Download or read book Large Scale Covariance Estimates for Portfolio Selection written by Francesco Lautizi and published by . This book was released on 2015 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose an estimator of the Covariance Matrix (SWSE) of a large number of assets. This estimator improves the Similarity Weighted Estimator (SWE) introduced in Munnix et al. (2014), by combining it with the shrinkage estimator of the sample covariance matrix towards the market factor developed by Ledoit and Wolf (2003). We compare the performance of our estimator to some alternatives already available form the literature and the industry. For this purpose we analyse both statistical and economic measures associated to the Global Minimum Variance (GMV) Portfolio, composed by the stocks included in the S&P 500 index and computed using the different estimators considered in our comparison.

Download or read book Asset Return Prediction and Covariance Matrix Estimation for Portfolio Selection in Large Dimensions written by Gianluca De Nard and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Estimation of High dimensional Covariance Matrices and Applications to Portfolio Selection written by Zehao Chen and published by . This book was released on 2008 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proposed new estimator is based on the modified Cholesky decomposition of the covariance matrix, and assumes sparsity in this parametrization. It uses a boosting algorithm with a modified Hannan-Quinn-type stopping criterion. For portfolio optimization applications, a factor model can be constructed and the covariance estimator can then be applied to the residuals, and an empirical study shows that this approach outperforms those that use the naive sample covariance matrix or shrinkage estimators. The main theoretical contributions of this thesis are consistency results for the boosting algorithm and stopping criterion and for the new high-dimensional covariance matrix estimator.

Download or read book Estimation and Forecasting of Large Realized Covariance Matrices and Portfolio Choice written by Laurent Callot and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-06-24 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.

Download or read book Parameter Uncertainty in Portfolio Selection written by Apostolos Kourtis and published by . This book was released on 2012 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The estimation of the inverse covariance matrix plays a crucial role in optimal portfolio choice. We propose a new estimation framework that focuses on enhancing portfolio performance. The framework applies the statistical methodology of shrinkage directly to the inverse covariance matrix using two non-parametric methods. The first minimises the out-of-sample portfolio variance while the second aims to increase out-of-sample risk-adjusted returns. We apply the resulting estimators to compute the minimum variance portfolio weights and obtain a set of new portfolio strategies. These strategies have an intuitive form which allows us to extend our framework to account for short-sale constraints, high transaction costs and singular covariance matrices. A comparative empirical analysis against several strategies from the literature shows that the new strategies generally offer higher risk-adjusted returns and lower levels of risk.

Download or read book Covariance Estimation in Dynamic Portfolio Optimization written by Lada M. Kyj and published by . This book was released on 2009 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Realized covariance estimation for large dimension problems is little explored and poses challenges in terms of computational burden and estimation error. In a global minimum volatility setting, we investigate the performance of covariance conditioning techniques applied to the realized covariance matrices of the 30 DJIA stocks. We find that not only is matrix conditioning necessary to deliver the benefits of high frequency data, but a single factor model, with a smoothed covariance estimate, outperforms the fully estimated realized covariance in one-step ahead forecasts. Furthermore, a mixed-frequency single-factor model - with factor coefficients estimated using low-frequency data and variances estimated using high-frequency data performs better than the realized single-factor estimator. The mixed-frequency model is not only parsimonious but it also avoids estimation of high-frequency covariances, an attractive feature for less frequently traded assets. Volatility dimension curves reveal that it is difficult to distinguish among estimators at low portfolio dimensions, but for well-conditioned estimators the performance gain relative to the benchmark 1/N portfolio increases with N.

Download or read book Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection written by Olivier Ledoit and published by . This book was released on 2000 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Portfolio Selection written by Harry Markowitz and published by Yale University Press. This book was released on 2008-10-01 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Embracing finance, economics, operations research, and computers, this book applies modern techniques of analysis and computation to find combinations of securities that best meet the needs of private or institutional investors.

Download or read book Spectral Analysis of Large Dimensional Random Matrices written by Zhidong Bai and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users. This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory.

Download or read book Advanced Derivatives Pricing and Risk Management written by Claudio Albanese and published by Academic Press. This book was released on 2006 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book and CDROM include the important topics and cutting-edge research in financial derivatives and risk management.

Download or read book Risk and Asset Allocation written by Attilio Meucci and published by Springer Science & Business Media. This book was released on 2009-05-22 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses in the practical and theoretical aspects of one-period asset allocation, i.e. market Modeling, invariants estimation, portfolia evaluation, and portfolio optimization in the prexence of estimation risk The book is software based, many of the exercises simulate in Matlab the solution to practical problems and can be downloaded from the book's web-site

Download or read book CAIA Level I written by Mark J. P. Anson and published by John Wiley & Sons. This book was released on 2012-04-24 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt: "CAIA Association has developed two examinations that are used to certify Chartered Alternative Investment Analysts. The Level I curriculum builds a foundation in both traditional and alternative investment markets--for example, the range of statistics that are used to define investment performance as well as the many types of hedge fund strategies. The readings for the Level II exam focus on the same strategies, but change the context to one of risk management and portfolio optimization. Level I CAIA exam takers have to work through an outline of terms, be able to identify and describe aspects of financial markets, develop reasoning skills, and in some cases make computations necessary to solve business problems"--

Download or read book Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection written by Olivier Ledoit and published by . This book was released on 2017 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markowitz (1952) portfolio selection requires an estimator of the covariance matrix of returns. To address this problem, we promote a nonlinear shrinkage estimator that is more flexible than previous linear shrinkage estimators and has just the right number of free parameters (that is, the Goldilocks principle). This number is the same as the number of assets. Our nonlinear shrinkage estimator is asymptotically optimal for portfolio selection when the number of assets is of the same magnitude as the sample size. In backtests with historical stock return data, it performs better than previous proposals and, in particular, it dominates linear shrinkage.

