Benford's Law and Bitcoin Price Manipulation¶
Benford's Law applied to Bitcoin price data provides independent statistical evidence of price manipulation in 2013, 2017, and 2019, corroborating the findings of Gandal [2018] and Griffin [2020]. Published in 2020, this research represents the first known application of Benford's Law to Bitcoin and demonstrates with near-100% confidence that Bitcoin's price has been fraudulently manipulated at some point since 2010.
Benford's Law¶
Benford's Law is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. In naturally occurring collections of numbers, the leading significant digit is likely to be small: the number 1 appears as the leading digit about 30% of the time, while 9 appears less than 5% of the time. The distribution resembles a Pareto distribution. Benford's Law also makes predictions about the distribution of second digits, third digits, and digit combinations.
Deviations from this expected distribution indicate an anomaly, and that anomaly is typically caused by some form of fraud. Application of Benford's Law to fraud detection dates to at least Varian [1972] and has been used to assess reported earnings, tax compliance, and auditing. It is a well-established methodology in forensic accounting.
Methodology¶
Using the daily price history from coinmetrics.io for July 2010 through June 2020, first-, second-, and third-digit tests were applied. Because extended periods may feature only one or two unique leading digits -- the S&P 500 started with a "1" or "2" from 2009 to 2019, making first-digit analysis meaningless over that span -- the methodology cascades from first-digit to second-digit to third-digit tests as needed. Each bin in the histogram required at least eight observations for statistical significance.
Empirical Results¶
Analysis of the full period found anomalies at 100% and 99% confidence levels using first-digit tests. Year-by-year analysis identified statistically significant anomalies in three specific years:
- 2013: 94.7% confidence of anomalous pricing (second-digit test)
- 2017: 94.9% confidence of anomalous pricing (second-digit test)
- 2019: 98.1% confidence of anomalous pricing (second-digit test)
No anomalies were detected at the 90% threshold for 2011, 2012, 2014, 2015, 2016, or 2018.
2013 and Mt. Gox¶
Gandal [2018] documented that the 2013 manipulation began with a hack and stolen bitcoins, followed by a software bot engaged in "painting the tape" -- publishing false volume and trading figures to induce trading. At trial, the CEO of Mt. Gox admitted such bots were running on the exchange in 2013.
2017 and Bitfinex¶
Griffin [2020] implied price manipulation in 2017 through a stablecoin scheme. The purported mechanism involved issuing a stablecoin pegged to the dollar, using affiliated exchange IOUs to purchase the stablecoin, then using the stablecoin to bid up Bitcoin's price. Bitcoin would later be sold at inflated prices for dollars, which were deposited to back the stablecoin retroactively. The U.S. Department of Justice opened an investigation into the matter and subpoenas were issued.
Benford analysis cannot ascertain the cause of fraud or identify perpetrators. It can only confirm that the price behavior of Bitcoin in 2017 was unnatural, with fraudulent manipulation being the most likely explanation.
2019 and PlusToken¶
A Ponzi scheme known as PlusToken may be responsible for the 2019 anomaly. PlusToken lured victims with promises of high returns. From January through June 2019, Bitcoin gained 212% to nearly $13,000. Operators left a note "Sorry we have run" in June 2019 and were arrested by Chinese authorities on June 29 -- a period corresponding with Bitcoin's 2019 price peak. Bitcoin's price subsequently declined to around $7,000 by December.
Implications for Analysis¶
The implications for Bitcoin valuation are profound. Technical price analysis over suspect periods is likely meaningless because Bitcoin's price during those intervals did not reflect equally motivated buyers and sellers and therefore cannot be indicative of market psychology. Fundamental analysis is also problematic: when price has been manipulated, comparisons of price to fundamental metrics are skewed, producing detrimental impacts on both the assessment of current value and forecasts of future price.