Is the cryptocurrency market efficient? Evidence from an analysis of fundamental factors for Bitcoin and Ethereum

Łęt, Blanka; Sobański, Konrad; Świder, Wojciech; Włosik, Katarzyna Article Is the cryptocurrency market efficient? Evidence from an analysis of fundamental factors for Bitcoin and Ethereum International Journal of Management and Economics Provided in Cooperation with: SGH Warsaw School of Economics, Warsaw Suggested Citation: Łęt, Blanka; Sobański, Konrad; Świder, Wojciech; Włosik, Katarzyna (2022) : Is the cryptocurrency market efficient? Evidence from an analysis of fundamental factors for Bitcoin and Ethereum, International Journal of Management and Economics, ISSN 2543-5361, Sciendo, Warsaw, Vol. 58, Iss. 4, pp. 351-370, https://doi.org/10.2478/ijme-2022-0030 This Version is available at: https://hdl.handle.net/10419/309769 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ International Journal of Management and Economics 2022; 58(4): 351–370 Blanka Łęt1, Konrad Sobański2,*, Wojciech Świder3, Katarzyna Włosik4 Is the cryptocurrency market efficient? Evidence from an analysis of fundamental factors for Bitcoin and Ethereum https://doi.org/10.2478/ijme-2022-0030 Received: August 26, 2022; accepted: December 14, 2022 Abstract: This article sheds new light on the informational efficiency of the cryptocurrency market by analyzing investment strategies based on structural factors related to on-chain data. The study aims to verify whether investors in the cryptocurrency market can outperform passive investment strategies by applying active strategies based on selected fundamental factors. The research uses daily data from 2015 to 2022 for the two major cryptocurrencies: Bitcoin (BTC) and Ethereum (ETH). The study applies statistical tests for differences. The findings indicate informational inefficiency of the BTC and ETH markets. They seem consistent over time and are confirmed during the COVID-19 pandemic. The research shows that the net unrealized profit/loss and percent of addresses in profit indicators are useful in designing active investment strategies in the cryptocurrency market. The factor-based strategies perform consistently better in terms of mean/median returns and Sharpe ratio than the passive “buy-and-hold” strategy. Moreover, the rate of success is close to 100%. Keywords: active strategies, cryptocurrency, fundamental factors, informational efficiency, Ledoit and Wolftest JEL Classification: F31, G11, G15 1 Introduction In the literature, divergent views on the informational efficiency of the cryptocurrency market exist. Yonghong et al. [2018] have not found the Bitcoin (BTC) market informationally efficient. Some researchers have showed that with time, it may be heading toward efficiency, and there are periods when it was informationally efficient [see e.g. Urquhart, 2016; Vidal-Tomás and Ibañez, 2018; Sensoy, 2019]. Another strand of the literature suggests that periods in which it can be considered efficient are intertwined with periods in which it is not efficient [see e.g. Alvarez-Ramirez et al., 2018; Khuntia and Pattanayak, 2018]. There are also authors who examine a wider group of cryptocurrencies, and there are indications that most of them are not informationally efficient [see e.g. Caporale et al., 2018; Hu et al., 2019; Kristoufek and Vosvrda, 2019]. A deviation from the efficient market hypothesis (EMH) [Fama, 1970] implies that the path of the price development for cryptocurrencies contains long-lasting asset bubbles as they cannot be quickly Empirical Paper Open Access. © 2023 Łęt et al., published by Sciendo. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 License. *Corresponding author: Konrad Sobański, Department of International Finance, Poznań University of Economics and Business, Poznań, Poland. E-mail: konr[email protected]znan.pl Blanka Łęt, Department of Applied Mathematics, Poznań University of Economics and Business, Poznań, Poland. Wojciech Świder, Department of Public Finance, Poznań University of Economics and Business, Poznań, Poland. Katarzyna Włosik, Department of Investment and Financial Markets, Poznań University of Economics and Business, Poznań,Poland. 