Download or read book Estimating High dimensional Mean variance Portfolio of Risky Assets written by Leheng Chen and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Dimensional Minimum Variance Portfolio Estimation Based on High Frequency Data written by Tony Cai and published by . This book was released on 2019 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators of the MVP and prove that our portfolios asymptotically achieve the minimum variance in a sharp sense. In addition, we introduce consistent estimators of the minimum variance, which provide reference targets. Simulation and empirical studies demonstrate the favorable performance of the proposed portfolios.

Download or read book Time Consistent Mean Variance Portfolio Selection with Only Risky Assets written by Chi Seng Pun and published by . This book was released on 2018 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-consistency and optimal diversification (minimum-variance) criteria are popular in the dynamic portfolio construction in practice. This paper is devoted to the exact analytic solution of the time-consistent mean-variance portfolio selection with assets that can be all risky in a continuous-time economy, of which the time-consistent global minimum-variance portfolio is a special case. Our solution generalizes the studies with a risk-free asset in the sense that one of the risky assets can be set as risk-free. By applying the extended dynamic programming, we manage to derive the exact analytic solution of the time-consistent mean-variance strategy with risky assets via the solution of the Abel differential equation. To stabilize the solution, we derive an analytical expansion for the Abel differential equation with any desired accuracy. In addition, we derive the statistical properties of the optimal strategy and prove a separation theorem. Moreover, we establish the links of time-consistent strategy with pre-commitment and myopic strategies and investigate the curse of dimensionality on the time-consistent strategies. We show that under the low-dimensional setting, the intertemporal hedging demands are significant; however, under the high-dimensional setting, the time-consistent strategies are approximately equivalent to myopic strategies, in the presence of estimation risk. Empirical studies are conducted to illustrate and verify our results.

Download or read book Elements of Financial Risk Management written by Peter Christoffersen and published by Academic Press. This book was released on 2011-11-22 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition of this best-selling book expands its advanced approach to financial risk models by covering market, credit, and integrated risk. With new data that cover the recent financial crisis, it combines Excel-based empirical exercises at the end of each chapter with online exercises so readers can use their own data. Its unified GARCH modeling approach, empirically sophisticated and relevant yet easy to implement, sets this book apart from others. Five new chapters and updated end-of-chapter questions and exercises, as well as Excel-solutions manual, support its step-by-step approach to choosing tools and solving problems. Examines market risk, credit risk, and operational risk Provides exceptional coverage of GARCH models Features online Excel-based empirical exercises

Download or read book Approaching Mean Variance Efficiency for Large Portfolios written by Mengmeng Ao and published by . This book was released on 2018 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a new approach to constructing optimal mean-variance portfolios. The approach relies on a novel unconstrained regression representation of the mean-variance optimization problem combined with high-dimensional sparse-regression methods. Our estimated portfolio, under a mild sparsity assumption, controls the risk and attains the maximum expected return as both the numbers of assets and observations grow. The superior properties of our approach are demonstrated through comprehensive simulation and empirical analysis. Notably, we fi nd that investing in individual stocks in addition to the Fama-French three factor portfolios using our strategy leads to substantially improved performance.

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 Characteristic based Mean variance Portfolio Choice written by Erik Hjalmarsson and published by . This book was released on 2009 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for "stock-picking" in international indexes, using characteristics such as value and momentum, with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.

