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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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.
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Seitenzahl: 353
Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title
Copyright
Preface
PART 1
1 Introduction to Portfolio Optimization
1.1. Fundamentals of portfolio optimization
1.2. An example case study
1.3. MATLAB® demonstrations
2 A Brief Primer on Metaheuristics
2.1. Metaheuristics framework
2.2. Exact methods versus metaheuristics
2.3. Population-based metaheuristics – Evolutionary Algorithms
2.4. Evolution Strategy.
2.5. Differential Evolution strategy
2.6. MATLAB® demonstrations
PART 2
3 Heuristic Portfolio Selection
3.1. Portfolio selection
3.2. Clustering
3.3.
k-
means clustering.
3.4. Heuristic selection of securities
3.5.
k-
portfolio performance
3.6. MATLAB® demonstrations
4 Metaheuristic Risk-Budgeted Portfolio Optimization
4.1. Risk budgeting
4.2. Long-Short portfolio
4.3. Risk-Budgeted Portfolio Optimization model
4.4. Differential Evolution with Hall of Fame
4.5. Repair strategy for handling unbounded linear constraints.
4.6. DE HOF-based Risk-budgeted portfolio optimization.
4.7. Case study global portfolio: results and analyses
4.8. MATLAB® demonstrations
5 Heuristic Optimization of Equity Market Neutral Portfolios
5.1. Market neutral portfolio
5.2. Optimizing a naïve equity market neutral portfolio
5.3. Risk-budgeted equity market neutral portfolio
5.4. Metaheuristic risk-budgeted equity market neutral portfolios
5.5. Experimental results and analyses
5.6. MATLAB® demonstrations
6 Metaheuristic 130-30 Portfolio Construction
6.1. 130-30 portfolio
6.2. 130-30 portfolio optimization: mathematical formulation
6.3. 130-30 portfolio optimization using MATLAB Financial Toolbox
™
6.4. Metaheuristic 130-30 portfolio optimization
6.5. MATLAB® demonstrations
7 Metaheuristic Portfolio Rebalancing with Transaction Costs
7.1. Portfolio rebalancing
7.2. Portfolio rebalancing mathematical model
7.3. Evolution Strategy with Hall of Fame for Portfolio Rebalancing
7.4. Experimental results.
7.5. Comparison of Non-Rebalanced and Rebalanced portfolios
7.6. MATLAB® demonstrations
Conclusion
Bibliography
Index
End User License Agreement
Guide
Cover
Table of Contents
Begin Reading
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e1
Metaheuristics Set
coordinated byNicolas Monmarché and Patrick Siarry
Volume 11
Metaheuristics for Portfolio Optimization
An Introduction using MATLAB®
G.A. Vijayalakshmi Pai
First published 2018 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com
© ISTE Ltd 2018
The rights of G.A. Vijayalakshmi Pai to be identified as the author of this work have been asserted by her in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2017955798
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-281-6
MATLAB® is a registered trademark of The MathWorks, Inc. MATLAB Financial Toolbox™,MATLAB Statistics Toolbox™ and MATLAB Optimization Toolbox™ are products of MATLAB®.
For MATLAB and SIMULINK product information, please contact:
The MathWorks, Inc.
3, Apple Hill Drive
Natick, MA, 01760-2098 USA
Tel: 508-647-7000, Fax: 508-647-7001
Email: [email protected]
Web: http://www.mathworks.com
How to buy: http://www.mathworks.com/store
Preface
Portfolio Optimization, that deals with the choice and appropriate allocation of capital over assets comprising a portfolio so that it is better off than any other, given the investment objectives and preferences of the investor, has been a traditional and hardcore discipline of Finance in general or Financial Engineering, in particular.
