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 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 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 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 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 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 Investment Risk Management written by Harold Kent Baker and published by Oxford University Press, USA. This book was released on 2015 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investment Risk Management provides an overview of developments in risk management and a synthesis of research on the subject. The chapters examine ways to alter exposures through measuring and managing risk exposures and provide an understanding of the latest strategies and trends within risk management.

Download or read book Portfolio Optimization with R Rmetrics written by and published by Rmetrics. This book was released on with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reconciling Factor Optimization with Portfolio Constraints written by Boris Gnedenko and published by . This book was released on 2017 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Allocation between factor portfolios can bring significant advantages over traditional portfolio optimization performed among individual assets or asset classes. One such advantage is a substantial dimension reduction when one's attention turns from many assets to few factors. This, however, comes at the cost of decreased flexibility in satisfying portfolio constraints.To address this problem, we suggest a natural approach inspired by a geometric interpretation of quadratic programming: among all feasible constrained portfolios, the optimal one minimizes tracking error with respect to the optimal unconstrained portfolio. Thus we obtain an optimal solution by "projecting" an optimal unconstrained factor portfolio onto a set of all feasible portfolios using tracking error as a distance measure. Doing so helps align alpha and risk factors in portfolio optimization.

Download or read book Systematic Trading written by Robert Carver and published by Harriman House Limited. This book was released on 2015-09-14 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is not just another book with yet another trading system. This is a complete guide to developing your own systems to help you make and execute trading and investing decisions. It is intended for everyone who wishes to systematise their financial decision making, either completely or to some degree. Author Robert Carver draws on financial theory, his experience managing systematic hedge fund strategies and his own in-depth research to explain why systematic trading makes sense and demonstrates how it can be done safely and profitably. Every aspect, from creating trading rules to position sizing, is thoroughly explained. The framework described here can be used with all assets, including equities, bonds, forex and commodities. There is no magic formula that will guarantee success, but cutting out simple mistakes will improve your performance. You'll learn how to avoid common pitfalls such as over-complicating your strategy, being too optimistic about likely returns, taking excessive risks and trading too frequently. Important features include: - The theory behind systematic trading: why and when it works, and when it doesn't. - Simple and effective ways to design effective strategies. - A complete position management framework which can be adapted for your needs. - How fully systematic traders can create or adapt trading rules to forecast prices. - Making discretionary trading decisions within a systematic framework for position management. - Why traditional long only investors should use systems to ensure proper diversification, and avoid costly and unnecessary portfolio churn. - Adapting strategies depending on the cost of trading and how much capital is being used. - Practical examples from UK, US and international markets showing how the framework can be used. Systematic Trading is detailed, comprehensive and full of practical advice. It provides a unique new approach to system development and a must for anyone considering using systems to make some, or all, of their investment decisions.

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 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 Introduction to Risk Parity and Budgeting written by Thierry Roncalli and published by CRC Press. This book was released on 2016-04-19 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although portfolio management didn't change much during the 40 years after the seminal works of Markowitz and Sharpe, the development of risk budgeting techniques marked an important milestone in the deepening of the relationship between risk and asset management. Risk parity then became a popular financial model of investment after the global fina

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 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.