Download or read book Statistical Inference for Markowitz Efficient Portfolios written by Yuanyuan Zhu and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Statistical Inference for Markowitz Efficient Portfolios" by Yuanyuan, Zhu, 朱淵遠, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled ST A TISTICAL INFERENCE FOR MARKOWITZ EFFICIENT POR TFOLIOS Submitted by ZHU, YUANYUAN for the degree of Do ctor of Philosophy at The University of Hong Kong in September 2015 Markowitz mean-v ariance mo del has been the foundation of modern portfolio theory . The Markowitz model attempts to maximize the portfolio expected return for a given level of portfolio risk, or equiv alently to minimize portfolio risk for a given level of expected return. Assuming multivariate normality of the asset returns, the optimal portfolio weights can be treated as a function of the unknown mean vector and covariance matrix. However it has b een criti- cized by many researchers the ineective and unstable performance of the op- timal portfolio under the model. This thesis intends to improve the Markowitz mean-variance model through two new methods. The rst method is to make use of generalized pivotal quantity (GPQ). The GPQ approach is widely used in constructing hypothesis tests and condence interv als. In this thesis, the GPQ approach is used to make statistical inference on the optimal portfolio weights. Dierent approaches are proposed for con- structing point estimator and simultaneous condence interv als for the optimal portfolio weights. Simulation studies has been conducted to compare the GPQ estimators with existing estimators based on Markowitz model, bootstrap andshrinkage methods. The results show that the GPQ based approach results in a smallest mean squared error for the point estimate of the portfolio weights in most cases and satisfactory coverage rate for the simultaneous condence interv als. F urthermore, an application on portfolio re-balancing problem is considered. Results show that the condence intervals help investors decide whether or not to update the p ortfolio weights so as to achieve a higher prot. This thesis not only focuses on the portfolio optimal weights, but also proposes a new estimator for the Sharpe ratio. Sharpe ratio serves as an important measure of the portfolio performance measure. Some researches have been done on the estimation of the distribution of Sharpe ratio when the number of assets is not too large but the sample size is big. This thesis makes use of GPQ to estimate the Sharpe ratio for high-dimensional data or small-sample-size data. The second method attempts to improve the estimation of the unknown cov ariance matrix. Note that the plug-in estimator for the optimal portfolio weights is biased and p erforms po orly due to the estimation error, especially in the cases of high dimensions. Instead of the sample covariance matrix, we consider the scaled sample cov ariance matrix to construct the new estimator for weights. The explicit formulae for both the mean and v ariance of the new estimator are derived. T wo approaches are prop osed to determine the optimal scale parameter of the covariance matrix estimator. Simulation studies show that the new estimators outperform the existing ones, especially when the number of assets is large. In addition, we illustrate the new estimators with an example from the US stock market. DOI: 10.5353/th_b5689290 Subjects: Portfolio management - Statistical methods

Download or read book An Analytic Derivation of the Efficient Portfolio Frontier written by Robert C. Merton and published by Legare Street Press. This book was released on 2022-10-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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 455 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.

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 Big Data Challenges of High Dimensional Continuous Time Mean Variance Portfolio Selection and a Remedy written by Mei Choi Chiu and published by . This book was released on 2017 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investors interested in the global financial market have to analyze financial securities internationally. The optimal global investment decision involves processing a huge amount of data for a high-dimensional portfolio. This paper investigates the big data challenges of two mean-variance optimal portfolios: continuous-time precommitment and constant-rebalancing strategies. We show that both optimized portfolios implemented with the traditional sample estimates converge to the worst performing portfolio when the portfolio size becomes large. The crux of the problem is the estimation error accumulated from the huge dimension of stock data. We then propose a linear programming optimal (LPO) portfolio framework, which applies a constrained l1 minimization to the theoretical optimal control to mitigate the risk associated with the dimensionality issue. The resulting portfolio becomes a sparse portfolio that selects stocks with a data-driven procedure and hence offers a stable mean-variance portfolio in practice. When the number of observations becomes large, the LPO portfolio converges to the oracle optimal portfolio, which is free of estimation error, even though the number of stocks grows faster than the number of observations. Our numerical and empirical studies demonstrate the superiority of the proposed approach.

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 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 Mean Variance Optimization Using Forward Looking Return Estimates written by Patrick Bielstein and published by . This book was released on 2017 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its theoretical appeal, Markowitz mean-variance portfolio optimization is plagued by practical issues. It is especially difficult to obtain reliable estimates of a stock's expected return. Recent research has therefore focused on minimum volatility portfolio optimization, which implicitly assumes that expected returns for all assets are equal. We argue that investors are better off using the implied cost of capital based on analysts' earnings forecasts as a forward-looking return estimate. Correcting for predictable analyst forecast errors, we demonstrate that mean-variance optimized portfolios based on these estimates outperform on both an absolute and a risk-adjusted basis the minimum volatility portfolio as well as naive benchmarks, such as the value-weighted and equally-weighted market portfolio. The results continue to hold when extending the sample to international markets, using different methods for estimating the forward-looking return, including transaction costs, and using different optimization constraints.

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 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.