352 B. Łęt et al. eliminated by rational investors who are able to estimate the fundamental price of assets. However, for the cryptocurrency market, with BTC at its core, the measurement of intrinsic value is highly disputable. On the one hand, researchers indicate that BTC has no fundamental value [Cheah and Fry, 2015]. Moreover, Detzel et al. [2021] have noted that the fundamental source of intrinsic value of cryptocurrencies remains unclear. The authors also have added that the fundamentals of cryptocurrencies have few, if any, predictive signals that would be publicly available (e.g. analyst coverage and accounting statements). On the other hand, some researchers suggest that, in a sense, demand and supply in this market can be considered fundamental factors [Gbadebo et al., 2021], sometimes giving priority to demand indicators [Li and Wang, 2017] or supply indicators such as the cost of mining [Hayes, 2017]. Regardless of the view, the lack of informational efficiency of the market induces that there are investment strategies that generate extraordinary returns over a prolonged period. The aim of this study is to verify whether investors in the cryptocurrency market can make excess returns by applying strategies based on fundamental factors. The study specifically investigates whether factor-based trading strategies generate higher returns than the passive “buy-and-hold” strategy, which is popular among investors known as “hodlers”.1 It should be noted that fundamental value and its indicators in the cryptocurrency market are highly debatable. The fundamental indicators analyzed in this study can be used to describe the structure of the cryptocurrency market. The examined set of indicators includes the net unrealized profit/loss (NUPL), the spent output profit ratio (SOPR), and the percent of addresses in profit (PAP). The study applies statistical tests for differences by Ledoit and Wolf [2008, 2018]. The analysis is based on daily data sourced from the Glassnode database for the period starting on 8 August 2015 and ending on 20 October 2022. The study calculates rates of returns and their volatility for several strategies based on fundamental (structural) factors for BTC and Ethereum (ETH). These cryptocurrencies have been selected based on two factors – their significant role in the ecosystem – taking account of volume as well as capitalization, and the availability of data.2 The performance measurement for these strategies is based on mean/median returns and the Sharpe ratio. Furthermore, the study verifies whether there are any differences between the pre-pandemic and COVID-19 periods. The study investigates the consistency of conclusions drawn for the main sample period (2015–2019) in the out-of-sample period. The usefulness of fundamental factors in making investment decisions is verified in the COVID-19 period (2020–2022). This allows checking the consistency of the results across different economic and social environments. To deepen the understanding of the cryptocurrency market and its efficiency, two research questions are formulated and discussed in the article: • Do trading strategies based on fundamental factors in the BTC and ETH markets outperform the “buyand-hold” strategy? • Are the BTC and ETH markets informationally efficient based on the insight from the fundamental factor analysis? The article aims to • verify whether investors in the cryptocurrency market can outperform passive investment strategies and make excess returns by applying active strategies based on selected fundamental factors, and • evaluate the efficiency of the BTC and ETH markets based on selected fundamental factors. 1 The so-called “hodl” can be defined as a buy and hold strategy in the cryptocurrency market. The name is derived from the misspelled word “hold” in one of the posts on the online forum – Bitcointalk, in 2013.This term is sometimes regarded as an acronym “hold on for dear life” [Kraken, n.a.]. The name “hodler” originates from the word “hodl”. 2 According to CoinMarketCap.com as of the beginning of November 2022, Bitcoin and Ethereum ranked first and second, respectively, in terms of market capitalization. They also took the second and third position in the ranking based on the trade volume only with Tether ahead of them. Nevertheless, the trade volume should be considered with caution as it may be artificially inflated by some entities [for discussion see e.g. Alexander and Dakos, 2020]. Bitcoin and Ethereum market efficiency 353 The study formulates and tests a hypothesis describing the efficiency of the cryptocurrency market. The hypothesis states that investment strategies designed based on structural indicators may generate higher returns and outperform the “buy-and-hold” strategy (B&H), and consequently, the cryptocurrency market is not efficient. The article contributes to the literature in several ways. First, it sheds new light on the efficiency of the cryptocurrency market by analyzing investment strategies based on fundamental (structural) factors and comparing their performance with that of the passive strategy. To the best of the authors’ knowledge, such a topic has not been addressed in the literature, despite the fact that the analyzed indicators are used by cryptocurrency market practitioners. For