Scaling Laws And Statistical Properties of The Transaction Flows And Holding Times of Bitcoin

Didier Sornette and Yu Zhang
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Didier Sornette: Risks-X, Southern University of Science and Technology (SUSTech); Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Tokyo Institute of Technology
Yu Zhang: University of Zurich - Department of Informantics

No 24-02, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We study the temporal evolution of the holding-time distribution of bitcoins and find that the average distribution of holding-time is a heavy-tailed power law extending from one day to over at least 200 weeks with an exponent approximately equal to 0.9, indicating very long memory effects. We also report significant sample-to-sample variations of the distribution of holding times, which can be best characterized as multiscaling, with power-law exponents varying between 0.3 and 2.5 depending on bitcoin price regimes. We document significant differences between the distributions of book-to-market and of realized returns, showing that traders obtain far from optimal performance. We also report strong direct qualitative and quantitative evidence of the disposition effect in the Bitcoin Blockchain data. Defining age-dependent transaction flows as the fraction of bitcoins that are traded at a given time and that were born (last traded) at some specific earlier time, we document that the time-averaged transaction flow fraction has a power law dependence as a function of age, with an exponent close to -1.5, a value compatible with priority queuing theory. We document the existence of multifractality on the measure defined as the normalized number of bitcoins exchanged at a given time.

Keywords: Bitcoin blockchain; Bitcoin holding time; bubbles; drawdowns; multiscaling; book-to-market returns; realized return; disposition effect; multifractality (search for similar items in EconPapers)
JEL-codes: C19 C41 G01 G41 (search for similar items in EconPapers)
Pages: 49 pages
Date: 2024-01
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2402

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