Least-Squares Approach to Risk Parity in Portfolio Selection PDF Download

Author: Bai, Xi
Publisher:
ISBN:
Category :
Languages : en
Pages : 27

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Book Description
The risk parity optimization problem aims to find such portfolios for which the contributions of risk from all assets are equally weighted. Portfolios constructed using risk parity approach are a compromise between two well-known diversification techniques: minimum variance optimization approach and the equal weighting approach. In this paper, we discuss the problem of finding portfolios that satisfy risk parity of either individual assets or groups of assets. We describe the set of all risk parity solutions by using convex optimization techniques over orthants and we show that this set may contain exponential number of solutions. We then propose an alternative nonconvex least-square model whose set of optimal solutions includes all risk parity solutions, and propose a modified formulation which aims at selecting the most desirable risk parity solution (according to some criteria). When general bounds are considered, a risk parity solution may not exist. The nonconvex least-square model then seeks a feasible portfolio which is as close to risk parity as possible. Furthermore, we propose an alternating linearization framework to solve this nonconvex model. Numerical experiments indicate the effectiveness of our technique in terms of both speed and accuracy.

Author: Francesco Cesarone
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
Risk Parity (RP), also called equally weighted risk contribution, is a recent approach to risk diversification for portfolio selection. RP is based on the principle that the fractions of the capital invested in each asset should be chosen so as to make the total risk contributions of all assets equal among them. We show here that the Risk Parity approach is theoretically dominated by an alternative similar approach that does not actually require equally weighted risk contribution of all assets but only an equal upper bound on all such risks. This alternative approach, called Equal Risk Bounding (ERB), requires the solution of a nonconvex quadratically constrained optimization problem. The ERB approach, while starting from different requirements, turns out to be strictly linked to the RP approach. Indeed, when short selling is allowed, we prove that an ERB portfolio is actually an RP portfolio with minimum variance. When short selling is not allowed, there is a unique RP portfolio and it contains all assets in the market. In this case, the ERB approach might lead to the RP portfolio or it might lead to portfolios with smaller variance that do not contain all assets, and where the risk contributions of each asset included in the portfolio is strictly smaller than in the RP portfolio. We define a new riskiness index for assets that allows to identify those assets that are more likely to be excluded from the ERB portfolio. With these tools we then provide an exact method for small size nonconvex ERB models and a very efficient and accurate heuristic for larger problems of this type. In the case of a common constant pairwise correlation among all assets, a closed form solution to the ERB model is obtained and used to perform a parametric analysis when varying the level of correlation. The practical advantages of the ERB approach over the RP strategy are illustrated with some numerical examples. Computational experience on real-world and on simulated data confirms accuracy and efficiency of our heuristic approach to the ERB model also in comparison with some state-of-the-art local and global optimization codes.

Author: BlackRock, Inc.
Publisher: John Wiley & Sons
ISBN: 111988487X
Category : Business & Economics
Languages : en
Pages : 455

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Book Description
An irreplaceable roadmap to modern risk management from renowned experts on the subject Edited by a co-founder and the former Chief Risk Officer of BlackRock—the world’s largest asset manager—BlackRock’s Guide to Fixed-Income Risk Management delivers an insightful blueprint to the implementation of a comprehensive investment risk management framework for buy-side firms. Leveraging the unprecedented academic and professional experience of current and former senior leaders in BlackRock’s risk and portfolio management functions, as well as trading, financial modeling, and analytics experts, the book serves a practitioner’s guide to investment risk management, leveraging BlackRock’s risk management framework. The included chapters combine to provide chief investment officers, risk managers, portfolio managers, researchers, and compliance professionals an approach to investment risk management well-suited for today's and tomorrow's markets. The book also presents: Critical elements that underpin a strong risk management program and culture Fixed income risk management concepts and theories that can be applied to other asset classes Lessons learned from financial crises and the COVID-19 Pandemic Ideal for undergraduate students and students and scholars of business, finance, and risk management, BlackRock’s Guide to Fixed-Income Risk Management is a one-of-a-kind combination of modern theory with proven, practical risk management strategies.

Author: Dirk Tasche
Publisher:
ISBN:
Category :
Languages : en
Pages : 22

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Book Description
An evergreen debate in Finance concerns the rules for making portfolio hedge decisions. A traditional tool proposed in the literature is the well-known standard deviation based Sharpe Ratio, which has been recently generalized in order to involve also other popular risk measures p, such as VaR (Value-at-Risk) or CVaR (Conditional Value at Risk). This approach gives the correct choice of portfolio selection in a mean-p world as long as p is homogeneous of order 1. But, unfortunately, in important cases calculating the exact incremental Sharpe Ratio for ranking profitable portfolios turns out to be computationally too costly. Therefore, more easy-to-use rules for a rapid portfolio selection are needed. The research in this direction for VaR is just the aim of the paper. Approximation formulae are carried out which are based on certain derivatives of VaR and involve quantities similar to the skewness and kurtosis of the random variables under consid-eration. Starting point for the approximations is the observation that the partial derivatives of portfolio VaR with respect to the portfolio weights are just the conditional expectations of the asset returns given that the portfolio return equals VaR. Since the conditional expec-tation of a random variable Y given another random variable X can be considered the best possible regression of Y versus X in least squares sense, the idea is to replace the conditional expectation by polynomial regression or, more generally, by finite-dimensional regression of Y versus X. In case of the variables obeying an elliptical joint distribution, the resulting approximation formulae coincide with the exact formula for the standard deviation taken as risk measure. By means of a number of numerical examples and counter-examples the properties of the formulae are discussed.

