Blockchain Characteristics and the Cross-Section of Cryptocurrency Returns

DISCUSSION PAPER SERIES

DP13724 (v. 8)

Siddharth Bhambhwani, Stefanos Delikouras and George Korniotis

FINANCIAL ECONOMICS ISSN 0265-8003 Blockchain Characteristics and the Cross-Section of Cryptocurrency Returns

Siddharth Bhambhwani, Stefanos Delikouras and George Korniotis

Discussion Paper DP13724 First Published 09 May 2019 This Revision 23 July 2021

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Copyright: Siddharth Bhambhwani, Stefanos Delikouras and George Korniotis Blockchain Characteristics and the Cross-Section of Cryptocurrency Returns

Abstract

We show that cryptocurrency returns relate to asset pricing factors derived from two blockchain characteristics, growth in aggregate computing power and network size. Consistent with theoretical models, cryptocurrency returns have positive risk exposures to these blockchain-based factors, which carry positive risk prices. A stochastic discount factor with computing power and network explains the cross-sectional variation in expected cryptocurrency returns at least as well as models with cryptocurrency return-based factors like size and momentum. The explanatory power of the blockchain factors also increases as the cryptocurrency market matures. Overall, theoretically motivated factors are important sources of risk for cryptocurrency expected returns.

JEL Classification: E4, G12, G15

Keywords: Hashrate, network, Factor Analysis, GMM, Rolling Estimation

Siddharth Bhambhwani - [email protected] University of Miami

Stefanos Delikouras - [email protected] University of Miami

George Korniotis - [email protected] University of Miami and CEPR

Acknowledgements We thank Nic Carter, Jacob Franek, Kevin Lu, and Tim Rice of Coinmetrics.io for their help with the data. We thank Ilona Babenka, Michael Barnett, Thomas Bates, Dirk Baur, Tyler Beason, Gennaro Bernile, Hendrik Bessembinder, Sreedhar Bharath, Dario Cestau, Indraneel Chakraborty, Andreas Charitou, Ilhan Demiralp, Evangelos Dioikitopoulos, Pedro Gete, Sara Holland, Allen Huang, Alok Kumar, Petri Jylha, George Kapetanios, Irene Karamanou, Matti Keloharju, Laura Lindsey, Scott Linn, Matthijs Lof, Andreas Milidonis, Dino Palazzo, George Nishiotis, Marios Panayides, Filippos Papakonstantinou, Simon Rottke, Yuri Tserlukevich, Vahid Saadi, Christoph Schiller, Mark Seasholes, Sean Seunghun Shin, Denis Sosyura, Jared Stanfield, Bryan Stanhouse, Luke Stein, Michael Ungeheuer, Jessie Wang, Tong Wang, Stavros Zenios, Zhuo Zhong as well as seminar participants at Aalto University, Arizona State University, IE Madrid, King's College London, 2019 Luxembourg Asset Management Summit, Miami Herbert Business School, University of Oklahoma, the 13th NUS Risk Management Institute Conference, the 2nd UWA Blockchain, Cryptocurrency, and FinTech Conference, 2019 FIRN Melbourne Asset Pricing Meeting, the NFA 2019 Conference, Tokyo Institute of Technology, Kyoto University, and University of Cyprus for helpful comments. Andrew Burch, Stanley Wai, and Irene Xiao provided excellent research assistance. All errors are our own.

Siddharth M. Bhambhwani∗ Stefanos Delikouras† George M. Korniotis‡

July 23, 2021 Abstract We show that cryptocurrency returns relate to asset pricing factors derived from two blockchain characteristics, growth in aggregate computing power and network size. Consistent with theoretical models, cryptocurrency returns have positive risk exposures to these blockchain-based factors, which carry positive risk prices. A stochastic discount factor with computing power and network explains the cross-sectional variation in expected cryptocurrency returns at least as well as models with cryptocurrency return-based factors like size and momentum. The explanatory power of the blockchain factors also increases as the cryptocurrency market matures. Overall, theoretically motivated factors are important sources of risk for cryptocurrency expected returns.

Keywords: Hashrate, Network, Factor Analysis, GMM, Rolling Estimation. JEL Classiﬁcation: E4, G12, G15

∗Siddharth M. Bhambhwani, Hong Kong University of Science and Technology, email: [email protected] †Stefanos Delikouras, University of Miami, email: [email protected] ‡George M. Korniotis, University of Miami and CEPR, email: [email protected] We thank Nic Carter, Jacob Franek, Kevin Lu, and Tim Rice of Coinmetrics.io for their help with the data. We thank Ilona Babenka, Michael Barnett, Thomas Bates, Dirk Baur, Tyler Beason, Gennaro Bernile, Hendrik Bessembinder, Sreedhar Bharath, Dario Cestau, Indraneel Chakraborty, Andreas Charitou, Ilhan Demiralp, Evangelos Dioikitopoulos, Pedro Gete, Sara Holland, Allen Huang, Alok Kumar, Petri Jylha, George Kapetanios, Irene Karamanou, Matti Keloharju, Laura Lindsey, Scott Linn, Matthijs Lof, Andreas Milidonis, Dino Palazzo, George Nishiotis, Marios Panayides, Filippos Papakonstantinou, Simon Rottke, Yuri Tserlukevich, Vahid Saadi, Christoph Schiller, Mark Seasholes, Sean Seunghun Shin, Denis Sosyura, Jared Stanﬁeld, Bryan Stanhouse, Luke Stein, Michael Ungeheuer, Jessie Wang, Tong Wang, Stavros Zenios, Zhuo Zhong as well as seminar participants at Aalto University, Arizona State University, IE Madrid, King’s College London, 2019 Luxembourg Asset Management Summit, Miami Herbert Business School, University of Oklahoma, the 13th NUS Risk Management Institute Conference, the 2nd UWA Blockchain, Cryptocur- rency, and FinTech Conference, 2019 FIRN Melbourne Asset Pricing Meeting, the NFA 2019 Conference, Tokyo Institute of Technology, Kyoto University, and University of Cyprus for helpful comments. Andrew Burch, Stanley Wai, and Irene Xiao provided excellent research assistance. All errors are our own. Introduction

Cryptocurrencies are a significant financial innovation. Yet, it is unclear which are the asset pricing factors that determine their expected returns. On the one hand, most empirical research focuses on the influence of investor sentiment and other non-fundamental factors on cryptocurrency prices and returns.1 On the other hand, theory suggests that blockchain characteristics such as computing power and network size are key determinants of cryptocurrency prices.2 However, there is little empirical work on the importance of these blockchain fundamentals for the cross-section of cryptocurrency expected returns.3 To fill this gap, we focus on aggregate computing power and aggregate network size and examine whether they can price cryptocurrency expected returns. Our analysis centers around two conjectures. First, we posit that aggregate computing power and network size are fundamental indicators of the state of the cryptocurrency market. Aggregate computing power proxies for the cumulative resources expended on mining and relates to the overall reliability and security of cryptocurrency blockchains. Aggregate network size captures the general adoption levels of cryptocurrencies. Therefore, these two factors offer important insights about the state of the cryptocurrency market and should affect expected returns of cryptocurrencies. Second, we posit that the pricing power of these blockchain-based factors should increase over time as the cryptocurrency market becomes more established. This conjecture follows from Pástorand Veronesi(2003; 2006), who argue that valuation uncertainty is initially high for new assets leading to price run-ups at the time of their introduction. As the assets

1See Griffin and Shams(2020), Makarov and Schoar(2020), and Liu, Tsyvinski, and Wu(2021). 2See Pagnotta and Buraschi(2018), Biais, Bisiere, Bouvard, and Casamatta(2019), Biais, Bisiere, Bou- vard, Casamatta, and Menkveld(2020), and Cong, Li, and Wang(2020). 3Exceptions include Liu and Tsyvinski(2020) who show that over the 2011 to 2018 period, Bitcoin’s network comoves with average cryptocurrency returns while variables related to Bitcoin’s mining do not. Liu and Tsyvinski(2020) proxy for Bitcoin mining activity using the price of Bitmain’s mining hardware and the cost of electricity in the U.S. and China. In contrast to their paper, we use hashrates because they are available for all Proof-of-Work cryptocurrencies and are measured at the daily level, thereby providing better information about aggregate mining activity at a very high-frequency level. Biais et al.(2020) focus on Bitcoin and highlight the importance of transaction benefits and network security. Pagnotta(2021) finds that the prices of Bitcoin, Ethereum, and Litecoin are positively related to their hashrates.

1 mature, this uncertainty dissipates and returns begin to line up with fundamentals. We examine our hypotheses with a comprehensive set of asset pricing tests (Fama and MacBeth, 1973; Cochrane, 2005, 2011) where aggregate computing power and network size are the main asset pricing factors. The fact that computing power and network size are endogenous economic variables does not invalidate our tests. We address this endogeneity following the framework used in testing the pricing ability of theoretically-motivated factors (Cochrane, 2005). For example, tests of the consumption CAPM treat aggregate consumption, an endogenous variable, as given and examine whether aggregate consumption prices the cross-section of expected equity returns. While we adopt this approach, we also test the pricing performance of the two blockchain-based factors with cryptocurrencies whose blockchain characteristics are not used in the construction of these factors. Our sample period is from 9/4/2015 to 5/28/2021. The sample starts in September of 2015 since many important cryptocurrencies were introduced around that time. For this period, we collect data on computing power (hashrates) and network size (number of unique addresses transacting on a blockchain) for ten baseline currencies, i.e., Bitcoin, Ethereum, Litecoin, Dash, Dogecoin, Vertcoin, Monero, Ripple, NEM, and Maidsafecoin. We select these currencies because they are some of the largest currencies at the beginning of our sample period comprising approximately up to 98% share of the market. They also have reliable and vetted data on computing power and network size for the entire sample period. Using this data, we create a balanced panel of cryptocurrencies and aggregate the growth rates in computing power and network size across the ten baseline currencies. These two blockchain characteristics are the main asset pricing factors in our empirical tests. We structure our empirical analysis around the stochastic discount factor paradigm (Cochrane 2005, 2011). Speciﬁcally, we ﬁrst estimate factor models. The main factors are the aggregate weekly growth rates of computing power (gCP ) and network size (gNET ) of the ten baseline currencies. Our goal is to show that the blockchain-based factors have positive risk exposures as advocated by existing theories (e.g., Pagnotta and Buraschi(2018)). Following Liu and Tsyvinski(2020), the factor models also control for a cryptocurrency

2 momentum factor, a cryptocurrency size factor, and Bitcoin’s return. Since Bitcoin is the largest cryptocurrency, its return can proxy for cryptocurrency market-wide risk. In the factor regressions, the test assets are 30 currencies. They include the ten baseline currencies used to derive the computing power and network factors. We also use 20 additional test cryptocurrencies whose blockchain fundamentals are not included in the gCP and gNET factors. Considering these 20 additional currencies addresses concerns related to possible endogeneity biases inflating the significance of the blockchain-based factors. We select these 20 currencies because they have valid and vetted return data for our entire sample period. For the factor regressions, we estimate two-factor models with the blockchain-based factors, three-factor models with the cryptocurrency return-based factors, and five-factor models with all the factors. We find that the estimated exposures to the gCP and gNET factors are positive and statistically significant even after controlling for the cryptocurrency return- based factors (i.e., Bitcoin’s return, size, and momentum). The positive betas on the gCP and gNET suggest that these factors are procyclical. Next, we turn to cross-sectional tests based on regressions of expected cryptocurrency returns on factor betas. We want to show that gCP and gNET , as procyclical factors in the cryptocurrency market, have positive risk prices and explain a significant portion of the variation in expected cryptocurrency returns. Cross-sectional tests are important because spurious factors can have significant betas in time series regressions but they usually have no explanatory power in cross-sectional regressions of expected returns (Daniel and Titman (1997); Lewellen, Nagel, and Shanken(2010)). For our cross-sectional tests, we adopt the rolling window estimation approach of Fama and MacBeth(1973) (FMB) because the cryptocurrency market has been evolving. We set the rolling window to 156 weeks (i.e., approximately three years). For each period, we use the Generalized Method of Moments (GMM) approach to estimate cross-sectional regressions and obtain the factor risk prices. We opt for the GMM methodology because it estimates the factor betas from the time series and simultaneously runs the cross-sectional regressions. From the rolling cross-sectional regressions, we obtain a time series of estimated prices of

3 risk. As in Fama and MacBeth(1973), we focus on the average prices of risk and find that they are positive and significant for both gCP and gNET . The FMB results also show that the cross-sectional dispersion in expected cryptocurrency returns is significantly related to the computing power and network factors. Specifically, these two factors explain about 28% of the cross-sectional variation in expected returns for the set of the 30 cryptocurrencies. This fit is comparable to the cross-sectional fit (about 22%) of a model with Bitcoin’s return, the size factor, and the momentum factor. Further, the explanatory power of the blockchain-based factors is not subsumed by the cryptocurrency return-based factors. Specifically, a model with all five factors has a cross-sectional fit of about 42%, while the computing power and network factors remain significant. We also examine the cross-sectional fit of the factor models across time. We find that the models that include the gCP and gNET factors either have similar or higher cross- sectional fit than the three-factor model with Bitcoin’s return, size, and cryptocurrency momentum. We also find that the pricing ability of the blockchain-based factors improves over time. This evidence suggests that as the market matures, the blockchain-based factors become increasingly more important for the cross-section of cryptocurrency expected returns. Overall, our findings are consistent with our conjecture that aggregate computing power and network growth are important sources of risk for cryptocurrencies. We conclude with various robustness tests. First, to ensure that Bitcoin’s fundamentals are not driving the significance of the blockchain-based factors, we construct versions of the computing power and network factors that exclude Bitcoin’s blockchain measures. Second, we expand our sample of 30 test cryptocurrencies with an additional 22 currencies. Reli- able data for these currencies are only available for a shorter time period (i.e., 1/6/17 to 5/28/21). In both robustness tests, we estimate FMB regressions using GMM. We find that the computing power and network factors, as well as their Bitcoin-free versions, have positive risk prices. They also explain a similar or a larger portion of the cross-sectional variation in expected returns than models with the three cryptocurrency return-based factors (i.e., Bitcoin’s return, size and momentum).

