The Use of Risk Budgets in Portfolio Optimization


Book Description

Risk budgeting models set risk diversification as objective in portfolio allocation and are mainly promoted from the asset management industry. Albina Unger examines the portfolios based on different risk measures in several aspects from the academic perspective (Utility, Performance, Risk, Different Market Phases, Robustness, and Factor Exposures) to investigate the use of these models for asset allocation. Beside the risk budgeting models, alternatives of risk-based investment styles are also presented and examined. The results show that equalizing the risk across the assets does not prevent losses, especially in crisis periods and the performance can mainly be explained by exposures to known asset pricing factors. Thus, the advantages of these approaches compared to known minimum risk portfolios are doubtful.




Introduction to Risk Parity and Budgeting


Book Description

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




Portfolio Construction and Risk Budgeting


Book Description

It provides the key concepts and methods to implement quantitatively-driven portfolio construction. Areas include satellite investing, estimation error heuristics, scenario optimisation, mean variance investing, Bayesian methods, budgeting active risk, non-normality and multiple manager allocation. The emphasis is on practical applications and problem-solving written in a highly accessible style. The title contains quantitative analysis that is supported by extensive examples, tables and charts to help practitioners adopt the subject matter in their day-to-day work.




Risk Budgeting Portfolios Under a Modern Optimization and Machine Learning Lens


Book Description

The mean-variance optimization framework has been the traditional approach to decide portfolio allocations based on return-risk trade-offs. However, it faces practical drawbacks, including sensitivity to estimated input parameters and concentration of portfolio risk. Risk budgeting portfolio optimization is a popular risk-based asset allocation technique where risk budgets are assigned to each assets' risk contribution, and equalizing all risk budgets in the portfolio is known as risk parity strategy. Unlike mean-variance, the risk parity strategy provides a balanced risk concentration in the portfolio and does not require expected asset return estimates as input. However, its performance can depend on the selected asset universe. Furthermore, its mathematical formulation imposes some computational challenges due to the non-convex structure.In this thesis, the risk budgeting problem is studied with modern optimization and machine learning approaches to enhance the portfolio model and address the aforementioned challenges. The second chapter introduces regime-switching risk parity portfolios with two primary components: regime modeling and prediction with supervised learning methods and identifying a regime-based strategy to improve the performance of a nominal risk parity portfolio. In the third chapter, we formulate a multi-period risk parity portfolio optimization problem in a transaction cost environment with a model predictive control approach. We provide a successive convex program algorithm that provides faster and more robust solutions. Lastly, we present an end-to-end portfolio allocation method by embedding the risk budget optimization problem as an implicit layer in a neural network. This approach combines prediction and optimization tasks in a single decision-making pipeline and constructs dynamic risk budgeting portfolios. Furthermore, we introduce a novel asset selection property with stochastic gates that protects the risk budgeting portfolio against the unprofitable assets.







Modern Portfolio Optimization with NuOPT™, S-PLUS®, and S+Bayes™


Book Description

Portfolio optimization and construction methodologies have become an critical ingredient of asset and fund management, while at same time portfolio risk assesment has become an essential ingredient in risk management.




A Generalized Risk Budgeting Approach to Portfolio Construction


Book Description

Risk-based asset allocation models have received considerable attention in recent years. This increased popularity is due in part to the difficulty in estimating expected returns as well as the financial crisis of 2008 which has helped reinforce the key role of risk in asset allocation. In this study, we propose a generalized risk budgeting (GRB) approach to portfolio construction. In a GRB portfolio assets are grouped into possibly overlapping subsets and each subset is allocated a pre-specified risk budget. Minimum variance, risk parity and risk budgeting portfolios are all special instances of a GRB portfolio. The GRB portfolio optimization problem is to find a GRB portfolio with an optimal risk-return profile where risk is measured using any positively homogeneous risk measure. When the subsets form a partition, the assets all have the same expected return and we restrict ourselves to long-only portfolios, then the GRB problem can in fact be solved as a convex optimization problem. In general, however, the GRB problem is a constrained non-convex problem, for which we propose two solution approaches. The first approach uses a semidefinite programming (SDP) relaxation to obtain an (upper) bound on the optimal objective function value. In the second approach we develop a numerical algorithm that integrates augmented Lagrangian and Markov chain Monte Carlo (MCMC) methods in order to find a point in the vicinity of a very good local optimum. This point is then supplied to a standard non-linear optimization routine with the goal of finding this local optimum. It should be emphasized that the merit of this second approach is in its generic nature: in particular, it provides a starting-point strategy for any non-linear optimization algorithm.




Efficient Asset Management


Book Description

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.




Risk Budgeting


Book Description

Institutionelle Anleger, Fonds- und Portfoliomanager müssen Risiken eingehen, wenn sie Spitzengewinne erzielen wollen. Die Frage ist nur wieviel Risiko. "Risk Budgeting: Portfolio Problem Solving with VaR" liefert die Antwort auf diese Frage. Beim Konzept des Risk Budgeting geht es um Risiko- und Kapitalallokation auf der Grundlage erwarteter Erträge und Risiken, mit dem Ziel, höhere Renditen zu erwirtschaften im Rahmen eines vordefinierten Gesamtrisikoniveaus. Mit Hilfe quantitativer Methoden zur Risikomessung, einschließlich der Value at Risk-Methode läßt sich das Risiko ermitteln und bewerten. Value at Risk (VaR) ist ein Verfahren zur Risikobewertung, das Banken ursprünglich zur Messung und Begrenzung von Marktpreisrisiken eingesetzt haben. Heute wird die VaR-Methode auch verstärkt im Risikomanagement eingesetzt. Dieses Buch bietet eine fundierte Einführung in die VaR-Methode sowie in Verfahren zur Risikomessung bei Extremereignissen und Krisenszenarien (Stress Testing). Darüber hinaus erklärt es, wie man mit Hilfe des Risk Budgeting ein effizienteres Portfoliomanagement erreicht. "Risk Budgeting: Portfolio Problem Solving with VaR" ist das einzige Buch auf dem Markt, das Risk Budgeting und VaR - zwei brandaktuelle Themen im Portfoliomanagement - speziell für institutionelle Investment- und Portfolio-Manager aufbereitet. Eine unverzichtbare Lektüre.




Robust Portfolio Optimization and Management


Book Description

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