The Price of a Digital Currency

Arash Aloosh∗

April 15, 2018

Abstract

This paper introduces a pricing relation for digital currencies as globally priced assets in competitive markets. Using the pricing relation, the study finds that the U.S. dollar price changes of Bitcoin, unlike other globally traded assets such as commodities and fiat currencies, are slightly negatively correlated with the U.S. dollar price changes of a basket of G10 currencies. It also documents Bitcoin price disparities and discrepancies for various pairs of denominated currencies, namely the U.S. dollar, Euro, British pound, Japanese yen, Canadian dollar, Chinese yuan, and Polish zloty. The Bitcoin price discrepancies are 25% higher than Bitcoin price disparities. Finally, this study examines the theoretical price and volatility of cryptocurrencies with zero fundamental values and finds that they have low price volatility. Consequently, they are much easier to regulate, use, and hold.

Keywords: Bitcoin; Pricing; Global Value; Volatility; Zero Fundamental Value.

∗Department of Finance at Neoma Business School; [email protected]; 1 Rue du Mar´echal Juin, 76130 Mont-Saint-Aignan, France. First version: June 15, 2017. The author would like to thank Campbell Harvey and David Yermack for invaluable comments and input. He also thanks Ed Saiedi (dis- cussant) and conference and seminar participants at the Federal Reserve Bank of Philadelphia, the Fifth Crowdinvesting Symposium in Berlin, the First Annual Toronto FinTech Conference, the Montpellier Business School, and the NEOMA Business School for their helpful comments and suggestions.

1 1 Introduction

A major innovation in financial technology (FinTech), such as blockchain, has great potential to impact the world economy. For example, the foreign exchange market is the world’s largest, with an average trading turnover of $5 trillion per day,1 and crypto- graphic digital currencies (cryptocurrencies) that use blockchain technology can change this market through direct international peer-to-peer electronic payments and forgoing conventional currency trading channels. Additionally, these changes may increase cus- tomer welfare while significantly reducing banks’ revenues from currency trading fees and governments’ revenues from currency trading taxes. However, Bitcoin trading is only around 0.001 percent of the total foreign exchange trading turnover.2 For a much higher turnover, Bitcoin and other digital currencies face two major challenges: first, their prices are too volatile; and second, domestic and international regulations are still lacking. These two challenges are connected and complex. In fact, the lack of regulations may increase digital currency price volatility, and high price volatility makes international regulation more complex. To highlight their complexity, we should consider that pricing and regulating even fiat currencies is difficult and complex. Thus, pricing and regulating digital currencies that use new technologies and have many unknown aspects, is indeed very complex. To shed some light on digital currency pricing, this paper introduces a simple pricing relation for globally traded digital currencies in frictionless markets. The pricing relation is an extended version of the triangular arbitrage relation, which suggests no price discrepancy among any three exchange rates in a frictionless market. Therefore, a competitive digital currency should be exchangeable with any competitive currency without a pricing discrepancy in the absence of triangular arbitrage. Consequently, we can study the price of digital currencies from a global perspective, and not necessarily from the perspective of a U.S. representative agent. In particular, the relation suggests that the appreciation rate of a digital currency against a fiat currency relates to changes in the global value of the fiat currency and changes in the global value of the digital currency. By applying the pricing relation to the data, this study provides some evidence that the U.S. dollar price changes of Bitcoin, unlike other globally traded assets such as commodities and fiat currencies, are slightly negatively correlated with the U.S. dollar price changes of a basket of G10 currencies. In addition, the study also documents Bitcoin price disparities and discrepancies for various fiat currencies, including the U.S. dollar, Euro, British pound, Japanese yen, Canadian dollar, Chinese yuan, and Polish zloty, whose

1Trading in foreign exchange markets averaged $5.1 trillion per day in April 2016, see BIS(2017). 2Bitcoin trading averages $50 million per day, or a market share of about 0.001 percent (≈ $50M/$5T). For more statistics on Bitcoin trading, see B¨ohme,Christin, Edelman, and Moore(2015).

2 bid-ask spread data are available for at least two platforms. This is consistent with the fact that frictions exist in the Bitcoin markets (see Kroeger and Sarkar(2017)) or the price of Bitcoin is manipulated (see Gandal, Hamrick, Moore, and Oberman(2018)). Furthermore, the Bitcoin price discrepancies are 25% higher than the Bitcoin price disparities. More importantly, the suggested pricing relation helps us study the price and volatility of digital currencies with zero fundamental value (see Cheah and Fry(2015) and Athey, Parashkevov, Sarukkai, and Xia(2016)). In particular, the pricing relation suggests that the price of a digital currency with a zero fundamental value should not change against a basket of fiat currencies. The intuition is that there is no fundamental value, such as a claim on a commodity or some lawful money to strengthen or weaken the digital currency relative to fiat currencies. However, when a fiat currency appreciates relative to other fiat currencies, it should also appreciate relative to globally traded digital currencies. Thus, the bilateral price of a digital currency may change relative to a numeraire fiat currency, but does not change against a basket of fiat currencies. Consequently, the price of a digital currency with zero fundamental value should be closely related to the price of numeraire fiat currencies without being pegged to any fiat currency; otherwise, its fundamental value is not zero. In addition, the volatility of a zero-fundamental-value digital currency is even slightly lower than the global volatility of each fiat currency. Therefore, regulating, using, and holding a digital currency with zero fundamental value is much easier than the extant cryptocurrencies. When the price of a digital currency does not vary relative to a basket of fiat currencies, the digital currency performs as a medium of exchange, a store of value, and a unit of account. These characteristics of fiat currencies should hold for a “real” digital currency, as Yermack(2014) suggests. In addition, reassuring users about the value of a digital currency disentangles them from predicting the return and volatility of digital currency price fluctuations, which is a very important concern for digital currency users, which existing cryptocurrenies (like Bitcoin) do not address. In contrast, when the price of a digital currency varies relative to a basket of fiat currencies, it generates volatility that brings extra costs to digital currency users, because users may need to spend time and resources predicting the digital currency price and volatility, which are hard exercises even for fiat currencies. In addition, users may bear extra regulation costs (risks) due to the lack or complexity of regulations. Consequently, because the legitimate core competency of digital currencies is to provide the standard functions of fiat currencies with fewer transaction costs, such as less transaction time and fewer transaction fees,3 the higher volatility of a digital currency may affect its core

3A digital currency may be used in illegal trading, money laundering, and tax evasion (B¨ohme,

3 competency. In other words, the higher utilization costs of a volatile digital currency may oﬀset its lower transaction costs. Finally, this study examines an economy with zero-fundamental-value digital currencies and various participants, including digital currency issuers, miners, market makers, users, and speculators.

