IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1902.05710.html
   My bibliography  Save this paper

Constrained Risk Budgeting Portfolios: Theory, Algorithms, Applications & Puzzles

Author

Listed:
  • Jean-Charles Richard
  • Thierry Roncalli

Abstract

This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the optimization program is particularly critical in order to determine the right risk budgeting portfolio. We also show that numerical solutions can be found using methods that are used in large-scale machine learning problems. Indeed, we develop an algorithm that mixes the method of cyclical coordinate descent (CCD), alternating direction method of multipliers (ADMM), proximal operators and Dykstra's algorithm. This theoretical body is then applied to some investment problems. In particular, we show how to dynamically control the turnover of a risk parity portfolio and how to build smart beta portfolios based on the ERC approach by improving the liquidity of the portfolio or reducing the small cap bias. Finally, we highlight the importance of the homogeneity property of risk measures and discuss the related scaling puzzle.

Suggested Citation

  • Jean-Charles Richard & Thierry Roncalli, 2019. "Constrained Risk Budgeting Portfolios: Theory, Algorithms, Applications & Puzzles," Papers 1902.05710, arXiv.org.
    • Handle: RePEc:arx:papers:1902.05710
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1902.05710
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. B. S. He & H. Yang & S. L. Wang, 2000. "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 337-356, August.
    2. Thierry Roncalli, 2015. "Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Asset Allocation," Bankers, Markets & Investors, ESKA Publishing, issue 138, pages 18-28, September.
    3. T. Roncalli & G. Weisang, 2016. "Risk parity portfolios with risk factors," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 377-388, March.
    4. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    5. Roncalli, Thierry, 2013. "Introduction to Risk Parity and Budgeting," MPRA Paper 47679, University Library of Munich, Germany.
    6. Griveau-Billion, Théophile & Richard, Jean-Charles & Roncalli, Thierry, 2013. "A Fast Algorithm for Computing High-dimensional Risk Parity Portfolios," MPRA Paper 49822, University Library of Munich, Germany.
    7. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    8. repec:dau:papers:123456789/4688 is not listed on IDEAS
    9. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Xi Bai & Katya Scheinberg & Reha Tutuncu, 2016. "Least-squares approach to risk parity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 357-376, March.
    11. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    12. Michael Kalkbrener, 2005. "An Axiomatic Approach To Capital Allocation," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 425-437, July.
    13. Dirk Tasche, 2007. "Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle," Papers 0708.2542, arXiv.org, revised Jun 2008.
    14. S. L. Wang & L. Z. Liao, 2001. "Decomposition Method with a Variable Parameter for a Class of Monotone Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 415-429, May.
    15. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sarah Perrin & Thierry Roncalli, 2019. "Machine Learning Optimization Algorithms & Portfolio Allocation," Papers 1909.10233, arXiv.org.
    2. Joan Gonzalvez & Edmond Lezmi & Thierry Roncalli & Jiali Xu, 2019. "Financial Applications of Gaussian Processes and Bayesian Optimization," Papers 1903.04841, arXiv.org.
    3. Ayse Sinem Uysal & Xiaoyue Li & John M. Mulvey, 2021. "End-to-End Risk Budgeting Portfolio Optimization with Neural Networks," Papers 2107.04636, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sarah Perrin & Thierry Roncalli, 2019. "Machine Learning Optimization Algorithms & Portfolio Allocation," Papers 1909.10233, arXiv.org.
    2. Sebastian Jaimungal & Silvana M. Pesenti & Yuri F. Saporito & Rodrigo S. Targino, 2023. "Risk Budgeting Allocation for Dynamic Risk Measures," Papers 2305.11319, arXiv.org, revised Mar 2024.
    3. Mingyi Hong & Tsung-Hui Chang & Xiangfeng Wang & Meisam Razaviyayn & Shiqian Ma & Zhi-Quan Luo, 2020. "A Block Successive Upper-Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 833-861, August.
    4. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    5. Thibault Bourgeron & Edmond Lezmi & Thierry Roncalli, 2019. "Robust Asset Allocation for Robo-Advisors," Papers 1902.07449, arXiv.org.
    6. da Costa, B. Freitas Paulo & Pesenti, Silvana M. & Targino, Rodrigo S., 2023. "Risk budgeting portfolios from simulations," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1040-1056.
    7. Anis, Hassan T. & Kwon, Roy H., 2022. "Cardinality-constrained risk parity portfolios," European Journal of Operational Research, Elsevier, vol. 302(1), pages 392-402.
    8. David Degras, 2021. "Sparse group fused lasso for model segmentation: a hybrid approach," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 625-671, September.
    9. Tadese, Mekonnen & Drapeau, Samuel, 2020. "Relative bound and asymptotic comparison of expectile with respect to expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 387-399.
    10. Benjamin Bruder & Nazar Kostyuchyk & Thierry Roncalli, 2022. "Risk Parity Portfolios with Skewness Risk: An Application to Factor Investing and Alternative Risk Premia," Papers 2202.10721, arXiv.org.
    11. Griveau-Billion, Théophile & Richard, Jean-Charles & Roncalli, Thierry, 2013. "A Fast Algorithm for Computing High-dimensional Risk Parity Portfolios," MPRA Paper 49822, University Library of Munich, Germany.
    12. Adil Rengim Cetingoz & Olivier Gu'eant, 2023. "Factor Risk Budgeting and Beyond," Papers 2312.11132, arXiv.org.
    13. Giorgio Costa & Roy H. Kwon, 2020. "Generalized risk parity portfolio optimization: an ADMM approach," Journal of Global Optimization, Springer, vol. 78(1), pages 207-238, September.
    14. M. Barkhagen & S. García & J. Gondzio & J. Kalcsics & J. Kroeske & S. Sabanis & A. Staal, 2023. "Optimising portfolio diversification and dimensionality," Journal of Global Optimization, Springer, vol. 85(1), pages 185-234, January.
    15. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    16. Vaughn Gambeta & Roy Kwon, 2020. "Risk Return Trade-Off in Relaxed Risk Parity Portfolio Optimization," JRFM, MDPI, vol. 13(10), pages 1-28, October.
    17. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.
    18. Bernardo Freitas Paulo da Costa & Silvana M. Pesenti & Rodrigo S. Targino, 2023. "Risk Budgeting Portfolios from Simulations," Papers 2302.01196, arXiv.org.
    19. Ben R. Craig & Margherita Giuzio & Sandra Paterlini, 2019. "The Effect of Possible EU Diversification Requirements on the Risk of Banks’ Sovereign Bond Portfolios," Working Papers 19-12, Federal Reserve Bank of Cleveland.
    20. TAYLOR, Adrien B. & HENDRICKX, Julien M. & François GLINEUR, 2016. "Exact worst-case performance of first-order methods for composite convex optimization," LIDAM Discussion Papers CORE 2016052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1902.05710. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.