4 Third, we examine the robustness of the factor betas of the computing power and network factors by expanding the set of control factors. Specifically, we estimate factor regressions with Bitcoin’s return, the cryptocurrency size and momentum factors, as well as factors based on Google searches, Reddit activity, aggregate trading volume, geopolitical risk, and the three U.S. Fama-French equity factors. We also control for the lead and lag values of gCP and gNET as well as the lead and lagged returns of the respective cryptocurrencies. We find that when controlling for these 16 additional factors, the estimated betas of gCP and gNET and their Bitcoin-free counterparts remain positive and statistically significant. Our work makes several contributions to the literature. We are the first to use aggregate blockchain characteristics in asset pricing tests and show that they are related to cryptocurrency returns. To the contrary, existing studies suggest that cryptocurrencies’ returns are driven by investor sentiment (e.g., Cheah and Fry(2015)). This evidence is not surprising since many studies focus on Bitcoin, which is susceptible to manipulation (e.g., Griffin and Shams(2020)). For large cryptocurrencies, like Bitcoin, there are also price differences across exchanges (Makarov and Schoar, 2020). Compared to this work, our goal is not to study a handful of major cryptocurrencies or to examine price differences of a currency across different exchanges. Instead, we consider a larger set of currencies (52 in total) and examine whether the aggregate blockchain factors are related to their average returns. In a related paper, Liu et al.(2021) argue that cryptocurrency returns are explained by factors related to a cryptocurrency market portfolio, a size factor, and a momentum factor. These factors are return generated and are perceptible to the criticisms of Cochrane (2011) and Harvey, Liu, and Zhu(2016) about the lack of economic interpretation of return- generated factors. In contrast, we use asset pricing factors based on blockchain fundamentals, which have theoretical foundations (e.g., Biais et al.(2020), Pagnotta(2021)). The pricing ability of these blockchain-based factors holds after controlling for return-based factors such as Bitcoin’s return, size, and momentum. Further, Liu and Tsyvinski(2020) show that cryptocurrency returns are affected by Bitcoin’s network but not by proxies related to Bitcoin’s production. Their main production

5 proxies are the cost of electricity in the U.S. and China, and the prices of Bitmain Antminer, a Bitcoin mining hardware. Our work is different along many dimensions. First, Liu and Tsyvinski(2020) do not use hashrates to capture the resources expended for mining. Instead, we use hashrates because they can be measured daily whereas electricity costs or hardware prices are not available at high frequencies since they do not change in real time. Hashrates are also available for all mineable currencies. Thus, aggregate hashrates provide broad and accurate information about the current mining activity of the market. Furthermore, hashrates are advocated by theoretical models as an important measure of blockchain security (e.g., Pagnotta and Buraschi(2018), Pagnotta(2021), Prat and Walter(2021)). Second, we go beyond Bitcoin and consider the blockchain characteristics of nine additional currencies. Third, Liu and Tsyvinski(2020) use data until 2018 while our analysis extends to May 2021. Considering a more recent sample is important because before 2018 many new currencies emerged, which initially had high returns that are not representative of expected returns.4 With post-2018 data, we capture a more mature period of the market that is more informative about the long-term sources of risk. Finally, our balanced-panel approach is different from the approach of Liu and Tsyvinski (2020) who update their sample as currencies enter and exit from the market. However, turnover in the universe of currencies is significant and not random. Currencies with small market shares disappear as miners do not maintain their blockchains. Others are introduced to capitalize on market upswings. Some disappear due to fraud, persistent hacks, or delistings from multiple exchanges. Such non-random turnover creates biases not easily addressed econometrically.5 Given the underlying econometric complexities, we opt for the balanced- panel approach, which does not create biases in standard asset pricing tests. Our findings are consistent with existing models for cryptocurrency prices. Pagnotta and Buraschi(2018) link cryptocurrency prices to blockchain trustworthiness, defined as the absence of fraud and protection from cyber-attacks, and network externalities, captured by

4Figure 2 in Liu and Tsyvinski(2020) illustrates this pattern in returns before and after late 2017. 5See Fitzgerald, Gottschalk, and Moﬃtt(1998), Hirano, Imbens, Ridder, and Rubin(2001), and Baltagi (2008) for proposed remedies to sample attrition.

6 the number of users. Sockin and Xiong(2020) note that the “trustless” nature of decentralized networks contributes to their value. Biais et al.(2020) build a model connecting the fundamental value of cryptocurrencies to transactional benefits and the risk of a hack. They estimate their model with a structural econometric approach using data on Bitcoin. Pagnotta(2021) sets up a model predicting that the price of proof-of-work currencies should be related to their blockchain security, which can be captured by their hashrates. He also finds that Bitcoin’s prices go through booms and busts that seem unrelated to hashrate changes. Complementing the above papers, we capture blockchain trustworthiness and security using computing power and transaction benefits using the size of the network. In related research, Yermack(2017) argues that blockchain usage improves corporate governance. Abadi and Brunnermeier(2018) study record-keeping via distributed ledgers and Schilling and Uhlig(2019) study the monetary policy implications of Bitcoin’s production. Biais et al.(2019) and Prat and Walter(2021) analyze the equilibrium behavior of miners. Cong and He(2019) highlight how blockchains allow for efficient execution of contracts and Chiu and Koeppl(2019) argue that blockchains improve the settlement of securities. Easley, O’Hara, and Basu(2019) show that transaction fees paid to miners become more important as more blocks are being mined. Foley, Karlsen, and Putni¸nˇs(2019) find that before 2013 many of Bitcoin’s transactions were related to illegal activities. Howell, Niessner, and Yermack(2019) and Gan, Tsoukalas, and Netessine(2021) study initial coin offerings. Cong et al.(2020) relate the value of cryptocurrency tokens to their transactional demand. Cong, He, and Li(2020) highlight the high energy costs of proof-of-work blockchains. Alsabah and Capponi(2020) study proof-of-work protocols and find that the mining industry has moved towards centralization as opposed to decentralization. Lastly, Härdle,Harvey, and Reule(2020) provide a general overview of cryptocurrencies. The above studies mostly focus on micro-level aspects of the cryptocurrency market. In contrast, we adopt a more aggregate approach and examine the determination of the cross-section of cryptocurrency expected returns using aggregate blockchain-based factors.6

6In other related work, Chod, Trichakis, Tsoukalas, Aspegren, and Weber(2020) and Cui, Gaur, and Liu (2020) examine how blockchains can improve supply-chains. Tsoukalas and Falk(2020) study the optimality

7 The rest of the paper is organized as follows. Section1 describes the data. Sections2 and3 respectively present the asset pricing factors and the asset pricing paradigm we use. Section4 reports results from factor regressions and Section5 presents the cross-sectional analysis. Section6 includes robustness tests and Section7 concludes the paper.

1 Data Description and Summary Statistics

This section describes the data and reports summary statistics for the main variables.

1.1 Balanced Panel Approach and Data Reliability

In our empirical analysis, we adopt a balanced-panel approach. Specifically, the sample starts on 9/4/2015 since many cryptocurrencies had been introduced by the middle of 2015. The sample ends on 5/28/2021. Our sample is long enough to allow for meaningful estimations of time-series factor regressions. Further, it includes enough cryptocurrencies to allow for meaningful estimations of the cross-sectional regressions of expected cryptocurrency returns. Because the cryptocurrency market is new, we carefully construct our sample only using high quality data. Data quality is a major concern because turnover in the universe of cryptocurrencies is significant and not random. Currencies with small market shares typically disappear. Other get delisted due to fraud or persistent hacks. To illustrate the high volatility in the sample of cryptocurrencies, we describe how the sample of the top 100 currencies, reported by Coinmarketcap at the beginning of our sample (September 4, 2015) has changed. Out of the top 100 currencies on September 4, 2015, Coinmarketcap stopped tracking 32 of them (as of May 28th, 2021), which suggests that they were either defunct, fraudulent, or they had negligible trading volume. The rank of of token-weighted voting. Iyengar, Saleh, Sethuraman, and Wang(2020) analyze the welfare implications of blockchain adoption while Ro¸suand Saleh(2021) and Saleh(2021) study Proof-of-Stake blockchains. Our work also complements theoretical (Weber, 2016; Athey, Parashkevov, Sarukkai, and Xia, 2016; Huberman, Leshno, and Moallemi, 2019; Jermann, 2021; Routledge, Zetlin-Jones, et al., 2018), empirical (Wang and Vergne, 2017; Stoffels, 2017; Mai, Shan, Bai, Wang, and Chiang, 2018; Auer and Claessens, 2018; Borri, 2019; Borri and Shakhnov, 2019; Hu, Parlour, and Rajan, 2019), and other work on cryptocurrencies (Corbet, Lucey, Urquhart, and Yarovaya, 2019; Shanaev, Sharma, Ghimire, and Shuraeva, 2020).

8 many of the remaining 68 dropped significantly with 18 dropping below rank 100 and 38 even dropping below rank 1,000. Out of the remaining 12 currencies, three of them are stablecoins that are linked 1:1 to the U.S. Dollar or the Chinese Yuan and are therefore excluded from our asset pricing tests. The remaining nine are all currently in the top 100 and are in our sample along with Vertcoin, which is currently ranked around 506. To minimize biases related to such high sample turnover, we adopt a balanced-panel approach and choose cryptocurrencies for which we can obtain reliable and vetted data for our entire sample period. The source of the original cryptocurrency data is also important since many exchanges are unreliable and report manipulated data.7 For instance, Coinbase, the only publicly-traded exchange, in 2015 and 2016 primarily listed only 5 currencies (Bitcoin, Litecoin, Ethereum, Ripple, and Dash). Today, Coinbase only lists 54 currencies (exclusive of stablecoins), most of which were added only very recently in late 2020 and early 2021. To ensure high data quality, we obtain data from Coinmetrics.io. This data provider does not report the blockchain characteristics of currencies that are fraudulent or defunct. It also reports price information from the most reputable exchanges. Specifically, it uses 35 criteria to filter out illiquid or unreliable exchanges. Coinbase, Kraken, and Bittrex are some of the exchanges used by Coinmetrics.io. Exchanges like CoinBene, OkEX, IDAX, Exrates, and BitForex, which have been found to report suspicious volume data, are not part of our sample. The exchanges selected by Coinmetrics.io are similar to those in Makarov and Schoar (2020). Because of the strict criteria imposed, Coinmetrics reports data for a smaller sample of currencies compared to other data providers. For example, Coinmarketcap, another data provider used by existing studies (e.g., (Liu and Tsyvinski, 2020; Liu et al., 2021)), generally has not imposed strict selection criteria on the exchanges from which it sources data or cryptocurrencies it follows. For this reason it reports data on over 10,000 cryptocurrencies (as of May 28, 2021). Our second source of data is Bittrex, which is one of the most trusted exchanges.8 We

7See Bitwise’s report to the SEC at https://static.bitwiseinvestments.com/Research/Bitwise-Asset- Management-Analysis-of-Real-Bitcoin-Trade-Volume.pdf. 8See the list provided by Bitwise Asset Management at https://www.bitcointradevolume.com/ and a list by FTX, a cryptocurrency derivatives exchange, at https://ftx.com/volume-monitor.

