{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/constrained-risk-budgeting-portfolios-theory","title":"Constrained Risk Budgeting Portfolios: Theory, Algorithms, Applications & Puzzles","arxiv_id":"1902.05710","date":"2019-02-15","proceeding":null,"authors":[],"abstract":"This article develops the theory of risk budgeting portfolios, when we would\nlike to impose weight constraints. It appears that the mathematical problem is\nmore complex than the traditional risk budgeting problem. The formulation of\nthe optimization program is particularly critical in order to determine the\nright risk budgeting portfolio. We also show that numerical solutions can be\nfound using methods that are used in large-scale machine learning problems.\nIndeed, we develop an algorithm that mixes the method of cyclical coordinate\ndescent (CCD), alternating direction method of multipliers (ADMM), proximal\noperators and Dykstra's algorithm. This theoretical body is then applied to\nsome investment problems. In particular, we show how to dynamically control the\nturnover of a risk parity portfolio and how to build smart beta portfolios\nbased on the ERC approach by improving the liquidity of the portfolio or\nreducing the small cap bias. Finally, we highlight the importance of the\nhomogeneity property of risk measures and discuss the related scaling puzzle.","url_abs":"http://arxiv.org/abs/1902.05710v1","url_pdf":"http://arxiv.org/pdf/1902.05710v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"constrained-risk-budgeting-portfolios-theory","repo_url":"https://github.com/jcrichard/pyrb","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"admm","method_name":"ADMM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}