Further Evidence of Bitcoin Price Manipulation.
CryptoClub: this article, an excerpt of research on #BTC manipulation
Executive Summary.
- Unmolested prices have been shown to exhibit an
expected, natural distribution characterized by
Benford’s law. Benford’s law has been used to
identify and investigate financial anomalies and
fraud for nearly 30 years. We believe this is the
first application of Benford’s law to bitcoin. - We can say with nearly 100% confidence that
bitcoin’s price was manipulated at some point
since 2010. We can say with 95% confidence that
bitcoin’s price was manipulated in 2013, 2017,
and 2019. Our research corroborates the general
findings of Gandal [2018] and Griffin [2020].
Bitcoin’s price during these periods is not reflective
of natural supply and demand by equally
motivated buyers and sellers. - Both technical and fundamental analysis of bitcoin
that include suspect periods is likewise suspect
unless the issue is recognized and adjustments are
made. When price has been manipulated, any
comparisons of price to fundamental metrics
would be flawed. Such analysis is likely to have a
detrimental impact on both the assessment of
current value and forecasts of future price.
Prior Research.
Past research on this topic includes Monamo [2016],
Gandal [2018] (which is contemporaneously
summarized at reference note 18), Chen [2019],
Bitwise [2019], and Griffin [2020].
Benford’s Law.
Benford's law is an observation about the frequency
distribution of leading digits in many real-life sets of
numerical data. The law states that in many naturally
occurring collections of numbers, the leading
significant digit is likely to be small [Benford, 1938].
Specifically, the number 1 appears as the leading
significant digit about 30% of the time, while 9
appears as the leading significant digit less than 5%
of the time. Benford's law also makes predictions
about the distribution of second digits, third digits,
digit combinations, and so on. A Benford distribution
resembles a Pareto distribution
(Exhibit 1).
Deviations from this distribution indicate an anomaly,
and typically that anomaly is caused by some type of
fraud. Application of Benford’s law to fraud detection
dates to at least Varian [1972] as a test of validity of
scientific data. It has been used to assess reported
earnings [Carslaw 1988], [Thomas 1989], tax
compliance [Nigrini 1996], and auditing [Durtschi 2004].
Data and Methodology.
Data is sourced from the daily price history dataset
from coinmetrics.io.
We use the methodologies set out in Benford [1938],
Durtschi [2004], and Stambaugh [2012]. We use the
first-, second-, and third-digit tests. For bitcoin prices
less than $1.00 we ignore leading zeros after the
decimal.
To ensure there is statistical significance in our
distribution results, we required that each bin [0..9] in
our histogram be populated with at least eight
observations. If this condition is not met for the first-digit test, we rely on the second-digit test. If this
condition is not met for the second-digit test, we rely
on the third-digit test.
A key reason for this approach is that there could be
extended periods where the first digit may only be
comprised of one or two unique numbers. For
example, the S&P 500 started with a “1” or a “2”
from 2009 to 2019. First-digit Benford analysis over
this time period would be meaningless.
We conducted an analysis for the entire period July
2010 through June 2020. We also conducted analyses
for calendar years 2011-2019 (we exclude the 2010
and 2020 partial years as having too few
observations.) Because Benford analysis requires large
datasets, it is difficult to narrow down anomalies to a
granularity of less than one year.
Empirical Results.
Table 1 shows results for those tests where there was
a 90% or greater probability of anomalous pricing.
Position test indicates whether the first-digit, second-
digit, or third-digit test was used.
nd is the number of observations in the bin where an
anomalous result was detected. This is not the
number of anomalous events. nd / N gives the
observed distribution, whereas the expected
distribution is governed by Benford’s law.
N is the total number of observations in the test.
z is the z-score for the test.
Conf. is the assumed normal distribution confidence
level that an anomalous event occurred during the
tested period.
nd / N nd / N gives the observed distribution, whereas
the expected distribution is governed by Benford’s
law.
1* See Gandal, 2018. “Price Manipulation in the Bitcoin
Ecosystem.”
https://www.youtube.com/watch?v=N0033FbywEg
Discussion.
To those familiar with prior research on bitcoin price
manipulation these results are not entirely surprising.
What is unique is that a commonly accepted and
independent methodology corroborates evidence of
price manipulation.
