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Resolution of Optimization Problems and Construction of Efficient Portfolios

Resolution of Optimization Problems and Construction of Efficient Portfolios
Author: Victor Adame-Garcia
Publisher:
Total Pages: 43
Release: 2017
Genre:
ISBN:
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We assess the effectiveness of various portfolio optimization strategies (only long allocations) applied to the components of the Euro Stoxx 50 index during the period 2002-2015. The sample under study contemplates episodes of high volatility and instability in financial markets, such as the Global Financial Crisis and the European Debt Crisis. This implies a real challenge in portfolio optimization strategies, since all the methodologies used are restricted to the assignment of positive weights. We use the daily returns for the asset allocation with a three year estimation window, keeping the assets in portfolio for one year.In the context of strategies with short-selling constraints, we contribute to the debate on whether naive diversification proves to be an effective alternative for the construction of the portfolio, as opposed to the portfolio optimization models. To that end, we analyse the out-of-sample performance of 16 strategies for the selection of assets and weights in the main stock index of the euro area. Our results suggest that a large number of strategies outperform both the naive strategy and the Euro Stoxx 50 index in terms of the profitability and Sharpe's ratio. Furthermore, the portfolio strategy based on the maximization of the diversification ratio provides the highest return and the classical strategy of mean-variance renders the highest Sharpe ratio, which is statistically different from the Euro Stoxx 50 index in the period under study.

Robust Portfolio Optimization and Management

Robust Portfolio Optimization and Management
Author: Frank J. Fabozzi
Publisher: John Wiley & Sons
Total Pages: 513
Release: 2007-04-27
Genre: Business & Economics
ISBN: 0470164891
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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

Efficient Asset Management

Efficient Asset Management
Author: Richard O. Michaud
Publisher: Oxford University Press
Total Pages: 145
Release: 2008-03-03
Genre: Business & Economics
ISBN: 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.

Linear and Mixed Integer Programming for Portfolio Optimization

Linear and Mixed Integer Programming for Portfolio Optimization
Author: Renata Mansini
Publisher: Springer
Total Pages: 131
Release: 2015-06-10
Genre: Business & Economics
ISBN: 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.

Portfolio Optimization

Portfolio Optimization
Author: Michael J. Best
Publisher: CRC Press
Total Pages: 238
Release: 2010-03-09
Genre: Mathematics
ISBN: 1420085840
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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 CD-ROM.

Implementation of Efficient Frontier in Portfolio Optimization

Implementation of Efficient Frontier in Portfolio Optimization
Author: Rowland Bismark Pasaribu
Publisher:
Total Pages:
Release: 2017
Genre:
ISBN:
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Traditionally, risky assets and risk-less asset are treated as two distinct classes. Observing the Indonesian liquid stock with very close maturity dates, we view risk-less asset as its natural limit. This unifying viewpoint is not only theoretically appealing, but also practically important. The purpose of research are to recapitulate the single-period results of Markowitz and Sharpe in the context of iso-elastic utility, and formally derive the solution to the unconstrained optimization problem and examine the mathematical properties of the resulting efficient frontier and efficient portfolios. This work relieves the burden of constructing efficient frontiers in asset allocation problems. More important, removing the restriction posed by the efficient frontiers, it allows for much better asset allocation decisions than the traditional methods.

Metaheuristic Approaches to Portfolio Optimization

Metaheuristic Approaches to Portfolio Optimization
Author: Ray, Jhuma
Publisher: IGI Global
Total Pages: 263
Release: 2019-06-22
Genre: Business & Economics
ISBN: 1522581049
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Control of an impartial balance between risks and returns has become important for investors, and having a combination of financial instruments within a portfolio is an advantage. Portfolio management has thus become very important for reaching a resolution in high-risk investment opportunities and addressing the risk-reward tradeoff by maximizing returns and minimizing risks within a given investment period for a variety of assets. Metaheuristic Approaches to Portfolio Optimization is an essential reference source that examines the proper selection of financial instruments in a financial portfolio management scenario in terms of metaheuristic approaches. It also explores common measures used for the evaluation of risks/returns of portfolios in real-life situations. Featuring research on topics such as closed-end funds, asset allocation, and risk-return paradigm, this book is ideally designed for investors, financial professionals, money managers, accountants, students, professionals, and researchers.

