Download or read book Estimating the Covariance Matrix for Portfolio Optimization written by David Disatnik and published by . This book was released on 2006 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: We discuss the estimation of the covariance matrix of stock returns for portfolio optimization and show that for constructing the global minimum variance portfolio (GMVP), there is no statistically-significant gain from using more sophisticated shrinkage estimators instead of simpler portfolios of estimators. We introduce a new quot;two block estimator,quot; which produces - in an unconstrained optimization - a positive GMVP, that can be found analytically and that is sensitive to even small changes in the covariance matrix. For constructing the GMVP, an example of our new estimator performs at least as well as a combination of imposing the short sale constraints and using the sample matrix.

Download or read book Covariance Matrix Estimation Methods for Constrained Portfolio Optimization in a South African Setting written by Jaison Pedzisai Madume and published by . This book was released on 2010 with total page 70 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 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 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 207 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 Portfolio Optimization with R Rmetrics written by and published by Rmetrics. This book was released on with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Robust Adaptive Beamforming written by Jian Li and published by John Wiley & Sons. This book was released on 2005-10-10 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest research and developments in robust adaptivebeamforming Recent work has made great strides toward devising robust adaptivebeamformers that vastly improve signal strength against backgroundnoise and directional interference. This dynamic technology hasdiverse applications, including radar, sonar, acoustics, astronomy,seismology, communications, and medical imaging. There are alsoexciting emerging applications such as smart antennas for wirelesscommunications, handheld ultrasound imaging systems, anddirectional hearing aids. Robust Adaptive Beamforming compiles the theories and work ofleading researchers investigating various approaches in onecomprehensive volume. Unlike previous efforts, these pioneeringstudies are based on theories that use an uncertainty set of thearray steering vector. The researchers define their theories,explain their methodologies, and present their conclusions. Methodspresented include: * Coupling the standard Capon beamformers with a spherical orellipsoidal uncertainty set of the array steering vector * Diagonal loading for finite sample size beamforming * Mean-squared error beamforming for signal estimation * Constant modulus beamforming * Robust wideband beamforming using a steered adaptive beamformerto adapt the weight vector within a generalized sidelobe cancellerformulation Robust Adaptive Beamforming provides a truly up-to-date resourceand reference for engineers, researchers, and graduate students inthis promising, rapidly expanding field.

Download or read book Improving Portfolios Global Performance with Robust Covariance Matrix Estimation written by Jay Emmanuelle and published by . This book was released on 2018 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the same improvements apply also in the other optimisation problems such as the Minimum Variance Portfolio. We assume that the most important information (or the latent factors) are embedded in correlated Elliptical Symmetric noise extending classical Gaussian assumptions. We propose here to focus on a recent method of model order selection allowing to efficiently estimate the subspace of main factors describing the market. This non-standard model order selection problem is solved through Random Matrix Theory and robust covariance matrix estimation. The proposed procedure will be explained through synthetic data and be applied and compared with standard techniques on real market data showing promising improvements.

Download or read book Essays on Applications of the Factor Model written by Xiaolin Sun and published by . This book was released on 2013 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimating the volatilities and correlations of asset returns plays an important role in portfolio and risk management. As of late, interest in the estimation of the covariance matrix of large dimensional portfolios has increased. Estimating large dimensional covariance poses a challenge in that the cross-sectional dimension is often similar to or bigger than the number of observations available. Simple estimators are often poorly conditioned with some small eigenvalues, and so are unsuitable for many real world applications, including portfolio optimization and tracking error minimization. The first chapter introduces our two large dimensional covariance matrix estimators. We estimate the large dimensional realized covariance matrix by using the methods of asymptotic principal components analysis based factor modeling and singular value decomposition. In the second chapter, we show though simulation that our proposed estimators are closer to the true covariance matrix than the current popular shrinkage estimator. We also simulate conducting the out sample portfolio performance tests and find that the portfolios constructed based on our proposed estimators have lower risk than portfolios constructed using the shrinkage matrix. Using S&P 500 stocks from 1926 to 2011, we back test our proposed covariance matrix. In addition, the portfolios constructed based on our proposed estimators exhibit lower risk than portfolios constructed using the shrinkage matrix. The third chapter proposes a new volatility index--a cross-sectional volatility index of residuals using factor model. The cross-sectional volatility index moves closely with the VIX for the S&P 500 stock universe. It is a non-parametric, model-free volatility index, which could be estimated at any frequency for any region, sector, and style of world equity market and also does not depend on any option pricing. We provide some interpretation of the cross-sectional volatility index of residuals as a proxy for aggregate economic uncertainty, and show a high correlation between the VIX index and the corresponding cross-sectional volatility index of residuals based on the S&P 500 universe. Our results show that the portfolio hedged based on the cross-sectional volatility index of residuals has a much higher Sharpe ratio than the portfolio without hedge. Overall, these findings suggest that the cross-sectional volatility index of residuals is intimately related to other volatility measures where and when such measures are available, and that it can be used as a reliable proxy for volatility when such measures are not available.

