Download or read book Estimating the Global Minimum Variance Portfolio written by Christoph Memmel and published by . This book was released on 2006 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to standard portfolio theory, the tangency portfolio is the only efficient stock portfolio. However, empirical studies show that an investment in the global minimum variance portfolio often yields better out-of-sample results than does an investment in the tangency portfolio and suggest investing in the global minimum variance portfolio. But little is known about the distributions of the weights and return parameters of this portfolio. Our contribution is to determine these distributions. By doing so, we answer several important questions in asset management.

Download or read book On the Estimation of the Global Minimum Variance Portfolio written by Alexander Kempf and published by . This book was released on 2003 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implementation of the Markowitz optimization requires the knowledge of the parameters of the return distribution. These parameters cannot be observed, but have to be estimated. Merton (1980) and Jorion (1985) point out that especially the expected returns are hard to estimate from time series data. The estimation risk is huge. The global minimum variance portfolio is the only efficient stock portfolio whose weights do not depend on the expected returns. Therefore, one can avoid extreme estimation risk by investing into this portfolio. Nevertheless, there remains a considerable estimation risk with respect to the covariance matrix. This article deals with the estimation of the weights of the global minimum variance portfolio. The literature suggests a two-step approach to determine the optimal portfolio weights. In the first step one estimates the return distribution parameters, and in the second step one optimizes the portfolio weights using the estimated parameters. The main contribution of our paper is to suggest new one-step approaches to estimate optimal portfolio weights. Our paper has four main results: 1) Our one-step regression approach is the best unbiased weight estimator. 2) The estimation risk for this best unbiased estimator is large. 3) (Biased) shrinkage estimators lead to portfolios with smaller out-of-sample return variances. 4) Our one-step shrinkage estimator beats the two step shrinkage approach proposed by Ledoit and Wolf (2003) significantly. The results 1 and 2 are shown analytically. The results 3 and 4 are derived from an extensive simulation study.

Download or read book Focused Shrinkage Estimators for the Global Minimum Variance Portfolio written by Filip Klimenka and published by . This book was released on 2017 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a shrinkage estimator for covariance matrices designed to minimize estimation error of the Global Minimum Variance (GMV) portfolio. Implementing the GMV portfolio requires estimating the asset covariance matrix and using this to obtain variance-minimizing portfolio weights. Standard estimation approaches for this application utilize shrinkage. These estimators use shrinkage weights that are not designed to directly minimize estimation error of the final object of interest: GMV portfolio weights. We develop a focused shrinkage approach to the problem. This method utilizes the form of the trading rule to derive a shrinkage estimator that directly controls estimation error of GMV portfolio weights. Extensive simulations are conducted to compare performance with nine standard competitors. Our estimator uniformly outperformed all competitors across portfolios of various sizes. The methods are applied to several standard portfolios of US and international assets. Similar improvements are found. Our estimator achieves the smallest out-of-sample portfolio variance in 25 of 28 data sets considered.

Download or read book Estimation of the Global Minimum Variance Portfolio in High Dimensions written by Taras Bodnar and published by . This book was released on 2013 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Dimensional Global Minimum Variance Portfolio written by Li Hua and published by . This book was released on 2015 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes the spectral corrected methodology to estimate the Global Minimum Variance Portfolio (GMVP) for the high dimensional data. In this paper, we analysis the limiting properties of the spectral corrected GMVP estimator as the dimension and the number of the sample set increase to infinity proportionally. In addition, we compare the spectral corrected estimation with the linear shrinkage and nonlinear shrinkage estimations and obtain that the performance of the spectral corrected methodology is best in the simulation study.

Download or read book Dominating Estimators for the Global Minimum Variance Portfolio written by Gabriel Frahm and published by . This book was released on 2009 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dominating Estimators for the Global Minimum Variance Portfolio written by Gabriel Frahm and published by . This book was released on 2016 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two shrinkage estimators for the global minimum variance portfolio that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return are derived. The presented results hold for any number of observations n >= d 2 and number of assets d >= 4. The small-sample properties of the shrinkage estimators and also their large-sample properties for fixed d but n -> infinity as well as n,d -> infinity but n/d -> q

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 Computational Finance and Financial Econometrics written by Eric Zivot and published by CRC Press. This book was released on 2017-01-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents mathematical, programming and statistical tools used in the real world analysis and modeling of financial data. The tools are used to model asset returns, measure risk, and construct optimized portfolios using the open source R programming language and Microsoft Excel. The author explains how to build probability models for asset returns, to apply statistical techniques to evaluate if asset returns are normally distributed, to use Monte Carlo simulation and bootstrapping techniques to evaluate statistical models, and to use optimization methods to construct efficient portfolios.