2013 and Mt. Gox
Gandal [2018] relates that the 2013 manipulation
started with a hack and stolen bitcoins, followed by a
software program (aka “bot”) that engaged in
“painting the tape.” Painting the tape involves
publishing false volume and trading figures to induce
investors to trade. A report by Bitwise [2019]
indicated that this practice is widespread even
recently.
At trial, the CEO of Mt. Gox admitted such bots were
running on the exchange in 2013, cementing the
notion that price was being manipulated.1
Peterson
[2018] confirmed Gandal’s findings using price
deviation from fundamental value.
2017 and Bitfinex.
Griffin [2020] implied that price was manipulated in
2017. One way to manipulate bitcoin’s price is to
issue a relatively worthless new token, and use that
token, say Token X, to purchase bitcoin. The problem is that it will take many X tokens to buy enough bitcoin
to impact price. Issuing more Token X only devalues
Token X further, making it even more difficult to buy
bitcoin. However, if Token X were pegged to a fiat
currency like the dollar, Token X would not lose value
in the short term.
The purported scheme is that investors use dollars to
buy stablecoin Token X, meaning Token X is “backed”
by dollars. Token X is then used to buy bitcoin.
If Exchange X and Token X are affiliated, then
Exchange X can issue IOUs to purchase Token X.
Token X is then used on Exchange X to bid up the price
of bitcoin. Bitcoin is later sold at an inflated price for
dollars, which is deposited into Token X’s account to
retire the IOU, giving the appearance, ex post facto,
that Token X was backed by dollars all along.
Anonymous blogger Bitfinex’d [2017] alleged this was
the scheme perpetrated by Tether and Bitfinex, in
response to a hack and theft of bitcoins on the Bitfinex
exchange in 2016. The allegation was apparently
enough that the U.S. Department of Justice opened
an investigation into the matter [Robinson 2018].
Subpoenas were issued [Leising 2018], but the status
of that investigation is to date unknown.
Benford analysis is unable to ascertain the cause of
fraud or price manipulation, let alone identify
perpetrators. Technically, it only provides evidence of
a deviation from an expected distribution. Our
analysis of 2017 prices cannot confirm specific
allegations of fraud, 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.
We are unaware of any studies (published or
otherwise) providing evidence of fraud or price
manipulation in 2019. There are allegations that a
ponzi scheme known as PlusToken may be
responsible. PlusToken was a classic ponzi scheme
that lured unsuspecting victims to invest with promises
of high returns and low investments [Michael 2020].
From January 1 – June 30, 2019, bitcoin gained 212%
to nearly $13,000. Shortly thereafter, bitcoin’s price
declined until December of that year where it traded
around $7,000. Operators of the scheme left a note
“Sorry we have run” in June 2019 and were arrested
by Chinese authorities on June 29th. This period (and
into July) corresponds with bitcoin’s price peak for
2019.
Presumably, the scheme involves
a) selling a worthless token PlusToken to
naïve investors for fiat currency;
b) purchasing bitcoin with PlusToken and
bidding up the price; then
c) selling bitcoin at an inflated price for
fiat currency.
If that is in fact the scheme, then this appears to be a
poor attempt at money laundering as well as price
manipulation.
Our research method cannot validate any such
specifics, only that prices in 2019 are suspected of
being manipulated. The PlusToken scheme, however,
appears to be more than a coincidence.
Conclusion.
Unmolested prices have been shown to exhibit an
expected, natural distribution characterized by
Benford’s law. Benford’s law has been used to identify
and investigate financial anomalies and fraud for
nearly 30 years. We believe this is the first application
of Benford’s law to bitcoin.
Our analysis confirmed anomalies in bitcoin prices for
2013, 2017, and 2019. Given past research on the
topic, we can say with near 100% confidence that
bitcoin’s price has been fraudulently manipulated at
some point in its lifespan since 2010. We can say with
95% confidence that bitcoin was manipulated in
2013; 95% confidence that bitcoin was manipulated
in 2018; and 98% confidence that bitcoin was
manipulated in 2019.
The implications for bitcoin valuation are profound.
First and foremost, it means that technical price
analysis of bitcoin over the suspect periods is likely
meaningless; bitcoin’s price did not reflect equally
motivated buyers and sellers, and therefore bitcoin’s
price cannot be indicative of market psychology.
