Noisy covariance matrices and portfolio optimization

RePEc: Research Papers in Economics, 2001

Recent studies inspired by results from random matrix theory (

Physical Review Letters, 1999

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.

Physica A-statistical Mechanics and Its Applications, 2004

We apply Random Matrix Theory (RMT) on an empirically-measured nancial 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 di erent 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 di erent 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 ltering C that has many advantages, from the stability point of view, over the existing method of cleaning.

Physica A: Statistical Mechanics and its Applications, 2004

Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of it's estimator (experimentally measured correlation matrix). These relations will be used to analyze a particular case of the correlations in financial series and to show that contrary to earlier claims, correlations can be measured also in the "random" part of the spectrum. Implications for the portfolio optimization are briefly discussed.

2004

We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate the spectrum of large exponentially weighted random matrices (whose upper band edge needs to be known for the implementation of the estimation) analytically, by a procedure analogous to that used for standard random matrices. Finally, we illustrate, on empirical data, the superiority of the newly introduced estimator in a portfolio optimization context over both the method of exponentially weighted moving averages and the uniformly-weighted random-matrix-theory-based filtering.

Physica A: Statistical Mechanics and its Applications, 2004

Financial correlations play a central role in financial theory and also in many practical applications. From theoretical point of view, the key interest is in a proper description of the structure and dynamics of correlations. From practical point of view, the emphasis is on the ability of the developed models to provide the adequate input for the numerous portfolio and risk management procedures used in the financial industry. This is crucial, since it has been long argued that correlation matrices determined from financial series contain a relatively large amount of noise and, in addition, most of the portfolio and risk management techniques used in practice can be quite sensitive to the inputs. In this paper we introduce a model (simulation)-based approach which can be used for a systematic investigation of the effect of the different sources of noise in financial correlations in the portfolio and risk management context. To illustrate the usefulness of this framework, we develop several toy models for the structure of correlations and, by considering the finiteness of the time series as the only source of noise, we compare the performance of several correlation matrix estimators introduced in the academic literature and which have since gained also a wide practical use. Based on this experience, we believe that our simulation-based approach can also be useful for the systematic investigation of several other problems of much interest in finance.

Quantitative Finance, 2012

We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise band is composed of multiple subbands that do not fully mix. Our findings allow us to construct effective generalized random matrix theory market models that are closely related to correlation and eigenvector clustering . We show how to use these models in a simulation that incorporates heavy tails. Finally, we demonstrate how a subtle purely stationary risk estimation bias can arise in the conventional cleaning prescription .

Hal-hal yang perlu dilakukan untuk mengembangkan Karakter Maritim pada diri seorang mahasiswa "Karakter Maritim adalah tujuh karakter yang diharapkan dimiliki oleh mahasiswa Unhas, yaitu Manusiawi, Arif, Religius, Integritas, Tangguh, Inovatif dan Mandiri,"kata Prof Dwia.

Diferencované efekty lokálnych riešení rómskej problematiky na príklade obcí Pečovská Nová Ves, Lipany a Ostrovany Slovensko patrí medzi krajiny s najvyšším zastúpením Rómskej menšiny v Európe. Podľa výsledkov z posledného Sčítania obyvateľov, domov a bytov (ŠÚ SR, 2012) žilo v roku 2011 na Slovensku 105 738 Rómov a ich podiel na celkovom počte obyvateľov tak vzrástol za desať rokov z 1,7 (2001) na 2,0% (2011). Objektivita týchto údajov je však často spochybňovaná z dôvodu, že sleduje iba deklarovanú etnicitu. Mnohí Rómovia tak deklarujú inú príslušnosť pred Rómskou. Objektivizovanie uvedených dát je preto založené na kvalifikovaných odhadoch, podľa ktorých v roku 2010 tvorila u nás skupina obyvateľov, ktorých majorita vníma ako Rómov viac ako 350 000 člennú komunitu (352 924 in Matlovičová a kol. 2012), ktorá z priestorového hľadiska je rozptýlená na území celého Slovenska. Najvyššie zastúpenie má však na východe a juhovýchode krajiny, kde sa podľa posledných odhadov nachádza najvä...

ÉPREUVE ÉCRITE / ÉPREUVE spécifique / oPtion tEchnologiqUE / Économie / Droit 2 APRès ClassE pRÉpaRaToIRE prepa concours ecricome Esprit dE l'éprEuvE L'épreuve d'économie-droit du concours Ecricome Prépa repose sur une maîtrise approfondie tant de connaissances que d'exigences méthodologiques. Elle dure 4 heures.