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Power-Law Scaling in Extreme Bitcoin Return Fluctuations

Article arXiv papers · Author: Stjepan Begušić et al.
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Summary

The study examines the tails of Bitcoin return distributions across different time intervals and digital exchanges. It tests for common scaling behavior and estimates the power-law exponent, with attention to whether the tails imply a finite second moment. The authors report slowly decaying, power-law tails across the examined intervals and exchanges, with an asymptotic exponent between 2 and 2.5.

They interpret this exponent as evidence that Bitcoin returns have heavier tails than stock returns, whose exponent is described as being around 3, while still having a finite second moment. That finding supports the possible use of covariance-based methods in risk management and portfolio optimization. The summary gives no sample dates, exchange names, estimation procedures, or uncertainty ranges, so it does not establish how stable the estimates are or whether the reported behavior persists across later market conditions.

Key ideas

  • Bitcoin returns are examined across multiple time intervals and digital exchanges.
  • The authors report slowly decaying power-law tails in the return distributions.
  • The estimated asymptotic exponent lies between 2 and 2.5.
  • The reported tails are heavier than those associated with stock returns.
  • The authors infer a finite second moment, supporting covariance-based risk and portfolio methods.

Tags

CryptoStatisticsVolatilityRisk managementPortfolio construction
Full text
# Scaling properties of extreme price fluctuations in Bitcoin markets


# Scaling properties of extreme price fluctuations in Bitcoin markets









Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting findings, such as the inverse cubic law in the tails of stock price fluctuation distributions. Motivated by the rise of novel digital assets based on blockchain technology, we study the distributions of cryptocurrency price fluctuations. We consider Bitcoin returns over various time intervals and from multiple digital exchanges, in order to investigate the existence of universal scaling behavior in the tails, and ascertain whether the scaling exponent supports the presence of a finite second moment. We provide empirical evidence on slowly decaying tails in the distributions of returns over multiple time intervals and different exchanges, corresponding to a power-law. We estimate the scaling exponent and find an asymptotic power-law behavior with 2 < α < 2.5 suggesting that Bitcoin returns, in addition to being more volatile, also exhibit heavier tails than stocks, which are known to be around 3. Our results also imply the existence of a finite second moment, thus providing a fundamental basis for the usage of standard financial theories and covariance-based techniques in risk management and portfolio optimization scenarios.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.