Download or read book Portfolio Optimization with Noisy Covariance Matrices written by Jose Menchero and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean-variance optimization provides a framework for constructing portfolios that have minimum risk for a given level of expected return. The required inputs are the expected asset returns, the asset covariance matrix, and a set of investment constraints. While portfolio optimization always leads to an increase in ex ante risk-adjusted performance, there is no guarantee that this performance improvement carries over ex post. The culprit is that both the expected return forecasts and the asset covariance matrix contain estimation error. In this paper, we explore the impact of sampling error in the covariance matrix when using mean-variance optimization for portfolio construction. In particular, we show that sampling error leads to several adverse effects, such as: (a) under-forecasting of risk, (b) increased out-of-sample volatility, (c) increased leverage and turnover, and (d) inefficient allocation of the risk budget.Moreover, we introduce a new framework to explain and understand the origin of these adverse effects. We decompose the optimal portfolio into an alpha portfolio which explains expected returns, and a hedge portfolio which has zero expected return but serves to reduce portfolio risk. We show that sampling error in the asset covariance matrix leads to systematic biases in the volatility and correlation forecasts of these portfolios.We also provide a geometric interpretation showing how these biases lead to the adverse effects described above.

Download or read book Estimation of Optimal Portfolio Weights Using Shrinkage Technique written by Takuya Kinkawa and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mean-variance optimization is one of the standard frameworks used to obtain optimal portfolio weights. This framework requires estimators for the mean vector and the covariance matrix of excess returns. The classical method is to adopt the usual sample estimates for the mean vector and the covariance matrix. However, it is well known that the optimal portfolio weights obtained by the classical approach are unstable and unreliable. In order to reduce the estimation error of the estimated mean-variance optimal portfolio weights, some previous studies have proposed applying shrinkage estimators. However, only a few studies have addressed this problem analytically. Since the form of the loss function used in this problem is not the quadratic one used in statistical literature, there have been some difficulties in showing analytically the general dominance results. In this Ph.D. dissertation, we show the dominance of a broader class of Stein type estimators for the mean-variance optimal portfolio weights, which shrink toward the origin, a fixed point, the grand mean, or more generally, toward a linear subspace when the covariance matrix is unknown and is estimated. Most of previous studies have addressed this problem when we have no constraint on portfolio weights. However, we also show the dominance when there are linear constraints on portfolio weights, similarly to Mori (2004), who has shown a result for that case. The obtained results enable us to clarify the conditions for some previously proposed estimators in finance to have smaller risks than the classical estimator which we obtain by plugging in the sample estimates. Jorion's (1986) estimator, Black and Litterman's (1992) estimator and Kan and Zhou's (2007) estimators have been considered. We also propose a new improved estimator which utilizes a prior information about Sharpe ratio, which is a well known performance measure of funds.

Download or read book Robust Portfolio Optimization and Management written by Frank J. Fabozzi and published by John Wiley & Sons. This book was released on 2007-04-27 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for Robust Portfolio Optimization and Management "In the half century since Harry Markowitz introduced his elegant theory for selecting portfolios, investors and scholars have extended and refined its application to a wide range of real-world problems, culminating in the contents of this masterful book. Fabozzi, Kolm, Pachamanova, and Focardi deserve high praise for producing a technically rigorous yet remarkably accessible guide to the latest advances in portfolio construction." --Mark Kritzman, President and CEO, Windham Capital Management, LLC "The topic of robust optimization (RO) has become 'hot' over the past several years, especially in real-world financial applications. This interest has been sparked, in part, by practitioners who implemented classical portfolio models for asset allocation without considering estimation and model robustness a part of their overall allocation methodology, and experienced poor performance. Anyone interested in these developments ought to own a copy of this book. The authors cover the recent developments of the RO area in an intuitive, easy-to-read manner, provide numerous examples, and discuss practical considerations. I highly recommend this book to finance professionals and students alike." --John M. Mulvey, Professor of Operations Research and Financial Engineering, Princeton University

Download or read book Portfolio Construction and Risk Budgeting written by 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 Handbook Of Financial Econometrics Mathematics Statistics And Machine Learning In 4 Volumes written by Cheng Few Lee and published by World Scientific. This book was released on 2020-07-30 with total page 5053 pages. Available in PDF, EPUB and Kindle. Book excerpt: This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

Download or read book Portfolio Selection With Robust Estimation written by Victor DeMiguel and published by . This book was released on 2007 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which relies solely on estimates of the covariance matrix, and thus, usually performs better out-of-sample. But even the minimum-variance portfolios are quite sensitive to estimation error and have unstable weights that fluctuate substantially over time. In this paper, we propose a class of portfolios that have better stability properties than the traditional minimum-variance portfolios. The proposed portfolios are constructed using certain robust estimators and can be computed by solving a single nonlinear program, where robust estimation and portfolio optimization are performed in a single step. We show analytically that the resulting portfolio weights are less sensitive to changes in the asset-return distribution than those of the traditional minimum-variance portfolios. Moreover, our numerical results on simulated and empirical data confirm that the proposed portfolios are more stable than the traditional minimum-variance portfolios, while preserving (or slightly improving) their relatively good out-of-sample performance.

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 Statistical Portfolio Estimation written by Masanobu Taniguchi and published by CRC Press. This book was released on 2017-09-01 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The composition of portfolios is one of the most fundamental and important methods in financial engineering, used to control the risk of investments. This book provides a comprehensive overview of statistical inference for portfolios and their various applications. A variety of asset processes are introduced, including non-Gaussian stationary processes, nonlinear processes, non-stationary processes, and the book provides a framework for statistical inference using local asymptotic normality (LAN). The approach is generalized for portfolio estimation, so that many important problems can be covered. This book can primarily be used as a reference by researchers from statistics, mathematics, finance, econometrics, and genomics. It can also be used as a textbook by senior undergraduate and graduate students in these fields.