this reason, the article aims to fill an important research gap. Second, the study identifies the best options for active investment strategies and assesses their effectiveness using selected statistical tests for the mean and the Sharpe ratio. Third, it considers recent trends in the efficiency of the cryptocurrency market by studying the COVID-19 pandemic alongside the pre-pandemic period. This approach also serves as a robustness check for the obtained results. The rest of the article is structured as follows. Section 2 reviews the relevant literature, mainly related to the efficiency of the cryptocurrency market. Section 3 contains the description of the data used in the study. Section 4 describes the methodology. Section 5 depicts and discusses empirical results, and Section 6 concludes. 2 Literature review According to Fama [1970], the market is informationally efficient from an economic point of view when stock prices reflect all information, and it is not possible to generate rates of returns higher than those with a passive strategy (“buy-and-hold”). In broader terms, the EMH applies to other markets in addition to stocks, including cryptocurrencies. From a theoretical point of view, on the one hand, the informational efficiency of the cryptocurrency market might be justified as the blockchain technology allows direct and quick access to information on all transactions. On the other hand, though, investors may lack the tools or technical skills to analyze blockchains and may not be able to make a proper use of the abundance of information that blockchains provide. Moreover, as mentioned in Introduction, there are divergent views on the fundamental value of cryptocurrencies. This makes it difficult for investors to establish whether a particular cryptocurrency is properly valued by the market, with all the information reflected in its prices, making this market informationally efficient. There are many methods used by researchers to assess the efficiency of the cryptocurrency market. These methods test, among others, the properties of the cryptocurrency time series – whether they follow a random walk, whether they are characterized by long memory, self-similarity and scaling patterns, autocorrelation, or independence [e.g. Urquhart, 2016; Nadarajah and Chu, 2017; Brauneis and Mestel, 2018; Wei, 2018; López‑Martín et al., 2021; Kakinaka and Umeno, 2022]. Moreover, researchers employ efficiency indices, which are synthetic measures that summarize either several statistical tests or results of one test in multiple sub-samples [e.g. Kristoufek, 2018; Yonghong et al., 2018; Kristoufek and Vosvrda, 2019; Tran and Leirvik, 2020]. They also detect pricing anomalies [e.g. Grobys and Sapkota, 2019; Cheng etal., 2019; Shen et al., 2020]. Another approach is to verify the profitability of investment strategies based on selected information, which is employed and expanded in this study. The problems with the identification of fundamental factors in the cryptocurrency market, highlighted in Introduction, may induce investors to employ the technical analysis to build profitable investment strategies in the cryptocurrency market. One strand of the literature examines the performance of technical analysis in the BTC trading. In general, the results indicate that employing strategies based on technical indicators is justified. Gerritsen et al. [2020] investigated whether seven selected technical trading rules may outperform a “buy-and-hold” strategy in the BTC market using daily data. Their results indicate that specific trading rules, mainly trading range breakout, outperform the “buy-and-hold” strategy. Detzel et al. [2021] analyzed daily BTC data and found that trading strategies based on ratios of prices to their moving averages outperform the “buy-and-hold” strategy – they generate large alphas and result in higher Sharpe 354 B. Łęt et al. ratios. Huang et al. [2019] built a classification tree-based model to predict BTC returns (specifically the range for the next day’s return). Next, they checked its usefulness. To do that, they used daily BTC data and 124 technical indicators that they divided into five groups (viz., cycle indicators, momentum indicators, overlap studies indicators, pattern recognition indicators, and volatility indicators). They found that their model has out-of-sample predictive power and outperformed the “buy-and-hold” strategy as well as classic strategies that they have investigated. Resta et al. [2020] considered both daily and intraday (5-min interval) data. They built trend-following and mean-reverting strategies to evaluate the performance of technical trading rules. The authors also found that the strategies based on daily data are more profitable than