Modern Portfolio Theory (MPT) – a theory pioneered by Harry Markowitz in his paper “Portfolio Selection” published in the Journal of Finance in 1952 and expounded in his book Portfolio Selection: Efficient Diversification, in 1959, which eventually won him the Nobel Prize in Economics in 1990, did make a huge impact on the discipline, despite its shortcomings pointed out by its critics. MPT harped on the expected risk and return of an asset, the benefits of diversification where one avoids putting all eggs in one basket, the categorization of risks as systematic and unsystematic, the role played by efficient frontier and risk-free assets in determining the expected portfolio returns and so on, which “…for over six decades… provided money managers and sophisticated investors with a tried-and-true way to select portfolios.” (“Harry Markowitz Father of Modern Portfolio Theory Still Diversified”, The Finance Professionals’ Post, December 28, 2011). This book subscribes to MPT and all the portfolio optimization models discussed in it are built over the MPT framework.
Nevertheless, Markowitz’s framework assumed a market devoid of transaction costs or taxes or short selling, to list a few, that resulted in simple portfolio optimization models that could be easily solved using a traditional method such as Quadratic Programming, to yield the optimal portfolios desired. However, markets in reality are not as naïve as they were assumed to be. In practice, market frictions, investor preferences, investment strategies, company policies of investment firms etc., have resulted in complex objectives and constraints that have made the problem of portfolio optimization difficult, if not intractable. The complex mathematical models defining the portfolio have found little help from traditional or analytical methods in their efforts to arrive at optimal portfolios, forcing the need to look for non-traditional algorithms and non-orthodox approaches from the broad discipline of Computational Intelligence. Fortunately, the emerging and fast-growing discipline of Metaheuristics, a sub discipline of Computational Intelligence, has refreshingly turned out to be a panacea for all the ills of such of these notorious problem models. Metaheuristics has not just turned out to be a viable alternative for solving difficult optimization problems, but in several cases has turned out to be the only alternative to solve the complex problem models concerned.
Metaheuristic approaches represent efficient ways to deal with complex optimization problems and are applicable to both continuous and combinatorial optimization problems. Nature-inspired Metaheuristics is a popular and active research area which relies on natural systems for the solution of optimization problem models and one of its genres, Evolutionary Algorithms, which is inspired by biological evolution, is what has been applied to solve the portfolio optimization problem models discussed in the book.
Objectives of the book
Metaheuristics for Portfolio Optimization elucidates Portfolio Optimization problems/models that employ metaheuristics for their effective solutions/decisions and demonstrates their application and results using MATLAB®. The book views a traditional hardcore finance discipline from an interdisciplinary perspective, with the cornerstones of:
– finance (Portfolio Optimization, in particular);
– metaheuristics (Evolutionary Algorithms, in particular), and
– computing (MATLAB®, in particular).
The book, therefore, presents a compilation of ideas, models, algorithms and experiments that were explored, investigated and worked upon by the author independently and in collaboration with the investment and finance industry, during a decade-old highly productive collaborative stint, beginning in 2006.
Notwithstanding the complex constraints that can make most Portfolio Optimization models difficult to solve using traditional methods, the presence of multiple objectives (two or more) in the model can render the problems even more difficult. Fortunately, metaheuristics endowed with their innate capabilities and strengths have exhibited strong potential to solve even such problems, finding what are called Pareto optimal solutions that are acceptable solutions. However, in this book the discussion is restricted only to single objective optimization models with complex constraints though.
The objective of the book, therefore, is not to get the readers lost in the labyrinth of encyclopedic work in the niche area of metaheuristic portfolio optimization. It is to lead them through a charted path on tested waters, just as a boatman does while taking the tourists on a pleasure trip across a lake! The book therefore, is target-specific and intensive in content, presenting a modest set of metaheuristic portfolio optimization models worked upon by a specific set of metaheuristic algorithms implemented in MATLAB®, to lead the reader slowly but surely through a selective set of systems. The aim is to demonstrate the tricks of the trade to the reader, so as to equip him/her to explore and innovate further, for solving their own complex problems in hand.