9 use Bittrex because it has historically listed plenty of cryptocurrencies compared to other top U.S. exchanges. In 2015, for example, Bittrex listed over 100 cryptocurrencies, of which 30 were still present as of May 28th, 2021, the last day of our sample. For comparison, Coinbase and Gemini, two regulated U.S.-based crypto-exchanges, only listed the top 3 cryptocurrencies in 2015. Overall, we focus on a select sample of currencies that are neither frauds nor are defunct and have reliable data for our entire sample period. This is diﬀerent from other studies (Liu and Tsyvinski, 2020; Liu et al., 2021) that use all the cryptocurrencies listed on sources such as Coinmarketcap. Our approach is similar to traditional asset pricing studies with equity data that exclude stocks that were delisted, were thinly traded, or had very low prices.

1.2 Baseline Cryptocurrencies

We construct our blockchain-based asset pricing factors using ten baseline currencies. The mineable currencies in the baseline sample are Bitcoin, Ethereum, Litecoin, Dash, Dogecoin, Vertcoin, and Monero. The non-mineable currencies or ‘tokens’ (Cong et al., 2020) are Ripple (XRP), NEM, and Maidsafecoin. These currencies are among the ten largest ones in terms of market capitalization at the beginning of our sample period (9/4/2015) that also have reliable and vetted data on prices and blockchain characteristics for our entire sample period (9/4/2015 to 5/28/2021). Specif- ically, they constitute up to 98% of the market capitalization of the top 30 cryptocurrencies during our sample period (see Table1). 9 They also span a wide cross-section of return variation.10 Given their size and consistent presence in the market, the evolution of their blockchain characteristics is a reliable indicator of the state of the cryptocurrency market.

9We calculate their capitalization relative to the top 30 cryptocurrencies as the aggregate number of cryptocurrencies has continuously been expanding from about 600 on September 4th, 2015 to over 10,000 on May 28th, 2021. The aggregate capitalization of currencies outside the top-30 has historically been relatively small comprising around 1-5% of the aggregate market. 10See Table2 and Panel A of Table A2 of the Appendix.

10 1.3 Blockchain Characteristics

In this section, we describe the two blockchain-based characteristics, aggregate computing power and network size, which we compute using the sample of ten baseline cryptocurrencies.

1.3.1 Computing Power, Resources, and Security

Computing power is measured in megahashes (106 hashes). We obtain computing power data for seven baseline cryptocurrencies from Coinmetrics.io. There is no data on computing power for Ripple (XRP), NEM (XEM), and Maidsafecoin (MAID) since they are non-mineable currencies that do not rely on the Proof-of-Work mining model used by mineable currencies. We construct the weekly growth rates of computing power by taking the first differences of the log values of the hashrates between consecutive Fridays. To reduce the influence of outliers, we winsorize the growth rates at the 1% and 99% levels, consistent with Liu and Tsyvinski(2020). Computing power is an important blockchain characteristic of Proof-of-Work mineable currencies as it affects the reliability and security of their blockchains. For instance, when computing power is high, miners are expending plentiful resources to efficiently and securely record transactions. Further, a blockchain can be hacked if rogue miners amass more than 50% of the existing computing power. This is highly improbable for cryptocurrencies with high computing power like Bitcoin (Kroll, Davey, and Felten, 2013; Eyal and Sirer, 2018). We also treat computing power as a sufficient statistic for the resources expended on operating a blockchain. Consistent with our intuition, De Vries(2018) and Saleh(2021) note that the annual energy consumption of the computational resources spent on mining Bitcoin is comparable to that used by countries such as Austria and Ireland. Even if computing power is a proxy for expended cryptomining resources, detailed data on the real resources expended by miners (e.g., electricity, hardware costs) is not available for all cryptocurrencies. To the contrary, accurate hashrate (i.e., computing power) data is available for all the baseline mineable cryptocurrencies in our sample.

11 1.3.2 Network Size and Adoption Levels

Another important characteristic of a blockchain is the size of its network, which is related to the number of users of the blockchain. Analogous to established fiat currencies that are accepted by a large number of entities as a means of transaction, a large network is indicative of greater adoption of the cryptocurrency. A large number of unique blockchain users is also suggestive of enhanced liquidity of the respective cryptocurrency. Network size is the number of unique active addresses that transact on the blockchain. We obtain this data from Coinmetrics.io.11 In the Coinmetrics data, active addresses with multiple transactions are not double-counted. We construct weekly network growth rates by taking the first differences of the log values of the unique active addresses between consecutive Fridays. We winsorize these first differences at the 1% and 99% levels. An alternative measure of the adoption level of a blockchain is the number of daily transactions. However, this measure magnifies the role of a few highly active addresses, such as exchanges that conduct a large number of transactions on a daily basis when receiving or sending cryptocurrencies. We acknowledge that the number of unique active addresses is also not a perfect measure of cryptocurrency adoption since a portion of active addresses arises from multiple transactions meant to obfuscate the movements of funds. Nevertheless, we use this measure because it is available for all the baseline currencies (excluding Monero).

1.4 Cryptocurrency Test Assets

The sample of test assets includes 30 currencies. These are the ten baseline currencies, from which we derive the blockchain-based factors, and 20 additional cryptocurrencies, whose blockchain characteristics are not included in the blockchain-based factors. Using test assets whose blockchain characteristics are not included in the blockchain-based factors should help alleviate endogeneity concerns. We report the list of the 20 additional currencies in Panel B of Table A2 of the Appendix.

11We do not use the network size of Monero because it masks transactions across multiple addresses, which dilutes the true address count (Narayanan, Bonneau, Felten, Miller, and Goldfeder, 2016).

12 These currencies have reliable price data on the Bittrex exchange for our entire sample period from 9/4/15 to 5/28/21. To be included in the sample, we also require that their market capitalization rates are at least 50,000 USD at the beginning of the sample period. We use a 50,000 USD ﬁlter because as of September 4th, 2015, there were only 27 cryptocurrencies with market capitalizations greater than USD 1 million and only about 15 of them were listed on Bittrex. Further, in Section 6.2, we use another 22 currencies (i.e., 52 cryptocurrencies in total), whose return data is available for a shorter time period (1/6/2017 to 5/28/2021).

1.5 Cryptocurrency Return Data

We compute weekly returns for all the baseline 10 cryptocurrencies using their daily prices. We obtain USD-denominated daily prices from Coinmetrics.io, which collects prices from exchanges worldwide and weights them by the trading volume of each exchange. For the additional 20 cryptocurrencies in our sample of test assets, we obtain their end-of-day prices from Bittrex.12 We use the daily prices to compute weekly returns by cumulating the daily returns of 7-day periods ending on Fridays. We use weekly returns to mitigate any day-of-the-week eﬀects (e.g., Biais et al.(2020)) and problems with outliers. We set the end of the 7-day period to Friday following the Friday convention in the weekly Fama-French factors.

1.6 Summary Statistics

The main variables in our tests are weekly cryptocurrency returns and growth rates of computing power and network size. We report their descriptive statistics in Table2. According to Panel A, the baseline cryptocurrencies have positive average returns. They also demonstrate significant return fluctuations as their standard deviations are larger than their respective means and medians. This finding is not surprising given that cryptocurrencies are a new asset class. For instance, Pástorand Veronesi(2003) find that the return volatilities of young

12For most currencies on Bittrex, we obtain their BTC-denominated prices, which we multiply by Bitcoin’s U.S.D. value for the same day-end to obtain their USD-equivalent price.

13 ﬁrms are much greater than their average returns. The growth rates of computing power and network also have standard deviations that are greater than their respective means. We oﬀer additional summary statistics for the extended samples of 20 and 22 currencies in Panels B and C of Table A2 of the Appendix, respectively. These statistics show that the additional test assets include a wide range of currencies in terms of size, average returns, and return volatilities. To ensure that our test assets are not highly correlated, we report in Table A3 of the Appendix the correlations among the returns of the ten baseline cryptocurrencies along with their minimum, average, and maximum correlations with the extended set of 20 cryptocurrencies. These correlations are not excessively high ranging from 0.03 to 0.54.

2 Asset Pricing Factors

Our analysis centers around two blockchain-based factors and three cryptocurrency return- based factors, which we describe next.

2.1 Blockchain-Based Factors

The blockchain factors are based on rank-weighted averages of the growth rates of computing power and network size of the ten baseline currencies.13 We denote the average growth in computing power and network size by gCP and gNET , respectively. We use rank-weighted averages to ensure that the factors are not dominated by the largest currencies. The more traditional value-weighted approach implies that our aggregate factors would simply be cap- turing the CP and NET growth of BTC that dominates the market in terms of capitalization. Hence, the value-weighted approach ignores the blockchain characteristics of smaller cryptocurrencies that are important to describe the overall state of the cryptocurrency market. Liu and Tsyvinski(2020) ﬁnd that Bitcoin’s network is related to cryptocurrency returns while its computing power is not. To verify that our results are not aﬀected by Bitcoin’s

13For example, for computing power, we rank the seven Proof-of-Work currencies with computing power using their capitalization rates as of the prior week. We assign ranks 1 to 7 to the currencies with the lowest to highest capitalization. We transform the ranks into weights and compute rank-weighted averages.

14 computing power and network size, we also construct factors that exclude the blockchain measures of Bitcoin. We denote the factors that exclude Bitcoin’s computing power and network growth by gCP \ BTC and gNET \ BTC, respectively.

2.2 Cryptocurrency Return-Based Factors

We consider three cryptocurrency return-based factors suggested by the literature (e.g., Liu and Tsyvinski(2020), Liu et al.(2021)). The ﬁrst one is the return of Bitcoin (BTC), which is the most prominent cryptocurrency. It constitutes 48% to 85% of the aggregate market capitalization of cryptocurrencies (see Table1). Because of its large size, Bitcoin is a good proxy for the cryptocurrency market factor of Liu et al.(2021). 14 The second cryptocurrency return-based factor is a size factor (Size) constructed following Liu et al. (2021). The third one is a momentum factor (Mom) constructed following Jegadeesh and Titman(1993). Detailed deﬁnitions of these factors are in Table A1 of the Appendix.

2.3 Descriptive Statistics and Correlations

Table3 reports summary statistics and correlations for the various asset pricing factors. In the case of the blockchain-based factors, the average weekly growth in aggregate computing power (gCP ) is 0.025 with a standard deviation of 0.055. The average weekly growth in aggregate network size (gNET ) is 0.006 with a standard deviation of 0.126. We also ﬁnd that gCP is almost orthogonal to gNET with a correlation of 0.07, which suggests that the two factors capture diﬀerent aspects of the cryptocurrency market.

3 Asset Pricing with Aggregate Blockchain Factors

With our sample of factors and test currencies, we examine whether aggregate computing power and network growth are important asset pricing factors for cryptocurrency returns.

14These authors note that the return of Bitcoin exhibits similar statistical properties with the cryptocurrency market.