the intraday approach. Moreover, they documented that simple moving averages yield best results when daily data are considered, whereas the “buy-and-hold” strategy outperforms the analyzed alternatives at the intraday frequency. Corbet et al. [2019] tested resistance and support levels and their performance using various technical trading rules based on high-frequency BTC returns. Their results support the choice of moving average strategies. The authors also indicated that the variable-length moving average rule yields the best results with buy signals compared to sell signals. Miller et al. [2019] searched for price patterns in the BTC 1-min price data with an algorithm using smoothing splines. They detected three patterns – head-and-shoulders, inverted head-and-shoulders, and triangle bottoms. Then, the authors constructed a trading strategy to assess the profitability of these patterns. The results indicate that the strategy yield returns that are significantly higher than the returns of unconditional/random strategies. Nakano et al. [2018] investigated trading strategies in the BTC market using artificial neural networks. They extracted trading signals from the technical indicators that are calculated based on intraday data (15-min intervals). The authors found that their approach helps obtain better results than those using the “buy-and-hold” strategy and primitive technical trading strategies. The profitability of technical analysis is also investigated with regard to a wider group of cryptocurrencies. Grobys et al. [2020] analyzed a group of 11 cryptocurrencies with high market capitalization and found one of the moving average trading strategies profitable. Hudson and Urquhart [2021] used almost 15,000 rules from five main classes of technical trading rules and applied them to data from two BTC markets and ETH, Litecoin, and Ripple data. The results indicate that each class of technical trading rules yields profits. The authors also indicated that employing these rules generates higher risk-adjusted returns compared with the “buy-and-hold” strategy. Anghel [2021] investigated 861 cryptocurrencies using technical analysis and machine learning and found that statistically significant positive excess returns are rarely generated. The author controlled for risk, data snooping, and market frictions. The conclusion holds irrespective of the test significance level, the type of the trading position, and data sampling frequency (the author used daily data; however, for four cryptocurrencies, he additionally analyzed hourly data). The employed machine learning methods usually underperform simple alternatives based on the technical analysis, particularly after controlling for trading costs. The author notes, however, that applied machine learning solutions outperform the technical analysis on less liquid and small cryptoasset markets. Nevertheless, excess returns are not significant when they are controlled for data snooping. To sum up, the research conducted so far generally shows evidence that the cryptocurrency market is not informationally efficient as above-average profits can be achieved based on technical analysis. Apart from the strategies based on the technical analysis presented earlier, Fang et al. [2021], in their extensive literature review on cryptocurrency trading, distinguished two other main types of systematic trading in this market – the usage of pairs trading [e.g. Lintilhac and Tourin, 2017] and informed trading [e.g. Feng et al., 2018]. This study extends this strand of literature further. To the best of our knowledge, this study is the first to use structural indicators derived from the on-chain data such as the NUPL or the SOPR to design investment strategies and test their performance. It is worth noting that data derived from blockchain were used in some previous studies, but in other contexts and to address other research problems [e.g. Maesa et al., 2017; Griffin and Shams, 2020; Mizerka et al., 2020]. Since the outbreak of the COVID-19 pandemic, researchers have started to analyze the cryptocurrency market developments under the new economic and social conditions. They examined the safe haven or hedging properties of selected cryptocurrencies [e.g. Demir et al., 2020; Ghorbel and Jeribi, 2021], volatility Bitcoin and Ethereum market efficiency 355 of cryptocurrencies [e.g. Segnon and Bekiros, 2020; Ftiti et al., 2021; Özdemir, 2022], interrelationships between volatility and liquidity in this market [e.g. Corbet et al., 2022], and its efficiency. Mnif et al. [2020], using a multifractal analysis, discovered a positive impact of the pandemic on the efficiency of the cryptocurrency market. Naeem et al. [2021], however, applying asymmetric multifractal detrended fluctuation analysis, found that the outbreak of the COVID-19 pandemic has adversely affected the efficiency of the four cryptocurrencies analyzed: BTC, ETH, Litecoin, and Ripple. Kakinaka and Umeno [2022] examined the efficiency of BTC and ETH markets and concluded that during the COVID-19 period, they became more inefficient in the short term. This article sheds new light on this matter by applying another approach and taking a closer look at the cryptocurrency market efficiency before and during the pandemic. 