2 Digital Currencies

Digital currencies allow for instantaneous domestic and international transactions and transfer-of-ownership. They can also be used for direct peer-to-peer electronic payments to avoid the transaction time and cost of going through a financial intermediary. However, such a transaction may be subject to a double-spending problem. Nakamoto(2008) proposes cryptography as a solution to prevent double-spending.4 Barber, Boyen, Shi, and Uzun(2012) studies the strengths and weaknesses of cryptography and ways to either improve or build on cryptocurrencies like Bitcoin.5 Catalini and Gans(2016) study the impact of the blockchain and cryptocurrencies in reducing transaction time and costs in detail, and identify two major reductions in verification and networking costs. Böhme, Christin, Edelman, and Moore(2015) find that updating the blockchain adds an undesirable delay that makes Bitcoin less competitive for domestic transactions. However, Tasca(2015) and He et al. (2016), among many others, suggest that digital currencies are very competitive for international transactions. Although both market participants and financial regulators agree on the time and cost advantage of digital currencies (see Khapko and Zoican(2017), Luther(2015) suggests that monetary stability and government support play a major role in the competitive- ness of digital currencies. Meanwhile, Evans(2014) finds that deficient incentives and government regulations make digital currencies inferior. Yermack(2014) raises the importance of Bitcoin’s price volatility and its current functionality, which does not match that of a real currency. A later study by Ali, Barrdear, Clews, and Southgate(2014) endorses these findings. 6. In particular, Yermack(2014) Christin, Edelman, and Moore(2015)). In addition, this paper does not consider the use of a digital currency to donate to organizations like Wikileaks or to conduct business anonymously. For more detail, see Grinberg(2011). 4Cryptography turns a hashing transaction into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work, the so-called blockchain. 5Grinberg(2011) suggests that potential users should be aware of various risks of a recently devel- oping digital currency like Bitcoin. Since then, several papers study various aspect of Bitcoins. For example, Moore and Christin(2013) reports a 45% risk of ceased operation in Bitcoin exchanges; Har- vey(2015) reviews Bitcoin technology; Athey, Catalini, and Tucker(2017) study the privacy aspects of Bitcoin through an experiment, and Yermack(2017) studies the impacts of the blockchain on corporate governance. 6For more information about Bitcoin price and volatility, see Kristoufek(2015), Hencic and

4 finds that Bitcoin’s price is much more volatile than that of extant fiat currencies, and that it prevents it from performing properly as a medium of exchange, a store of value, and a unit of account. Dwyer(2015) finds that Bitcoin’s complexity is a disadvantage, as it requires blind faith in anonymous people’s expertise. While domestic regulations of digital currencies are complex, He et al. (2016) argue that international regulations are even more difficult and complex. This complexity is not surprising, considering that even price modeling and international regulations of extant fiat currencies are very complex. In sum, developments in blockchain technology and the supporting legal and security issues created a foundation on which to develop digital currencies, which can reduce the costs of daily international payments. However, users and financial regulators of cryptocurrencies still share concerns about price volatility and international regulations. This paper investigates cryptocurrency price dynamics from an international perspective and finds that the price of a cryptocurrency with zero fundamental value is closely related to the price of fiat currencies, and that its volatility level is even slightly lower than those of fiat currencies. Therefore, international regulations for a zero-fundamental-value cryptocurrency are much easier because they avoid the high volatility and unruly price movement of extant cryptocurrencies.

3 Global Pricing

The global value of globally traded assets, like currencies, commodities, and cryptocurrencies, is better investigated from a global perspective. For example, the Australian dollar may slightly appreciate against the Canadian dollar, while its global value may depreciate signiﬁcantly at the same time. In other words, to investigate the global value of a currency, it is better to study its average appreciation rate relative to a basket of other currencies rather than bilateral rates. For more information about the relation between the global and bilateral appreciation rates of currencies, see Aloosh and Bekaert (2017). From the same perspective, commodity and currency prices, as well as major economic factors, are often given in U.S. dollars, and the appreciation rate of the U.S. dollar aﬀects the appreciation rate of asset prices. Thus, the price of globally traded assets, like commodities, currencies, and cryptocurrencies, is better investigated from a global perspective. In this section, I present a pricing relation for globally traded assets in

Gouri´eroux(2015), Donier and Bouchaud(2015), Kaminski and Gloor(2014), and Ciaian, Rajcaniova, and Kancs(2016). Additionally, for more on Bitcoin price modelling, see Athey, Parashkevov, Sarukkai, and Xia(2016), Balcilara, Bourid, Guptac, and Roubaud(2017), and Bolt and van Oordt(2016)

5 frictionless markets. In particular, I extend the triangular arbitrage relation to separate changes in the global value of a digital currency from changes in the value of its denominated ﬁat currency. Assume an agent uses a domestic ﬁat currency H and a digital currency D, and can exchange D and H as follows:

H H H ∆sD,t+1 = sD,t+1 − sD,t, (1)

H where sD,t+1 is the log exchange rate of domestic ﬁat currency H per unit of digital H currency D at time t, and ∆sD,t+1 is the log appreciation rate of currency D against currency H from time t to time t+1. In the absence of triangular arbitrage, we have

H H i sD,t+1 = si,t+1 + sD,t+1, ∀i, (2)

where, i is a currency in the market. Equation2 suggests that the observed exchange rate for currencies D and H equals their implicit exchange rate through exchanging currency i. In other words, in the absence of a triangular arbitrage opportunity, there is no discrepancy among any three exchange rates D, H, and i. When Equation2 always holds after time t, we get a similar relation among any three exchange rate changes, as follows:

H H i ∆sD,t+1 = ∆si,t+1 + ∆sD,t+1, ∀i (3) For an economy with N ﬁat currencies, Equation3 holds for N ﬁat currency ‘i’s. Additionally, by averaging across N equations, we get

N 1 X ∆sH = (∆sH + ∆si ), (4) D,t+1 N i,t+1 D,t+1 i or, N N 1 X 1 X ∆sH = (∆sH ) + (∆si ). (5) D,t+1 N i,t+1 N D,t+1 i i Equation4 suggests that the direct exchange rate for currencies D and H equals the average implicit exchange rate through exchanging for N fiat currency ‘i’s. In addition, Equation5 suggests that the appreciation rate of digital currency D against fiat currency H equals the average appreciation rate of a basket of N fiat currency ‘i’s against H plus the average appreciations rate of D against a basket of N fiat currency ‘i’s. As there are

6 H N-1 exchange rates among N ﬁat currencies (∆sH,t+1 = 0), we get

" N # " N # N − 1 1 X 1 X ∆sH = (∆sH ) + (∆si ) . (6) D,t+1 N N − 1 i,t+1 N D,t+1 i i

By the same token, Equation6 suggests that the appreciation rate of D against H equals a multiplier of the average appreciation rate of a basket of N-1 ﬁat currencies against H plus the average appreciation rate of D against a basket of N ﬁat currencies.

