IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2410.00854.html
   My bibliography  Save this paper

Impermanent loss and loss-vs-rebalancing I: some statistical properties

Author

Listed:
  • Abe Alexander
  • Lars Fritz

Abstract

There are two predominant metrics to assess the performance of automated market makers and their profitability for liquidity providers: 'impermanent loss' (IL) and 'loss-versus-rebalance' (LVR). In this short paper we shed light on the statistical aspects of both concepts and show that they are more similar than conventionally appreciated. Our analysis uses the properties of a random walk and some analytical properties of the statistical integral combined with the mechanics of a constant function market maker (CFMM). We consider non-toxic or rather unspecific trading in this paper. Our main finding can be summarized in one sentence: For Brownian motion with a given volatility, IL and LVR have identical expectation values but vastly differing distribution functions.

Suggested Citation

  • Abe Alexander & Lars Fritz, 2024. "Impermanent loss and loss-vs-rebalancing I: some statistical properties," Papers 2410.00854, arXiv.org.
    • Handle: RePEc:arx:papers:2410.00854
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2410.00854
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden & Anthony Lee Zhang, 2022. "Automated Market Making and Loss-Versus-Rebalancing," Papers 2208.06046, arXiv.org, revised May 2024.
    2. Robin Hanson, 2007. "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation," Journal of Prediction Markets, University of Buckingham Press, vol. 1(1), pages 3-15, February.
    3. Álvaro Cartea & Fayçal Drissi & Marcello Monga, 2023. "Predictable Losses of Liquidity Provision in Constant Function Markets and Concentrated Liquidity Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(2), pages 69-93, March.
    Full references (including those not matched with items on IDEAS)

    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. Rafael Frongillo, 2022. "Quantum Information Elicitation," Papers 2203.07469, arXiv.org.
    2. Karimi, Majid & Zaerpour, Nima, 2022. "Put your money where your forecast is: Supply chain collaborative forecasting with cost-function-based prediction markets," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1035-1049.
    3. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    4. Mikuláš Gangur & Miroslav Plevný, 2014. "Tools for Consumer Rights Protection in the Prediction of Electronic Virtual Market and Technological Changes," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 16(36), pages 578-578, May.
    5. Galanis Spyros & Kotronis Stelios, 2021. "Updating Awareness and Information Aggregation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 613-635, June.
    6. Patrick Buckley & Fergal O’Brien, 0. "The effect of malicious manipulations on prediction market accuracy," Information Systems Frontiers, Springer, vol. 0, pages 1-13.
    7. Dian Yu & Jianjun Gao & Weiping Wu & Zizhuo Wang, 2022. "Price Interpretability of Prediction Markets: A Convergence Analysis," Papers 2205.08913, arXiv.org, revised Nov 2023.
    8. Hanea, A.M. & McBride, M.F. & Burgman, M.A. & Wintle, B.C. & Fidler, F. & Flander, L. & Twardy, C.R. & Manning, B. & Mascaro, S., 2017. "I nvestigate D iscuss E stimate A ggregate for structured expert judgement," International Journal of Forecasting, Elsevier, vol. 33(1), pages 267-279.
    9. Ledyard, John & Hanson, Robin & Ishikida, Takashi, 2009. "An experimental test of combinatorial information markets," Journal of Economic Behavior & Organization, Elsevier, vol. 69(2), pages 182-189, February.
    10. Snowberg, Erik & Wolfers, Justin & Zitzewitz, Eric, 2013. "Prediction Markets for Economic Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 657-687, Elsevier.
    11. Ravi Kashyap, 2024. "The Democratization of Wealth Management: Hedged Mutual Fund Blockchain Protocol," Papers 2405.02302, arXiv.org, revised Jul 2024.
    12. Kelly, David L. & Letson, David & Nelson, Forrest & Nolan, David S. & Solís, Daniel, 2012. "Evolution of subjective hurricane risk perceptions: A Bayesian approach," Journal of Economic Behavior & Organization, Elsevier, vol. 81(2), pages 644-663.
    13. Frank M. A. Klingert & Matthias Meyer, 2012. "Effectively combining experimental economics and multi-agent simulation: suggestions for a procedural integration with an example from prediction markets research," Computational and Mathematical Organization Theory, Springer, vol. 18(1), pages 63-90, March.
    14. Ravi Kashyap, 2024. "To Trade Or Not To Trade: Cascading Waterfall Round Robin Rebalancing Mechanism for Cryptocurrencies," Papers 2407.12150, arXiv.org.
    15. Jinli Hu, 2012. "Combinatorial Modelling and Learning with Prediction Markets," Papers 1201.3851, arXiv.org.
    16. Buckley, Patrick, 2016. "Harnessing the wisdom of crowds: Decision spaces for prediction markets," Business Horizons, Elsevier, vol. 59(1), pages 85-94.
    17. Pivato, Marcus & Soh, Arnold, 2020. "Weighted representative democracy," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 52-63.
    18. Nicolas Della Penna & Mark D. Reid, 2011. "Bandit Market Makers," Papers 1112.0076, arXiv.org, revised Aug 2013.
    19. Patrick Buckley & Fergal O’Brien, 2017. "The effect of malicious manipulations on prediction market accuracy," Information Systems Frontiers, Springer, vol. 19(3), pages 611-623, June.
    20. Aseem Brahma & Sanmay Das & Malik Magdon-Ismail, 2010. "Comparing Prediction Market Structures, With an Application to Market Making," Papers 1009.1446, arXiv.org.

    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:2410.00854. 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.