Asset Market Equilibria in Cryptocurrency Markets: Evidence from a Study of Privacy and Non-Privacy Coins

This paper explores whether asset market equilibria in cryptocurrency markets exist. In doing so, it distinguishes between privacy and non-privacy coins. Most recently, privacy coins have attracted increasing attention in the public debate as non-privacy cryptocurrencies, such as Bitcoin, do not satisfy some users’ demands for anonymity. Analyzing ten cryptocurrencies with the highest market capitalization in each sub-market in the 2016–2018 period, we find that privacy coins and non-privacy coins exhibit two distinct market equilibria. Contributing to the current debate on the market efficiency of cryptocurrency markets, our findings provide evidence of market inefficiency. Moreover, the asset market equilibrium of privacy coins appears to be unrelated to the market equilibrium in the non-privacy coin markets, implying that the privacy coin market is emerging as a distinct asset market among cryptocurrency markets.


Introduction
Recently, empirical investigations of the cryptocurrency markets have attracted considerable attention in the academic literature. This is not surprising given that from an economic perspective the sums of money involved are substantial (Fry and Cheah, 2016, p.350).
Bitcoin (BTC), Ethereum (ETH), Ripple (XRP) are among the top three cryptocurrencies with the highest market capitalization 1 . Interestingly, in recent years, another type of cryptocurrency, exemplified by Monero (XMR), Dash (DASH), and Verge (XVG) came into existence claiming to provide transaction privacy and account balance privacy to their users that the public blockchains like BTC, ETH or XRP do not provide. Androulaki, Karame, Roeschlin, Scherer, and Capkun (2013) argue that almost 40% of Bitcoin users could be identified despite the privacy measures in place; today, however, virtually all Bitcoin users could be identified. Goldfeder, Kalodner, Reisman, and Narayanan (2018) show how thirdparty web trackers can de-anonymize users of cryptocurrencies. 2 By implementing sophisticated cryptographic protocols, privacy coins can hide senders and receivers addresses as well as the transaction amount while executing each transaction. The complete financial transparency of Bitcoin and other non-privacy coins is deterring many institutional and private investors from adopting these decentralized cryptocurrencies (Liu, Li, Karame and Asokan, 2018). Bitinfocharts website provides user level, account balance level and transaction level information for the top 100 richest wallet addresses of fourteen different cryptocurrencies 3 . Non privacy coins like Bitcoin are fully transparent; therefore institutions are hesitant to use it as a medium of exchange. Baur, Hong, and Lee (2018) show that Bitcoins are mainly used as a speculative asset rather than as a medium of exchange. 1 https://coinmarketcap.com/, accessed on 18.3.2019 2 Third parties typically receive user information for advertising purposes even if users pay via cryptocurrencies, which is enough to identify that particular user's blockchain transactions. By linking the user's cookie to that particular blockchain transaction, one can identify the real user behind it. 3 https://bitinfocharts.com, accessed on 18.3.2019 An alternative is presented by Brenig, Accorsi, and Müller (2015) who outline the structure of a money laundering process and anti-money-laundering controls to examine whether cryptocurrencies constitute a driver for money laundering or not. The study argues that privacy coins have potential benefits for criminals; an important yet neglected factor in the circulation of cryptocurrencies as a money laundering instrument. In this regard, Kethineni and Cao (2019) support Brenig et al. (2015) and argue that cryptocurrencies became the currency of choice for many drug dealers and extortionists because of the opportunities to hide behind the assumed privacy and anonymity.
Privacy coins also use the decentralized public blockchain, but by using many features like masternode technology, ring signature, and a stealth wallet address, privacy coins make it impossible for third parties to trace transactions to the real parties involved.
Privacy coins are different from non-privacy coins not only in the cryptographic level, but probably also at the user level. One reason why a separate user base for privacy coins might be growing could be due to the complete transparency of non-privacy coins like BTC and ETH. A certain degree of financial privacy about transaction and balance may be important for both the institutional and individual users. Therefore, one can hypothesize that the traders who favor privacy over complete transparency are emerging as a different subgroup in digital financial markets. Since the total supply of cryptocurrencies is (in most cases) predetermined, the price processes of cryptocurrencies depend solely on the demand side (e.g., the users). As a consequence, if the user base for privacy coins is different from that for non-privacy coins, we would expect that each submarket of cryptocurrencies potentially forms an individual asset market equilibrium.