Portfolio Management with Heuristic Optimization

Portfolio Management with Heuristic Optimization
Author: Dietmar G. Maringer
Publisher: Springer
Total Pages: 0
Release: 2011-01-05
Genre: Business & Economics
ISBN: 9781441938428
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Portfolio Management with Heuristic Optimization consist of two parts. The first part (Foundations) deals with the foundations of portfolio optimization, its assumptions, approaches and the limitations when "traditional" optimization techniques are to be applied. In addition, the basic concepts of several heuristic optimization techniques are presented along with examples of how to implement them for financial optimization problems. The second part (Applications and Contributions) consists of five chapters, covering different problems in financial optimization: the effects of (linear, proportional and combined) transaction costs together with integer constraints and limitations on the initital endowment to be invested; the diversification in small portfolios; the effect of cardinality constraints on the Markowitz efficient line; the effects (and hidden risks) of Value-at-Risk when used the relevant risk constraint; the problem factor selection for the Arbitrage Pricing Theory.

Multi-objective Evolutionary Methods for Time-changing Portfolio Optimization Problems

Multi-objective Evolutionary Methods for Time-changing Portfolio Optimization Problems
Author: Iason Hatzakis
Publisher:
Total Pages: 79
Release: 2007
Genre:
ISBN:
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This thesis is focused on the discovery of efficient asset allocations with the use of evolutionary algorithms. The portfolio optimization problem is a multi-objective optimization problem for the conflicting criteria of risk and expected return. Furthermore the nonstationary nature of the market makes it a time-changing problem in which the optimal solution is likely to change as time advances. Hence the portfolio optimization problem naturally lends itself to an exploration with multi-objective evolutionary algorithms for time-changing environments. Two different risk objectives are treated in this work: the established measure of standard deviation, and the Value-at-Risk. While standard deviation is convex as an objective function, historical Value-at-Risk is non-convex and often discontinuous, making it difficult to approach with most conventional optimization techniques. The value of evolutionary algorithms is demonstrated in this case by their ability to handle the Value-at-Risk objective, since they do not have any convexity or differentiability requirements. The D-QMOO time-changing evolutionary algorithm is applied to the portfolio optimization problem. Part of the philosophy behind D-QMOO is the exploitation of predictability in the optimal solution's motion. This problem however is characterized by minimal or non-existent predictability, since asset prices are hard to forecast. This encourages the development of new time-changing optimization heuristics for the efficient solution of this problem. Both the static and time-changing forms of the problem are treated and characteristic results are presented. The methodologies proposed are verified through comparison with established methods and through the performance of the produced portfolios as compared to the overall market. In general, this work demonstrates the potential for the use of evolutionary algorithms in time-changing portfolio optimization as a tool for portfolio managers and financial engineers.

Multicriteria Portfolio Construction with Python

Multicriteria Portfolio Construction with Python
Author: Elissaios Sarmas
Publisher: Springer Nature
Total Pages: 176
Release: 2020-10-17
Genre: Business & Economics
ISBN: 3030537439
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This book covers topics in portfolio management and multicriteria decision analysis (MCDA), presenting a transparent and unified methodology for the portfolio construction process. The most important feature of the book includes the proposed methodological framework that integrates two individual subsystems, the portfolio selection subsystem and the portfolio optimization subsystem. An additional highlight of the book includes the detailed, step-by-step implementation of the proposed multicriteria algorithms in Python. The implementation is presented in detail; each step is elaborately described, from the input of the data to the extraction of the results. Algorithms are organized into small cells of code, accompanied by targeted remarks and comments, in order to help the reader to fully understand their mechanics. Readers are provided with a link to access the source code through GitHub. This Work may also be considered as a reference which presents the state-of-art research on portfolio construction with multiple and complex investment objectives and constraints. The book consists of eight chapters. A brief introduction is provided in Chapter 1. The fundamental issues of modern portfolio theory are discussed in Chapter 2. In Chapter 3, the various multicriteria decision aid methods, either discrete or continuous, are concisely described. In Chapter 4, a comprehensive review of the published literature in the field of multicriteria portfolio management is considered. In Chapter 5, an integrated and original multicriteria portfolio construction methodology is developed. Chapter 6 presents the web-based information system, in which the suggested methodological framework has been implemented. In Chapter 7, the experimental application of the proposed methodology is discussed and in Chapter 8, the authors provide overall conclusions. The readership of the book aims to be a diverse group, including fund managers, risk managers, investment advisors, bankers, private investors, analytics scientists, operations researchers scientists, and computer engineers, to name just several. Portions of the book may be used as instructional for either advanced undergraduate or post-graduate courses in investment analysis, portfolio engineering, decision science, computer science, or financial engineering.