Author: Florian Ielpo
Publisher: Elsevier
ISBN: 0081011482
Category : Business & Economics
Languages : en
Pages : 432

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Book Description
Engineering Investment Process: Making Value Creation Repeatable explores the quantitative steps of a financial investment process. The authors study how these steps are articulated in order to make any value creation, whatever the asset class, consistent and robust. The discussion includes factors, portfolio allocation, statistical and economic backtesting, but also the influence of negative rates, dynamical trading, state-space models, stylized facts, liquidity issues, or data biases. Besides the quantitative concepts detailed here, the reader will find useful references to other works to develop an in-depth understanding of an investment process. - Blends academic research with practical experience from quants, fund managers, and economists - Puts financial mathematics and econometrics in their rightful place - Presents useful information that will increase the reader's understanding of markets - Clearly provides both the global framework, the investment process, and the useful econometric and financial tools that help in its construction - Includes efficient tools taken from up-to-date econometric and financial techniques

Author: Steven E. Pav
Publisher: CRC Press
ISBN: 1000442713
Category : Business & Economics
Languages : en
Pages : 498

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Book Description
The Sharpe Ratio: Statistics and Applications is the most widely used metric for comparing the performance of financial assets. The Markowitz portfolio is the portfolio with the highest Sharpe ratio. The Sharpe Ratio: Statistics and Applications examines the statistical properties of the Sharpe ratio and Markowitz portfolio, both under the simplifying assumption of Gaussian returns, and asymptotically. Connections are drawn between the financial measures and classical statistics including Student's t, Hotelling's T^2 and the Hotelling-Lawley trace. The robustness of these statistics to heteroskedasticity, autocorrelation, fat tails and skew of returns are considered. The construction of portfolios to maximize the Sharpe is expanded from the usual static unconditional model to include subspace constraints, hedging out assets, and the use of conditioning information on both expected returns and risk. The Sharpe Ratio: Statistics and Applications is the most comprehensive treatment of the statistical properties of the Sharpe ratio and Markowitz portfolio ever published. Features: 1. Material on single asset problems, market timing, unconditional and conditional portfolio problems, hedged portfolios. 2. Inference via both Frequentist and Bayesian paradigms. 3. A comprehensive treatment of overoptimism and overfitting of trading strategies. 4. Advice on backtesting strategies. 5. Dozens of examples and hundreds of exercises for self study. The Sharpe Ratio: Statistics and Applications is an essential reference for the practicing quant strategist and the researcher alike, and an invaluable textbook for the student.

Author: Fabio Bellini
Publisher:
ISBN:
Category :
Languages : en
Pages : 29

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Book Description
A recent popular approach to portfolio selection aims at diversifying risk by looking for the so called Risk Parity portfolios. These are defined by the condition that the risk contributions of all assets to the global risk of the portfolio are equal. The Risk Parity approach has been originally introduced for the volatility risk measure. In this paper we consider expectiles as risk measures, we refine results on their differentiability and additivity, and we show how to define Risk Parity portfolios when the expectiles are used as coherent risk measures. Furthermore, we propose several methods for practically finding Risk Parity portfolios with respect to expectiles and we compare their accuracy and efficiency on real-world data. Expectiles are also used as risk measures in the classical risk-return approach to portfolio selection, where we present a new linear programming formulation.

Author: Daniel Haesen
Publisher:
ISBN:
Category :
Languages : en
Pages : 34

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Book Description
Within the finance literature there is an apparent gap between the inherent risk premium ignorance of a risk parity approach on the one hand and the assumed risk premium clairvoyance of a mean variance approach on the other. We propose a portfolio selection framework that allows an investor to position herself between these two extremes. Depending on the confidence in one's risk premium estimates, the optimal portfolio will be tilted more towards the risk parity portfolio or to the mean variance portfolio. We illustrate the framework for an investor in an asset allocation context.

Author: Edward E. Qian
Publisher: CRC Press
ISBN: 149873880X
Category : Business & Economics
Languages : en
Pages : 245

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Book Description
Written by an experienced researcher and portfolio manager who coined the term "risk parity," this book provides readers with a practical understanding of the risk parity investment approach. It uses fundamental, quantitative, and historical analysis to address the merit of risk parity as well as the practical and underlying aspects of risk parity investing. Requiring no advanced degrees in quantitative fields, the book analyzes risk parity performance from historical periods and more recent market environments.

Author: Hui Yang
Publisher: Springer Nature
ISBN: 303075166X
Category : Business & Economics
Languages : en
Pages : 474

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Book Description
This volume offers the state-of-the-art research and developments in service science and related research, education and practice areas. It showcases emerging technology and applications in fields including healthcare, energy, finance, information technology, transportation, sports, logistics, and public services. Regardless of size and service, a service organization is a service system. Because of the socio-technical nature of a service system, a systems approach must be adopted to design, develop, and deliver services, aimed at meeting end users’ both utilitarian and socio-psychological needs. Effective understanding of service and service systems often requires combining multiple methods to consider how interactions of people, technology, organizations, and information create value under various conditions. Chapters highlight ways to approach such technical challenges in service science and are based on submissions from the 2020 INFORMS International Conference on Service Science.