N − 1 ∆sH = CBH + CBD , (7) D,t+1 N t+1 t+1 H CBt+1 is the average log appreciation rate of a basket of N-1 fiat currencies relative to D fiat currency H and CBt+1 is the average log appreciation rate of currency D relative to a basket of N fiat currencies. Equation7 expresses changes in the bilateral value of D against H as a function of changes in the global value of currency H and changes in the global value of currency D. Consequently, by modeling the changes in the global value of D digital currency D against a basket of fiat currencies, CBt+1, we can explain the changes in the bilateral value of D against any fiat currency. Although I developed the pricing relation in Equation7 to study digital currency prices, others can use it to study the global price of any globally traded asset. In other words, the pricing relation is independent of the underlying global asset D, and it assumes only that there is no pricing discrepancy in frictionless markets. The next section provides an application of Equation7.

3.1 Global Value of Bitcoin

Using Equation7 and the G10 currencies, I constructed the daily changes in the global value of Bitcoin. Table1 reports the mean and standard deviations of changes in the global value of Bitcoin (BGlobal), the U.S. dollar value of Bitcoin (BUSD), and the U.S. dollar value of a basket of G10 currencies (USD). As the table shows, the global value of Bitcoin appreciates by 78% on average against the G10 currencies and the bilateral value of Bitcoin appreciates by 73% on average against the U.S. dollar. Meanwhile, the basket of G10 currencies appreciates by 6% on average against the U.S. dollar in a sample period from January 1st, 2014 to November 5th, 2017. The standard deviation of

BGlobal and BUSD, 55%, is around 7 times higher than the standard deviation of USD, 8%. Bitcoin’s volatility is extremely higher than that of almost all economic factors, making international Bitcoin regulations problematic. Figure1 plots the observed U.S. dollar value of Bitcoin (the solid line) and its global value (the dashed line). As the global value of U.S. dollar appreciates over the sample

7 period, January 1st, 2014 to November 5th, 2017, the global value of Bitcoin is higher than its U.S. dollar value. In other words, the global value of Bitcoin is even more overpriced than its U.S. dollar value. For example, the global value of Bitcoin was around 16.9% more than the U.S. dollar value of Bitcoin ($7421.9) on November 5th, 2017.

In the next section, we compare the correlation properties of BGlobal with those of selected ﬁat currencies, including the U.S. dollar, Euro, British pound, Canadian dollar, and Japanese yen, and three commodities: oil, gold, and sugar.7

3.2 Correlations

To test whether Bitcoin is priced like a commodity or a fiat currency, I compare the correlation properties of changes in the value in Bitcoin with those of three major commodities and three major fiat currencies. When the U.S. dollar price of fiat currencies increases (decreases), we expect the U.S. dollar price of commodities to increase (de- crease). In other words, the U.S. price changes of fiat currencies and commodities should be positively correlated. Table2 Panel I reports the correlations between the U.S. dollar price changes of Bitcoin traded on various platforms and the U.S. dollar price changes of a basket of G10 currencies (USD). Panels II and III report the correlation between the USD and the U.S. dollar price changes of commodities and fiat currencies, respectively. The sample period varies from one platform to another. In Panel I, the U.S. dollar price changes of Bitcoin and the U.S. dollar price changes of a basket of G10 currencies (USD) are mostly negatively correlated at various horizons, except for campbx.8 However, changes in the global value of the U.S. dollar and changes in the U.S. dollar price of commodities and fiat currencies are highly positively correlated. Therefore, in contrast to the U.S. dollar price changes of commodities and fiat currencies, the U.S. dollar price changes of Bitcoin are not positively correlated with the changes in the global value of the U.S. dollar.

3.3 Single Perspective versus Global Perspective

The correlation between currencies and asset prices is critical for investment, risk man- agement, and currency hedging policies. In addition, as asset prices are denominated in a fiat currency (the U.S. dollar), their correlation depends on variations in their denominated fiat currency. Equation7 helps to separate the impact of denominated fiat currency variations and to understand asset price correlations better. The left panels of

7The U.S. dollar, Euro, British pound, Canadian dollar, and Japanese yen are the most liquid or traded ﬁat currencies; oil is the most important commodity, and gold and sugar represent investment and consumption goods, respectively. 8Campbx is a Bitcoin trading platform.

8 Table3 report the correlations among oil, gold, and sugar from a U.S. dollar and global perspective. For example, oil and gold are barely correlated based on their U.S. dollar price changes in the sample period from June 25, 2015 to October 31, 2017. However, they are 10% negatively correlated from a global perspective. In contrast, oil and sugar are 4% positively correlated based on their U.S. dollar values, while they are almost uncorrelated from a global perspective. All three cross-commodity correlations are lower in the bottom panel than in the top panel. We have similar results for fiat currency correlations. Some fiat currencies are positively correlated based on their U.S. dollar values, for example, the U.S. dollar and European currencies, but negatively correlated from a global perspective. By the same token, the Japanese yen and the British pound are almost uncorrelated from a U.S. dollar perspective, while they are actually 44% negatively correlated from a global perspective. All cross-currency correlations are much lower in the bottom panel than in the top panel. The top left panel of Table3 reports the correlations among Bitcoin prices in various fiat currencies and on various platforms.9 The Bitcoin correlations vary from 90% to 98%. Since the underlying asset Bitcoin is identical in every series, we may think that imperfect correlations are due to co-movements in their denominated fiat currency. However, the impact of the denominated fiat currency co-movements is eliminated in the bottom panel and the Bitcoin correlations are still far from perfect from a global perspective. Some correlations increased by 1%, but all are nearly the same in the top and bottom panels. Therefore, the imperfect Bitcoin correlations are not due to the impact of their denominated fiat currencies. This also confirms that Bitcoin price dynamic is not similar to that of commodities nor fiat currencies. In the next section, I test Bitcoin price discrepancies among fiat currencies traded on various platforms, and I compare Bitcoin price discrepancies and disparities.

3.4 Bitcoin Mispricing

A simple rule known as the law of one price implies that a currency should be traded at the same rate on various exchanges in the absence of friction. Yermack(2014) documents a disparity of around 7% between the high and low quotes of Bitcoin on ﬁve platforms with the highest trading volumes quoting Bitcoin prices in the U.S. dollar. In a recent study, Kroeger and Sarkar(2017) use bid-ask spread data from Bitcoinity, a new Bitcoin dataset, to study the U.S. dollar price disparities in Bitcoin further, documenting disparities on several platforms. Furthermore, Kroeger and Sarkar(2017) investigates Bitcoin market frictions and their impacts on Bitcoin price disparities. Using bid-ask spread data from

9For each ﬁat currency, I report Bitcoin prices for the platform with the highest trading volumes. For example, Kraken has the highest Bitcoin trading volume against the Euro.

