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The risk parity portfolio selection problem aims to find such portfolios for which the contributions of risk from all assets are equally weighted. Portfolios constructed using the risk parity approach are a compromise between two well-known diversification techniques: minimum variance optimization and the equal weighting approach. In this paper, we discuss the problem of finding portfolios that satisfy risk parity over 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 an exponential number of solutions. We then propose an alternative non-convex least-squares 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 a given criterion. When general bounds are considered, a risk parity solution may not exist. In this case, the non-convex least-squares model seeks a feasible portfolio which is as close to risk parity as possible. Furthermore, we propose an alternating linearization framework to solve this non-convex model. Numerical experiments indicate the effectiveness of our technique in terms of both speed and accuracy.
Gérard Cornuéjols合作论文数Department of Mathematical Sciences, Mellon College of Science, Carnegie Mellon University;Tepper School of Business, Carnegie Mellon University29
Javier F. Peña合作论文数Operations Management Faculty, Tepper School of Business, Carnegie Mellon University;Mathematical Sciences, Mellon College of Science, Carnegie Mellon University17
Michael J. Todd合作论文数School of Operations Research and Information Engineering, Cornell University9
Kim-Chuan Toh (卓金全)合作论文数Department of Mathematics, Faculty of Science, National University of Singapore;Department of Analytics & Operations, Business School, National University of Singapore7
Ana M. Monteiro合作论文数2
Raphael Hauser合作论文数Mathematical Institute, University of Oxford;The National Institute for Data Science and Artificial Intelligence, Alan Turing Institute of Data Science2
Steven E Shreve合作论文数Finance Faculty, Tepper School of Business, Carnegie Mellon University2
Luis Vicente合作论文数Departamento de Matemática Coimbra, Universidade de Coimbra2Manos Hatzakis合作论文数1
Xi Bai (白晰)合作论文数1
Andreas Waechter合作论文数Industrial Engineering and Management Sciences, McCormick School of Engineering and Applied Science, Northwestern University1
Akiko Takeda合作论文数1
Dmitry Kramkov合作论文数Mathematical Sciences, Mellon College of Science, Carnegie Mellon University/Center for Computational Finance, Carnegie Mellon University1
Bjarni V. Halldórsson合作论文数CODE Genet, de1Arturo M. Cervantes合作论文数1
Katya Scheinberg合作论文数School of Operations Research and Information Engineering, Cornell University1
Kasper Larsen合作论文数Department of Mathematical Sciences,Carnegie Mellon University1
Catalin Starica合作论文数university of gothenburg1
Mustafa Ç. Pinar合作论文数cited by collaborative colleagues1
Traian A. Pirvu合作论文数Department of Mathematics and Statistics, McMaster University1
Lorenz T. Biegler (洛伦茨·比格勒)合作论文数Chemical Engineering Department, Carnegie Mellon University1
Stefano Herzel合作论文数Department of Economics;University of Perugia1
