
nature than that seen in the New York Stock Exchange (NYSE). Further, the price
movement of different stocks are highly correlated in Indian markets.Comment: 10 pages, 7 figures, to appear in Proceedings of International
Workshop on "Econophysics of Stock Markets and Minority Games"
(Econophys-Kolkata II), Feb 14-17, 200
A correlated stochastic volatility model measuring leverage and other stylized facts
We present a stochastic volatility market model where volatility is
correlated with return and is represented by an Ornstein-Uhlenbeck process.
With this model we exactly measure the leverage effect and other stylized
facts, such as mean reversion, leptokurtosis and negative skewness. We also
obtain a close analytical expression for the characteristic function and study
the heavy tails of the probability distribution.Comment: 22 pages, 2 figures and 2 table
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
Cluster structure of EU-15 countries derived from the correlation matrix analysis of macroeconomic index fluctuations
The statistical distances between countries, calculated for various moving
average time windows, are mapped into the ultrametric subdominant space as in
classical Minimal Spanning Tree methods. The Moving Average Minimal Length Path
(MAMLP) algorithm allows a decoupling of fluctuations with respect to the mass
center of the system from the movement of the mass center itself. A Hamiltonian
representation given by a factor graph is used and plays the role of cost
function. The present analysis pertains to 11 macroeconomic (ME) indicators,
namely the GDP (x1), Final Consumption Expenditure (x2), Gross Capital
Formation (x3), Net Exports (x4), Consumer Price Index (y1), Rates of Interest
of the Central Banks (y2), Labour Force (z1), Unemployment (z2), GDP/hour
worked (z3), GDP/capita (w1) and Gini coefficient (w2). The target group of
countries is composed of 15 EU countries, data taken between 1995 and 2004. By
two different methods (the Bipartite Factor Graph Analysis and the Correlation
Matrix Eigensystem Analysis) it is found that the strongly correlated countries
with respect to the macroeconomic indicators fluctuations can be partitioned
into stable clusters
Random matrix theory for portfolio optimization: a stability approach
We apply Random Matrix Theory (RMT) on an empirically-measured financial correlation matrix, C, and show that this matrix contains a large amount of noise. In order to determine the sensitivity of the spectral properties of a random matrix to noise, we simulate a set of data and add different volumes of random noise. Having ascertained that the eigenspectrum is independent of the standard deviation of added noise, we use RMT to determine the noise percentage in a correlation matrix based on real data from S&P500. Eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart. Finally we attempt to separate the noisy part from the non-noisy part of C. We apply an existing technique to cleaning C and then discuss its associated problems. We propose a technique of filtering C which has many advantages, from a stability point of view over the existing method of cleaning
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