9 Bitcoinity, I further investigate Bitcoin price discrepancies and disparities for various fiat currencies, including the Euro, Canadian dollar, British pound, Chinese yuan, and Polish zloty, and compare the magnitude of Bitcoin price discrepancies and disparities for individual fiat currencies and for all fiat currencies together. When Bitcoin price disparities exist for various fiat currencies, there might be two simultaneous price disparities for different fiat currencies, and this may generate a price discrepancy higher than the price disparities.10 To test this conjecture, I focus on Bit- coin exchanged for the U.S. dollar, Euro, Canadian dollar, British pound, Japanese yen, Chinese yuan, and Polish zloty, whose bid-ask spread data are available on at least two platforms. Thus, I can examine at least one potential Bitcoin price disparity for each fiat currency and compare it with various Bitcoin price discrepancies across these fiat currencies.11 Therefore, using bid-ask spread and mid prices, I obtain two Bitcoin quotes for each denominated fiat currency, a bid and an ask quote, on each platform. When two platforms are available to trade Bitcoin for a fiat currency, we may observe different bid and ask quotes across platforms. If the Bitcoin ask-quote on one platform is lower than the Bitcoin bid-quote on another, it is profitable to buy Bitcoin at the lower price (ask) on the first platform and sell it simultaneously at the higher price (bid) on the second platform. By the same token, it might be even more profitable to buy Bitcoin at the lowest price (ask) in one fiat currency and selling it simultaneously at the highest price (bid) in another fiat currency and exchange the second fiat currency for the first. The earlier pricing mismatch is called a disparity and the latter is a discrepancy. Table5 reports Bitcoin price disparities and discrepancies for the U.S. dollar, Euro, Canadian dollar, British pound, Japanese yen, Chinese yuan, and Polish zloty. In Panel I, the diagonal elements report the highest Bitcoin price disparities for each fiat currency. For example, in row 3 of column 2, 4.72%, is the time series average of the highest U.S. dollar price disparities observed across Bitcoin trading platforms. In the same row, the other numbers are Bitcoin price discrepancies based on the lowest U.S. dollar ask quotes and the highest other fiat currency bid quotes. In the same column, the other numbers

10Another simple rule in foreign exchange markets is that a pricing discrepancy among any three exchange rates generates an arbitrage opportunity, which is usually exploited quickly by algorithmic traders in a competitive market. In other words, when an exchange rate between two currencies (e.g., USD/EUR) is not aligned with their implicit exchange rate through a third currency (e.g., USD/GBP times GBP/USD), a trader equipped with a machine recognizes it quickly and uses a triangular arbitrage strategy to exchange the three rates simultaneously (e.g., USD/GBP, GBP/USD, and USD/EUR) to obtain a zero-risk profit. Therefore, exchange rates adjust quickly and a profitable triangular arbitrage is very rare in a competitive exchange market. 11Otherwise, I can investigate Bitcoin price discrepancies for another 9 fiat currencies, including the Australian dollar, Brazilian real, Indonesian rupiah, Israeli shekel, Korean won, Mexican peso, Russian ruble, Singapore dollar, and Ukrainian hryvnia, and Philadelphia Gold and Silver Index (XAU), whose bid-ask spreads are available on only one platform. However, I cannot evaluate potential Bitcoin price disparities for these fiat currencies.

10 are Bitcoin price discrepancies based on the lowest ask quotes in other fiat currencies and the highest U.S. dollar bid quotes. As can be seen, the price discrepancies are higher than the price disparities in every row. There are also higher price discrepancies than price disparities in every column, except the in the second, which are for the U.S. dollar. To compare the highest price discrepancies and disparities for each fiat currency, Panel II reports the time series average of the highest price disparities for the observed lowest Bitcoin ask quote for each fiat currency. As can be seen, the average price discrepancies in Panel II are much higher than the diagonal price disparities in Panel I are. This is consistent with the higher price discrepancies than price disparities in Panel I. However, some may argue that the price discrepancies may include a high bid quote of the highest price disparities in other fiat currencies, and thus the highest price disparities might be higher than the highest price discrepancies. To address this concern, Panel III reports the time series average and maximum highest price disparities and discrepancies for the lowest observed Bitcoin ask price.12 The time series average of highest Bitcoin price discrepancies is 25% higher than the time series average of highest price disparities, 6.59%. The maximum highest Bitcoin price discrepancy, 117.09%, is also higher than the maximum highest Bitcoin price disparity, 103.16%. Figure1 plots the time series of Bitcoin price disparities (red points) and Bitcoin price discrepancies (blue points) for the U.S. dollar, Euro, Canadian dollar, British pound, Japanese yen, Chinese yuan, and Polish zloty. In addition, the bottom right graph of Figure1 plots the time series of maximum Bitcoin price disparities and discrepancies. Bit- coin price disparities are almost as high as the price discrepancies for the U.S. dollar and the Euro, and Bitcoin price disparities are much lower than the price discrepancies are for the other fiat currencies. Bitcoin price disparities and discrepancies across fiat currencies vary in line with each other. For example, the high Euro price disparities of Bitcoin in March 2016 provide high Bitcoin price discrepancies for the other fiat currencies. In the next section, I use Equation7 to study the theoretical price and volatility of digital currencies with zero fundamental values.

4 A Digital Currency with Zero Fundamental Value

Any currency should store some value, and a digital currency pegged to a ﬁat currency obviously does not have zero fundamental value. Thus, we need to ask whether can a non-pegged zero-fundamental-value digital currency can store value. Furthermore, de- spite many arguments about the fundamental value of digital currencies, we have no intuition for the price dynamics of a zero-fundamental-value digital currency. In partic-

12In other words, the actual highest Bitcoin price discrepancies may be slightly higher.

11 ular, a digital currency with zero fundamental value that is not tied to any economic or government value, should neither appreciate nor depreciate against fiat currencies. Then, we also need to ask what the price of zero-fundamental-value digital currency is in fiat currency units. As the global (denominated neutral) price of zero-fundamental-value digital currency D should not change relative to a basket of fiat currencies, Equation7 provides a simple and interesting relation:

D CBt+1 = 0. (8) Under this condition, the global value stored in a zero-fundamental-value digital currency does not change against a basket of fiat currencies. By replacing Equation8 in Equation7, the price change of zero-fundamental-value digital currency D against a fiat currency H equals N − 1 ∆sH = CBH . (9) D,t+1 N t+1 Consequently, the price of a digital currency D in units of fiat currency H closely follows the global value of currency H, which is a constant multiplier of the appreciation rate of a basket of fiat currencies against H. For example, when the value of currency H appreciates by 0.50% relative to a basket of 9 other fiat currencies, the value of currency H appreciates 9 by 0.45% (= 10 × 0.50%) relative to zero-fundamental-value digital currency D. In other words, the global value stored in zero-fundamental-value digital currency D is constant relative to a basket of fiat currencies, but it may change relative to an individual fiat currency depending on the global value change of the fiat currency. Interestingly, Equation9 suggests that the volatility of a zero-fundamental-value dig- H H ital currency is even lower than that of a fiat currency (σ(∆sD,t+1) < σ(CBt+1) as N−1 N < 1). In addition, the price of a digital currency with a zero fundamental value, as in Equation9, does not depend on the supply of the digital currency, competition between digital currencies, speculation in digital currency, or digital currency investors’ sentiments. Consequently, regulating, holding, and using such a digital currency is much easier. This is very important to regulators, as the prices of extant cryptocurrencies are highly volatile and unruly. In addition, as a digital currency with zero fundamental value has low volatility, it serves reliably as a store of value, as a unit of account in commercial markets, and as a medium of exchange. The next section studies an economy with a zero-fundamental-value digital currency.