15 3.1 Stochastic Discount Factor

We frame our tests within the stochastic discount factor (SDF) paradigm. Under general conditions, there exists an SDF Mt, which can price the returns of any asset i, Ri,t. That is, E Ri,tMt = 1. (1)

This pricing relationship dates back to Rubinstein(1976), Lucas(1978), Ross(1978), Har- rison and Kreps(1979), and Hansen and Richard(1987). Tirole(1985) also ﬁnds a similar SDF representation when pricing ﬁat money. Biais et al.(2020) extend the model of Tirole (1985) to include a cryptocurrency. Moreover, the pricing equation (1) implies that the theoretical expected returns are related to the covariances between returns and the SDF: E Ri,t = 1 − Cov(Ri,t,Mt) /E Mt . (2)

The functional form of the SDF is dictated by investor preferences. It also depends on investor portfolio and consumption decisions and it reﬂects the evolution of the marginal utility of total wealth. Since the preferences for cryptocurrency investors are unobservable, we cannot pin down the functional form of Mt and directly estimate the pricing equation

(2). Therefore, we follow Cochrane(2005, 2011) and assume that Mt is a linear function of observable factors. The factors are aggregate economic indicators that affect the portfolio decisions and total wealth of investors. Specifically, Mt is defined as

0 Mt = 1 − (ft − E[ft]) γ, (3) where ft are factors centered around their means and γ is the vector of SDF parameters. The linear SDF in equation (3) implies that the pricing model (2) is:

0 0 E Ri,t = 1 + Cov Ri,t, (ft − E[ft]) γ = 1 + E Ri,t(ft − E[ft]) γ. (4) Multiplying and dividing equation (4) by the covariance matrix of the factors, E (ft − 0 E[ft])(ft − E[ft]) , we obtain the beta representation of the pricing equation:

0 E Ri,t = 1 + βiλ. (5)

0 0 0−1 Above, βi = E Ri,t(ft − E[ft]) E (ft − E[ft])(ft − E[ft]) is the vector of factor betas

16 0 for cryptocurrency i and λ = E (ft − E[ft])(ft − E[ft]) γ is the vector of risk prices.

3.2 Beta Pricing Model and Cryptocurrency Expected Returns

The pricing equation (5) is the basis of our empirical tests. In our set up, the factors ft include the aggregate computing power and aggregate network growth rates. We conjecture that these factors affect the cryptocurrency SDF because according to existing theoretical models they should be positively correlated with the wealth of cryptocurrency investors. Specifically, Pagnotta and Buraschi(2018) and Biais et al.(2020) predict a positive relationship among computing power, network size, and prices. Therefore, the wealth of the average cryptocurrency investor should comove with aggregate computing power and network size. In this setting, investors require high premia for cryptocurrencies whose returns follow aggregate computing power and network growth. That is, risky cryptocurrencies are the ones whose returns covary with the aggregate blockchain characteristics. The relation between risk premia and the covariances with aggregate blockchain characteristics should hold for mineable and non-mineable currencies, even if the latter do not require the consumption of computing power for mining. As long as aggregate computing power affects the overall wealth of cryptocurrency investors, the SDF paradigm predicts that aggregate computing power should impact the risk premia of all currencies, even the non-mineable ones.15 Theoretical models (e.g., Biais et al.(2019), Biais et al.(2020)) also suggest that computing power and network size should be procyclical factors. Therefore, the blockchain factors should have positive exposures (β0s) and positive risk prices (λ’s) in the pricing equation (5). Furthermore, for the blockchain factors to be valid asset pricing factors they should explain a significant portion of the cross sectional variation in expected cryptocurrency returns (Daniel and Titman(1997); Lewellen et al.(2010)). We examine these predictions next.

15This is a reasonable assumption because the development of mining and blockchain technology can have positive externalities for non-mineable currencies. For example, greater development in a mineable cryptocurrency like Bitcoin can allow for batches of transactions using non-mineable cryptocurrencies like Ripple to be more securely aggregated and settled on Bitcoin’s blockchain. Therefore, the growth in computing power of a mineable currency can improve the transaction beneﬁts of non-mineable currencies, which ultimately increases the value of non-mineables.

17 4 Factor Regressions and Risk Exposures

In this section, we present the results of our factor regressions.

4.1 Graphical Comovement Evidence

To set the stage for the factor regressions, we first provide some graphical evidence of comovement between returns and the blockchain-based factors. Specifically, Figure1 plots 12-week moving averages of the returns of the 30 test assets and the aggregate growth rates of computing power and network. Panel A shows the graph for gCP and Panel B reports the plot for gNET . In these figures, gCP and gNET follow closely the average returns of the 30 cryptocurrencies. This pattern suggests that the gCP and gNET factors should have positive beta estimates in the factor regressions.

4.2 Factor Model Estimates

We use the 30 test assets and estimate various panel factor regressions, which we report in Table4. We estimate three-factor models with the cryptocurrency return-based factors and two-factor models with the blockchain-based factors. In the three-factor models in column (1), we find that Bitcoin’s return and the cryptocurrency size factor are statistically significant. In particular, the coefficient on Bitcoin’s return is 0.84 (t-statistic = 11.00) and the coefficient on the size factor is 0.21 (t-statistic = 1.94). Momentum effects are not significant in our sample. More importantly, in the two-factor models in column (2), we find that the exposures of the gCP and gNET factors are statistically significant at the 1% level. In particular, the coefficients on gCP and gNET are 0.65 (t-statistic = 3.92) and 0.34 (t-statistic = 5.13), respectively. We document similar results in column (3) when using the gCP \ BTC and gNET \ BTC factors, which are versions of gCP and gNET that exclude Bitcoin’s computing power and network growth.

18 To ensure that the significance of the gCP and gNET factors is unrelated to the return- based factors, we estimate five-factor models with all the factors. We report these results in columns (4) to (5) of Table4. We find that the estimates of the two blockchain factors remain statistically significant. In sum, the computing power and network factors comove with cryptocurrency returns and their significance is not affected when controlling for the cryptocurrency return-based factors.

5 Expected Returns and Prices of Risk

In the next set of tests, we estimate cross-sectional regressions of expected cryptocurrency returns on factor betas, which are estimated from the time series. We implement cross- sectional tests because spurious factors can have signiﬁcant beta estimates in time series factor regressions but they usually have poor cross-sectional ﬁt (Daniel and Titman(1997); Lewellen et al.(2010)). For example, Daniel and Titman(1997) suggest that the covariance structure of returns with the true asset pricing factors should line up with the average returns of the test assets. Cross-sectional tests precisely focus on estimating the relation between betas and average returns.

5.1 Rolling Fama-MacBeth Tests

We conduct cross-sectional tests following the methodology of Fama and MacBeth(1973) (FMB). Fama and MacBeth estimate rolling regressions by allowing for the risk-return trade- off to evolve across time. The FMB approach is appropriate for our analysis because the cryptocurrency market is relatively new and constantly evolving. For example, until 2018, the cryptocurrency market was in a ‘fledgling’ state. As such, the price dynamics at the beginning of our sample are quite different from the later part. In particular, cryptocurrency prices were generally increasing before 2018, with newly introduced currencies often having very high returns in the first weeks of trading. These return patterns are depicted in Figure 2 of Liu and Tsyvinski(2020). Their figure shows that the returns of their cryptocurrency

19 market factor were continuously increasing until the end of 2017 and then shifted downwards around early 2018, reﬂecting a signiﬁcant change in the cryptocurrency market. The FMB approach can account for these changes in market conditions by allowing the factor betas and prices of risk to vary over time.

5.2 FMB via GMM

To implement the FMB methodology, we follow Cochrane(2005) and use the following GMM system:     E Rt − α − β(ft − E[ft]) IN(K+1) 0N(K+1)×N   ×   = A × g = 0. (6)   E Rt − α − β(ft − E[ft]) ⊗ (ft − E[ft])  T 0 β0   K×N(K+1) E Rt − 1 − βλ

Above, N is the number of cryptocurrency test assets and K (K < N) is the number of factors. The matrix A is a N(K + 1) + K × N(K + 2) weighting matrix and gT is the N(K + 2) × 1 vector of moment conditions, which are functions of α, β, and λ. The vector α is the N × 1 vector of time series alphas, β is the N × K matrix of time series betas, and λ is the vector of the K risk prices.

The first two sets of moments in gT estimate the time series alphas and betas, respectively. The last set of moments runs the cross-sectional regression of expected returns on factor betas to estimate the prices of risk. The GMM system is over-identified since the first N × (K + 1) conditions exactly identify the N time series alphas and the N × K time series betas, while the final N moments identify the K prices of risk. We embed the GMM system in the FMB estimation. In particular, we set the rolling time window to 156 weeks, i.e., approximately three years. The window is updated weekly resulting in 145 cross-sectional regressions. The estimation window is long enough to provide reliable estimates of the factor exposures but short enough to enable us to estimate a sufficiently large number of cross-sectional regressions. For each window, we solve the GMM system of equation (6) that simultaneously estimates factor exposures and prices of risk. The

20 rolling estimation yields a time series of risk estimates λt. We follow Fama and MacBeth (1973) and report the average risk estimate λ¯. We compute the standard error of λ¯ following the Newey and West(1987) variance correction. 16 The GMM approach is an improvement over the original two-step methodology of Fama and MacBeth(1973), which was based on ordinary least square (OLS) regressions (Cochrane, 2005). Fama and MacBeth(1973) ﬁrst run OLS time series regressions of test asset on factors to obtain the β’s. Next, they separately estimate a series of repeated cross-sectional OLS regressions of average returns on factor betas to identify the λ’s. Instead, the GMM approach simultaneously estimates the time series and cross-sectional regressions and accounts for the fact that the β’s, i.e., the independent variables in the cross-sectional regressions, are generated regressors.

5.3 FMB Estimation Results

We estimate the GMM system with the main factors from our analysis in Section4. These factors are the computing power and network factors (gCP and gNET ) along with their Bitcoin-free versions (gCP \ BTC and gNET \ BTC). We also control for the cryptocurrency return-based factors: Bitcoin’s return (BTC), the cryptocurrency size factor (Size), and cryptocurrency momentum factor (Mom). We estimate two-factor models with the blockchain-based factors, three-factor models with the return-based factors, and five-factor models with all the factors. We tabulate the FMB results in Table5. We find that the risk-price estimates for Mom are insignificant across all models. In contrast, all the remaining factors have positive and statistically significant risk-price estimates. Moreover, in the five-factor models in columns (4) and (5), controlling for the return-based factors has almost no impact on the statistical significance of the risk-price estimates of computing power and network. We also document that the two-factor models with the blockchain-based factors explain a significant portion of the variation in expected returns (about 28%). Their fit is marginally

16In the variance correction, we use 40 lags because the price of risk estimates are persistent.

21 better than that of the three-factor model with the BTC, Size, and Mom factors (about 22%). This finding is important since we are comparing two fundamentals-based factors, which have full economic interpretation, against three return-generated factors. The five- factor models have the highest fit (about 42%), which suggests that the pricing power of the blockchain-based factors is almost orthogonal to that of the return-based factors. We further examine the fit of the various models in Figure2. The figure presents the theoretically-implied expected returns (1 + β0λ) against sample average returns, averaged across the 145 rolling regressions. The figure confirms that the two blockhain-based factors (gCP and gNET in Panel A) can explain the cross-section of cryptocurrencies just as well as the three return-generated factors (Bitcoin, size, momentum in Panel B). Further, the specification that combines all five factors (Panel C) performs the best.

5.4 Time-Variation in Model Fit

Over our sample period, the cryptocurrency market has been evolving from a fledgling state pre-2018 to a more established market post-2018. This evolution should affect the explanatory power of the asset pricing models. This intuition follows from Pástorand Veronesi (2003, 2006) who argue that valuation uncertainty is elevated for new assets, which can lead to price run-ups at the time of their initial public offerings. With time, returns begin to line up with fundamentals because valuation uncertainty dissipates as investors get access to more information about the new assets. Overall, the pricing ability of the aggregate blockchain measures should strengthen as the market matures. We assess the fit of the models across our sample period in Figure3, where we plot the time series of adjusted-R2’s from the 145 cross-sectional rolling regressions. The figure shows that the explanatory power of the models consistently increases across time. After July 2019, the model with the two blockchain-based factors almost always has higher adjusted- R2’s than the three-factor model with BTC, Size, and Mom. Since January 2021, the two specifications exhibit similar cross-sectional performance. This is probably due to the extreme fluctuation of cryptocurrency prices during the most recent period (i.e., January,

22 2021 to May, 2021) that might be fueled by sentiment trading and not fundamentals. In sum, the FMB tests show that the computing power and network factors have positive and signiﬁcant prices of risk. They also explain a large component of the cross-sectional dispersion in expected cryptocurrency returns. This evidence supports our conjecture that blockchain-based factors are important sources of risk for the cryptocurrency market.

6 Robustness Tests

We conclude our analysis with additional tests to verify the robustness of our ﬁndings.