Electronic copy available at: https://ssrn.com/abstract=3407300 Hence, we hypothesize that privacy coins form a distinct submarket in the cryptocurrency market. Following Urquhart (2016), Dyhrberg (2016), Bouri, Molnár, Azzi, Roubaud, and Hagfors (2017) who adopt the perspective that cryptocurrencies are an asset market, we consider the privacy and non-privacy coin markets to be two different asset markets. We explore whether market equilibria in those two submarkets exist, and also investigate their market efficiency. A test for market efficiency that does not require the specific formulation of an equilibrium price mechanism goes back to an argument by Granger (1986): If two or more asset prices show a stable common relationship in the long-run, it is possible that the movement of one asset price is linked to the movement of other asset prices.
In turn, the price of one asset does not only depend on its own past prices but also on the history of a different asset's prices. As a consequence, the weak-form of market efficiency is violated (Richards, 1995, p.632). In line with Engle and Granger's (1987) cointegration theory, we employ Johansen's (1991Johansen's ( , 1994Johansen's ( , 1995 multivariate methodology to model and test the long-term equilibrium process and short-term response to deviations from the equilibrium. The error correction mechanism implies that in the face of a deviation of one asset price from the induced long-run relationship, unused profit opportunities would automatically arise. Specifically, if the stable long-run relationship between asset prices is known to the market participants they are able to exploit them to make excess profits (Copeland, 1991, p. 187).
This paper contributes to the literature in several important ways. On the one hand, Urquhart (2016) and Al-Yahyaee, Mensi, and Yoon (2018) studied the market efficiency of Bitcoin and found the cryptocurrency to be inefficient; however, Nadarajah and Chu (2017) revisited Urquhart's (2016) paper and found that Bitcoin returns do satisfy the efficient market hypothesis. Moreover, Vidal-Tomás and Ibañez (2018) and Sensoy (2019) argue that Bitcoin has become more efficient over time, whereas Bariviera's (2017) findings suggest Electronic copy available at: https://ssrn.com/abstract=3407300 Bitcoin has met the standards of informational efficiency since 2014. The different views in the literature indicate there is no consensus on the market efficiency of cryptocurrencies.
While the past papers cited above consider a single asset (e.g., Bitcoin) our paper adds to this strand of literature by taking a market-wide perspective. In doing so, we consider a whole set of cryptocurrencies that exhibit the largest market capitalization and employ Johansen's (1991Johansen's ( , 1994Johansen's ( , 1995 multivariate cointegration methodology to explore whether or not asset market equilibria in line with Engle and Granger's (1987) cointegration theory exist.
There is also a new strand of literature emerging that discusses the features of privacy and non-privacy coins. This literature however mostly adopts a technological perspective and explores the privacy implications of Bitcoin (Androulaki et al., 2013), identification of a particular user's blockchain transactions (Goldfeder et al., 2018, Khalilov andLevi 2018), technological interventions that could address the privacy issues of cryptocurrencies (Ouaddah, Elkalam, and Ouahman, 2017;Kopp, Mödinger, Hauck, Kargl, and Bösch, 2017), and potential failures to guarantee privacy in terms of unlinkability and untraceability (Kumar, Fischer, Tople, and Saxena, 2017;Möser, Soska, Heilman, Lee, Heffan, Srivastava, Hogan, Hennessey, Miller, Narayanan, and Christin, 2018). Inspired by Cheah and Fry (2015) and Osterrieder and Lorenz (2017) who discuss the need for academic research on cryptocurrency from a financial point of view, our paper adopts the financial perspective and considers cryptocurrency markets as an asset market comprising two submarkets, the privacy coin market and the non-privacy coin market. This is the first paper that explicitly explores the existence of cointegration relationships among asset prices in those two cryptocurrency submarkets. We hypothesize that if those two submarkets are distinct and have different user bases, potential asset price equilibria will not be related to each other.
Finally, there is a wide strand of literature performing market efficiency tests using cointegration analysis of traditional currencies. Studies that also employ multivariate cointegration analysis as a methodological framework for exploring the European Monetary System (EMS) are Norrbin (1996), Woo (1999, Haug, MacKinnon, and Michels (2000), Rangvid and Sorensen (2002), and Aroskar, Sarkar, and Swanson (2004). Interestingly, those studies are mostly able to reject the null hypothesis of no cointegration for the EMS currencies. No paper has explicitly examined cryptocurrency markets for cointegration. 4 Hence, our paper extends the literature to reveal potential cointegration equilibria in new digital currency markets.