Download or read book Linear Statistical Inference for Global and Local Minimum Variance Portfolios written by Gabriel Frahm and published by . This book was released on 2012 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional portfolio optimization has often been criticized for not taking estimation risk into account. Estimation risk is mainly driven by the parameter uncertainty regarding the expected asset returns rather than their variances and covariances. The global minimum variance portfolio has been advocated by many authors as an appropriate alternative to the tangential portfolio. This is because there are no expectations which have to be estimated and thus the impact of estimation errors can be substantially reduced. However, in many practical situations an investor is not willing to choose the global minimum variance portfolio but he wants to minimize the variance of the portfolio return under specific constraints for the portfolio weights. Such a portfolio is called 'local minimum variance portfolio'. Small-sample hypothesis tests for global and local minimum variance portfolios are derived and the exact distributions of the estimated portfolio weights are calculated in the present work. The first two moments of the estimator for the expected portfolio returns are also provided and the presented instruments are illustrated by an empirical study.

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 On the Estimation Error in Mean Variance Efficient Portfolio Weights written by Frans de Roon and published by . This book was released on 2004 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives the asymptotic covariance matrix of estimated mean-variance efficient portfolio weights, both for gross returns (without a riskfree asset available) and for excess returns (in excess of the riskfree rate). When returns are assumed to be normally distributed, we obtain simple formulas for the covariance matrices. The results show that the estimation error increases as the risk aversion underlying the portfolio decreases and as the (asymptotic) slope or Sharpe ratio of the mean-variance frontier increases. For the tangency portfolio, there is an additional estimation risk because the location of the tangency portfolio is not known beforehand. The empirical analysis of efficient portfolios based on the G7 countries indicates that the estimation error can be big in practice. It also shows that the standard errors that assume normality are usually very close to the standard errors that do not assume normality in returns, except for portfolios close to the Global Minimum Variance portfolio.

Download or read book Predicting the Global Minimum Variance Portfolio written by Laura Reh and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a novel dynamic approach to forecast the weights of the global minimum variance portfolio (GMVP). The GMVP weights are the population coefficients of a linear regression of a benchmark return on a vector of return differences. This representation enables us to derive a consistent loss function from which we can infer the optimal GMVP weights without imposing any distributional assumptions on the returns. In order to capture time variation in the returns' conditional covariance structure, we model the portfolio weights through a recursive least squares (RLS) scheme as well as by generalized autoregressive score (GAS) type dynamics. Sparse parameterizations combined with targeting towards nonlinear shrinkage estimates of the long-run GMVP weights ensure scalability with respect to the number of assets. An empirical analysis of daily and monthly financial returns shows that the proposed models perform well in- and out-of-sample in comparison to existing approaches.

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 Multivariate T Distributions and Their Applications written by Samuel Kotz and published by Cambridge University Press. This book was released on 2004-02-16 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.

Download or read book Global Minimum Variance Portfolio written by Majeed Simaan and published by . This book was released on 2018 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We conduct a horse race using three asset return volatility estimates: the sample variance, the exponential smoother used by RiskMetrics, and the generalized autoregressive conditional heteroskedasticity (GARCH). Our results are performed in both univariate and multivariate analysis. Our goal is to test whether using econometric tools achieves better economic performance. Economic performance is captured by portfolio performance as in DeMiguel et al (2009), who use three metrics to evaluate portfolios: risk-return, Sharpe-ratio, and turnover. Our portfolio of interest is the global minimum variance (GMV) portfolio since its inputs are determined solely by the variances and covariances of the asset returns. Computing the three portfolio performances for the three volatility candidate, we provide an evidence in support of the GARCH approach; however, this edge is undermined by greater portfolio turnover and larger estimation error, when the number assets in the portfolio is large.

Download or read book Portfolio Analysis written by John P. Dickinson and published by Saxon House Lexington Mass.. This book was released on 1974 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: