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 Dramatically Improved Portfolio Optimization Results with Noise Filtered Covariance written by Alexander Izmailov and published by . This book was released on 2014 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstration that in-sample Markowitz type mean-variance optimization, carried out with noise filtered covariance matrices, results in asset allocation that leads to 2-3 times increase of the Sharpe ratio compared to the same optimization carried out without noise filtering.Demonstration of 2-3 times increase of the Sharpe ratio due to asset allocation obtained via optimization, carried out with noise filtered covariance matrices, for two possible optimization scenarios - maximization of portfolio return at a fixed volatility and minimization of portfolio volatility at a fixed return.

Download or read book Markowitz Portfolio Optimization with Misspecified Covariance Matrices written by Yuan Wang and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider portfolio optimization problems in which the true covariance matrix is misspecified and its value may be obtained by solving a suitably defined learning problem. We consider two types of learning problems to aid in such a resolution: (i) sparse covariance selection; and (ii) sparse precision matrix selection. A tradi- tional sequential approach for addressing such a problem requires first solving the learning problem and then using the solution of this problem in solving the result- ing computational problem. Unfortunately, exact solutions to the learning problem may only be obtained asymptotically; consequently, practical implementations of the sequential approach may provide approximate solutions, at best. Instead, we consider a simultaneous approach that solves both the learning problem and port- folio optimization problems simultaneously. In particular, we use the alternating direction method of multipliers (ADMM) to solve the learning problem while the projected gradient method is used to solve the computational problem. Asymp- totic convergence statements and rate analysis is conducted for the simultaneous scheme. Preliminary numerics on a class of misspecified portfolio optimization problems suggests that the scheme provides accurate solutions with a comparable performance with the sequential approach.

Download or read book Portfolio Optimization Using a Block Structure for the Covariance Matrix written by David J. Disatnik and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Sensitivity Analysis for Changes in the Covariance Matrix in Portfolio Optimization written by Julia Huang and published by . This book was released on 2001 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Portfolio Optimization written by Michael J. Best and published by CRC Press. This book was released on 2010-03-09 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eschewing a more theoretical approach, Portfolio Optimization shows how the mathematical tools of linear algebra and optimization can quickly and clearly formulate important ideas on the subject. This practical book extends the concepts of the Markowitz "budget constraint only" model to a linearly constrained model. Only requiring elementary linear algebra, the text begins with the necessary and sufficient conditions for optimal quadratic minimization that is subject to linear equality constraints. It then develops the key properties of the efficient frontier, extends the results to problems with a risk-free asset, and presents Sharpe ratios and implied risk-free rates. After focusing on quadratic programming, the author discusses a constrained portfolio optimization problem and uses an algorithm to determine the entire (constrained) efficient frontier, its corner portfolios, the piecewise linear expected returns, and the piecewise quadratic variances. The final chapter illustrates infinitely many implied risk returns for certain market portfolios. Drawing on the author’s experiences in the academic world and as a consultant to many financial institutions, this text provides a hands-on foundation in portfolio optimization. Although the author clearly describes how to implement each technique by hand, he includes several MATLAB® programs designed to implement the methods and offers these programs on the accompanying downloadable resources.

Download or read book Robust Equity Portfolio Management written by Woo Chang Kim and published by John Wiley & Sons. This book was released on 2015-11-30 with total page 259 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 Risk Based and Factor Investing written by Emmanuel Jurczenko and published by Elsevier. This book was released on 2015-11-24 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of recent articles written by leading academics and practitioners in the area of risk-based and factor investing (RBFI). The articles are intended to introduce readers to some of the latest, cutting edge research encountered by academics and professionals dealing with RBFI solutions. Together the authors detail both alternative non-return based portfolio construction techniques and investing style risk premia strategies. Each chapter deals with new methods of building strategic and tactical risk-based portfolios, constructing and combining systematic factor strategies and assessing the related rules-based investment performances. This book can assist portfolio managers, asset owners, consultants, academics and students who wish to further their understanding of the science and art of risk-based and factor investing. Contains up-to-date research from the areas of RBFI Features contributions from leading academics and practitioners in this field Features discussions of new methods of building strategic and tactical risk-based portfolios for practitioners, academics and students

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 Metaheuristics for Portfolio Optimization written by G. A. Vijayalakshmi Pai and published by John Wiley & Sons. This book was released on 2017-12-27 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a monograph in the cross disciplinary area of Computational Intelligence in Finance and elucidates a collection of practical and strategic Portfolio Optimization models in Finance, that employ Metaheuristics for their effective solutions and demonstrates the results using MATLAB implementations, over live portfolios invested across global stock universes. The book has been structured in such a way that, even novices in finance or metaheuristics should be able to comprehend and work on the hybrid models discussed in the book.

