Analysis of Bitcoin prices across exchanges in U.S.
Pratish Patel
2022-01-17
Introduction
Imagine buying one TSLA share on the Robinhood App at a price of \(x\) dollars. During the transaction process, the investor expects best execution based on price and time. The investor expects the TSLA share on Ameritrade — a different exchange — will also be \(x\). Afterall, if the price was \(y > x\) on Ameritrade, hedgefunds and investors (arbitrageurs in general) short TSLA stock on Ameritrade and use the proceeds to buy TSLA stock on Robinhood. The competition between hedge funds, retail investors and institutions ensures that discrepancy in TSLA prices on Robinhood and Ameritrade are negligible. The investor knows that the price \(x\) is the unique market price. Now imagine buying one Bitcoin (BTC). In this article, I analyze whether competition drives the BTC prices across exchanges to converge at a unique price.
Price uniqueness depends on the arbitrage principle. That is, an investor cannot invest zero dollars and expect a positive return. This deal is too good to be true. Practically, arbitrage depends on trading regulations and the trading mechanism. For example, arbitrage depends on whether an investor has the ability to short the TSLA stock. Unlike equities, trading regulations for BTC and other crypto tokens remain murky. One can trade across Decentralized Exchanges (DeFI), which operate without regulations. As far as I know, there is no trusted source of data documenting the trading volume across DeFI exchanges. Even within the realm of centralized exchanges, the regulations differ. In fact, in some cases, it is not even clear which government body has the jurisdiction. Tesla share is classified as a “security” and hence investors are protected by the Securities and Exchange Commission (SEC). BTC is classified as a commodity (store of value like gold) — not a security. Commodities Futures Trading Commission (CFTC) regulates derivatives trading for commodities, but in America, there is no governing body regulating the commodity spot markets. The jurisdictional uncertainty is best understood with Ripple (XRP) lawsuit. On one hand, SEC claims Ripple raised funds, beginning in 2013, through the sale of digital assets known as XRP in an unregistered security offering to investors in the U.S. and worldwide. SEC views XRP as a security and claims that it has jurisdiction. Ripple claims it is a commodity and SEC does not have the jurisdiction.
Unlike equities, trading one BTC is also costly. To validate a transaction that claims that the investor owns that BTC, the average cost is $243.65 as of January 02 2022. On Robinhood, the investor can buy TSLA shares for free (ignoring small indirect costs). The high transaction cost is akin to trading TSLA shares before May 1, 1975 (May day). Prior to May day, brokers charged a fixed rate commission irrespective of the trade size hurting small investors. After Mayday, SEC asked the brokers to abolish fixed commissions which resulted in an increase in trading volume by individual investors. The high validation cost is the lower bound actually. Coinbase — the biggest crypto exchange in America — does not allow shorting which makes arbitrage trades even more expensive.
Unlike equities, trading one BTC is also time consuming. To validate a transaction, the average confirmation time is $4.28 minutes as of January 02 2022. On Robinhood, the transaction takes fractions of a second.
The regulatory uncertainty, the high transaction cost and the large amount of time it takes to confirm a transaction may imply that there is no unique BTC price. In this article, we empirically measure the deviations across exchanges and explore the time series properties of the deviations. Specifically, we seek to answer three questions:
- How big are the deviations across exchanges?
- How does the deviation depend on the average transaction cost?
- How does the deviation depend on the average transaction time?
Bitcoin Trading Across various Exchanges
In United States, as of January 17 2022, based on the data from CoinGecko, Coinbase is the most popular exchange to trade BTC followed by Kraken and Binance US. But, across the world, the most popular exchanges to trade BTC are Binance and OKEx. The headquarters for Binance is in Cayman Islands; the headquarters for OKEx is Belize. CoinBase ranks third.
| Country | Total_BTC_Volume | NumExchanges | ShareVolume |
|---|---|---|---|
| Cayman Islands | 427,242 | 6 | 30.7% |
| Seychelles | 232,739 | 10 | 16.7% |
| Belize | 122,247 | 2 | 8.8% |
| United States | 107,538 | 7 | 7.7% |
| Bahamas | 91,828 | 1 | 6.6% |
| Singapore | 65,633 | 7 | 4.7% |
| South Korea | 59,615 | 4 | 4.3% |
Table 1 shows the spatial distribution of the BTC exchanges as of January 17 2022. Cayman Islands serves as a host to 6 exchanges which combine to trade 30.7% of the total BTC trades. The United States does not rank at the top. Upon first inspection, the ranking may not make sense. After all, because of the American market size, it makes little sense for any exchange to exclude American citizens. The demand to include Americans is clear by the latest sporting events. On the Christmas eve of 2021, the famed Staples center, which houses the Los Angeles Lakers, became the Crypto.com (headquartered in Cayman Islands) arena. In baseball, starting July 13, 2021, FTX.US logo began appearing on every MLB player’s sleeve (Antigua and Barbuda serves as the host country to FTX — the parent company of FTX.US.).
Trading on American exchanges is limited. American citizens, for example, cannot short BTC on Coinbase. The regulatory uncertainty and the associated stringent KYC rules forced Binance to start a different exchange named Binance US. American citizens cannot trade on Kucoin or FTX or Binance exchanges. Moreover, Americans cannot trade options on most exchanges except for LedgerX which remains relatively unknown. An investor can, theoretically, short using CME futures but the 50% margin requirement is onerous. Moreover, CME futures are cash settled and does not allow an investor to own a physical BTC. To summarize, shorting Bitcoin for Americans remains expensive because of either explicit or implicit constraints.