The motivation behind the choice of MATLAB® for the implementation and experimentation of the metaheuristic portfolio optimization models discussed in the book is the availability of an interactive programming environment and accessibility to a repertoire of toolboxes and libraries that render the tasks of coding, testing, execution and simulation easier. Also, the accessibility to a toolbox such as MATLAB’s Financial Toolbox™ together with MATLAB’s Statistics Toolbox™ and MATLAB’s Optimization Toolbox™, coupled with the exclusive Command Line Mode execution of MATLAB®, for example, can help users execute most of their fundamental Portfolio Optimization tasks with minimal or nil program scripts. Some examples to this effect have been illustrated in the book at appropriate places of discussion. While a working knowledge of MATLAB® can help understand the implementations presented in the book better, the algorithms and concepts pertaining to the metaheuristic portfolio optimization models have been kept software independent, so that a reader who comprehends the ideas discussed can implement the same in a software of his/her choice.
The coding style adopted by the MATLAB® code fragments and functions presented in the book has been kept simple and direct to favor readers who are novices in MATLAB®. Nevertheless, such readers are advised to refer to the extensive and elaborate help manuals provided by MATLAB®.
Target audience of the book
Being an interdisciplinary work, the book targets:
– finance practitioners, theorists and “quants”, who are interested to know how Metaheuristics, an ally of Computational Intelligence, can serve to solve their complex portfolio optimization models;
– computer scientists and information technologists with little or no knowledge of Metaheuristics as a specialization, who wish to foray into the exciting world of Portfolio Management as practitioners;
– metaheuristic researchers wanting to make inroads into the fertile ground of Portfolio Optimization in particular or Computational Finance in general, to explore applications of their innovative algorithms;
– academic researchers from both Finance and Computer Science / Information Technology communities, and
– graduate/senior undergraduate students from the disciplines of STEM (Science, Technology, Engineering and Management) aspiring to get into the interdisciplinary field, either out of curricular or career interests.
Organization of the book
The book comprises seven chapters grouped under two parts, Part 1 and Part 2. Part 1 of the book comprising chapters 1 and 2, serves as a compact introduction to the disciplines of Portfolio Optimization and Metaheuristics respectively, to readers unfamiliar with the same.
Part 2 of the book comprising chapters 3–7, elaborately discusses five different metaheuristic portfolio selection/optimization models that are built over the fundamentals discussed in Part 1 of the book.
All the Portfolio Optimization concepts and models have been experimented or demonstrated over realistic portfolios, selected from global stock universes, S&P BSE200 Index (Bombay Stock Exchange, India) and Nikkei 225 Index (Tokyo Stock Exchange, Japan), to name a few. The MATLAB® demonstrations of the functions and algorithms governing the portfolio models or discussions in the chapters concerned have been included at the end of each chapter of the book. Projects to be undertaken to reinforce learning and application of concepts discussed in the chapters concerned and suggested material for further reading are included at the end of each chapter.
A brief outline of the chapter contents are as follows:
Chapter 1– Introduction to Portfolio Optimization, introduces the fundamentals of Portfolio Optimization based on Modern Portfolio Theory, targeting readers who are unfamiliar with concepts and theories surrounding financial portfolios. However, the discussion on the fundamentals has been kept very specific and comprehensive enough only to follow the portfolio optimization models discussed in the subsequent chapters.
Chapter 2 – A Brief Primer on Metaheuristics, introduces the broad metaheuristics framework and elaborates on two popular genres of metaheuristic methods, namely Evolution Strategy and Differential Evolution Strategy, their approach, algorithms and performance characteristics. This chapter targets readers who are unfamiliar with metaheuristics and therefore the discussion has been deliberately restricted to the aforementioned two genres on which the Portfolio Optimization models discussed in the rest of the book are dependent upon.
Chapter 3 – Heuristic Portfolio Selection, elaborates on how a heuristic algorithm such as k-means clustering can be effectively used to select securities in a portfolio. The heuristic selection has been demonstrated over two benchmark portfolios, which are equal weighted portfolios and inverse volatility weighted portfolios.
Chapter 4 – Metaheuristic Risk Budgeted Portfolio Optimization, details the application of metaheuristics for a popular investment strategy such as Risk Budgeting. Differential Evolution strategy is employed for the optimization of risk budgeted long-short portfolios with the objective of maximizing its Sharpe Ratio.