Also, this finding means that even fundamental
analysis of bitcoin is problematic. Fundamental
analysis typically relies on historical relationships
between price and some other metric to ascertain if
an asset is overvalued or undervalued. When price has
been manipulated, any such comparisons are then
skewed, and would likely have a detrimental impact
on both the assessment of current value and forecasts
of future price.
References.
1. Benford, F. 1938. “The Law of Anomalous Numbers.”
Proceedings of the American Philosophical Society. 78(4):
551-572. https://www.jstor.org/stable/984802
2. Bitfinex’d. 2017. “Bitfinex never ‘repaid’ their tokens, Bitfinex
started a ponzi scheme.”
https://medium.com/@bitfinexed/bitfinex-never-repaid-their-
tokens-bitfinex-started-a-ponzi-scheme-86a9291add29
3. Bitwise Asset Management. 2019. “Meeting with Bitwise
Asset Management / Presentation to the U.S. Securities and
Exchange Commission.” https://www.sec.gov/comments/sr-
nysearca-2019-01/srnysearca201901-5164833-183434.pdf
4. Carslaw, C.A.P.N. 1988. “Anomalies in Income Numbers:
Evidence of Goal Oriented Behavior.” The Accounting
Review. 63(2): 321-327.
5. Chen, W., et al. 2019. “Market Manipulation of Bitcoin:
Evidence from Mining the Mt. Gox Transaction Network.”
IEEE INFOCOM 2019 - IEEE Conference on Computer
Communications, doi:10.1109/infocom.2019.8737364.
6. Durtschi, C., et al.2004. “The Effective Use of Benford’s Law
to Assist in Detecting Fraud in Accounting Data.” Journal of
Forensic Accounting. 5: 17-34.
7. Gandal, N., et al. 2018. “Price Manipulation in the Bitcoin
Ecosystem.” Journal of Monetary Economics. (95): 86–96.,
doi:10.1016/j.jmoneco.2017.12.004.
8. Griffin, J. M., and A. Shams. 2020. “Is Bitcoin Really
Untethered?” The Journal of Finance, forthcoming,
doi:10.1111/jofi.12903
9. Leising, M. 2018. “U.S. Regulators Subpoena Crypto
Exchange Bitfinex, Tether.” Bloomberg.
www.bloomberg.com/news/articles/2018-01-30/crypto-
exchange-bitfinex-tether-said-to-get-subpoenaed-by-cftc
10. Michael. 2020. “Plus Token (PLUS) Scam – Anatomy of a
Ponzi.” Boxmining. https://boxmining.com/plus-token-
ponzi.
11. Monamo, Patrick, et al. 2016. “Unsupervised Learning for
Robust Bitcoin Fraud Detection.” Information Security for
South Africa (ISSA). doi:10.1109/issa.2016.7802939.
12. Nigrini, M.J. 1996. “Taxpayer Compliance Application of
Benford’s Law.” Journal of the American Taxation
Association. 18(1):72-92.
13. Peterson, T. 2018. “Metcalfe's Law as a Model for Bitcoin's
Value.” Alternative Investment Analyst Review. 7(2): 9-18.
14. Robinson, M., and T. Shoenberg. 2018. “Bitcoin-Rigging
Criminal Probe Focused on Tie to Tether.” Bloomberg.
https://www.bloomberg.com/news/articles/2018-11-
20/bitcoin-rigging-criminal-probe-is-said-to-focus-on-tie-to-
tether
15. Stambaugh, C., et al. 2012. “Using Benford Analysis to
Detect Fraud.” Internal Auditing. May/June:21-29.
16. Thomas, J.K. 1989. “Unusual Patterns in Reported
Earnings.” The Accounting Review. 64(4): 773-787.
17. Varian, H.R. 1972. “Benford’s Law.” The American
Statistician. 26: 65-66.
18. The Willy Report. 26 May 2014. “Proof of Massive Fraudulent
Trading Activity at Mt. Gox, and How It Has Affected the Price
of Bitcoin.” willyreport.wordpress.com/2014/05/25/the-willy-
report-proof-of-massive-fraudulent-trading-activity-at
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