Download or read book Another Look at Portfolio Optimization under Tracking Error Constraints written by Philippe Bertrand and published by . This book was released on 2008 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today, the use of a benchmark portfolio is common practice in the financial management industry. This setup allows the investor to evaluate the added value in line with the risks undertaken. But the relevant concept of risk is relative risk as defined by tracking-error volatility.The problem of minimizing the volatility of tracking error was originally solved by Roll (1992). He noticed that the optimal portfolios obtained have several undesirable properties and then suggested introducing an additional constraint on the beta of the portfolio.More recently, Jorion (2003) elegantly tackled this problem again, pointing out that constant-TEV portfolios are described by an ellipse. He showed that because of the flat shape of this ellipse, adding a constraint on total portfolio volatility can substantially improve the performance of the managed portfolio.This paper looks at the problem from another angle. Instead of considering constant TEV frontiers as Jorion does, we allow tracking error to vary but we fix the risk aversion. It is shown that the resulting optimal portfolios have several desirable properties.

Download or read book Portfolio Optimization Under Tracking Error and Weights Constraints written by Isabelle G. Bajeux-Besnainou and published by . This book was released on 2007 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: Active portfolio manager performances are commonly assessed against a benchmark. In this case, his/her performance is often measured by the Information Ratio, the maximization of which is equivalent to the maximization of an expected return under a tracking error constraint. In addition, asset managers often deal with weights constraints (for instance, no more than 10% in equity). These constraints are regulatory or inherent to the fund's policy. We consider a fund manager complying simultaneously with a tracking error (computed for instance, vis-a-vis a bond index) and a weights constraints. These two constraints are not necessarily redundant even when the benchmark complies with the weights constraint. We show, theoretically and through numerical examples that the weights and the tracking error constraints can be simultaneously binding, we consider both equality and inequality weights constraints, derive the analytical and geometrical solutions in both cases and provide financial interpretations based on funds separation. We compute the loss in the Information Ratio due to a weights constraint and analyze the implications on asset allocation and performance measures. In particular, due to the weights constraint, the asset manager may operate under a smaller Information Ratio when free to deviate more from the benchmark (higher Tracking Error). This result undermines the coherence of the Information Ratio as a measure of the ability of asset managers.

Download or read book Portfolio Optimisation Under the Tracking Error Constraint written by and published by . This book was released on 2019 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: Active management -- Tracking error -- Benchmarks -- Portfolio asset allocation.

Download or read book Portfolio Optimization with Tracking Error Constraints written by Philippe Jorion and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article explores the risk and return relationship of active portfolios subject to a constraint on tracking-error volatility (TEV), which can also be interpreted in terms of value at risk. Such a constrained portfolio is the typical setup for active managers who are given the task of beating a benchmark. The problem with this setup is that the portfolio manager pays no attention to total portfolio risk, which results in seriously inefficient portfolios unless some additional constraints are imposed. The development in this article shows that TEV-constrained portfolios are described by an ellipse on the traditional mean-variance plane. This finding yields a number of new insights. Because of the flat shape of this ellipse, adding a constraint on total portfolio volatility can substantially improve the performance of the active portfolio. In general, plan sponsors should concentrate on controlling total portfolio risk.

Download or read book Risk Attribution and Portfolio Optimizations Under Tracking Error Constraints written by Philippe Bertrand and published by . This book was released on 2008 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines wether risk attribution process is consistent with portfolio optimizations under tracking-error constraints. Since Mina (2003), Bertrand (2005) and Menchero and Hu (2006), risk attribution has been widely used in the performance attribution process.This article presents an extension of our previous work on risk attribution to others portfolio optimization contexts. It is shown that only optimization under the tracking-error constraint alone is consistent with the risk attribution process. Indeed, as soon as additional constraints (e.g. on total risk) are introduced, the risk attribution method conflicts with the performance attribution process, preventing us from legitimating all the optimal decisions taken by a portfolio manager.

Download or read book Risk Adjusted Performance Attribution and Portfolio Optimizations Under Tracking Error Constraints written by Philippe Bertrand and published by . This book was released on 2008 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines whether the risk-adjusted performance attribution process is consistent with portfolio optimization under tracking-error constraints. Since Mina (2003), Bertrand (2005) and Menchero and Hu (2006), risk attribution has been widely used in the performance attribution process.This article analyzes and discusses the information ratio decomposition proposed by Menchero (2007) in the light of the analysis of risk-adjusted performance attribution developed in Bertrand (2005). It is also shown that only optimization under the tracking-error constraint alone is consistent with the risk-adjusted performance attribution process. Indeed, as soon as additional constraints (e.g. on total risk) are introduced, the component information ratios of the decisions are no longer uniform nor equal to the information ratio of the whole portfolio. This means that no equilibrium between expected return and relative risk has been reached.