Chapter 5 – Heuristic Optimization of Equity Market Neutral Portfolios, discusses how metaheuristics can help ensure market-neutral investing, a popular form of investing. A refined version of Differential Evolution strategy is used to optimize equity market neutral portfolios that incorporate risk budgets.
Chapter 6 – Metaheuristic 130-30 Portfolio Construction, elaborates on the application of Differential Evolution Strategy and MATLAB’s Financial ToolboxTM, for the construction of 130-30 portfolios and a comparison of the same with long-only portfolios.
Chapter 7 – Metaheuristic Portfolio Rebalancing with Transaction Costs, discusses the application of Evolution Strategy for rebalancing a portfolio with the additional constraint of curtailing transaction costs and with the objective of maximizing its Diversification Ratio.
Software Download
The MATLAB® demonstrations discussed in this book were implemented using MATLAB® R2011b and MATLAB® R2012 versions. The programs and functions can be downloaded from the MATLAB® Central File Exchange https://www.mathworks.com/matlabcentral/fileexchange/64507-matlab-demonstrations-in-the-book--metaheuristics-for-portfolio-optimization--authored-by-g-a-v-pai
Acknowledgements
The author would like to express her profound gratitude to Thierry Michel, presently Systematic Portfolio Manager, TOBAM, Paris, France, for introducing her to the challenging discipline of Portfolio Optimization, way back in 2006, during the course of his lectures at the CIMPA-UNESCO-IMAMIS School on Financial Information Systems, organized by Centre international de mathématiques pures et appliquées, Nice, France, at Kuala Lumpur, Malaysia. This exciting field in hardcore finance, which eventually turned out to be a fertile ground for applications of algorithms and approaches from the broad field of Computational Intelligence, led to a long, highly productive collaborative stint with Thierry Michel, spanning over a decade and resulting in a spate of research publications in journals and conferences, about 14 in all, besides sanctioning of a funded Major Research Project by University Grants Commission, New Delhi, India, 2011–14, in recognition of the work undertaken in the cross-discipline. The ideas gathered, the rich intellectual experience gained and the lessons learned, the hard way though, metamorphosed into writing a monograph, for the sheer joy of disseminating the knowledge discovered to the research fraternity at large. In all these regards, the unstinted support and help provided by Thierry Michel, during every stage of the saga of learning and research, including finding time to read all the chapters of this monograph and offering valuable suggestions, is gratefully acknowledged.
The author expresses her sincere thanks to Vitaliy Feoktistov, author of Differential Evolution, In search of solutions (Springer, 2006), an inspiring book that influenced several aspects of her work discussed in this book, besides the useful correspondence that emboldened her to observe more freedom with regard to interpretation and application of concepts to the problems in hand, which served to tide over stumbling blocks during her explorations.
The author expresses her grateful thanks to Patrick Siarry, Université de Paris 12, France and Nicolas Monmarché, University of Tours, France, coordinators of the Metaheuristics Set of ISTE Ltd for accepting this book and sharing their reviews and suggestions.
The support extended by the production team of ISTE Ltd is gratefully acknowledged.
The assistance and support provided by The MathWorks, Inc., USA to upload the MATLAB® Demonstrations illustrated in the book in the MATLAB® Central File Exchange and promote its narratives, is sincerely acknowledged.
The explorations that contributed to writing this monograph were undertaken in the Soft Computing Research Laboratory, during the tenure of Major Research Projects sanctioned by the University Grants Commission (UGC), New Delhi, India and All India Council of Technical Education (AICTE), New Delhi, India and thereafter. The state-of-the-art equipment, software and infrastructure support for the laboratory, funded by UGC and AICTE, besides PSG College of Technology, Coimbatore, India, is gratefully acknowledged.
The author places on record her deep admiration for her father, Late Prof G A Krishna Pai, for teaching her things without saying words, her mother Rohini Krishna Pai, for her boundless encouragement and prayers and her sisters, Dr Rekha Pai and Udaya Pai, for their unstinted support and help whenever and wherever she wanted them, without all of which this work would never have fructified.
G.A. Vijayalakshmi Pai
October 2017