6.1 Additional Factors and Risk Exposures

We ﬁrst extend our factor regressions with a broader set of factors to verify that the robustness of the exposure estimates of the blockchain-based factors are robust. The set of additional control factors includes the Fama-French U.S. three factors, i.e., MKTRF , SMB, and HML. We also use factors related to investor attention, sentiment, and trading activity in the cryptocurrency markets. These are the weekly growth in Google searches for cryptocurrency-related terms along with the growth in the number of user posts on various cryptocurrency forums on Reddit. We control for trading volume since Baker and Stein (2004) note that investor sentiment is linked to higher trading volume. Additionally, we consider the geopolitical uncertainty factor of Baker, Bloom, and Davis (2016) to account for potential hedging beneﬁts of cryptocurrencies against global uncertainty.17 Further, we use the lead and lag returns of each cryptocurrency as a control variable to further account for the cryptocurrency momentum phenomenon. Lastly, we include the lead and lag values of our gCP and gNET factors to account for potential feedback between the growth in computing power and network with cryptocurrency returns. We estimate panel factor regressions with the sample of 30 currencies. Each model consists of the two blockchain-based factors and the additional 16 control variables. We 17We provide more details on the construction of the Google searches, Reddit, volume, and geopolitical risk factors in Table A1 of the Appendix.

23 report the results in Table6. We ﬁnd that the estimated exposures of the gCP and gNET factors, and their Bitcoin-free versions, are similar to those in Table4 and they remain statistically signiﬁcant.

6.2 More Test Assets, Shorter Sample Period

Our main asset pricing tests are based on a balanced panel of 30 cryptocurrencies. For our second robustness test, we examine whether our main findings extend to a larger sample of currencies that includes an additional 22 currencies. We report the list of these 22 cryptocurrencies in Panel C of Table A2 of the Appendix. To identify them, we searched for cryptocurrencies listed on the Bittrex exchange with reliable return data for the entire period from 1/6/2017 to 5/28/2021. The time period starts on January, 2017 instead of September, 2015 to maintain a balanced panel since these 22 currencies emerged later on. First, similar to our analysis for the sample of 30 cryptocurrencies in Table4, we run factor regressions using the sample of 52 cryptocurrencies. We report the new results in Panel A of Table7. We find that the exposures of the gCP and gNET factors, and their Bitcoin-free versions, retain their statistical significance. Second, we repeat the rolling FMB estimation of Section5 with the sample of the 52 test assets. We use a 156-week rolling window, which implies that the sample of the first rolling regression is from 1/6/2017 to 12/27/2019. We report the estimation results in Panel B of Table7. We find that that both the gNET and gCP factors have positive risk-price estimates. The risk prices of the network factor are always statistically significant. However, the computing power factor is less significant. Despite the weaker significance of gCP , the blockchain-based factors have higher cross-sectional fit (about 42-44%) compared to the return-based factors (about 26%). Graphical evidence in Figure A1 of the Appendix confirm the improved fit of the blockchain-based factors. The figure shows that the expected returns predicted by the blockchain-based factors line up well with the sample average returns. In Figure A2, we present the evolution of the fit of the two-factor model with gCP and gNET and the three-factor model with BTC, Size, and Mom. The figure shows that in

24 the first part of the sample the fit of the two blockchain-based factors is better than the return-based factors. Since January 2021, the fit of the two models is comparable. Similar to the original sample of 30 cryptocurrencies, this pattern is probably due to the extreme fluctuation in cryptocurrency prices during the most recent period (i.e., January, 2021 to May, 2021). Overall, the graphical evidence demonstrates that the computing power and network factors accurately capture the cross-sectional dispersion of expected returns in the sample of 52 cryptocurrencies. More importantly, their explanatory power is better than that of the return-based factors.

6.3 A Validation Test: Cryptocurrency-Level Analysis

We end our analysis with a validation test. The test is based on the theoretical prediction that the price of each cryptocurrency should depend on its own blockchain measures (e.g., Pagnotta and Buraschi(2018), Pagnotta(2021)). The results of our prior asset-pricing tests are consistent with this prediction. Nevertheless, for robustness, we present evidence that this theoretical prediction is also supported at the cryptocurrency-level. For this analysis, we focus on the ten baseline currencies from Panel A of Table A2.

6.3.1 DOLS Regression Methodology

Estimating the relation between cryptocurrency prices, computing power, and network is challenging since these variables are jointly determined in equilibrium and are all non- stationary processes.18 Thus, we cannot estimate this relation with ordinary least squares because such regression results would be spurious (e.g., Phillips(1986)). Instead, we use coin- tegration analysis, which we implement with the dynamic ordinary least squares (DOLS) of Stock and Watson(1993). Lettau and Ludvigson(2001) employ DOLS to estimate the relationship of aggregate consumption with income and wealth. Lustig and Van Nieuwerburgh (2005) use DOLS to show that U.S. housing wealth is related to aggregate U.S. income.

18In unreported results, we implement the augmented Dickey and Fuller(1979) test and ﬁnd that the prices, computing power, and network size of the ten baseline currencies are unit-root processes.

25 To implement the DOLS, we assume that there is a linear cointegrating relation between log prices (P ), log computing power (CP ), and log network (NET ). As in Lustig and Van Nieuwerburgh(2005), we impose the restriction that the cointegrating relation elimi- nates any deterministic trends. This set up implies the following DOLS regression:

k k X X Pt = α + δ · t + βCP CPt + βNET NETt + βCP,τ ∆CPt+τ + βNET,τ ∆NETt+τ + t. (7) τ=−k τ=−k

Above, ∆CP and ∆NET are the ﬁrst diﬀerences of CP and NET , respectively. Stock and Watson(1993) show that under mild conditions, the ordinary least squares estimates of

βCP and βNET from the DOLS regression in equation (7) are not affected by endogeneity. Intuitively, endogeneity creates feedback loops between prices, CP , and NET . By controlling for the first differences of CP and NET , we can account for these loops. In the estimation, we use one lead and one lag for the first differences in equation (7) (i.e., k = 1). The results are similar when using up to four leads and lags. We compute the t-statistics of the estimated parameters with robust Newey-West standard errors corrected for autocorrelation, whose length is determined by automatic bandwidth selection.

6.3.2 DOLS Regression Estimates

We report the DOLS results in Table8. The results confirm our main empirical findings and the existing theoretical models, which suggest that βCP and βNET should be positive (e.g., Pagnotta and Buraschi(2018), Biais et al.(2020), Pagnotta(2021)). Specifically, almost all the coefficients on CP are positive and statistically significant at the 1% level. The exceptions are Litecoin, which is only significant at the 5% level and Dogecoin whose βCP is positive but insignificant. With regards to estimates of the network variable, we find that all the βNET estimates are positive and statistically significant except for Ethereum and Dash. Collectively, the DOLS results provide micro-level evidence that there is a common trend between cryptocurrency prices and blockchain fundamentals.

26 7 Conclusion

The main hypothesis of this paper is that aggregate blockchain-based computing power and network size are important risk factors in the cryptocurrency market. We examine this hypothesis using the blockchain characteristics of ten important cryptocurrencies (i.e., Bitcoin, Ethereum, Litecoin, Dash, Dogecoin, Vertcoin, Monero, Ripple, NEM, and Maidsafecoin). We aggregate their computing power and network growth rates and create two blockchain- based asset pricing factors for computing power and network. We find that these two factors have positive and significant risk exposures. Cross-sectional regressions indicate that these blockchain-based factors have positive prices of risk and their explanatory power for the cross-section of expected cryptocurrency returns has been improving as the cryptocurrency market matures. Furhter, their ability to explain average cryptocurrency returns is at least as good as that of models with return- generated factors such as a model with Bitcoin’s return, size, and momentum. Overall, our paper is an important step towards better understanding cryptocurrency prices. In particular, we are the first to provide evidence that cryptocurrency returns are related to aggregate computing power and network size. As the cryptocurrency market further matures additional asset pricing factors might become relevant. Our analysis can serve as a tool for studying these additional factors.

27 Figure 1: Growth in Blockchain Characteristics and Cryptocurrency Returns

This ﬁgure plots 12-week moving averages of the weekly growth in computing power (gCP ) and network (gNET ), as well as the weekly cross-sectional average returns of 30 cryptocurrencies, which are listed in Panels A and B of Table A2. In Panels A and B of this ﬁgure, we plot gCP and gNET , respectively, with the average returns of the 30 cryptocurrencies. The sample period is from 9/4/2015 to 5/28/2021.

28 Figure 2: Fitted and Sample Average Cryptocurrency Returns

The figure presents a summary of the fitted expected and average returns from the rolling Fama-MacBeth regressions. For each rolling regression, we compute the fitted expected returns, i.e., factor betas × risk prices, and the sample average returns at the weekly frequency. In the graph, we plot the mean of the fitted and average returns from the 145 cross-sectional rolling regressions. In Figure A, the factors are the return of Bitcoin, BTC, cryptocurrency size, Size, and cryptocurrency momentum, Mom. In Figure B, the factors are the blockchain-based gCP and gNET . In Figure C, we consider all five factors. The reported average adjusted R2 is the time series average of the cross-sectional adjusted R2’s across the rolling regressions. The test assets consist of the 30 cryptocurrencies from Panels A and B of Table A2. The estimation of the models is based on the GMM approach described in Section 5.1.

A) BTC + Size + Mom (Time Series Averages) B) gCP + gNET (Times Series Averages) 0.08 0.08

0.07 0.07

0.06 0.06

0.05 0.05

0.04 0.04

0.03 0.03

0.02 0.02

FITTED EXPECTED RETURNS 0.01 FITTED EXPECTED RETURNS 0.01

0 0 2 Average Adjusted R = 0.22 Average Adjusted R2 = 0.28 -0.01 -0.01 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 SAMPLE AVERAGE RETURNS SAMPLE AVERAGE RETURNS

C) BTC + Size + Mom + gCP + gNET (Time Series Averages) 0.08

0.07

0.06

0.05

0.04

0.03

0.02

FITTED EXPECTED RETURNS 0.01

0 Average Adjusted R2 = 0.42 -0.01 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 SAMPLE AVERAGE RETURNS

29 Figure 3: Cross-Sectional Adjusted-R2’s from Rolling Fama-MacBeth Regressions

The ﬁgure plots the time series of the cross-sectional adjusted R2’s for the rolling Fama-MacBeth regressions of expected cryptocurrency returns on factor betas. The rolling window is 156 weeks and it is updated weekly for a total of 145 regressions. The dashed line corresponds to the factor model with Bitcoin (BTC), cryptocurrency size (Size), and cryptocurrency momentum (Mom). The solid line corresponds to the factor model with the blockchain-based computing power (gCP ) and network size (gNET ) factors. The test assets are the 30 cryptocurrencies from Panels A and B of Table A2. The sample period is from 9/4/2015 to 5/28/2021.

0.8

0.6

0.4 2

0.2 ADJUSTED R ADJUSTED 0

-0.2 BTC + Size + Mom gCP + gNET

-0.4 Jan 2019 Jul 2019 Jan 2020 Jul 2020 Jan 2021 ROLLING REGRESSION END DATE

30 Table 1: Cryptocurrency Market Capitalization Rates

The table reports the market capitalization (in USD millions) of the ten baseline cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), Dash (DSH), Dogecoin (DOGE), Vertcoin (VTC), Monero (XMR), Ripple (XRP), NEM (XEM), and Maidsafecoin (MAID). Market capitalization data are from Coinmarketcap’s public API for 8/31/2015, 8/31/2016, 8/31/2017, 8/31/2018, 8/31/2019, 8/31/2020, and 5/28/2021. Rank is the rank of each cryptocurrency in terms of capitalization. P ercentage of top 30 is the ratio of the capitalization of each cryptocurrency over the total capitalization of the top-30 cryptocurrencies. The total capitalization of the top-30 cryptocurrencies, on average, accounts for approximately 98% of the market capitalization of all cryptocurrencies in our sample period from 9/4/2015 to 5/28/2021.