Download or read book Optimization Methods in Finance written by Gerard Cornuejols and published by Cambridge University Press. This book was released on 2006-12-21 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

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 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 Value at Risk 3rd Ed written by Philippe Jorion and published by McGraw Hill Professional. This book was released on 2006-11-09 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its original publication, Value at Risk has become the industry standard in risk management. Now in its Third Edition, this international bestseller addresses the fundamental changes in the field that have occurred across the globe in recent years. Philippe Jorion provides the most current information needed to understand and implement VAR-as well as manage newer dimensions of financial risk. Featured updates include: An increased emphasis on operational risk Using VAR for integrated risk management and to measure economic capital Applications of VAR to risk budgeting in investment management Discussion of new risk-management techniques, including extreme value theory, principal components, and copulas Extensive coverage of the recently finalized Basel II capital adequacy rules for commercial banks, integrated throughout the book A major new feature of the Third Edition is the addition of short questions and exercises at the end of each chapter, making it even easier to check progress. Detailed answers are posted on the companion web site www.pjorion.com/var/. The web site contains other materials, including additional questions that course instructors can assign to their students. Jorion leaves no stone unturned, addressing the building blocks of VAR from computing and backtesting models to forecasting risk and correlations. He outlines the use of VAR to measure and control risk for trading, for investment management, and for enterprise-wide risk management. He also points out key pitfalls to watch out for in risk-management systems. The value-at-risk approach continues to improve worldwide standards for managing numerous types of risk. Now more than ever, professionals can depend on Value at Risk for comprehensive, authoritative counsel on VAR, its application, and its results-and to keep ahead of the curve.

Download or read book Supply Chain and Finance written by Panos M. Pardalos and published by World Scientific. This book was released on 2004 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes recently developed mathematical models, methodologies, and case studies in diverse areas, including stock market analysis, portfolio optimization, classification techniques in economics, supply chain optimization, development of e-commerce applications, etc. It will be of interest to both theoreticians and practitioners working in economics and finance.

Download or read book Perspectives in Sustainable Equity Investing written by Guillaume Coqueret and published by CRC Press. This book was released on 2022-03-08 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sustainable investing has recently gained traction throughout the world. This trend has multiple sources, which span from genuine ethical concerns to hopes of performance boosting, and also encompass risk mitigation. The resulting appetite for green assets is impacting the decisions of many investors. Perspectives in Sustainable Equity Investing is an up-to-date review of the academic literature on sustainable equity investing. It covers more than 800 academic sources grouped into six thematic chapters. Designed for corporate sustainability and financial management professionals, this is an ideal reference for ESG-driven financiers (both retail and institutional). Students majoring in finance or economics with some background or interest in ESG concerns would also find this compact overview useful. Key Features: Introduces the reader to terms and nomenclature used in the field. Surveys the link between sustainability and performance (including risk). Details the integration of sustainable criteria in complex portfolio optimization. Reviews the financial liabilities induced by climate change.

Download or read book Bond Portfolio Optimization written by Michael Puhle and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book analyzes how modern portfolio theory and dynamic term structure models can be applied to government bond portfolio optimization problems. The author studies the necessary adjustments, examines the models with regard to the plausibility of their results and compares the outcomes to portfolio selection techniques used by practitioners. Both single-period and continuous-time bond portfolio optimization problems are considered.

Download or read book Linear and Mixed Integer Programming for Portfolio Optimization written by Renata Mansini and published by Springer. This book was released on 2015-06-10 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents solutions to the general problem of single period portfolio optimization. It introduces different linear models, arising from different performance measures, and the mixed integer linear models resulting from the introduction of real features. Other linear models, such as models for portfolio rebalancing and index tracking, are also covered. The book discusses computational issues and provides a theoretical framework, including the concepts of risk-averse preferences, stochastic dominance and coherent risk measures. The material is presented in a style that requires no background in finance or in portfolio optimization; some experience in linear and mixed integer models, however, is required. The book is thoroughly didactic, supplementing the concepts with comments and illustrative examples.

Download or read book Multi Period Trading Via Convex Optimization written by Stephen Boyd and published by . This book was released on 2017-07-28 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph collects in one place the basic definitions, a careful description of the model, and discussion of how convex optimization can be used in multi-period trading, all in a common notation and framework.

Download or read book Portfolio Mathematics with General Linear and Quadratic Constraints written by David L. Stowe and published by . This book was released on 2017 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimizing investment portfolios is one of the oldest research areas in finance. It has been studied most prolifically in the context of mean/variance optimization problems. Modern investment management is facilitated primarily by delegated managers in principal/agent relationships. Agents optimize not in mean and variance but in excess return above a benchmark and tracking error to a benchmark. Although the mathematics behind such relationships are similar to the mean/variance problem, the differences are subtle and significant. In this paper, I derive the general portfolio optimization problems with a constraint to tracking error (a quadratic constraint), the most pervasive constraint placed on delegated portfolio managers. I also analyze the general linear constraint when applied to Sharpe Ratio maximization.

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