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 On the Estimation Error in Mean variance Efficient Portfolio Weights written by Frans Adrianus Roon and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Estimation Error in Mean varince 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:

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 Estimation Error in Mean Returns and the Mean Variance Efficient Frontier written by Majeed Simaan and published by . This book was released on 2017 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we build estimation error in mean returns into the mean-variance (MV) portfolio theory under the assumption that returns on individual assets follow a joint normal distribution. We derive the conditional sampling distribution of the MV portfolio along with its mean and risk return when the sample covariance matrix is equal to a constant matrix. We use the mean squared error (MSE) to characterize the effects of estimation error in mean returns on the joint sampling distributions and examine how such error affects the risk-return tradeoff of the MV portfolios. We show that the negative effects of error in mean returns on the joint sampling distributions increase with the decision maker's risk tolerance and the number of assets in a portfolio, but decrease with the sample size.

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 Robust Equity Portfolio Management written by Woo Chang Kim and published by John Wiley & Sons. This book was released on 2015-11-25 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive portfolio optimization guide, with provided MATLAB code Robust Equity Portfolio Management + Website offers the most comprehensive coverage available in this burgeoning field. Beginning with the fundamentals before moving into advanced techniques, this book provides useful coverage for both beginners and advanced readers. MATLAB code is provided to allow readers of all levels to begin implementing robust models immediately, with detailed explanations and applications in the equity market included to help you grasp the real-world use of each technique. The discussion includes the most up-to-date thinking and cutting-edge methods, including a much-needed alternative to the traditional Markowitz mean-variance model. Unparalleled in depth and breadth, this book is an invaluable reference for all risk managers, portfolio managers, and analysts. Portfolio construction models originating from the standard Markowitz mean-variance model have a high input sensitivity that threatens optimization, spawning a flurry of research into new analytic techniques. This book covers the latest developments along with the basics, to give you a truly comprehensive understanding backed by a robust, practical skill set. Get up to speed on the latest developments in portfolio optimization Implement robust models using provided MATLAB code Learn advanced optimization methods with equity portfolio applications Understand the formulations, performances, and properties of robust portfolios The Markowitz mean-variance model remains the standard framework for portfolio optimization, but the interest in—and need for—an alternative is rapidly increasing. Resolving the sensitivity issue and dramatically reducing portfolio risk is a major focus of today's portfolio manager. Robust Equity Portfolio Management + Website provides a viable alternative framework, and the hard skills to implement any optimization method.

Download or read book A Practitioner s Guide to Asset Allocation written by William Kinlaw and published by John Wiley & Sons. This book was released on 2017-05-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the formalization of asset allocation in 1952 with the publication of Portfolio Selection by Harry Markowitz, there have been great strides made to enhance the application of this groundbreaking theory. However, progress has been uneven. It has been punctuated with instances of misleading research, which has contributed to the stubborn persistence of certain fallacies about asset allocation. A Practitioner's Guide to Asset Allocation fills a void in the literature by offering a hands-on resource that describes the many important innovations that address key challenges to asset allocation and dispels common fallacies about asset allocation. The authors cover the fundamentals of asset allocation, including a discussion of the attributes that qualify a group of securities as an asset class and a detailed description of the conventional application of mean-variance analysis to asset allocation.. The authors review a number of common fallacies about asset allocation and dispel these misconceptions with logic or hard evidence. The fallacies debunked include such notions as: asset allocation determines more than 90% of investment performance; time diversifies risk; optimization is hypersensitive to estimation error; factors provide greater diversification than assets and are more effective at reducing noise; and that equally weighted portfolios perform more reliably out of sample than optimized portfolios. A Practitioner's Guide to Asset Allocation also explores the innovations that address key challenges to asset allocation and presents an alternative optimization procedure to address the idea that some investors have complex preferences and returns may not be elliptically distributed. Among the challenges highlighted, the authors explain how to overcome inefficiencies that result from constraints by expanding the optimization objective function to incorporate absolute and relative goals simultaneously. The text also explores the challenge of currency risk, describes how to use shadow assets and liabilities to unify liquidity with expected return and risk, and shows how to evaluate alternative asset mixes by assessing exposure to loss throughout the investment horizon based on regime-dependent risk. This practical text contains an illustrative example of asset allocation which is used to demonstrate the impact of the innovations described throughout the book. In addition, the book includes supplemental material that summarizes the key takeaways and includes information on relevant statistical and theoretical concepts, as well as a comprehensive glossary of terms.

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 Theory and Methodology of Tactical Asset Allocation written by Wai Lee and published by John Wiley & Sons. This book was released on 2000-08-15 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asset allocation has long been viewed as a safe bet for reducing risk in a portfolio. Asset allocators strive to buy when prices are low and sell when prices rise. Tactical asset allocation (TAA) practitioners tend to emphasize shorter-term adjustments, reducing exposure when recent market performance has been good, and increasing exposure in a slipping market (in contrast to dynamic asset allocation, or portfolio insurance). As interest in this technique continues to grow, J.P. Morgan's Wai Lee provides comprehensive coverage of the analytical tools needed to successfully implement and monitor tactical asset allocation.

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 Adjusting for Estimation Error in the Mean variance Portfolio Model written by Kent Handi and published by . This book was released on 2000 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mean Variance Portfolio Selection with Tracking Error Penalization written by William Lefebvre and published by . This book was released on 2020 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in case of misspecified parameters, by “fitting” it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean-Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

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 Your Essential Guide to Quantitative Hedge Fund Investing written by Marat Molyboga and published by CRC Press. This book was released on 2023-07-18 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your Essential Guide to Quantitative Hedge Fund Investing provides a conceptual framework for understanding effective hedge fund investment strategies. The book offers a mathematically rigorous exploration of different topics, framed in an easy to digest set of examples and analogies, including stories from some legendary hedge fund investors. Readers will be guided from the historical to the cutting edge, while building a framework of understanding that encompasses it all. Features Filled with novel examples and analogies from within and beyond the world of finance Suitable for practitioners and graduate-level students with a passion for understanding the complexities that lie behind the raw mechanics of quantitative hedge fund investment A unique insight from an author with experience of both the practical and academic spheres.

Download or read book Modern Portfolio Optimization with NuOPTTM S PLUS and S BayesTM written by Bernd Scherer and published by Springer Science & Business Media. This book was released on 2007-09-05 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years portfolio optimization and construction methodologies have become an increasingly critical ingredient of asset and fund management, while at the same time portfolio risk assessment has become an essential ingredient in risk management. This trend will only accelerate in the coming years. This practical handbook fills the gap between current university instruction and current industry practice. It provides a comprehensive computationally-oriented treatment of modern portfolio optimization and construction methods using the powerful NUOPT for S-PLUS optimizer.