Optimization Methods for Financial Index Tracking
Optimization Methods for Financial Index Tracking

Author: Konstantinos Benidis

Publisher:

Published: 2018

Total Pages: 109

ISBN-13: 9781680834659

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Index tracking is a very popular passive investment strategy. Since an index cannot be traded directly, index tracking refers to the process of creating a portfolio that approximates its performance. A straightforward way to do that is to purchase all the assets that compose an index in appropriate quantities. However, to simplify the execution, avoid small and illiquid positions, and large transaction costs, it is desired that the tracking portfolio consists of a small number of assets, id est, we wish to create a sparse portfolio. Although index tracking is driven from the financial industry, it is in fact a pure signal processing problem: a regression of the financial historical data subject to some portfolio constraints with some caveats and particularities. Furthermore, the sparse index tracking problem is similar to many sparsity formulations in the signal processing area in the sense that it is a regression problem with some sparsity requirements. In its original form, sparse index tracking can be formulated as a combinatorial optimization problem. A commonly used approach is to use mixed-integer programming (MIP) to solve small sized problems. Nevertheless, MIP solvers are not applicable for high-dimensional problems since the running time can be prohibiting for practical use. The goal of this monograph is to provide an in-depth overview of the index tracking problem and analyze all the caveats and practical issues an investor might have, such as the frequent rebalancing of weights, the changes in the index composition, the transaction costs, et cetera Furthermore, a unified framework for a large variety of sparse index tracking formulations is provided. The derived algorithms are very attractive for practical use since they provide efficient tracking portfolios orders of magnitude faster than MIP solvers.

Optimization Methods for Financial Index Tracking
Optimization Methods for Financial Index Tracking

Author: Konstantinos Benidis

Publisher: Foundations and Trends (R) in Optimization

Published: 2018-06-07

Total Pages: 122

ISBN-13: 9781680834642

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An in-depth overview of the index tracking problem analyzing all the caveats and practical issues an investor might have, such as the frequent rebalancing of weights, the changes in the index composition, the transaction costs, etc.

Optimization Methods in Finance
Optimization Methods in Finance

Author: Gerard Cornuejols

Publisher: Cambridge University Press

Published: 2006-12-21

Total Pages: 358

ISBN-13: 9780521861700

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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.

Portfoliomanagement
Portfoliomanagement

Author: Klaus Grobys

Publisher: BoD – Books on Demand

Published: 2009

Total Pages: 138

ISBN-13: 3839107318

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Peter Norman, who is in the head management of Sjunde AP-fonden, which is one of the five largest pension funds in Sweden and accounts for 66 milliard Swedish crones, admits that they have decided to employ passive Index-Tracking strategies, because they expect to receive a higher profit by investing in passive strategies. Sidea [2009], who works as editor of the magazine Veckans Affärer, argues that traditional active funds management is built on the management's analysis to figure out and invest in stocks which are underpriced. Considering this, these strategies are built on expectations which may be quite different from each other. This relatively expansive sort of active management needs a high degree of analyst competence, forecast making and trading which involve clearly high costs. This book presents an overview about passive Index-Tracking Strategies as well as an empirical application. The reader will be able to understand the discussed methods and be able to construct strategies of their own, too. Apart from traditional strategies, Klaus Grobys presents the application of more sophisticated models based on cointegration theory as well as a new Pricing model, introduced in his academic final thesis at the University of Kiel.

Optimization Methods in Finance
Optimization Methods in Finance

Author: Gerard Cornuejols

Publisher: Cambridge University Press

Published: 2006-12-21

Total Pages: 3

ISBN-13: 1139460560

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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.

Sparse Portfolios for High-Dimensional Financial Index Tracking
Sparse Portfolios for High-Dimensional Financial Index Tracking

Author: Konstantinos Benidis

Publisher:

Published: 2018

Total Pages: 16

ISBN-13:

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Index tracking is a popular passive portfolio management strategy that aims at constructing a portfolio that replicates or tracks the performance of a financial index. The tracking error can be minimized by purchasing all the assets of the index in appropriate amounts. However, to avoid small and illiquid positions and large transaction costs, it is desired that the tracking portfolio consists of a small number of assets, i.e., a sparse portfolio. The optimal asset selection and capital allocation can be formulated as a combinatorial problem. A commonly used approach is to use mixed-integer programming (MIP) to solve small sized problems. Nevertheless, MIP solvers can fail for high-dimensional problems while the running time can be prohibiting for practical use. In this paper we propose efficient and fast index tracking algorithms that automatically perform asset selection and capital allocation under a set of general convex constraints. A special consideration is given to the case of the non-convex holding constraints and to the downside risk tracking measure. Further, we derive specialized algorithms with closed-form updates for particular sets of constraints. Numerical simulations show that the proposed algorithms match or outperform existing methods in terms of performance, while their running time is lower by many orders of magnitude.

Linear and Mixed Integer Programming for Portfolio Optimization
Linear and Mixed Integer Programming for Portfolio Optimization

Author: Renata Mansini

Publisher: Springer

Published: 2015-06-10

Total Pages: 131

ISBN-13: 3319184822

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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.

Efficient Asset Management
Efficient Asset Management

Author: Richard O. Michaud

Publisher: Oxford University Press

Published: 2008-03-03

Total Pages: 145

ISBN-13: 0199715793

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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.

Index Tracking
Index Tracking

Author: Ren-Raw Chen

Publisher:

Published: 2022

Total Pages: 0

ISBN-13:

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Index tracking has long been of interest for both industry of fund management andacademia. Various methods have been proposed and tested and various issues arediscussed throughout the past 30 years. Yet one issue remains unresolved is how toperform stock selection optimally. In this paper, I propose to use an artificial intelligentmethod - particle swarm optimization (or PSO) to select the most effective stocks totrack a target index most closely.I track the S&P 500 index using a small number of its constituents from 1990 till 2019.Practical constraints such as liquidity (in a form of bid-ask spread), transaction costs(commission), capital requirement are considered. The overall out-of-sample error isconsistent with the literature and shown to be greatly reduced if the rebalancing horizonis shorter and the number of stocks is increased. Also turnovers are lower if rebalancingis more frequent and if more stocks are chosen. Hence, there is a clear tradeoff betweenrebalancing cost and tracking accuracy.

Stochastic Optimization Models in Finance
Stochastic Optimization Models in Finance

Author: William T. Ziemba

Publisher: World Scientific

Published: 2006

Total Pages: 756

ISBN-13: 981256800X

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A reprint of one of the classic volumes on portfolio theory and investment, this book has been used by the leading professors at universities such as Stanford, Berkeley, and Carnegie-Mellon. It contains five parts, each with a review of the literature and about 150 pages of computational and review exercises and further in-depth, challenging problems.Frequently referenced and highly usable, the material remains as fresh and relevant for a portfolio theory course as ever.