Download or read book Portfolio Diversification and the Use of Shrinking written by Maja Kuhnell Frederiksen and published by . This book was released on 2008 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: An examination of the performance of the improved estimator of the covariance matrix was conducted on the Danish stock market, the UK stock market and the German stock market. The test results of the Danish and German stock markets revealed a very bad performance of the improved estimator. Even though the levels of the shrinkage intensities were very much in accordance with previous research conducted on the US stock market by Ledoit and Wolf (2003) the improved estimator failed to perform better than the estimated covariance matrix based on Sharpe's (1963) single index model. The test results of the UK stock market were in favor of the improved estimator. The shrinkage intensity yielded an investment strategy that was significantly less volatile than similar strategies based on the traditional sample covariance matrix by Markowitz's (1959) and the single index model. Furthermore, the shrinkage intensity was found to be rather stable over time whereas the shrinkage intensities of the Danish market tended to decrease over time and shrinkage intensities of the German market showed indications of an upward sloping trend. A benchmark test conducted on a small sample of UK stocks showed that the performance of the improved method weakens when the sample size decreases. The weak performance of the improved estimator of Danish and German stock portfolios may therefore have been caused from using too small samples of stocks in the estimation process. Finally the results of the German market may indicate that the improved covariance matrix estimator is sensitive to thin trading.

Download or read book Efficient Asset Management written by Richard O. Michaud and published by Oxford University Press. This book was released on 2008-03-03 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of theoretical benefits, Markowitz mean-variance (MV) optimized portfolios often fail to meet practical investment goals of marketability, usability, and performance, prompting many investors to seek simpler alternatives. Financial experts Richard and Robert Michaud demonstrate that the limitations of MV optimization are not the result of conceptual flaws in Markowitz theory but unrealistic representation of investment information. What is missing is a realistic treatment of estimation error in the optimization and rebalancing process. The text provides a non-technical review of classical Markowitz optimization and traditional objections. The authors demonstrate that in practice the single most important limitation of MV optimization is oversensitivity to estimation error. Portfolio optimization requires a modern statistical perspective. Efficient Asset Management, Second Edition uses Monte Carlo resampling to address information uncertainty and define Resampled Efficiency (RE) technology. RE optimized portfolios represent a new definition of portfolio optimality that is more investment intuitive, robust, and provably investment effective. RE rebalancing provides the first rigorous portfolio trading, monitoring, and asset importance rules, avoiding widespread ad hoc methods in current practice. The Second Edition resolves several open issues and misunderstandings that have emerged since the original edition. The new edition includes new proofs of effectiveness, substantial revisions of statistical estimation, extensive discussion of long-short optimization, and new tools for dealing with estimation error in applications and enhancing computational efficiency. RE optimization is shown to be a Bayesian-based generalization and enhancement of Markowitz's solution. RE technology corrects many current practices that may adversely impact the investment value of trillions of dollars under current asset management. RE optimization technology may also be useful in other financial optimizations and more generally in multivariate estimation contexts of information uncertainty with Bayesian linear constraints. Michaud and Michaud's new book includes numerous additional proposals to enhance investment value including Stein and Bayesian methods for improved input estimation, the use of portfolio priors, and an economic perspective for asset-liability optimization. Applications include investment policy, asset allocation, and equity portfolio optimization. A simple global asset allocation problem illustrates portfolio optimization techniques. A final chapter includes practical advice for avoiding simple portfolio design errors. With its important implications for investment practice, Efficient Asset Management 's highly intuitive yet rigorous approach to defining optimal portfolios will appeal to investment management executives, consultants, brokers, and anyone seeking to stay abreast of current investment technology. Through practical examples and illustrations, Michaud and Michaud update the practice of optimization for modern investment management.

Download or read book How Robust Is Robust Covariance Evidence from International Portfolio Selection written by Tsung-Wu Ho and published by . This book was released on 2015 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates whether the use of robust covariance improves portfolio performance and, in the presence of uncertainty, whether the 1/N strategy is as good as you think. In addition to sample covariance, we use a battery of robust covariance matrix. Our empirical evidence has two findings: First, the range of in-sample estimation horizon and out-of-sample holding period matter the most; secondly, generally, assets selected by robust covariance does not matter, the only exception is covariance estimated by multivariate t distribution Although the 1/N strategy is as optimal as the literature suggests, it does not cover all assets, yet n assets selected out of N by certain strategy perform better. Whether the out-of-sample holding period is set to be 1 and 3 months, our empirical illustration shows that: n assets selected from 90-day estimation window performs best, portfolio with 1/n weight consistently outperforms that with pre-optimized weights. As a result, robust investment strategy matters the most, rather than robust covariance. The factors that affect covariance estimator is not outliers, but the one that balance information.