Our results show strong evidence for two separate cointegration relationships.
Specifically, the privacy coin market and the non-privacy coin market form two distinct asset market equilibria. Employing ten cryptocurrencies exhibiting the highest market capitalization for each market, we find that at least six out of seven coins are a part of the market-specific cointegration equilibrium. The t-statistics for the parameters of the loading matrix reveal that only some of the coins adjust to disturbances to the market equilibrium.
Our results are in line with the literature offering evidence of cointegration equilibria in traditional currency markets such as the European Monetary System (Norrbin, 1996;Woo, 1999;Haug, MacKinnon, and Michels, 2000;Rangvid and Sorensen, 2002;Aroskar, Sarkar, and Swanson, 2004). The presence of cointegration equilibria is also in line with Urquhart (2016) and Al-Yahyaee, Mensi, and Yoon (2018) who argue that Bitcoin is inefficient because a cointegration relationship implies weak-form market inefficiency. Finally, our results provide some new evidence on market heterogeneity: Privacy coins appear to build their own submarket of cryptocurrencies as they form their own market equilibrium that is unrelated to the asset market equilibrium of non-privacy coins. This market heterogeneity phenomenon in the cryptocurrency market may be subject to future investigations.

Methodology
For each group-privacy and non-privacy coins-we retrieved daily closing prices 5 for ten cryptocurrencies that exhibit the highest market capitalization as of January 3, 2016. We also downloaded data for Bitcoin, which dominates the cryptocurrency market. Our sample is from January 1, 2016 until December 31, 2018 accounting for 1096 daily observations. For all asset prices we compound the log-price series that we used in the following analyses.  Table 1 illustrates that at the beginning of our sample period, the average market capitalization of non-privacy coins (excluding Bitcoin) is about 19 times larger than that of privacy coins. Interestingly, the three-year growth in market capitalization of these top ten cryptocurrencies in each category is about three times higher for privacy coins than for nonprivacy coins. This suggests that the relative popularity of privacy coins has increased over time. Even though both privacy and non-privacy categories of cryptocurrencies use the decentralized public blockchain technology, they differ on other technological levels, particularly in relation to either the public node, wallet form, or the signature. Privacy coins also differ from non-privacy coins in terms of their usage. People who use non-privacy coins face complete financial transparency which might be less appealing in a competitive environment. Traders might want to maintain a certain degree of financial privacy at both the transaction and account balance level. Thus, we hypothesize that these two subgroups are emerging as independent players in digital currency markets.
To investigate whether or not equilibria in those two subgroups of assets exist and to explore how they relate to each other, the first step of our empirical analysis is to identify whether or not our set of cryptocurrencies exhibits stationarity. This is an important step because cointegration equilibria require that the input variables are integrated of order one, that is, I(1) stochastic processes. To test the order of integration, we follow the common literature and employ the well-known Augmented Dickey Fuller (ADF) unit root test (Dickey-Fuller, 1979). The model for estimating the test statistics is given by: where , denotes the log-price of cryptocurrency i at time t, 0 is the corresponding estimate for the intercept of the regression, 1 is the corresponding estimate for the time trend t, 2+ is the estimate for the lagged differences in log prices of lag 2 + where = 1, … , , denotes a white-noise error term, and the parameter 2 is assumed to be zero under the null hypothesis. Under the null hypothesis, , is an I(1) stochastic process. Given our research context, we assume stationarity under the alternative hypothesis. Moreover, we follow a common practice by choosing the lag-order j with respect to the Schwarz criterion.
