Download or read book Least Squares Approach to Risk Parity in Portfolio Selection written by Bai, Xi and published by . This book was released on 2016 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Equal Risk Bounding Is Better Than Risk Parity for Portfolio Selection written by Francesco Cesarone and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book BlackRock s Guide to Fixed Income Risk Management written by BlackRock, Inc. and published by John Wiley & Sons. This book was released on 2023-10-31 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Approximations for the Value at Risk Approach to Risk Return Analysis written by Dirk Tasche and published by . This book was released on 2014 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Engineering Investment Process written by Florian Ielpo and published by Elsevier. This book was released on 2017-03-22 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book The Sharpe Ratio written by Steven E. Pav and published by CRC Press. This book was released on 2021-09-22 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Risk Parity with Expectiles written by Fabio Bellini and published by . This book was released on 2019 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Enhancing Risk Parity by Including Views written by Daniel Haesen and published by . This book was released on 2016 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Risk Parity Fundamentals written by Edward E. Qian and published by CRC Press. This book was released on 2016-02-10 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book AI and Analytics for Public Health written by Hui Yang and published by Springer Nature. This book was released on 2022-01-03 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Artificial Intelligence written by Marco Antonio Aceves-Fernandez and published by BoD – Books on Demand. This book was released on 2018-06-27 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artificial intelligence (AI) is taking an increasingly important role in our society. From cars, smartphones, airplanes, consumer applications, and even medical equipment, the impact of AI is changing the world around us. The ability of machines to demonstrate advanced cognitive skills in taking decisions, learn and perceive the environment, predict certain behavior, and process written or spoken languages, among other skills, makes this discipline of paramount importance in today's world. Although AI is changing the world for the better in many applications, it also comes with its challenges. This book encompasses many applications as well as new techniques, challenges, and opportunities in this fascinating area.

Download or read book Introduction to Risk Parity and Budgeting written by Thierry Roncalli and published by CRC Press. This book was released on 2016-04-19 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Minimum Risk Vs Capital and Risk Diversification Strategies for Portfolio Construction written by Francesco Cesarone and published by . This book was released on 2015 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we propose an extensive empirical analysis on three different categories of portfolio selection models, each focused on different objectives: minimization of risk, maximization of capital diversification, and uniform distribution of risk allocation. This latter approach, also called Risk Parity (RP) or Equal Risk Contribution (ERC), is a recent strategy for asset allocation, where the risk measure commonly used to select RP portfolios is volatility. We propose here new developments on the ERC approach based on Conditional Value-at-Risk as risk measure.We investigate how these classes of portfolio models (Minimum-Risk, Capital and Risk Diversification) work on seven investment universes, each with different sources of risk, which consist of equities, bonds and mixed assets. Then we highlight some strengths and weaknesses of all portfolio strategies in terms of various performance measures.

Download or read book Hierarchical Bayes Methods for Market Model Estimation and Portfolio Selection written by Martin R. Young and published by . This book was released on 1997 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applications of Evolutionary Computation written by Antonio M. Mora and published by Springer. This book was released on 2015-03-16 with total page 914 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed conference proceedings of the 18th International Conference on the Applications of Evolutionary Computation, EvoApplications 2015, held in Copenhagen, Spain, in April 2015, colocated with the Evo 2015 events EuroGP, EvoCOP, and EvoMUSART. The 72 revised full papers presented were carefully reviewed and selected from 125 submissions. EvoApplications 2015 consisted of the following 13 tracks: EvoBIO (evolutionary computation, machine learning and data mining in computational biology), EvoCOMNET (nature-inspired techniques for telecommunication networks and other parallel and distributed systems), EvoCOMPLEX (evolutionary algorithms and complex systems), EvoENERGY (evolutionary computation in energy applications), EvoFIN (evolutionary and natural computation in finance and economics), EvoGAMES (bio-inspired algorithms in games), EvoIASP (evolutionary computation in image analysis, signal processing, and pattern recognition), EvoINDUSTRY (nature-inspired techniques in industrial settings), EvoNUM (bio-inspired algorithms for continuous parameter optimization), EvoPAR (parallel implementation of evolutionary algorithms), EvoRISK (computational intelligence for risk management, security and defence applications), EvoROBOT (evolutionary computation in robotics), and EvoSTOC (evolutionary algorithms in stochastic and dynamic environments).

Download or read book Advances and Trends in Optimization with Engineering Applications written by Tamas Terlaky and published by SIAM. This book was released on 2017-04-26 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques. In recent years, the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications. Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area and discusses a range of real-world problems. The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand the importance of optimization methods to engineering and the capabilities of these methods.

Download or read book A Multi Greedy Approach to Optimal Diversified Portfolio Selection written by Francesco Cesarone and published by . This book was released on 2018 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical approaches to optimal portfolio selection call for finding a feasible portfolio that optimizes a risk measure, or a gain measure, or a combination thereof by means of a utility function or of a performance measure. However, the optimization approach tends to amplify the estimation errors on the parameters required by the model, such as expected returns and covariances. For this reason, the risk parity model, a novel risk diversification approach to portfolio selection, has been recently theoretically developed and used in practice, mainly for the case of the volatility risk measure.Here we first provide new theoretical results for the risk parity approach for general risk measures. Then we propose a novel framework for portfolio selection that combines the diversification and the optimization approaches through the solution of a hard nonlinear mixed integer or pseudo Boolean problem. For the latter problem we propose an efficient and accurate Multi-Greedy heuristic that extends the classical single-threaded greedy approach to a multiple-threaded setting. Finally, we provide empirical results on real-world data showing that the diversified optimal portfolios are only slightly suboptimal in-sample with respect to optimal portfolios, and generally show improved out-of-sample performance with respect to their purely diversified or purely optimized counterparts.