Related papers: Noisy Covariance Matrices and Portfolio Optimizati…
According to recent findings [1,2], empirical covariance matrices deduced from financial return series contain such a high amount of noise that, apart from a few large eigenvalues and the corresponding eigenvectors, their structure can…
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…
We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the…
This paper examines the applicability of Random Matrix Theory to portfolio management in finance. Starting from a group of normally distributed stochastic processes with given correlations we devise an algorithm for removing noise from the…
We study empirical covariance matrices in finance. Due to the limited amount of available input information, these objects incorporate a huge amount of noise, so their naive use in optimization procedures, such as portfolio selection, may…
Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed''. We develop a new and alternative method to…
In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the…
This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…
We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and…
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…
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…
The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is…
The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance…
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…
This thesis mainly focuses on two problems in capital structure and individual's life-cycle portfolio choice. In the first problem, we derive a stochastic control model to optimize banks' dividend and recapitalization policies and calibrate…
Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to…
Noisy optimization is the optimization of objective functions corrupted by noise. A portfolio of solvers is a set of solvers equipped with an algorithm selection tool for distributing the computational power among them. Portfolios are…
We investigate simulation-based bandpower covariance matrices commonly used in cosmological parameter inferences such as the estimation of the tensor-to-scalar ratio $r$. We find that upper limits on $r$ can be biased low by tens of…
When shrinking a covariance matrix towards (a multiple) of the identity matrix, the trace of the covariance matrix arises naturally as the optimal scaling factor for the identity target. The trace also appears in other context, for example…
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…