Specifically, under some circumstances, a linear combination of some I(1) processes becomes a stationary process, that is, an I(0) process. According to Granger (1986), and Engle and Granger (1987), those = 1, … , stochastic processes are said to be co-integrated of order (1, …, 1), denoted as CI(1, …, 1). To test the order of cointegration, we employ the trace test for each submarket of cryptocurrencies, given by: where = 10, and are the eigenvalues obtained by applying RR regression techniques to the fully unrestricted Vector-Error Correction model (VECM) (Johansen 1991(Johansen , 1992a(Johansen , 1992b(Johansen , 1994(Johansen , 1995 given by: where the 10x1 vector Δ , contains the log-returns of privacy coins if = 1 or non-privacy coins if = 2. 6 Moreover, ,0 and ,1 denote constant and trend, and ,1 , ,2 , …, , −1 are KxK parameter matrices. The trace test tests the sequence of hypotheses given by: The corresponding cointegration rank is selected when the null hypothesis cannot be rejected for the first time. 7 If a cointegration relationship of order r exists, the matrix has a reduced rank form and can be decomposed into ′, where and are Kxr. In this regard, the term ′ ( , −1 − ,0 − ,1 ( − 1)) contains the cointegration equilibrium relationships, whereas is the loading matrix. Each cryptocurrency in submarket that has an insignificant weight attached to the respective cointegration relationship is said to be exogenous as it does not respond to disturbances of the long-term equilibrium. 7 Using the general-to-specific rule, we made use of the fully unrestricted VECM as given in Eq. (3).

Results
The results of testing the order of integration are presented in Table 2. Initially imposing the restriction 1, = 0, we find that none of the privacy coins appears to be stationary, whereas the null hypothesis is rejected for only two non-privacy coins (e.g., Ethereum and MaidSafeCoin). However, when estimating the fully unrestricted ADF test-involving testing a random walk with drift under the null hypothesis against a trend-stationary process under the alternative-we find that all cryptocurrencies appear to be I(1). This result is in line with the earlier literature indicating that Bitcoin is an I(1) process (Urquhart, 2016). cointegration equilibrium relationship (see Table 3). 8 Using our subset of non-privacy cryptocurrencies shows the same patterns: there is one cointegration equilibrium spanning the asset prices of non-privacy coins.  To check the robustness of our findings, we also employed maximum eigenvalue tests for cointegration. The corresponding results are reported in Tables A.1 and A.2 and support our findings. Since Bitcoin dominates the non-privacy cryptocurrency market, it would be useful to understand how the results are affected when including Bitcoin in the non-privacy coin sample. When we added Bitcoin to our set of ten non-privacy coins and re-ran the trace test we found including Bitcoin did not alter the finding that there is only one cointegration equilibrium relationship (see Table 5). Again, as a robustness check, we conducted the maximum eigenvalue test for cointegration (for results, see Table A.3). Our conclusions remain unchanged. While earlier studies found cointegration relationships in traditional currency markets (Norrbin, 1996;Woo, 1999;Haug et al., 2000;Rangvid and Sorensen, 2002;Aroskar et al., 2004) our novel findings suggest the presence of cointegration equilibria even in new digital currency markets. Establishing the existence of a cointegration relationship in our two submarkets makes it possible to estimate the reduced form of model (3) using ′ where the dimension of and is Kx1. We order both vectors Δ 1, (e.g., privacy coins) and Δ 2, (e.g., nonprivacy coins) by the market capitalization in a decreasing order, that is, the first variable in Δ 1, (Δ 2, ) is DASH (XRP), the second is BCN (LTC), and so on.
Next, we estimated fully specified VECMs for both submarkets. 9 Since we are interested in the equilibria, we report the point estimates for 1 and 1 , and 2 and 2 , respectively (see Tables 6 and 7). Investigating the privacy coin market, we observe that at least six out of ten cryptocurrencies are a part of the cointegration equilibrium (see Table 6). 10 However, only two coins, namely NAV and XVG, appear to adjust to deviations from the long-term cointegration equilibrium. Specifically, the loading vector shows that 2-3% of the disequilibrium error is corrected in one time period. In addition, the time trend is statistically significant on any level, implying that the chosen fully unrestricted VECM represents the underlying data generating process appropriately.

Table 6
Vector-Error Correction model estimates using privacy coins. Note: This table reports the estimates for a fully specified Vector-Error-Correction Model using our set of privacy coins. The model accounts for an intercept and a time trend in the cointegration equilibrium relationship. Our model uses daily data of log prices. The model has a lag-order of = 5. We report the estimates for the cointegration vector and the estimates for the adjustment parameter vector . The sample period is from January 1, 2016 until December 31, 2018 corresponding to 1096 observations. ** Statistically significant on a 5% level. *** Statistically significant on a 1% level.
The following step was to turn our attention to the non-privacy coin market, while excluding Bitcoin owing to its overwhelming market dominance. Again, we estimate a fully unrestricted VECM. The results are reported in Table 7.