BTC ETH LTC DSH DOGE VTC XMR XRP XEM MAID August 31st, 2015 Market Capitalization $3,350 $99 $120 $15 $13 $1 $4 $256 $1 $10 Rank 1 4 3 5 6 23 15 2 31 9 Percentage of top 30 85% 3% 3% 0.4% 0.3% 0% 0.1% 6% 0% 0.3% August 31st, 2016 Market Capitalization $9,117 $975 $180 $80 $25 $1 $110 $214 $51 $48 Rank 1 2 4 8 13 70 6 3 9 10 Percentage of top 30 84% 9% 2% 1% 0.2% 0% 1% 2% 0.5% 0.4% 31 August 31st, 2017 Market Capitalization $77,775 $36,142 $3,746 $2,847 $228 $38 $2,108 $9,801 $3,034 $298 Rank 1 2 5 7 36 108 9 3 6 27 Percentage of top 30 48% 22% 2% 2% 0.1% 0% 1% 6% 2% 0.2% August 31st, 2018 Market Capitalization $121,347 $28,775 $3,597 $1,613 $556 $35 $1,909 $13,296 $949 $122 Rank 1 2 7 13 22 144 11 3 18 60 Percentage of top 30 58% 14% 2% 1% 0.3% 0% 1% 6% 0.5% 0.1% August 31st, 2019 Market Capitalization $172,471 $18,550 $4,078 $723 $304 $14 $1,161 $11,142 $434 $76 Rank 1 2 5 16 30 247 12 3 24 84 Percentage of top 30 72% 8% 2% 0.3% 0.1% 0% 0.5% 5% 0.2% 0% August 31st, 2020 Market Capitalization $215,818 $48,909 $3,994 $841 $406 $16 $1,651 $12,678 $1,275 $52 Rank 1 2 7 29 47 383 16 4 20 205 Percentage of top 30 62% 14% 1% 0.2% 0.1% 0% 0.5% 4% 0.4% 0% May 28th, 2021 Market Capitalization $668,284 $280,864 $11,837 $1,860 $40,391 $41 $4,710 $41,536 $1,622 $234 Rank 1 2 14 53 7 506 26 6 59 147 Percentage of top 30 48% 20% 0.8% 0.1% 2.9% 0% 0.3% 3% 0.1% 0% Table 2: Descriptive Statistics: Cryptocurrency Returns, Computing Power, and Network Growth

The table reports descriptive statistics for the weekly returns and the weekly growth rates of computing power (CP) and network (NET) of the ten baseline cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), Dash (DSH), Dogecoin (DOGE), Vertcoin (VTC), Monero (XMR), Ripple (XRP), NEM (XEM), and MaidSafeCoin (MAID). Weekly returns are the cumulative daily returns of seven-day periods ending on Fridays. Weekly growth rates of computing power and network are the ﬁrst diﬀerences of the Friday log values of hashrate and unique active addresses, respectively. The statistics for the growth rates in computing power do not include Ripple (XRP), NEM (XEM), and MaidSafeCoin (MAID), which are non-mineable currencies. The statistics for the growth rates in network do not include Monero (XMR), whose true active addresses count is not available as it is a privacy-focused currency. The sample period is from 9/4/2015 to 5/28/2021.

Returns CP Growth Rate NET growth rate Mean Median St. Dev. Mean Median St. Dev. Mean Median St. Dev. N

BTC 0.022 0.015 0.107 0.019 0.018 0.127 0.004 0.007 0.099 300

32 ETH 0.041 0.011 0.193 0.026 0.024 0.063 0.020 0.011 0.170 300 LT C 0.026 0.005 0.169 0.018 0.017 0.096 0.008 0.003 0.233 300 DSH 0.028 0.002 0.175 0.036 0.022 0.129 0.007 0.018 0.278 300 DOGE 0.062 −0.006 0.444 0.018 0.020 0.087 0.003 0.015 0.268 300 VTC 0.032 −0.012 0.247 0.027 0.014 0.234 0.003 −0.010 0.280 300 XMR 0.035 0.017 0.186 0.021 0.019 0.120 300 XRP 0.036 −0.013 0.242 0.001 −0.013 0.332 300 XEM 0.048 −0.010 0.247 0.009 0.012 0.437 300 MAID 0.025 0.011 0.173 0.007 0.000 0.607 300 Table 3: Descriptive Statistics and Correlations of Asset Pricing Factors

The table reports descriptive statistics of the asset pricing factors used in our empirical analysis. The cryptocurrency return-based factors include the return of Bitcoin (BTC), a cryptocurrency size factor (Size), and a cryptocurrency momentum factor (Mom). The blockchain-based factors are the aggregate growth in computing power (gCP ) and network size (gNET ) across the ten baseline cryptocurrencies, as well as their versions that exclude Bitcoin’s computing power and network growth (gCP \ BTC and gNET \ BTC, respectively). We also report summary statistics and correlations for the average returns of the sample of 30 cryptocurrencies (AvgRet30 ), which are listed in Panels A and B of Table A2. Details on the construction of the variables are provided in Table A1 of the Appendix. The sample period is from 9/4/2015 to 5/28/2021.

Mean SD BTC Size Mom gCP gNET gCP \ BT C gNET \ BTC AvgRet30

BTC 0.022 0.107 1.00

Size 0.006 0.132 −0.01 1.00

33 Mom 0.005 0.180 0.08 0.14∗∗ 1.00

gCP 0.025 0.055 0.18∗∗∗ 0.09 −0.03 1.00

gNET 0.006 0.126 0.36∗∗∗ −0.13∗∗ 0.03 0.07 1.00

gCP \ BTC 0.026 0.059 0.19∗∗∗ 0.10∗ 0.01 0.81∗∗∗ 0.02 1.00

gNET \ BTC 0.006 0.151 0.33∗∗∗ −0.12∗∗ 0.04 0.02 0.99∗∗∗ 0.01 1.00

AvgRet30 0.041 0.144 0.62∗∗∗ 0.18∗∗∗ 0.03 0.27∗∗∗ 0.32∗∗∗ 0.26∗∗∗ 0.31∗∗∗ 1.00 Table 4: Factor Regressions and Risk Exposures

The table reports estimates from factor regressions of weekly cryptocurrency returns. The test assets are 30 cryptocurrencies, which are listed in Panels A and B of Table A2. The cryptocurrency return-based factors are the return of Bitcoin (BTC), a cryptocurrency size factor (Size), and a cryptocurrency momentum factor (Mom). The blockchain-based factors are gCP , gNET , gCP \ BTC, and gNET \ BTC. The superscripts ***, **, and * indicate signiﬁcance at the 0.01, 0.05, and 0.10 level, respectively. Standard errors are double-clustered by currency and week. The sample runs from 9/4/2015 to 5/28/2021.

(1) (2) (3) (4) (5) BTC 0.84∗∗∗ 0.74∗∗∗ 0.74∗∗∗ (11.00) (8.52) (8.61) Size 0.21∗ 0.21∗∗ 0.21∗∗ (1.94) (2.07) (2.06) Mom −0.04 −0.04 −0.04 (−0.55) (−0.53) (−0.61)

gCP 0.65∗∗∗ 0.37∗∗∗ (3.92) (2.75) gNET 0.34∗∗∗ 0.15∗∗ (5.13) (2.10) gCP\ BTC 0.63∗∗∗ 0.33∗∗∗ (4.10) (2.83) gNET\ BTC 0.29∗∗∗ 0.14∗∗ (5.17) (2.29)

α(×100) 2.09∗∗∗ 2.27∗∗∗ 2.25∗∗∗ 1.29∗∗ 1.34∗∗ (3.35) (2.83) (2.69) (2.14) (2.15) Adjusted R2 0.10 0.04 0.04 0.11 0.11 Currencies 30 30 30 30 30 Weeks 300 300 300 300 300

34 Table 5: Fama-MacBeth Regressions of Expected Returns on Factor Betas

The table reports results of estimates from rolling Fama-MacBeth regressions of expected cryptocurrency returns on factor betas. The cross-sectional regressions of expected returns on factor betas are jointly estimated with the time series regressions for the factor betas (untabulated) via the ﬁrst-stage GMM system of equation (6). The table reports time series averages of the estimated cross-sectional risk prices for the corresponding factor betas. The rolling time window is 156 weeks and it is updated every week leading to 145 regressions. The test assets are the 30 cryptocurrencies listed in Panels A and B of Table A2. The superscripts ***, **, and * indicate signiﬁcant price of risk estimates at the 0.01, 0.05, and 0.10 level, respectively. The t-statistics of the average estimates are adjusted for autocorrelation with the Newey and West(1987) correction. We also report the time series averages of the χ2-statistic, degrees of freedom (dof), and p-value for the test that all moment conditions in the GMM system are jointly zero. Finally, the average adjusted R2 and average RMSE are the time series averages of the cross-sectional adjusted R2’s and the root-mean-square-error, respectively. The sample runs from 9/4/2015 to 5/28/2021.

(1) (2) (3) (4) (5) BTC 0.03∗∗∗ 0.03∗∗∗ 0.03∗∗∗ (3.89) (4.40) (4.05) Size 0.01∗∗ 0.01∗ 0.01∗ (2.23) (1.77) (1.84) Mom −0.00 −0.00 0.00 (−1.00) (−0.68) (0.25) gCP 0.01∗∗ 0.01∗∗ (2.40) (2.01) gNET 0.06∗∗∗ 0.05∗∗∗ (8.04) (10.21) gCP \ BTC 0.02∗∗∗ 0.01∗∗∗ (3.12) (6.91) gNET \ BTC 0.07∗∗∗ 0.05∗∗∗ (8.34) (11.12) χ2 19.69 18.91 18.16 17.88 17.39 dof 27 28 28 25 25 p 0.81 0.87 0.89 0.80 0.83 Average Adjusted R2 0.22 0.28 0.28 0.42 0.42 Average RMSE 1.34% 1.32% 1.31% 1.12% 1.12%

35 Table 6: Expanded Factor Regressions

The table reports factor regressions of weekly cryptocurrency returns on asset pricing factors. The test assets are the 30 currencies described in Panels A and B of Table A2. The factors are the return of Bitcoin, a size factor, a momentum factor, the blockchain-based factors for computing power and network, the three U.S. Fama-French factors, the growth rate in Google Searches, the growth in cryptocurrency-related Reddit posts, the growth in trading volume, the geopolitical uncertainty index of Baker et al.(2016), the lead and lag returns of the respective cryptocurrency, and the lead and lag values of the computing power and network factors. The sample is from 9/4/2015 to 5/21/2021. The superscripts ***, **, and * indicate signiﬁcance at the 0.01, 0.05, and 0.10 level, respectively. Standard errors are double-clustered by currency and week. Variable deﬁnitions are in Table A1.

Estimates t-stats Estimates t-stats

(1) (2)

BTC 0.69∗∗∗ (7.61) 0.70∗∗∗ (7.74) Size 0.23∗∗ (2.42) 0.23∗∗ (2.42) Mom −0.04 (−0.64) −0.04 (−0.67) gCP 0.35∗∗∗ (2.82) gNET 0.21∗∗∗ (2.62) gCP \ BTC 0.26∗∗ (2.36) gNET \ BTC 0.18∗∗∗ (2.63) MKTRF 0.34 (1.50) 0.33 (1.46) SMB −0.12 (−0.30) 0.02 (0.04) HML −0.17 (−0.69) −0.16 (−0.64) ∆GoogleSearches −0.01∗ (−1.67) −0.01∗ (−1.67) ∆RedditP 0.01 (0.86) 0.01 (0.91) ∆T radeV olume 0.00 (0.26) 0.00 (0.18) ∆GEP U −0.17∗ (−1.69) −0.15 (−1.56)

Returnt+1 0.03 (1.18) 0.03 (1.17)

Returnt−1 0.00 (1.09) 0.00 (1.07)

gCPt−1 0.05 (0.47) ∗∗ gNETt−1 0.13 (2.01) ∗∗∗ gCPt+1 0.37 (3.44)

gNETt+1 0.02 (0.39)

gCP \ BTCt−1 0.08 (0.71) ∗∗ gNET \ BTCt−1 0.12 (2.16) ∗∗ gCP \ BTCt+1 0.25 (2.20)

gNET \ BTCt+1 0.02 (0.34) α(×100) 0.22 (0.40) 0.55 (0.99)

Adjusted R2 0.12 0.12 Currencies 30 30 Weeks 299 299

36 Table 7: Asset Pricing Tests with 52 Test Cryptocurrencies

The table reports results of asset pricing tests where the test assets are the 52 cryptocurrencies described in Table A2. In Panel A, we report the beta estimates from time series regressions of various factor models. In Panel B, we report time series averages of the estimated cross-sectional risk prices from the rolling Fama-MacBeth regressions. The rolling time window is 156 weeks and there are 75 regressions. The t- statistics in Panel B are adjusted for autocorrelation with the Newey and West(1987) correction. We also report the time series averages of the χ2-statistic, degrees of freedom (dof), and p-value for the test that all moment conditions in the GMM system of the Fama-MacBeth regressions are jointly zero. Finally, the average adjusted R2 and average RMSE are the time series averages of the cross-sectional adjusted R2’s and the root-mean-square-error, respectively. The superscripts ***, **, and * indicate signiﬁcant price of risk estimates at the 0.01, 0.05, and 0.10 level, respectively. The sample runs from 1/6/2017 to 5/28/2021.