3 Data and fundamental factors The analysis is based on daily data for BTC and ETH sourced from the Glassnode database for the period from August 8, 2015 to October 20, 2022. The starting point of the analysis was based on the availability of the time series examined. The Glassnode database is a comprehensive library of the cryptocurrency data which provides different metrics as well as a wide range of indicators derived from cryptocurrency blockchains. It is used in scientific research [e.g. Hoang and Baur, 2022; Urquhart, 2022] and also by international financial institutions [e.g. Bank for International Settlements – Auer et al., 2022]. It is also among the top databases with on-chain data in Internet rankings [e.g. Oladotun, 2022]. The fundamental indicators analyzed in this study can be used to describe the structure of the cryptocurrency market. The factors studied include3 • net unrealized profit/loss (NUPL), • spent output profit ratio (SOPR), and • percent of addresses in profit (PAP). The structural factors were selected based on two considerations. First, the study chooses from indicators calculated using the on-chain data. The on-chain analysis is a popular method among crypto community members for exploring information from a blockchain ledger to ascertain market sentiment. Second, only factors that generate enough transaction signals to evaluate investment strategies are used. This allows meeting assumptions of the statistical tests and drawing general conclusions. In other words, the study recognizes that indicators that generate rare signals are not practicable. The NUPL indicator [Schultze-Kraft, 2019] considers the difference between relative unrealized profit and relative unrealized loss to determine whether the network as a whole is currently in a state of profit or loss (see Formula [1]). The relative unrealized profit represents the total profit accrued by the unspent coins (unspent transaction output, UTXO), which were created when the price of the asset was lower than the current price compared with the current market capitalization.4 Consequently, the relative unrealized loss represents the total loss accrued by the unspent coins, which were created when the price of the asset was higher than the current price compared with the current market capitalization. The NUPL indicator can also 3 The description of the methodology for calculating structural indicators is based on the Glassnode database. All indicators for BTC and ETH are available at: https://studio.glassnode.com/metrics?a=BTC&category=&m=indicators.NetUnrealizedProfitLoss https://studio.glassnode.com/metrics?a=ETH&category=&m=indicators.NetUnrealizedProfitLoss https://studio.glassnode.com/metrics?a=BTC&category=&m=indicators.Sopr https://studio.glassnode.com/metrics?a=ETH&category=&m=indicators.Sopr https://studio.glassnode.com/metrics?a=BTC&category=&m=addresses.ProfitRelative https://studio.glassnode.com/metrics?a=ETH&category=&m=addresses.ProfitRelative 4 The unspent transaction output (UTXO) refers to digital currency someone has left in his or her wallet after executing a cryptocurrency transaction. 356 B. Łęt et al. be calculated by subtracting realized capitalization from market capitalization, and dividing the result by the market capitalization [Demeester et al., 2019; see Formula [4]]. The realized capitalization is a variation of market capitalization that values each unspent coin based on the price when it was last transferred (moved), as opposed to its current value. As such, the realized capitalization represents the realized value of all the coins in the network, as opposed to their current market value. The NUPL metric tries to answer the following question: if all units of a given cryptocurrency were sold today, how much would investors stand to gain or lose? If the NUPL indicator is positive (NUPL>0), the network is in a state of net profit. If the NUPL indicator is negative (NUPL<0), the network is in a state of net loss. In general, the further NUPL deviates from zero, the closer the market trends toward tops and bottoms. As such, NUPL can help investors identify when to take profit and when to re-enter the market. Figure 1 depicts the NUPL indicator