472 research outputs found
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
Risk Minimization through Portfolio Replication
We use a replica approach to deal with portfolio optimization problems. A
given risk measure is minimized using empirical estimates of asset values
correlations. We study the phase transition which happens when the time series
is too short with respect to the size of the portfolio. We also study the noise
sensitivity of portfolio allocation when this transition is approached. We
consider explicitely the cases where the absolute deviation and the conditional
value-at-risk are chosen as a risk measure. We show how the replica method can
study a wide range of risk measures, and deal with various types of time series
correlations, including realistic ones with volatility clustering.Comment: 12 pages, APFA5 conferenc
Random matrix approach in search for weak signals immersed in background noise
We present new, original and alternative method for searching signals coded
in noisy data. The method is based on the properties of random matrix
eigenvalue spectra. First, we describe general ideas and support them with
results of numerical simulations for basic periodic signals immersed in
artificial stochastic noise. Then, the main effort is put to examine the
strength of a new method in investigation of data content taken from the real
astrophysical NAUTILUS detector, searching for the presence of gravitational
waves. Our method discovers some previously unknown problems with data
aggregation in this experiment. We provide also the results of new method
applied to the entire respond signal from ground based detectors in future
experimental activities with reduced background noise level. We indicate good
performance of our method what makes it a positive predictor for further
applications in many areas.Comment: 15 pages, 16 figure
Coexistence of solutions in dynamical mean-field theory of the Mott transition
In this paper, I discuss the finite-temperature metal-insulator transition of
the paramagnetic Hubbard model within dynamical mean-field theory. I show that
coexisting solutions, the hallmark of such a transition, can be obtained in a
consistent way both from Quantum Monte Carlo (QMC) simulations and from the
Exact Diagonalization method. I pay special attention to discretization errors
within QMC. These errors explain why it is difficult to obtain the solutions by
QMC close to the boundaries of the coexistence region.Comment: 3 pages, 2 figures, RevTe
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
Quantum Monte Carlo calculation of the finite temperature Mott-Hubbard transition
We present clear numerical evidence for the coexistence of metallic and
insulating dynamical mean field theory(DMFT) solutions in a half-filled
single-band Hubbard model with bare semicircular density of states at finite
temperatures. Quantum Monte Carlo(QMC) method is used to solve the DMFT
equations. We discuss important technical aspects of the DMFT-QMC which need to
be taken into account in order to obtain the reliable results near the
coexistence region. Among them are the critical slowing down of the iterative
solutions near phase boundaries, the convergence criteria for the DMFT
iterations, the interpolation of the discretized Green's function and the
reduction of QMC statistical and systematic errors. Comparison of our results
with those of other numerical methods is presented in a phase diagram.Comment: 4 pages, 5 figure
Data clustering and noise undressing for correlation matrices
We discuss a new approach to data clustering. We find that maximum likelihood
leads naturally to an Hamiltonian of Potts variables which depends on the
correlation matrix and whose low temperature behavior describes the correlation
structure of the data. For random, uncorrelated data sets no correlation
structure emerges. On the other hand for data sets with a built-in cluster
structure, the method is able to detect and recover efficiently that structure.
Finally we apply the method to financial time series, where the low temperature
behavior reveals a non trivial clustering.Comment: 8 pages, 5 figures, completely rewritten and enlarged version of
cond-mat/0003241. Submitted to Phys. Rev.
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