Panel A: Factor Regressions (1) (2) (3) (4) (5) BTC 0.92∗∗∗ 0.80∗∗∗ 0.80∗∗∗ (11.96) (8.53) (8.74) Size 0.17 0.18 0.18 (1.35) (1.62) (1.59) Mom −0.05 −0.05 −0.06 (−0.60) (−0.60) (−0.72) gCP 0.77∗∗∗ 0.44∗∗∗ (4.29) (3.10) gNET 0.42∗∗∗ 0.18∗∗ (5.68) (2.29) gCP \ BTC 0.72∗∗∗ 0.38∗∗∗ (4.15) (3.03) gNET \ BTC 0.35∗∗∗ 0.16∗∗ (5.54) (2.37) α (×100) 2.24∗∗∗ 2.26∗∗ 2.25∗∗ 1.39∗ 1.46∗ (2.90) (2.30) (2.14) (1.93) (1.88) Adjusted R2 0.12 0.05 0 .05 0.13 0.13 Currencies 52 52 52 52 52 Weeks 230 230 230 230 230 Panel B: Fama-MacBeth Regressions (1) (2) (3) (4) (5) BTC 0.02∗∗∗ 0.02∗∗∗ 0.01∗∗∗ (2.72) (3.40) (3.35) Size 0.00 −0.00 −0.00 (1.58) (−0.28) (−0.07) Mom −0.01∗∗∗ −0.00 0.00 (−5.02) (−0.34) (0.33) gCP 0.00 0.00 (1.32) (0.77) gNET 0.05∗∗∗ 0.04∗∗∗ (7.08) (4.88) gCP \ BTC 0.01 0.01∗ (1.61) (1.95) gNET \ BTC 0.05∗∗∗ 0.05∗∗∗ (9.46) (5.53) χ2 40.26 39.46 37.65 36.90 35.24 dof 49 50 50 47 47 p 0.73 0.81 0.86 0.81 0.85 Average Adjusted R2 0.26 0.42 0.44 0.47 0.49 Average RMSE 1.17% 1.01% 0.99% 0.95% 0.93% 37 Table 8: Cointegrating Relation between Prices, Computing Power, and Network Size This table reports estimates of the cointegrating relation between cryptocurrency prices (Price), computing power (CP), and network size (NET) for the ten baseline cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), Dash (DSH), Dogecoin (DOGE), Vertcoin (VTC), Mon- ero (XMR), Ripple (XRP), NEM (XEM), and Maidsafecoin (MAID). The cointegrating relation is Pricet = α +δ +βCP ×CPt +βNET ×NETt and it is estimated with the dynamic ordinary least squares (DOLS) methodology of Stock and Watson(1993) using equation (7). The superscripts ***, **, and * indicate signiﬁcant price of risk estimates at the 0.01, 0.05, and 0.10 level, respectively. The t-statistics, reported in parenthesis, are based on Newey-West standard errors with automatic bandwidth selection. The sample runs from 9/4/2015 to 5/28/2021.

BTC ETH LTC DSH DOG VTC XMR XRP XEM MAID (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) ∗∗ ∗∗∗ ∗∗ ∗∗∗ ∗∗∗ ∗∗∗ βCP 0.57 0.70 0.21 0.38 0.05 0.28 1.54 (2.39) (2.93) (2.48) (2.84) (0.18) (8.58) (9.00) ∗∗∗ ∗∗∗ ∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ βNET 2.02 0.42 1.08 1.05 1.40 1.10 1.56 1.10 0.67 (3.80) (1.55) (9.20) (1.44) (1.93) (13.92) (8.93) (4.63) (6.01)

∗∗∗ ∆CPt+1 0.17 0.03 0.17 0.16 −0.06 −0.06 1.08 (1.24) (0.08) (1.20) (0.97) (−0.19) (−0.81) (7.28)

38 ∗ ∗∗∗ ∆CPt −0.07 0.02 0.29 0.02 −0.36 −0.11 0.65 (−0.71) (0.05) (1.66) (0.09) (−0.77) (−1.38) (4.13) ∗∗ ∗∗ ∗∗∗ ∆CPt−1 −0.12 0.23 0.24 0.01 −0.21 −0.07 0.28 (−2.06) (1.31) (2.09) (0.06) (−0.60) (−1.33) (2.99)

∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∆NETt+1 0.82 0.18 0.46 0.40 0.43 0.46 0.91 0.46 0.27 (3.14) (1.24) (6.42) (1.18) (1.47) (6.03) (6.15) (4.00) (4.80) ∗∗∗ ∗∗ ∗∗∗ ∗∗ ∗∗ ∆NETt 0.21 −0.04 0.17 0.05 −0.06 0.17 0.33 0.14 0.07 (1.50) (−0.53) (3.40) (0.37) (−0.50) (1.99) (3.63) (2.15) (2.37)

∆NETt−1 −0.05 −0.05 0.03 −0.05 −0.13 0.03 0.04 0.01 0.01 (−0.63) (−0.87) (0.84) (−1.04) (−1.42) (0.50) (0.77) (0.18) (0.42)

∗∗ ∗∗∗ ∗∗∗ ∗∗ ∗∗∗ δt −0.00 −0.00 −0.00 −0.02 0.01 0.01 −0.01 0.00 0.00 0.01 (−0.51) (−1.00) (−1.47) (−2.56) (1.30) (7.57) (−3.48) (2.16) (0.74) (6.11)

α −35.79∗∗∗ −12.27∗∗∗ −11.62∗∗∗ −11.60∗∗ −23.42∗∗∗ −13.50∗∗∗ −2.78∗∗∗ −16.22∗∗∗ −11.37∗∗∗ −5.51∗∗∗ (−3.64) (−7.58) (−13.49) (−2.14) (−5.01) (−17.19) (−5.46) (−11.90) (−11.77) (−12.01)

Weeks 299 299 299 299 299 299 299 299 299 299 References

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43 Appendix: Supplemental Figures and Tables

Figure A1: Fitted and Sample Average Cryptocurrency Returns: 52 Cryptocurrencies

This figure presents a summary of the fitted expected and average returns from the rolling Fama-Macbeth regressions. For each rolling regression, we compute the fitted expected returns, i.e., factor betas × risk prices, and the sample average returns at the weekly frequency. In the graph, we plot the mean of the fitted and average returns from the 75 cross-sectional rolling regressions. In Figure A, the factors are the return of Bitcoin (BTC), the cryptocurrency size factor (Size), and the crypto-momentum factor (Mom). In Figure B, the factors are the blockchain-based gCP and gNET . In Figure C, we consider all five factors. The reported average adjusted R2 is the time series average of the cross-sectional adjusted R2’s across the rolling regressions. The test assets consist of the 52 cryptocurrencies from Table A2. The estimation of the models is based on the GMM approach described in Section 5.1.

A) BTC + Size + Mom (Time Series Averages) B) gCP + gNET (Time Series Averages) 0.05 0.05

0.04 0.04

0.03 0.03

0.02 0.02

0.01 0.01 FITTED EXPECTED RETURNS FITTED EXPECTED RETURNS 0 0

Average Adjusted R2 = 0.26 Average Adjusted R2 = 0.42 -0.01 -0.01 -0.01 0 0.01 0.02 0.03 0.04 0.05 -0.01 0 0.01 0.02 0.03 0.04 0.05 SAMPLE AVERAGE RETURNS SAMPLE AVERAGE RETURNS

C) BTC + Size + Mom + gCP +gNET (Time Series Averages) 0.05

0.04

0.03

0.02

0.01 FITTED EXPECTED RETURNS 0

Average Adjusted R2 = 0.46 -0.01 -0.01 0 0.01 0.02 0.03 0.04 0.05 SAMPLE AVERAGE RETURNS

44 Figure A2: Cross-Sectional Adjusted-R2’s from Rolling Fama-MacBeth Regressions: 52 Cryptocurrencies

The ﬁgure plots the time series of the cross-sectional adjusted R2’s from rolling Fama-MacBeth regressions of expected cryptocurrency returns on factor betas. The rolling window is 156 weeks and it is updated weekly for a total of 75 regressions. The dashed line corresponds to the factor model with the the return of Bitcoin (BTC), cryptocurrency size (Size), and cryptocurrency momentum (Mom). The solid line corresponds to the factor model with the blockchain-based computing power and network size factors. The test assets consist of the 52 cryptocurrencies listed in Table A2. The sample period is from 1/6/2017 to 5/28/2021.

0.7

0.6

0.5

0.4 2

0.3

0.2 ADJUSTED R ADJUSTED 0.1

-0.1 BTC + Size + Mom gCP + gNET -0.2 Jan 2020 Apr 2020 Jul 2020 Oct 2020 Jan 2021 Apr 2021 ROLLING REGRESSION END DATE

45 Table A1: Variable Descriptions This table presents detailed descriptions of the main variables used in our analysis.

Variable Description Cryptocurrency Variables Return Weekly returns based on cumulative daily returns of seven-day periods ending on Fridays. P rice Natural logarithm of price as of Friday. The price is the fixed closing price at midnight UTC time on Friday. It is denominated in U.S. dollars. Daily prices are from Coinmetrics.io’s fixing/reference rate service. CP Natural logarithm of the hashrate value (in megahashes) as of Friday. The hashrate values are obtained from Coinmetrics.io, which gathers data directly from the cryptocurrencies’ blockchains. Hashrate data for Ripple (XRP), NEM (XEM), and Maidsafecoin (MAID) are not available as these currencies are non-mineable, i.e., they do not use a Proof-of-Work mecha- nism that relies on computing power to support the blockchain. ∆CP Weekly first differences of CP . NET Natural logarithm of unique active addresses on the blockchain as of Fri- day. Unique active addresses are the number of addresses from (or to) which transactions are conducted on the blockchain. The daily active address count is from Coinmetrics.io, which gathers data directly from the cryptocurrencies’ blockchains. We do not collect network data for Monero (XMR) because the true active addresses count on Monero’s blockchain is not available as it is a privacy-focused cryptocurrency. ∆NET Weekly first differences of NET .

Cryptocurrency Blockchain-based Factors gCP Weighted average of the weekly growth rates of computing power (∆CP ) for seven of the ten baseline cryptocurrencies excluding Ripple (XRP), NEM (XEM), and Maidsafecoin (MAID). The weights are based on market capitalization ranks. Specifically, we first rank the seven cryptocurrencies by market capitalization as of the prior week. Then, we assign ranks 1 to 7 to the seven mineable cryptocurrencies based on their ascending market capitalization. Finally, we transform the ranks 1, 2, 3, 4, 5, 6, and 7 into the respective weights: 1/28, 2/28, 3/28, 4/28, 5/28, 6/28, and 7/28. gNET Weighted average of the weekly growth rate of network size (∆NET ) for nine of the ten baseline cryptocurrencies excluding Monero (XMR). The weights are based on market capitalization ranks. Specifically, we first rank the nine cryptocurrencies by market capitalization as of the prior week. Then, we assign ranks 1 to 9 to the nine cryptocurrencies based on their ascending market capitalization. Finally, we transform the ranks 1, 2, 3, 4, 5, 6, 7, 8, and 9 into weights. gCP \ BTC Rank-weighted growth rate of computing power (∆CP ) for six of the ten baseline cryptocurrencies excluding Bitcoin (BTC), Ripple (XRP), NEM (XEM), and Maidsafecoin (MAID). To calculate the rank weights, we first rank the six cryptocurrencies by their market capitalization as of the prior week. Then, we assign ranks 1 to 6 to the six mineable cryptocurrencies based on their ascending market capitalization. Finally, we transform the ranks 1, 2, 3, 4, 5, and 6 into weights.

46 Table A1: Variable Descriptions (continued)

Variable Description gNET \ BTC Rank-weighted growth rate of network size (∆NET ) for eight of the ten baseline cryptocurrencies excluding Bitcoin (BTC) and Monero (XMR). To calculate the rank weights, we ﬁrst rank the eight cryptocurrencies by their market capitalization as of the prior week. Then, we assign ranks 1 to 8 to the eight cryptocurrencies based on their ascending market capitalization. Finally, we transform the ranks 1, 2, 3, 4, 5, 6, 7, and 8 into weights.