12 4.1 Market Conditions for a Zero-Fundamental-Value Digital Currency

In this section, I explore the details of a market for a digital currency that follows the price condition suggested in Equation9. In particular, I study its market quotes, bid- ask spread, blockchain type, market making, speculating, users’ exchange risk, and an economy with several such digital currencies.

4.1.1 Price of a Zero-Fundamental-Value Digital Currency

Assuming that the initial price of zero-fundamental-value digital currency D in units of currency H is given, together with real-time bid and ask rates of fiat currencies, we can use changes in the mid-price of fiat currency H against a basket of fiat currencies to determine the price changes of zero-fundamental-value digital currency D against H, as follows:

N − 1 sH = sH + CBH,mid. (10) D,t+1 D,t N t+1 This equation is similar to Equation9. The only difference is that the global value changes of fiat currency H is calculated using mid-quotes for practical purposes.13 For example, assuming that a zero-fundamental-value digital currency is introduced to the H market at time t at the price of sD,t against currency H, then its future price against currency H follows changes in the global value of currency H, as in Equation 10. Buying and selling orders match at the quoted price of the zero-fundamental-value digital currency. Assuming trading costs, users buy and sell digital currencies at slightly different quotes, as follows: bid quote: H,bid H H,bid sD,t+1 = sD,t+1 − fD,t+1, (11) ask quote: H,ask H H,ask sD,t+1 = sD,t+1 + fD,t+1, (12)

H,bid H,ask where 0 ≤ fD,t+1 is the selling cost and 0 ≤ fD,t+1 is the buying cost for a zero- fundamental-value digital currency.

4.1.2 Bid-Ask Spreads

Assume that a user with a domestic fiat currency H buys (sells) a product from (to) a foreign company, and that she can make (receive) her payment in a foreign fiat currency K in two ways. She can either exchange domestic and foreign fiat currencies (H-K) directly

13See AppendixA for details.

13 in a fiat currency exchange market, or use a digital currency for an indirect exchange of domestic and foreign fiat currency (H-D and D-K) in a digital currency exchange market. The difference between the choices is that her payment is subject to one bid-ask spread in the first method and to two bid-ask spreads in the second. To ensure better deals in a digital currency market than a fiat currency market, the sum of the two transaction costs in the digital currency market should be lower than the transaction cost in the fiat currency market. Consequently, transaction costs are half as much as or less than in the digital currency market. In other words, the bid-ask spread of exchanging H for D should be less than half the minimum bid-ask spread of exchanging H for any other fiat currency. See AppendixB for details.

4.1.3 Blockchain

Extant cryptocurrencies use two types of blockchain: a permissionless blockchain like Bit- coin, and a permissioned blockchain like Ripple. In a permissionless blockchain, anyone can join the blockchain network and compete to verify transactions for a cryptocurrency reward, known as a mining reward. However, in a permissioned blockchain, only a re- stricted set of users can verify transactions. Therefore, in contrast to a permissionless blockchain, the identity of users is known to the ledger and the transaction speed is higher. The issuer of a zero-fundamental-value digital currency may choose either type of blockchain.

4.1.4 Market Making

When liquidity decreases and the bid-ask spread widens in the digital currency market, a digital currency market maker may provide liquidity for a profit equal to her quoted bid-ask spread per unit of transactions. Thus, she makes a smaller profit than the bid-ask spread for every unit pair of the digital currency that she buys and sells (see AppendixC for details). Meanwhile, the trading volume, liquidity, and bid-ask spreads of extant digital currencies are much lower than those of fiat currencies are. Therefore, market making is less profitable for zero-fundamental-value digital currencies than for fiat currencies.

4.1.5 Speculation

In a zero-fundamental-value digital currency market, speculation proﬁt is closely related to the changes in the global value of ﬁat currencies and the bid-ask spread of trading zero- fundamental-value digital currencies. Since volatile markets attract speculators, such as extant cryptocurrency markets, speculation in zero-fundamental-digital currency markets

14 is much less attractive than it is for both extant cryptocurrencies and ﬁat currencies. See AppendixD for details.

4.1.6 Digital Currency Users

Individuals and companies who buy or sell products and services in foreign currencies are increasingly interested in digital currencies. It is crucial for them to evaluate the exchange rate risk of digital currencies. Costumers prefer a less volatile digital currency, and companies prefer less volatile cash flows to reduce their cost of financing. If costumers and companies hold assets in digital currencies that are more volatile than fiat currencies are, they are exposed to more risk. Consequently, they should not hold such digital currencies, but use them only as media of exchange when they pay or receive funds. In particular, when digital currency price changes relative to a basket of fiat currencies, D CBt+1 6= 0:

N − 12 N − 1 σ2 ∆sH = σ2 CBH +σ2 CBD +2 cov CBH ,CBD . (13) D,t+1 N t+1 t+1 N t+1 t+1

This equation suggests that when the covariance between currencies D and H have small fluctuations, even a tiny volatility in the price of currency D against a basket of fiat D currencies, σ CBt+1 , increases the volatility of the exchange rate between fiat currency H H and digital currency D, σ ∆sD,t+1 . Unfortunately, extant digital currencies are extremely volatile and have a low covariance with fiat currencies. These increase users’ exchange rate risk significantly. Furthermore, dollar currencies, such as the U.S. dollar, Canadian dollar, and Aus- tralian dollar, are negatively correlated with European currencies, such as the Euro, Swiss franc, Norwegian krona, and Swedish krona.14 Therefore, it is almost impossi- ble to introduce a digital currency that correlates negatively with all fiat currencies. Consequently, any digital currency with a volatile value against a basket of fiat cur- D rencies 0 < σ CBt+1 increases the exchange rate risk for some users. However, a zero-fundamental-value digital currency, whose value does not vary against a basket of fiat currencies, as in Equation8, does not increase users’ exchange rate risk.

4.1.7 An Economy with Several Zero-Fundamental-Value Digital Currencies

Political, economic, and many other factors may lead to a global economy with multiple zero-fundamental-value digital currencies, where one zero-fundamental-value digital cur- 14For more information about correlation between currency-basket factors, see Aloosh and Bekaert (2017).