Transaction Cost related to Bitcoin trading
Figure 1: Transaction cost and time related to Bitcoin validation
Panel A of Figure1 shows the time series of the average cost to mine Bitcoin; Panel B shows the time series of the time to validate a transaction. Overall, the cost to mine Bitcoin has increased over time. Panel B is more interesting. After 2012, the shortest median time to validate a transaction is 3.37 minutes — the time is significantly more than a fraction of a second.
To summarize, because of the trading restrictions across exchanges, because of the high transaction cost and because of the validation time, the concept of a unique Bitcoin price may not exist. In the next section, I explore price deviations across exchanges.
Price deviations across exchanges
Summary Statistics
I now extend the analysis to understanding price deviations across U.S. exchanges. I analyze deviations using prices from cryptodatadownload at an hourly frequency. At the top of every hour, I compare prices across six exchanges: Bittrex, CEXIO, Bitfinex, Bitstamp, Poloniex and Gemini. I choose these exchanges because of data availability.
To understand the price deviations, I consider two measures: Absolute and Relative price deviations. Absolute price deviation is the difference between the maximum and minimum Bitcoin prices across exchanges. Relative deviation is the ratio of the Absolute deviation and the average price across exchanges. The table below summarizes both types of deviations. The results form the basis of the article. At 1:00 a.m. GMT, on Christmas eve, the price of Bitcoin on Bittrex exchange was $13,180 and the price of Bitcoin on CEXIO was $16,400. The absolute deviation across exchanges is $3,220 and the relative deviation is 22%. On average, the absolute deviation is $166 and the relative deviation is 2% — the deviation is higher than Tesla stock deviation across equity exchanges.
The average transaction cost is also $51 while the mean transaction time is 11 minutes. The transaction cost is not zero and the mean transaction time is certainly more than a fraction of second.
| Statistic | N | Mean | St. Dev. | Min | Pctl(25) | Pctl(75) | Max |
| AbsoluteDeviation | 29,730 | 166.08 | 338.48 | 1.13 | 31.43 | 124.69 | 3,220.00 |
| RelativeDeviation | 29,730 | 0.02 | 0.03 | 0.000 | 0.004 | 0.03 | 0.26 |
| TransactionCost | 29,730 | 51.47 | 25.38 | 18.00 | 32.27 | 60.71 | 161.69 |
| TransactionTime | 20,418 | 10.71 | 3.70 | 3.37 | 7.93 | 12.82 | 28.95 |
Figure 2: Absolute and Relative deviations through time
The two panels show that both absolute and relative deviations decrease over time. The spikes in the deviations were more pronounced in 2017 relative to 2020. Figure 3 compares the average absolute deviation across years. Consistent with Panel A of Figure 2, the average are statistically different — the averages decrease over time.
Figure 3: Comparing Absolute deviations across years
Does the Absolute Deviation vary by Days of the week or by Hours of the day?
Figure 4: Comparing Absolute deviations across years
Figure 4 shows a box plot of absolute deviation across days of the week. There is no evidence that the absolute deviations vary by the days of the week starting from number zero which represents Sunday. The means across all days are not statistically different from each other.
Figure 5: This figure the p value from a t-test comparing the average absolute value across each hour. Since all p-values are above 0.5, there is no evidence that the absolute deviations vary across hours of the day.
Relationship between Absolute and Relative deviation with the Transaction Cost.
Figure 6: This figure shows the scatter plot and the best fit line of the log Absolute Deviation and log Transaction cost grouped by year.
Figure 6 shows the relationship between log absolute deviation and log transaction cost. We transform the variables to log scale so that the variables are unitless. We only consider price at 4:00 p.m. EST, which is also when the stock market closes. We performed the same analysis for other hours and the results do not change. Consider year 2017 (red line) first. Evidently, the transaction cost by itself explains 83% of the variation in absolute deviation. Now consider Year 2020 (purple line). Consistent with Figure 3, the purple dots hover around zero. More importantly, since the R-square is closest ot zero, the variation in the absolute deviation does not depend on the transaction cost — absolute deviation is idiosyncratic. The blue line representing year 2019 is more interesting. Evidently, the relationship between transaction cost and absolute deviation is negative which does not make sense.
Figure 7: This figure shows the scatter plot and the best fit line of Relative Deviation and log Transaction cost grouped by year.
Figure 7 shows the relationship between relative deviation and log transaction cost. Since relative deviation is unitless, we do not transform that variable. The results are similar to that of Figure 6.
Relationship between Absolute and Relative deviation with the Transaction Time.
Figure 8: This figure shows the scatter plot and the best fit line of the log Absolute Deviation and log Transaction time grouped by year.
Figure 8 shows the relationship between log absolute deviation and log transaction time. We transform the variables to log scale so that the variables are unitless. Even though the best fit lines have positive slope across every year, the R square is small suggesting a weak relationship.
Figure 9: This figure shows the scatter plot and the best fit line of Relative Deviation and log Transaction time grouped by year.
Figure 7 shows the relationship between relative deviation and log transaction time. The low R squares imply that the relationship is weak.