Dynamic Portfolio Choice With Linear Rebalancing Rules
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| Author | : Ciamac C. Moallemi |
| Publisher | : |
| Total Pages | : 59 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
We consider a broad class of dynamic portfolio optimization problems that allow for complex models of return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. We propose a class of linear rebalancing rules, and describe an efficient computational procedure to optimize with this class. We illustrate this method in the context of portfolio execution, and show that it achieves near optimal performance. We consider another numerical example involving dynamic trading with mean-variance preferences and demonstrate that our method can result in economically large benefits.
| Author | : Letian Ding |
| Publisher | : |
| Total Pages | : 25 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
This paper develops a framework for constructing portfolios with superior out-of-sample performance in the presence of estimation errors. Our framework relies on solving the classical mean-variance problem with dynamic portfolio rebalancing at a comparatively-high frequency level. With the employment of A-DCC GARCH model, we found that the usage of turnover constraints will tend to enhance the performance of the portfolios sufficiently high to overcome transaction costs in practice. For a long-only optimal portfolio based on a linear combination of two different strategies we find a return exceeding 51% per annual with annual volatility equal to 35% over the 1998-2007 period. We argue that the advantage of our framework comes from the mean-reverting nature of the stock market and the impact of the estimation errors in high frequency level. Our works indicate that one can successfully move from ordinary monthly or weekly adjusting strategies to high frequency and dynamic asset management without the significant increase of transaction costs.
| Author | : Poomyos Wimonkittiwat |
| Publisher | : |
| Total Pages | : 95 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
We study two important generalizations of dynamic portfolio choice problems: a portfolio choice problem with market impact costs and a portfolio choice problem under the Hidden Markov Model. In the first problem, we allow the presence of market impact and illiquidity. Illiquidity and market impact refer to the situation where it may be costly or difficult to trade a desired quantity of assets over a desire period of time. In this work, we formulate a simple model of dynamic portfolio choice that incorporates liquidity effects. The resulting problem is a stochastic linear quadratic control problem where liquidity costs are modeled as a quadratic penalty on the trading rate. Though easily computable via Riccati equations, we also derive a multiple time scale asymptotic expansion of the value function and optimal trading rate in the regime of vanishing market impact costs. This expansion reveals an interesting but intuitive relationship between the optimal trading rate for the illiquid problem and the classical Merton model for dynamic portfolio selection in perfectly liquid markets. It also gives rise to the notion of a liquidity time scale. Furthermore, the solution to our illiquid portfolio problem shows promising performance and robustness properties. In the second problem, we study dynamic portfolio choice problems under regime switching market. We assume the market follows the Hidden Markov Model with unknown transition probabilities and unknown observation statistics. The main difficulty of this dynamic programming problem is its high-dimensional state variables. The joint probability density function of the hidden regimes and the unknown quantities is part of the state variables, and this makes the problem suffer from the curse of dimensionality. Though the problem cannot be solved by any standard fashions, we propose approximate methods that tractably solve the problem. The key is to approximate the value function by that of a simpler problem where the regime is not hidden and the parameters are observable (the C-problem). This approximation allows the optimal portfolio to be computed in a semi-explicit way. The approximate solution shares the same structure with the solution of C-problem, but at the same time it provides clear insight into the unobservable extension. In addition, the performance of the proposed methods is reasonably close to the upper-bound obtained from the information relaxation problem.
| Author | : Giorgio Consigli |
| Publisher | : Springer |
| Total Pages | : 310 |
| Release | : 2016-10-17 |
| Genre | : Business & Economics |
| ISBN | : 3319416138 |
The scope of this volume is primarily to analyze from different methodological perspectives similar valuation and optimization problems arising in financial applications, aimed at facilitating a theoretical and computational integration between methods largely regarded as alternatives. Increasingly in recent years, financial management problems such as strategic asset allocation, asset-liability management, as well as asset pricing problems, have been presented in the literature adopting formulation and solution approaches rooted in stochastic programming, robust optimization, stochastic dynamic programming (including approximate SDP) methods, as well as policy rule optimization, heuristic approaches and others. The aim of the volume is to facilitate the comprehension of the modeling and methodological potentials of those methods, thus their common assumptions and peculiarities, relying on similar financial problems. The volume will address different valuation problems common in finance related to: asset pricing, optimal portfolio management, risk measurement, risk control and asset-liability management. The volume features chapters of theoretical and practical relevance clarifying recent advances in the associated applied field from different standpoints, relying on similar valuation problems and, as mentioned, facilitating a mutual and beneficial methodological and theoretical knowledge transfer. The distinctive aspects of the volume can be summarized as follows: Strong benchmarking philosophy, with contributors explicitly asked to underline current limits and desirable developments in their areas. Theoretical contributions, aimed at advancing the state-of-the-art in the given domain with a clear potential for applications The inclusion of an algorithmic-computational discussion of issues arising on similar valuation problems across different methods. Variety of applications: rarely is it possible within a single volume to consider and analyze different, and possibly competing, alternative optimization techniques applied to well-identified financial valuation problems. Clear definition of the current state-of-the-art in each methodological and applied area to facilitate future research directions.
| Author | : Renata Mansini |
| Publisher | : Springer |
| Total Pages | : 131 |
| Release | : 2015-06-10 |
| Genre | : Business & Economics |
| ISBN | : 3319184822 |
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.
| Author | : Brian Thomas |
| Publisher | : Columbia University Press |
| Total Pages | : 273 |
| Release | : 2016-11-22 |
| Genre | : Business & Economics |
| ISBN | : 0231540841 |
Featuring interviews with topflight scholars discussing their work and that of their colleagues, this retrospective of the first hundred years of Columbia Business School recounts the role of the preeminent institution in transforming education, industry, and global society. From its early years as the birthplace of value investing to its seminal influence on Warren Buffett and Benjamin Graham, the school has been a profound incubator of ideas and talent, determining the direction of American business. In ten chapters, each representing a single subject of the school's research, senior faculty members recount the collaborative efforts and innovative approaches that led to revolutionary business methods in fields like finance, economics, and accounting. They describe the pioneering work that helped create new quantitative and stochastic tools to enhance corporate decision making, and they revisit the groundbreaking twentieth-century marketing and management paradigms that continue to affect the fundamentals of global business. The volume profiles several prominent centers and programs that have helped the school adapt to recent advancements in international business, entrepreneurship, and social enterprise. Columbia Business School has long offered its diverse students access to the best leaders and thinkers in the industry. This book not only reflects on these relationships but also imagines what might be accomplished in the next hundred years.
| Author | : Stephen Boyd |
| Publisher | : |
| Total Pages | : 92 |
| Release | : 2017-07-28 |
| Genre | : Mathematics |
| ISBN | : 9781680833287 |
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.
| Author | : F. Spinnewyn |
| Publisher | : |
| Total Pages | : 60 |
| Release | : 1974 |
| Genre | : |
| ISBN | : |
| Author | : Nikolai Dokuchaev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 232 |
| Release | : 2002-01-31 |
| Genre | : Business & Economics |
| ISBN | : 9780792376484 |
An investigation of optimal investment problems for stochastic financial market models, this book is addressed to academics and students who are interested in the mathematics of finance, stochastic processes and optimal control. It should also be useful to practitioners in risk management and quantitative analysis who are interested in new strategies and methods of stochastic analysis.
| Author | : Richard O. Michaud |
| Publisher | : Oxford University Press |
| Total Pages | : 207 |
| Release | : 2008-03-03 |
| Genre | : Business & Economics |
| ISBN | : 0199887195 |
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.