Download or read book Dynamics of Top Eigenvalues of Empirical Covariance Matrices of Financial Data written by Lijia Wang and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Covariance matrices of financial data and their inverses play an important role in algorithmic portfolio optimization and risk management. For example, PCA (principal component analysis) based strategies in algorithmic portfolio trading, and Markowitz portfolio theory in risk control and portfolio construction. However, since the true covariance matrix is neither perfectly known nor constant in time, the dynamics of the empirical covariance covariances is of great importance, as the volatilities and correlations evolve with time. It is obviously too heavy to carry the whole empirical covariance matrices all the time, especially when they contain a lot of noise. As PCA strategies suggest, most of the meaningful economic information is contained in the large eigenvalues and eigenvectors of covariance matrices, especially, the largest eigenvalue and eigenvector correspond to a collective market mode. As also suggested in risk control, the largest eigenvalue and eigenvector represent the most risky direction in a financial context. The largest eigenvalue of the empirical covariance matrix and the corresponding eigenvector are of considerable importance and we want to analyze their stability over time and characterize their fluctuations. We thus study the dynamics of the top eigenvalues and eigenvectors, instead of the whole matrices. In the thesis, we use a one factor continuous time model and study the dynamics of the top eigenvalues of the empirical covariance matrices. We first model the dynamics of stock returns and construct the empirical covariance matrices through an exponential moving average of the returns. We then derive a stochastic differential equation for the deviation part of the empirical covariance matrix from the true covariance matrix. We also establish a weak convergence result for the top eigenvalue of the deviation matrix at the equilibrium level, and show that the dynamics of the top eigenvalues of the deviation matrices satisfies in probability a reflecting stochastic differential equation for large N (size of covariance matrix) and a large true top eigenvalue. Numerical results are presented at the end to validate our theoretical results.

Download or read book High dimensionality in Statistics and Portfolio Optimization written by Konstantin Glombek and published by BoD – Books on Demand. This book was released on 2012 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Practical Fruits of Econophysics written by Hideki Takayasu and published by Springer Science & Business Media. This book was released on 2006-01-05 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the Third Nikkei Econophysics Symposium, "Business Models in the 21st Century - Risk Management and Expectations for Econophysics," held in Tokyo in November 2004, are gathered herein. Cutting-edge research on the practical application of econophysics is included, covering such topics as the predictability of markets, the analysis of rare events, the mechanism of crashes and bubbles, markets’ correlation and risk management, investment strategy, stochastic market simulations, agent-based market simulations, wealth distribution, and network structures in economics, most of which are beyond the scope of standard financial technology. New market models and financial-data analysis methods are introduced, and dynamic aspects of markets and economy are highlighted. Professionals, researchers, and students will find an invaluable resource in this first book of its kind to summarize the latest work in the field of econophysics.

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 Portfolio Rebalancing with Reinvestment Based on Noise Filtered Correlation Covariance Matrices and the Case of NASDAQ 100 written by Alexander Izmailov and published by . This book was released on 2014 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alexander Izmailov, Ph.D (theoretical physics) and Brian Shay, Ph.D (mathematics) of Market Memory Trading, L.L.C. present, in a series of nine (9) white papers, aspects of a revolutionary advance in uncovering hidden dependencies via filtering noise from correlation matrices developed by the New York based company, Market Memory Trading, L.L.C. (MMT). Correlations are quantitative measures of these dependencies and noise filtering increases their accuracy as a decision-making tool, from asset allocation to LIBOR Surveillance and cyber security.“PORTFOLIO REBALANCING BASED ON NOISE FILTERED CORRELATION/COVARIANCE MATRICES the Case of NASDAQ 100.” White Paper 2, dated December 2, 2013, provides a demonstration of outstanding investment performance due to noise filtering of covariance matrices in optimum portfolio selection exercises. This demonstration is based on the out-of-sample simulation of rebalancing trading done daily, weekly, biweekly and monthly; and exhibits of investment performance for a number of long-short and mostly long portfolios consisting of NASDAQ 100 names. The reported results clearly favor filtered covariance matrices. In extreme cases, 100 % additional performance (annualized returns) can be derived from using noise filtered matrices in optimization rather than using unfiltered matrices. This particular portfolio selection method succeeded in “beating the index” even without filtering, in all exhibits during a 7 year period including the most recent financial crisis: 2006-2013. Refer to Appendix A for Complete Series.

Download or read book Fast Recursive Portfolio Optimization written by Laurence Irlicht and published by . This book was released on 2014 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Institutional equity portfolios are typically constructed via taking expected stock returns and then applying the computationally expensive processes of covariance matrix estimation and mean-variance optimization. Unfortunately, these computational costs make it prohibitive to comprehensively backtest and tune higher frequency strategies over long histories. In this paper, we introduce a recursive algorithm which significantly lowers the computational cost of calculating the covariance matrix and its inverse as well as an iterative heuristic which provides a very fast approximation to mean-variance optimization. Together, these techniques cut backtesting time to a fraction of that of standard techniques. Where possible, the additional step of caching pre-calculated covariance matrices, can result in overall backtesting speeds up to orders of magnitude faster than the standard methods. We demonstrate the efficacy of our approach by selecting a prediction strategy in a fraction of the time taken by standard methods.