Scaling Laws And Statistical Properties of The Transaction Flows And Holding Times of Bitcoin (2401.04702v1)

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.

• The paper introduces a mathematical framework to analyze Bitcoin holding times and transaction flows, revealing distinct behavioral patterns among investor types.
• It finds that realized returns are consistently lower than book-to-market returns, uncovering trading inefficiencies during varying market conditions.
• It identifies heavy-tailed distributions and multifractality in holding times, signaling long-memory effects and complex dynamics in the Bitcoin market.

Analyzing Bitcoin Transaction Dynamics: A Detailed Exploration of Holding Times and Transaction Flows

The paper "Scaling Laws And Statistical Properties Of The Transaction Flows And Holding Times of Bitcoin" explores an in-depth analysis of Bitcoin's transaction dynamics, focusing on the statistical properties of holding times and transaction flows. This paper leverages the transparent and detailed nature of the Bitcoin blockchain to extract valuable insights into investor behavior, which are typically obscured in conventional financial markets.

Methodological Framework

The authors establish a comprehensive mathematical framework to model Bitcoin transaction flows, with particular emphasis on holding times—the duration a Bitcoin is held before being exchanged again. They utilize the public ledger of Bitcoin to trace every transaction from the inception of Bitcoin, a task made feasible by the unique structure of blockchain technology. Through meticulous processing of the blockchain's substantial data, the researchers analyze the age distribution of Bitcoin, revealing crucial insights into the behavior of distinct investor categories.

Key Findings

Age Distribution and Holding Patterns

The paper highlights notable differences in the dynamics of short-, medium-, and long-term Bitcoin holders. Long-term holders, for example, display a propensity to sell their assets as prices rise, while short-term holders often display contrasting behavior. The authors also observe a stark anti-correlation between medium-term and long-term holders' activity, which suggests a distinct pattern of asset transfer among different investor types.

Book-to-Market vs. Realized Returns

A significant portion of the research is dedicated to comparing book-to-market (theoretical gains or losses) versus realized returns (actual gains or losses post-transaction). The paper unveils a crucial discrepancy—realized returns tend to be smaller than the projected book-to-market returns, especially during peak price periods, which underscores the prevalent trading inefficiencies. The research aligns with the well-documented disposition effect, where investors hastily realize gains while postponing the realization of losses.

Power Laws and Heavy-Tailed Distributions

A pivotal finding relates to the heavy-tailed nature of Bitcoin holding times, characterized by a power law with an exponent of approximately 0.87. This indicates the presence of long memory effects within the market, suggesting that a significant fraction of Bitcoin holders tend to retain their assets for extended periods. The paper asserts the existence of multiscaling properties in holding times, with varying power-law exponents manifesting across different market conditions and price regimes.

Transaction Flows and Priority Queuing

The research provides empirical evidence of a power law governing average transaction flow fractions concerning age, closely aligning with priority queuing theory. This suggests that the dynamics of Bitcoin transactions mirror congested priority queues, where the timing of transactions is influenced by a combination of age and competing priorities.

Multifractality in Bitcoin Transactions

The authors further extend their analysis to explore the multifractality in Bitcoin transactions through the lens of normalized transaction volumes. They utilize a multifractal moment assessment to confirm the nonlinear scaling properties indicative of multifractality, adding a layer of complexity to the market’s transaction dynamics.

Implications and Future Directions

This paper presents profound implications both practically and theoretically. The identification of distinct behavioral patterns among investors based on holding times and transaction preferences can inform the design of financial instruments and trading strategies. The insights into power-law distributions and multifractality enrich the understanding of market dynamics, suggesting potential areas for further research, such as the development of predictive models based on these statistical properties.

In conclusion, the paper provides a meticulous and quantitative exploration of Bitcoin's holding and transaction characteristics, leveraging blockchain's transparent ledger. The insights gained not only enhance the understanding of Bitcoin markets but also have broader applications in analyzing other financial systems incorporating similar blockchain technologies. Future research could benefit from expanding these methodologies to diverse asset classes, enhancing the generalizability and applicability of the findings in the broader financial landscape.