15 rency is used in a region or for a speciﬁc purpose, and another zero-fundamental-value digital currency used in another region or for another purpose. Thus, it is useful to know the relative prices of two zero-fundamental-value digital currencies. As I suggest in this study, the price of a zero-fundamental-value digital currency is constant relative to a basket of ﬁat currencies. Therefore, the prices of zero-fundamental-value digital currencies are constant relative to each other. See AppendixE for details.

5 Conclusions

To shed some light on digital currency pricing, this paper introduces a pricing relation for digital currencies as globally priced assets in frictionless markets. The pricing relation is an extended version of the triangular arbitrage relation and helps to distinguish changes in the global value of denominated fiat currency from changes in the global value of the underlying assets, such as digital currencies, fiat currencies, and commodities. Using the pricing relation, I find that the U.S. dollar price changes of Bitcoin, unlike other globally traded assets such as commodities and fiat currencies, are slightly negatively correlated with the U.S. dollar price changes of a basket of G10 currencies. In particular, Bitcoin price changes exhibit different correlations from those of commodities and fiat currencies. For example, in contrast to the U.S. dollar price changes of commodities and fiat currencies, the U.S. dollar price changes of Bitcoin are not positively correlated with the U.S. dollar price changes of a basket of fiat currencies. In addition, Bitcoin’s value against various fiat currencies on various platforms does not correlate perfectly. Specifically, their correlation varies from 88% to 96%, and these imperfect correlations do not depend on co-movements in their denominated fiat currencies. In addition, I document Bitcoin price disparities and discrepancies for various pairs of denominated currencies, including the U.S. dollar, Euro, British pound, Japanese yen, Canadian dollar, Chinese yuan, and Polish zloty. The Bitcoin price discrepancies for each fiat currency are much higher on average than its Bitcoin price disparity. On average, the maximum Bitcoin price discrepancies are 25% higher than the maximum Bitcoin price disparities. Finally, I study the theoretical price and volatility of digital currencies with zero fundamental values and find that they have low price volatility. Therefore, they are much easier to regulate, use, and hold. This is important to regulators, investors, and users because existing cryptocurrencies are extremely volatile, which makes their pricing and international regulation very complex.

16 References

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19 A Global value of ﬁat currency H

Using bid and ask quotes of currency H against other fiat currencies, the appreciation rate of a basket of fiat currencies with respect to the mid-quote of fiat currency H is as follows: N " H,bid H,ask ! H,bid H,ask !# X si,t+1 + si,t+1 si,t + si,t CBH,mid = − , (14) t+1 2 2 i=1 B Bid-Ask Spreads in a Digital Currency Market

When the bid-ask spread of exchanging H for D is less than or equal to half the minimum bid-ask spread of exchanging H for any other ﬁat currency:

( H,ask ) ( H,bid ) f f f H,ask ≤ min i,t+1 & f H,bid ≤ min i,t+1 ∀i. (15) D,t+1 2 D,t+1 2

The intuition is that a user pays only one transaction cost to exchange currencies H and K, while she pays two transaction costs in the digital currency market for an equivalent exchange of currencies H and K. In addition, when the transaction cost in a digital currency market does not vary for various ﬁat currencies, Equation 15 should hold to ensure a better exchange deal in a digital currency market than in a ﬁat currency market.15 For example, assume that she should pay for a product in currency K. Through an indirect exchange for digital currency D, she gets:

K,ask D,ask K,mid K,ask D,mid D,ask sD,t+1 − sH,t+1 = sD,t+1 + fD,t+1 − sH,t+1 − fH,t+1 , (16)

K,ask D,ask K,mid K,ask D,ask sD,t+1 − sH,t+1 = sH,t+1 + fD,t+1 + fH,t+1 . (17)

H,ask D,bid 16 Assuming that fD,t+1 = fH,t+1, we get:

K,ask D,ask K,mid K,ask H,bid sD,t+1 − sH,t+1 = sH,t+1 + fD,t+1 + fD,t+1 , (18)

15When the user exchanges K for D, the equation would be:

(f K,ask ) (f K,bid ) f K,ask ≤ min i,t+1 & f K,bid ≤ min i,t+1 ∀i. D,t+1 2 D,t+1 2

16 H,ask 1 D,bid The accurate equation is fD,t+1 = D,mid fH,t+1. However, to simplify the notations, I assume that sH,t+1 H,ask D,bid fD,t+1 = fH,t+1 for the same amount of trading. For example, assume that the transaction cost of exchanging 1.0H for 0.5K is 0.001H, and then assume a transaction cost of 0.5K for 1.0H is 0.001H, which is equivalent to a transaction cost of 0.002H to exchange 1.0K for 2.0H.

20 By substituting Equation 15 into Equation 18, we get:

f K,ask + f H,bid sK,ask − sD,ask ≤ sK,mid + H,t+1 K,t+1 , (19) D,t+1 H,t+1 H,t+1 2

K,ask H,ask K,bid H,bid assuming that fH,t+1 = fK,t+1 = fH,t+1 = fK,t+1, we get:

K,ask D,ask K,mid K,ask sD,t+1 − sH,t+1 ≤ sH,t+1 + fH,t+1 , (20)

K,ask D,ask K,ask sD,t+1 − sH,t+1 ≤ sH,t+1, (21) Therefore, as the transaction costs are half as much as or less in the digital currency market, Equation 15 ensures that the user is better off transacting through a digital currency, D. In other words, if the two parties exchange their fiat currencies directly in the fiat currency market, they either pay more or receive less money, as they should pay higher transaction fees.

C Market Making Proﬁt

H,bid H,ask When the bid-ask spread widens, 0 fD,t+1 & 0 fD,t+1, a market maker provides liquidity for a proﬁt per-unit of a buy-sell transaction, which equals his quoted bid-ask spread. Therefore, the market maker’s return (MMR) per buy-sell transaction of one unit of digital currency is as follows:

N − 1 N − 1 MMR = sH + CBH,mid + f MM,ask − sH + CBH,mid − f MM,bid , D,t N t+1 t+1 D,t N t+1 t+1 (22) MM,bid H,ask MM,ask H,bid where, ft+1 ≤ fD,t+1 & ft+1 ≤ fD,t+1; thus,

MM,bid MM,ask H,ask H,bid MMR = ft+1 + ft+1 ≤ fD,t+1 + fD,t+1, (23) Equation 23 shows that a market maker will make a smaller proﬁt than the bid-ask spread.

D Speculation Proﬁt

When domestic ﬁat currency H appreciates relative to digital currency D at time t, speculators buy currency D and hold it until time T, when H depreciates. Then, they

21 sell their currency D to make a proﬁt, as follows: Speculator’s Return

H,bid H,bid = sD,T +1 − sD,t+1 − r(T − t), (24)

N − 1 N − 1 = sH + CBH,mid − f H,bid − sH − CBH,mid − f H,ask − r(T − t), (25) D,T N T +1 D,T +1 D,t N t+1 D,t+1

T ! N − 1 X = CBH,mid − f H,ask + f H,bid − r(T − t), (26) N i+1 D,t+1 D,T +1 i=t where r is the continuously compounding interest rate.