Cryptocurrency Market-Based Factors BTC The weekly return of Bitcoin. Size The diﬀerence between the average returns of the smallest three out of the nine baseline cryptocurrencies (excluding Bitcoin) by market capitalization as of the prior week and the average returns of the largest three out of the nine baseline cryptocurrencies by market capitalization as of the prior week (excluding Bitcoin). We exclude Bitcoin’s return from the calculation because the contemporaneous return of Bitcoin is included in our empirical analysis as a separate factor. Mom Average of the contemporaneous returns of three of the ten baseline cryptocurrencies with the highest returns (winners) in the prior week minus the average of the contemporaneous returns of three of the ten baseline cryptocurrencies with the lowest returns (losers) in the prior week, excluding Bitcoin. We exclude Bitcoin’s return from the calculation because the contemporaneous return of Bitcoin is included in our empirical analysis as a separate factor.

Fama-French U.S. 3 Factors (Weekly) MKTRF Aggregate stock market return in excess of the risk-free rate. Obtained from Kenneth French’s data library at https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html SMB Return of the Small minus Big portfolios (size factor). Obtained from Ken- neth French’s data library. HML Return of the High minus Low portfolios (value factor). Obtained from Kenneth French’s data library.

Cryptocurrency Non-Blockchain-Based Factors ∆GoogleSearches First diﬀerences of the natural log of the weekly average values of worldwide Google searches downloaded from Google Trends for the terms ‘bitcoin’, ‘ethereum’, ‘litecoin’, ‘dash cryptocurrency’ (‘dash’ has multiple meanings), ‘dogecoin’, ‘monero’, ‘vertcoin’, ‘ripple cryptocurrency’, ‘ripple xrp’ (as ‘ripple’ has multiple meanings), ‘nem cryptocurrency’ (‘nem’ is ambiguous), and ‘maidsafecoin’. The Google searches are scaled into an index with the maximum value reported as 100 in the data. ∆RedditP First diﬀerences of the natural log of the weekly sum of the number of new Reddit posts on the subreddits of the ten baseline cryptocurrencies along with the number of posts on a general cryptocurrency subreddit. The number of new posts is summed over the 7-day weekly period ending Friday. The subreddits used in our paper are ‘r/Cryptocurrency’, ‘r/Bitcoin’, ‘r/Eth- Trader’, ‘r/Litecoin’, ‘r/Dashpay’, ‘r/Dogecoin’, ‘r/Vertcoin’, ‘r/Monero’, ‘r/Ripple’, ‘r/NEM’, and ‘r/Safenetwork’. The data are obtained by pars- ing Reddit’s public API.

47 Table A1: Variable Descriptions (continued)

Variable Description ∆T radeV olume First difference in the natural log of the weekly total units traded (bought and sold) multiplied by the average of last week’s price. This sum, is based on units traded each week for the ten baseline cryptocurrencies: Bitcoin, Ethereum, Litecoin, Dash, Dogecoin, Vertcoin, Monero , Ripple, NEM, and Maidsafecoin. The volume data are provided by Coinmetrics.io and includes trades from a set of cryptocurrency exchanges that is almost identical to the exchanges used in Makarov and Schoar(2020). To obtain the weekly total volume, we first aggregate the number of units of the cryptocurrency traded each week for the seven-day period ending Friday 00:00 UTC time. Next, we multiply the number of units traded by the average of last week’s price in USD. We then aggregate the values across the ten baseline crytocurrencies to create the aggregate trading volume. We use last week’s price as opposed to the current week’s price to mitigate mechanical correlations between price and volume. ∆GEP U Monthly values of the global economic policy uncertainty index (GEPU) constructed by Davis(2016) and obtained from https://www.policyuncertainty.com/global monthly.html. The GEPU index is constructed by counting the number of times economic-uncertainty related words appear in leading global newspapers from 21 countries. Specifically, Davis(2016) counts the number of times the words ‘economic’ and ‘uncertain’ (along with their variations) appear along with a policy term such as ‘deficit’, ‘legislation’, and ‘regulation’. Some examples of the newspapers used to construct the economic policy uncertainty (EPU) index for the U.S.A. are The New York Times, The Wall Street Journal, and The Washington Post. After constructing the EPU Index for each country, the GEPU index is calculated by taking the GDP-weighted average of the EPU indices from the following 21 countries: Australia, Brazil, Canada, Chile, China, Colombia, France, Germany, Greece, India, Ireland, Italy, Japan, Mexico, the Netherlands, Russia, South Korea, Spain, Sweden, the United Kingdom, and the United States. The methodology used by Davis(2016) to construct the GEPU is adapted from Baker et al.(2016). We extrapolate the monthly values into weekly values to create a weekly version of the GEPU index. Using the natural logs of these values, we construct weekly growth rates for the global economic policy risk that we denote by ∆GEP U.

48 Table A2: Descriptive Statistics for Sample Cryptocurrencies This table presents descriptive statistics for the cryptocurrencies in our sample. We report averages for the log of computing power (CP ), log of network size (NET ), prices in USD, log-prices, market capitalization rates (in millions USD), and cryptocurrency returns. We also report the standard deviation of returns. In Panel A, we report these statistics for the ten baseline cryptocurrencies, which are Bitcoin, Ethereum, Litecoin, Dash, Dogecoin, Vertcoin, Monero , Ripple, NEM, and Maidsafecoin. Related statistics for the set of the additional 20 cryptocurrencies are listed in Panel B. The samples in Panels A and B are from 9/4/2015 to 5/28/2021. In Panel C, we report related statistics for an extended set of 22 cryptocurrencies over the period from 1/6/2017 to 5/28/2021.

Panel A: 10 Baseline Cryptocurrencies Averages St. Dev. CP NET Price Ln(Price) MktCap (millions) Ret Ret Bitcoin 30.43 13.46 8,676 8.24 156,581 0.02 0.11 Ethereum 17.66 11.68 349 4.61 37,637 0.04 0.19 Litecoin 17.49 10.86 64 3.41 3,870 0.03 0.17 Dash 18.74 10.50 147 4.12 1,224 0.03 0.18 Dogecoin 17.38 10.73 0.01 −6.44 1,725 0.06 0.44 Vertcoin 12.39 6.94 0.70 −1.42 31 0.03 0.25 Monero 5.32 85 3.44 1,424 0.04 0.19 Ripple 8.56 0.30 −2.22 29,819 0.04 0.24 NEM 6.78 0.13 −3.44 1,169 0.05 0.25 Maidsafecoin 3.52 0.22 −1.92 100 0.02 0.17 Average 23,358 0.04 0.22

Panel B: 20 Additional Cryptocurrencies Averages St. Dev. Price Ln(Price) MktCap (millions) Ret Ret Aeon 0.86 −0.65 10 0.04 0.27 Bitshares 0.06 −3.22 183 0.03 0.24 Burst 0.01 −5.16 14 0.05 0.30 Curecoin 0.13 −2.38 3 0.02 0.22 Digibyte 0.02 −4.32 210 0.05 0.30 FLO 0.05 −3.19 6 0.04 0.24 Gamecredits 0.68 −1.60 36 0.03 0.26 Groestlcoin 0.40 −1.48 23 0.06 0.31 Iocoin 0.66 −1.34 9 0.02 0.22 Monacoin 1.84 0.10 87 0.07 0.57 Navcoin 0.44 −1.43 21 0.04 0.41 Gulden 0.04 −3.67 14 0.02 0.20 Pinkcoin 0.01 −5.46 3 0.04 0.28 Reddcoin 0.00 −6.62 56 0.07 0.49 Syscoin 0.14 −2.60 58 0.04 0.23 Viacoin 0.78 −0.82 14 0.04 0.23 Vericoin 0.20 −2.30 5 0.03 0.22 Digitalnote 0.00 −6.57 18 0.07 0.41 Myriad 0.00 −6.25 11 0.04 0.27 Stealth 0.14 −2.48 3 0.06 0.42 Average 39 0.04 0.30 49 Panel C: Extended Sample of 22 Cryptocurrencies (1/6/17 - 5/28/21) Averages St. Dev. Price Ln(Price) MktCap (millions) Ret Ret Ardor 0.16 −2.37 161 0.03 0.20 Decred 41.56 3.30 388 0.04 0.19 Einsteinium 0.13 −2.75 29 0.06 0.33 EthereumClassic 11.76 2.13 1,212 0.04 0.24 ExclusiveCoin 0.38 −1.81 2 0.06 0.38 Expanse 0.78 −1.54 7 0.02 0.24 GeoCoin 0.72 −0.93 2 0.05 0.41 Lisk 3.78 0.67 432 0.04 0.24 Memetic 0.09 −3.49 2 0.07 0.53 MonetaryUnit 0.05 −4.07 6 0.04 0.29 NEO 24.86 2.49 1,643 0.05 0.27 Nexus 0.89 −0.73 51 0.04 0.29 OkCash 0.08 −3.16 6 0.03 0.25 PIVX 1.55 −0.26 88 0.05 0.30 SteemDollars 1.92 0.30 13 0.05 0.55 Salus 17.70 2.43 16 0.05 0.31 Sphere 0.94 −1.15 4 0.06 0.42 SteemDollars 0.84 −0.80 229 0.03 0.23 Validity 2.17 0.22 8 0.04 0.31 Waves 3.92 0.87 388 0.04 0.20 Stellar 0.15 −2.51 2,960 0.05 0.30 Verge 0.02 −5.17 247 0.09 0.51 Average 359 0.05 0.32

50 Table A3: Correlations between Fundamentals-based Factors and Cryptocurrency Returns

This table reports cross-correlations of the aggregate computing power and network growth factors (gCP , gNET , gCP \ BTC, and gNET \ BTC) with the weekly returns of the ten baseline cryptocurrencies from Panel A of Table A2: Bitcoin (BTC), Ethereum (ETH), Ripple (XRP), Litecoin (LTC), Dash (DSH), Monero (XMR), Dogecoin (DOGE), NEM (XEM), Vertcoin (VTC), and Maidsafecoin (MAID). We also report their cross-correlations with the average return of the extended sample of 30 cryptocurrencies (AvgRet30 ), which includes the 20 additional cryptocurrencies from Panel B of Table A2. The sample period begins on 9/4/2015 and ends on 5/28/2021.

gCP gNET gCP \ BT C gNET \ BT C BT C ET H LT C DSH DOGE V T C XMR XRP XEM MAID AvgRet30 gCP 1.00

gNET 0.07 1.00

gCP \ BTC 0.81 0.02 1.00

gNET \ BTC 0.02 0.99 0.01 1.00

BTC 0.18 0.36 0.19 0.33 1.00

51 ETH 0.15 0.35 0.14 0.35 0.39 1.00

LT C 0.19 0.32 0.22 0.31 0.62 0.41 1.00

DSH 0.19 0.22 0.21 0.22 0.45 0.52 0.47 1.00

DOGE −0.03 0.24 0.00 0.25 0.24 0.23 0.30 0.25 1.00

VTC 0.20 0.16 0.23 0.16 0.36 0.32 0.32 0.32 0.14 1.00

XMR 0.23 0.20 0.26 0.19 0.45 0.42 0.40 0.53 0.19 0.39 1.00

XRP 0.12 0.29 0.11 0.28 0.33 0.33 0.61 0.29 0.28 0.29 0.27 1.00

XEM 0.21 0.22 0.21 0.21 0.38 0.29 0.26 0.33 0.17 0.20 0.27 0.33 1.00

MAID 0.13 0.27 0.10 0.27 0.41 0.41 0.33 0.30 0.16 0.30 0.35 0.27 0.30 1.00

AvgRet30 0.27 0.32 0.26 0.31 0.62 0.54 0.58 0.55 0.45 0.59 0.57 0.56 0.49 0.52 1.00

Correlations with the 20 Out-of-Sample cryptocurrencies

Minimum 0.02 0.04 0.04 0.03 0.12 0.13 0.12 0.11 0.08 0.09 0.12 0.15 0.10 0.03 0.27

Average 0.15 0.13 0.13 0.13 0.30 0.25 0.27 0.25 0.19 0.31 0.27 0.27 0.24 0.26 0.54

Maximum 0.29 0.31 0.25 0.31 0.45 0.43 0.47 0.34 0.45 0.49 0.54 0.40 0.42 0.40 0.69