Table 7
Vector-Error Correction model estimates using non-privacy coins. Note: This table reports the estimates for a fully specified Vector-Error-Correction Model using our set of nonprivacy coins. The model accounts for an intercept and a time trend in the cointegration equilibrium relationship. Our model uses daily data of log prices. The model has a lag-order of = 5. We report the estimates for the cointegration vector and the estimates for the adjustment parameter vector . The sample period is from January 1, 2016 until December 31, 2018 corresponding to 1096 observations. * Statistically significant on a 10% level. ** Statistically significant on a 5% level. *** Statistically significant on a 1% level. Surprisingly, we again find that at least six out of ten cryptocurrencies are a part of the cointegration equilibrium relationship. 11 The loading vector 2 reveals that at least three cryptocurrencies are endogenous as their point estimate indicates statistical significance on at least a 5% level. Subsequently, we explored the cointegration equilibrium conditions in more detail. In Figure 1, we plot the cointegration equilibrium for both models over our sample period. The correlation is estimated at -0.10 implying that those two market equilibria are two distinct phenomena. Since our results from Tables 6 and 7 suggest that not all coins are a part of the cointegration equilibria and, moreover, only some of them are endogenous, we set restrictions on those parameters that do not indicate statistical significance on a common 5% level. 11 XRP, ETH, DOGE, BTS, NXT, MAID. Specifically, for our first model, we test the restrictions 1,3 = 0, 1,5 = 0, 1,6 = 0, 1,8 = 0, 1,1 = 0, 1,2 = 0, 1,3 = 0, 1,4 = 0, 1,5 = 0, 1,6 = 0, 1,7 = 0, and 1,8 = 0. The corresponding test statistic is distributed as chi-square with 12 degrees of freedom under the null hypothesis. The estimated test statistic is 9.66 corresponding to a p-value of 0.65. Hence, we cannot reject our null hypothesis. The restricted model shows that the adjustment parameters of the coins NAV and XVG are -1.22% and -0.48% per day with corresponding tstatistics of -7.43 and -2.52 indicating statistical significance on at least a 5% level.
Finally, it would be useful to understand how sensitive the results are with respect to the selected lag-order of the VECM model, because the ADF tests showed an optimal lagorder of four only for one coin. Since the potential bias accruing from omitting variables is far more severe than that associated with adding redundant lags to the model, we limited our robustness check to varying the number of lags for the cointegration tests. In the appendix, we report the trace test results for using four and three lags respectively in the model (see Tables A.4 -A.7). The results confirm our previous findings and indicate only one cointegration equilibrium in both submarkets. We also performed Granger causality tests for the cointegration equilibria (results unreported). 12 We did not find any evidence of Granger causality, implying that those two market equilibria are indeed unrelated to each other.

Conclusion
Using cointegration analysis to investigate a subset of ten cryptocurrencies exhibiting the highest market capitalization shows that privacy and non-privacy coins form two distinct market equilibria. Notably, in both models, the majority of cryptocurrencies are a part of that market equilibrium. An examination of the market of privacy coins reveals only two out of six coins adjust to deviations from the long-term equilibrium (e.g., NAV and XVG). With regard to the unrestricted model estimates, NAV's adjustment parameter shows that it takes roughly 34 days until the equilibrium is restored, all other things being equal. The adjustment process seems to be more complex in the market for non-privacy coins as four out of six coins adjust to market equilibrium disturbances. The presence of cointegration equilibria has some important implications.
First, an immediate implication of cointegration is the existence of Granger-causal orderings among cointegrated series, which implies that asset prices determined in a weakly efficient market cannot be cointegrated. Hence, our findings provide evidence for market inefficiency in both submarkets of privacy and non-privacy coins. Second, the cointegration equilibria appear to be disconnected from each other. The market equilibria show a lack of correlation and do not trigger Granger causality in each other. A novel aspect of our study is it providing evidence that the underlying forces that cause privacy coins equilibrium are unrelated to those at work in the non-privacy coins market. One explanation could be behavioral type: It could be that the market actors in the privacy coin market are different from those that trade in the non-privacy coin market. However, future studies might explore the market heterogeneity in the cryptocurrency market in more detail. Moreover, potential factors that might have caused the cointegration relationships should be the subject of future research. Third, if the stable cointegration relationship between asset prices is known to the market participants they would be able to exploit it and be in a position to profit. There is a        Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon- Haug-Michelis (1999) p-values