IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1511.03704.html
   My bibliography  Save this paper

Foundations for Wash Sales

Author

Listed:
  • Phillip G. Bradford

Abstract

Consider an ephemeral sale-and-repurchase of a security resulting in the same position before the sale and after the repurchase. A sale-and-repurchase is a wash sale if these transactions result in a loss within $\pm 30$ calendar days. Since a portfolio is essentially the same after a wash sale, any tax advantage from such a loss is not allowed. That is, after a wash sale a portfolio is unchanged so any loss captured by the wash sale is deemed to be solely for tax advantage and not investment purposes. This paper starts by exploring variations of the birthday problem to model wash sales. The birthday problem is: Determine the number of independent and identically distributed random variables required so there is a probability of at least 1/2 that two or more of these random variables share the same outcome. This paper gives necessary conditions for wash sales based on variations on the birthday problem. This allows us to answer questions such as: What is the likelihood of a wash sale in an unmanaged portfolio where purchases and sales are independent, uniform, and random? This paper ends by exploring the Littlewood-Offord problem as it relates capital gains and losses with wash sales.

Suggested Citation

  • Phillip G. Bradford, 2015. "Foundations for Wash Sales," Papers 1511.03704, arXiv.org, revised Jun 2016.
    • Handle: RePEc:arx:papers:1511.03704
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1511.03704
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Astrup Jensen, Bjarne & Marekwica, Marcel, 2011. "Optimal portfolio choice with wash sale constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1916-1937.
    2. Kazuo Nishimura & Masaaki Sibuya, 1988. "Occupancy with two types of balls," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(1), pages 77-91, March.
    3. Michael N. Katehakis & Arthur F. Veinott, 1987. "The Multi-Armed Bandit Problem: Decomposition and Computation," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 262-268, May.
    4. Wendl, Michael C., 2003. "Collision probability between sets of random variables," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 249-254, September.
    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. Derek Liu & Francesco Piccoli & Katie Chen & Adrina Tang & Victor Fang, 2023. "NFT Wash Trading Detection," Papers 2305.01543, 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. Marco Pollanen, 2024. "A Double Birthday Paradox in the Study of Coincidences," Mathematics, MDPI, vol. 12(24), pages 1-14, December.
    2. Paul Ehling & Michael Gallmeyer & Sanjay Srivastava & Stathis Tompaidis & Chunyu Yang, 2018. "Portfolio Tax Trading with Carryover Losses," Management Science, INFORMS, vol. 64(9), pages 4156-4176, September.
    3. Lodewijk Kallenberg, 2013. "Derman’s book as inspiration: some results on LP for MDPs," Annals of Operations Research, Springer, vol. 208(1), pages 63-94, September.
    4. Sonin, Isaac M., 2008. "A generalized Gittins index for a Markov chain and its recursive calculation," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1526-1533, September.
    5. Shigeru Mase, 1992. "Approximations to the birthday problem with unequal occurrence probabilities and their application to the surname problem in Japan," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(3), pages 479-499, September.
    6. W. Jason Choi & Amin Sayedi, 2019. "Learning in Online Advertising," Marketing Science, INFORMS, vol. 38(4), pages 584-608, July.
    7. Belleh Fontem, 2022. "An optimal stopping policy for car rental businesses with purchasing customers," Annals of Operations Research, Springer, vol. 317(1), pages 47-76, October.
    8. R. T. Dunn & K. D. Glazebrook, 2004. "Discounted Multiarmed Bandit Problems on a Collection of Machines with Varying Speeds," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 266-279, May.
    9. Fischer, Marcel & Kraft, Holger & Munk, Claus, 2013. "Asset allocation over the life cycle: How much do taxes matter?," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2217-2240.
    10. Nicolas Gast & Bruno Gaujal & Kimang Khun, 2023. "Testing indexability and computing Whittle and Gittins index in subcubic time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 391-436, June.
    11. Jiatu Cai & Xinfu Chen & Min Dai, 2018. "Portfolio Selection with Capital Gains Tax, Recursive Utility, and Regime Switching," Management Science, INFORMS, vol. 64(5), pages 2308-2324, May.
    12. Hesam Ahmadi & Uday V. Shanbhag, 2020. "On the resolution of misspecified convex optimization and monotone variational inequality problems," Computational Optimization and Applications, Springer, vol. 77(1), pages 125-161, September.
    13. Mattias Rydenfelt & Hernan G Garcia & Robert Sidney Cox III & Rob Phillips, 2014. "The Influence of Promoter Architectures and Regulatory Motifs on Gene Expression in Escherichia coli," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-31, December.
    14. Isaac M. Sonin & Constantine Steinberg, 2016. "Continue, quit, restart probability model," Annals of Operations Research, Springer, vol. 241(1), pages 295-318, June.
    15. Qihao Wu & Jiangxue Han & Yimo Yan & Yong-Hong Kuo & Zuo-Jun Max Shen, 2025. "Reinforcement learning for healthcare operations management: methodological framework, recent developments, and future research directions," Health Care Management Science, Springer, vol. 28(2), pages 298-333, June.
    16. Ilya O. Ryzhov & Warren B. Powell & Peter I. Frazier, 2012. "The Knowledge Gradient Algorithm for a General Class of Online Learning Problems," Operations Research, INFORMS, vol. 60(1), pages 180-195, February.
    17. Malekipirbazari, Milad & Çavuş, Özlem, 2024. "Index policy for multiarmed bandit problem with dynamic risk measures," European Journal of Operational Research, Elsevier, vol. 312(2), pages 627-640.
    18. Loris Cannelli & Giuseppe Nuti & Marzio Sala & Oleg Szehr, 2020. "Hedging using reinforcement learning: Contextual $k$-Armed Bandit versus $Q$-learning," Papers 2007.01623, arXiv.org, revised Feb 2022.
    19. Tasos Papagiannis & Georgios Alexandridis & Andreas Stafylopatis, 2022. "Pruning Stochastic Game Trees Using Neural Networks for Reduced Action Space Approximation," Mathematics, MDPI, vol. 10(9), pages 1-16, May.
    20. K. D. Glazebrook & C. Kirkbride & H. M. Mitchell & D. P. Gaver & P. A. Jacobs, 2007. "Index Policies for Shooting Problems," Operations Research, INFORMS, vol. 55(4), pages 769-781, August.

    More about this item

    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:1511.03704. 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.