E Relative Price of Zero-Fundamental-Value Digital Currencies

H H H H H H Following Equation1, we have: sD,t+1 = sD,t + ∆sD,t+1 and sD0,t+1 = sD0,t + ∆sD0,t+1, H H where, D and D’ are two zero-fundamental-value digital currencies, and sD,t and sD0,t are their log exchange rates against ﬁat currency H, respectively. According to Equation8, H H N−1 H we have: ∆sD,t+1 = ∆sD0,t+1 = N CBt+1. Thus, we get;

H H H H D0 sD,t+1 − sD0,t+1 = sD,t − sD0,t = sD (27)

This equation suggests that the diﬀerence between the log exchange rates of the two zero-fundamental-value digital currencies against a ﬁat currency are constant over time. In other words, under the suggested price condition in Equation8, the exchange rate of D0 the two zero-fundamental-value digital currencies, sD , is constant over time.

22 Figure 1: The U.S. Dollar and the Global Value of Bitcoin The ﬁgure plots the observed U.S. dollar price of Bitcoin (the solid line) and the changes in the global value of Bitcoin w.r.t. the G10 currencies, as in Equation7 (the dashed line). As the U.S. dollar appreciates against a basket of G10 currencies in the sample period, the global value of Bitcoin (Bitcoin Global) is higher than its U.S. dollar price (Bitcoin USD). The sample period is from January 1st, 2014 to November 5th, 2017.

23 Figure 2: Bitcoin Price Disparities and Discrepancies. The figure reports the percentage Bitcoin price disparities and discrepancies for the U.S. dollar, Euro, Canadian dollar, British pound, Japanese yen, Chinese yuan, and Polish zloty. For example, in the top left graph, the Bitcoin price disparities (red points) represent the differences between the maximum USD bid and minimum USD ask quotes for Bitcoin across various platforms divided by the minimum USD ask quote. The Bitcoin price discrepancies (blue points) represent the differences between maximum other24 fiat currency bid quotes for Bitcoin multiplied by the USD bid quotes of fiat currencies divided by the minimum USD ask quotes for Bitcoin across various platforms minus one. Sample periods are limited to the availability of bid-ask spreads on Bitcoinity (see Table4). Table 1: Descriptive Statistics

BGlobal BUSD USD Mean 0.78 0.73 -0.06 S.D. 0.55 0.55 0.08

The table reports the daily means and standard deviations (S.D.) for the U.S. dollar price changes of a basket of G10 currencies (USD), the observed U.S. dollar price changes of Bitcoin (BUSD), and the global value changes of Bitcoin against a basket of G10 currencies (BGlobal), as in Equation7. The sample period is from January 1 st, 2014 to November 5th, 2017.

25 Table 2: Correlations

Panel I Panel I Panel III Platform Name #Obs USD Gold Oil Sugar EUR JPY GBP

bitbay 580 -0.06 0.45 0.22 0.10 0.80 0.64 0.65 bitcurex 236 -0.03 0.32 0.25 0.16 0.83 0.35 0.67 bitﬁnex 1144 -0.02 0.37 0.20 0.12 0.80 0.51 0.65 bitstamp 1488 -0.02 0.40 0.24 0.14 0.82 0.44 0.66 bitx 691 -0.04 0.39 0.22 0.14 0.80 0.49 0.64 btce 1179 -0.01 0.37 0.21 0.12 0.79 0.48 0.65 campbx 1249 0.04 0.35 0.27 0.17 0.83 0.41 0.67 cexio 538 -0.04 0.37 0.21 0.12 0.81 0.47 0.66 coinbase 692 -0.01 USD 0.39 0.23 0.12 0.79 0.48 0.64 exmo 619 -0.04 0.38 0.21 0.10 0.82 0.47 0.65 gemini 507 -0.04 0.37 0.22 0.11 0.82 0.48 0.66 hitbtc 947 -0.02 0.37 0.21 0.11 0.80 0.50 0.64 itbit 925 0.00 0.35 0.21 0.10 0.80 0.50 0.64 kraken 902 -0.03 0.37 0.22 0.11 0.80 0.50 0.64 lakebtc 726 -0.02 0.36 0.23 0.12 0.79 0.49 0.65 okcoin 790 -0.02 0.39 0.22 0.12 0.80 0.51 0.65 therocktrading 1127 -0.05 0.38 0.22 0.12 0.80 0.46 0.64

The table reports the correlations and number of observations for Bitcoin platforms that trade the U.S. dollar. Panel I reports the correlations between Bitcoin’s USD-price changes and the G10 currency basket USD-price changes. Panels II and III report the correlations between the G10 currency basket USD-price changes and three major commodities’ USD-price changes and three major ﬁat currencies’ USD-price changes, respectively. The three major commodities are gold, oil, sugar; and the three major ﬁat currencies are the Euro, Japanese yen, and British pound. The sample periods vary from July 8th, 2012 to November 5th, 2017.

26 Table 3: Single-Perspective versus Global-Perspective Correlations

Single Perspective

EUR CAD GBP JPY CNY P LN Gold Oil Sugar EUR CAD GBP JPY CNY PLN Bkraken Bquadrigacx Bcoinfloor Bbitflyer Bokcoin Bbitmarketpl EUR Gold 1.00 EUR 1.00 Bkraken 1.00 CAD Oil -0.01 1.00 CAD 0.28 1.00 Bquadrigacx 0.96 1.00 GBP Sugar 0.04 0.10 1.00 GBP 0.49 0.37 1.00 Bcoinfloor 0.98 0.95 1.00 JPY JPY 0.43 0.07 0.02 1.00 Bbitflyer 0.95 0.92 0.93 1.00 CNY CNY 0.33 0.28 0.32 0.27 1.00 Bokcoin 0.91 0.91 0.91 0.92 1.00 P LN PLN 0.80 0.39 0.55 0.26 0.33 1.00 Bbitmarketpl 0.96 0.94 0.96 0.92 0.90 1.00 Global Perspective 27 EUR CAD GBP JPY CNY P LN Gold Oil Sugar EUR CAD GBP JPY CNY PLN Bkraken Bquadrigacx Bcoinfloor Bbitflyer Bokcoin Bbitmarketpl EUR Gold 1.00 EUR 1.00 Bkraken 1.00 CAD Oil -0.10 1.00 CAD -0.53 1.00 Bquadrigacx 0.95 1.00 GBP Sugar 0.01 0.08 1.00 GBP -0.07 -0.10 1.00 Bcoinfloor 0.98 0.95 1.00 JPY JPY 0.09 -0.31 -0.44 1.00 Bbitflyer 0.95 0.92 0.94 1.00 CNY CNY -0.17 0.10 -0.08 0.17 1.00 Bokcoin 0.91 0.90 0.92 0.92 1.00 P LN PLN 0.49 -0.24 0.12 -0.22 -0.26 1.00 Bbitmarketpl 0.96 0.93 0.95 0.92 0.89 1.00

The table reports the daily correlations among commodities, ﬁat currencies, and Bitcoin from a single currency perspective and a G10 currency basket (global) perspective in the top and bottom panels, respectively. The left panels report correlations among oil, sugar, and gold. The middle panels report the correlations among the Euro, Canadian dollar, British pound, Japanese yen, Chinese yuan, and Polish Zloty. The right panels report the correlations among Bitcoin prices for Euro, Canadian dollar, British pound, Japanese yen, Chinese yuan, and Polish Zloty. The sample period is from June 25th, 2015 to October 31st, 2017. Table 4: Summary of Bitcoin Exchange Platforms

Denominated Fiat Currencies Platform Name CAD CNY EUR GBP JPY PLN USD bitbay 13/10/15 - 05/11/17 13/10/15 - 05/11/17 13/10/15 - 05/11/17 bitcoinde 03/02/14 - 05/11/17 bitcoincentral 18/03/13 - 14/06/16 bitcurex 04/03/13 - 14/10/16 04/03/13 - 14/10/16 04/03/15 - 14/10/16 bitfinex 09/10/13 - 05/11/17 bitflyer 11/02/17 - 05/11/17 bitmarketpl 08/12/15 - 05/11/17 08/12/15 - 05/11/17 bitstamp 30/05/16 - 05/11/17 06/11/12 - 05/11/17 bitx 17/08/15 - 05/11/17 17/08/15 - 05/11/17 17/08/15 - 05/11/17 btcchina 09/04/13 - 30/09/17 btce 15/02/13 - 25/07/17 08/07/12 - 25/07/17 campbx 14/04/13 - 05/11/17 cexio 26/08/15 - 05/11/17 26/08/15 - 05/11/17 28 clevercoin 04/03/16 - 29/06/16 coinbase 01/09/15 - 29/07/16 02/05/15 - 05/11/17 02/05/15 - 05/11/17 26/01/15 - 05/11/17 coinfloor 10/0814 - 05/11/17 exmo 14/04/15 - 05/11/17 14/04/15 - 05/11/17 gemini 08/10/15 - 05/11/17 hitbtc 01/08/14 - 05/11/17 01/08/14 - 05/11/17 huobi 23/12/13 - 20/05/17 itbit 08/03/14 - 05/11/17 22/01/14 - 05/11/17 kraken 04/08/15 - 05/11/17 20/09/13 - 05/11/17 04/08/15 - 05/11/17 04/08/15 - 05/11/17 15/02/14 - 05/11/17 lakebtc 19/08/14 - 17/01/17 19/08/14 - 01/04/17 okcoin 28/05/14 - 13/06/17 29/07/14 - 13/06/17 paymium 09/01/17 - 05/11/17 quadrigacx 29/10/15 - 05/11/17 therocktrading 27/11/16 - 05/11/17 27/11/16 - 05/11/17

The table reports the availability of daily bid-ask spread of Bitcoin exchanges for seven denominated ﬁat currencies, including the U.S. dollar (USD), Euro (EUR), Canadian dollar (CAD), British pound (GBP), Japanese yen (JPY), Chinese yuan (CNY), and Polish zloty (PLN). To compare Bitcoin price disparities and discrepancies, the table includes only denominated ﬁat currencies traded on at least two Bitcoin exchange platforms. Table 5: Descriptive Statistics for Bitcoin Price Disparities and Discrepancies

Disparity and Discrepancy Panel I USDUSD EURUSD CADUSD GBPUSD JPYUSD CNYUSD PLNUSD Mean 4.72% 5.32% 3.63% 2.95% 3.26% 2.91% 2.56% Max 94.99% 89.32% 90.26% 86.56% 87.20% 100.26% 87.97% USDEUR EUREUR CADEUR GBPEUR JPYEUR CNYEUR PLNEUR Mean 4.30% 4.26% 3.49% 2.64% 3.24% 2.05% 1.86% Max 109.23% 103.16% 91.95% 92.87% 117.09% 95.70% 92.68% USDCAD EURCAD CADCAD GBPCAD JPYCAD CNYCAD PLNCAD Mean 2.75% 2.60% 0.71% 0.78% 0.83% 1.24% 0.81% Max 64.75% 24.99% 9.49% 6.74% 18.89% 12.02% 7.15% USDGBP EURGBP CADGBP GBPGBP JPYGBP CNYGBP PLNGBP Mean 3.54% 3.56% 1.19% 0.79% 0.98% 0.84% 0.75% Max 66.74% 79.94% 15.96% 16.27% 23.01% 12.78% 13.56% USDJPY EURJPY CADJPY GBPJPY JPYJPY CNYJPY PLNJPY Mean 1.85% 1.76% 0.54% 0.47% 0.16% 0.53% 0.31% Max 55.70% 23.16% 8.14% 11.08% 10.91% 8.29% 8.25% USDCNY EURCNY CADCNY GBPCNY JPYCNY CNYCNY PLNCNY Mean 3.62% 3.77% 2.24% 1.74% 2.24% 0.21% 1.49% Max 60.20% 82.03% 25.87% 28.33% 33.97% 3.79% 25.58% USDPLN EURPLN CADPLN GBPPLN JPYPLN CNYPLN PLNPLN Mean 2.68% 2.74% 0.84% 0.70% 0.68% 1.04% 0.04% Max 63.68% 81.59% 7.44% 8.60% 18.47% 43.98% 2.27% Discrepancy Panel II USD EUR CAD GBP JPY CNY PLN Mean 6.22% 5.05% 4.32% 4.93% 3.15% 4.82% 4.01% Max 100.26% 117.09% 64.75% 79.94% 55.70% 82.03% 81.59% Disparity Discrepancy Panel III Maximum Among all Seven Rates Mean 6.59 % 8.27 % Max 103.16 % 117.09 %

The table reports the daily Bitcoin price disparities and discrepancies for seven denominated ﬁat currencies: U.S. dollar (USD), Euro (EUR), Canadian dollar (CAD), British pound (GBP), Japanese yen (JPY), Chinese yuan (CNY), and Polish zloty (PLN). Panel I reports the means and maximums for Bitcoin price disparities and discrepancies. For example, column 2 of row 2 reports the USD price disparity of Bitcoin and column 4 of row 5 reports the CAD-EUR price discrepancy of Bitcoin. Panel II reports the maximum observed discrepancies for each rate. Panel III reports the means and maximums of maximum observed disparities and discrepancies across all seven rates. 29