for BTC and ETH, respectively, in the period investigated (August 8, 2015 – October 20, 2022). =- NUPL Relative Unrealised Profit Relative Unrealised Loss (1) ( ) ⋅- = ∑ max 0, current realised UTXOs value price price Relative Unrealised Profit Market capitalisation (2) ( ) ⋅- = ∑ max 0, realised current UTXOs value price price Relative Unrealised Loss Market capitalisation (3) - = Market capitalisation Realised capitalisation NUPL Market capitalisation (4) The SOPR indicator provides insights into macro-market sentiment, profits, and losses taken over a particular time frame [Shirakashi, 2019]. It captures the aggregate profit and loss realized on a particular day. Both the absolute value of the SOPR indicator and the prevailing trend provide insights into the market spending behavior. In general, the higher the SOPR value, the larger the profit realized on that day by investors. A SOPR value greater than 1 (SOPR > 1) implies that the coins transferred (moved) on that day are, on average, selling at a profit. A SOPR value less than 1 (SOPR < 1) implies that the coins transferred on that day are, on average, selling at a loss. A SOPR value amounting to 1 (SOPR = 1) implies that the coins transferred on that day are, on average, selling at break even. A SOPR value trending higher implies profits are being realized with potential for previously illiquid supply being returned to liquid circulation. A SOPR value trending lower implies losses are being realized, or profitable coins are not being spent. The SOPR Figure 1. NUPL in the period from August 8, 2015 to October 20, 2022. Source: own compilation based on the Glassnode data. Notes: The left panel depicts NUPL for BTC. The right panel depicts NUPL for ETH. BTC, Bitcoin; ETH, Ethereum; NUPL, net unrealized profit/loss. Bitcoin and Ethereum market efficiency 357 indicator is calculated by dividing the realized value of all spent outputs (in USD) by the value of these coins at creation (in USD) (see Formula) [5]. Figure 2 depicts the SOPR indicator for BTC and ETH, respectively, in the period investigated (August 8, 2015 – October 20, 2022). ( ) ( )  ⋅ = ⋅  spent created Coin volume Price USD of all spent outputs SOPR Coin volume Price USD of all spent outputs (5) The PAP refers to unique addresses whose funds have an average buy price, which is lower than the current price. The “buy price” is defined as the price at the time when coins were transferred into an address. The PAP indicator is calculated by dividing the number of addresses in profit by the total number of addresses in the network of a given cryptocurrency (see Formula) [6]. This metric represents an oscillator that describes the current state of the market for a given coin. In general, higher values may suggest market tops, while lower values may signal bottoms. Figure 3 depicts the PAP indicator for BTC and ETH, respectively, in the period investigated (August 8, 2015 – October 20, 2022). =⋅ Number of addresses in profit PAP 100% Number of all addresses in the network (6) Figure 2. SOPR in the period from August 8, 2015 to October 20, 2022. Source: own compilation based on the Glassnode data. Notes: The left panel depicts SOPR for BTC. The right panel depicts SOPR for ETH. BTC, Bitcoin; ETH, Ethereum; SOPR, spent output profit ratio. Figure 3. PAP in the period from August 8, 2015 to October 20, 2022. Source: own compilation based on the Glassnode data. Notes: The left panel depicts PAP for BTC. The right panel depicts PAP for ETH. BTC, Bitcoin; ETH, Ethereum; PAP, percent of addresses in profit. 358 B. Łęt et al. 4 Methodology 4.1 Active strategies In general, there are two groups of investment strategies based on price dynamics: momentum strategies [e.g. Jagadeesh and Titman, 1993, 1995; Schiereck et al., 1999] and contrarian strategies [e.g. De Bondt and Thaler, 1985; Ball et al., 1995]. The study applies strategies belonging to the “contrarian category.” The assumptions of these strategies are described in the following text. The strategy based on the NUPL indicator uses the following assumptions: • Open long position: whenever NUPL is in the capitulation phase. In the study, three levels of entry are considered (NUPL 1 < 0, NUPL 2 < 0.05, and NUPL 3 < 0.10). • Close long position: when NUPL is in the belief–denial phase. Then, all long positions are closing. In the study, three levels of exit are considered (NUPL 1 > 0.5, NUPL 2 > 0.45, and NUPL 3 > 0.4). • There are no short positions in the strategy – only long. The strategy based on the SOPR indicator is realized under the following assumptions: • Open long position: in the case of BTC, whenever SOPR is below 0.990 (SOPR 1), 0.992 (SOPR 2), and 0.995 (SOPR 3). In the case of ETH, the threshold values are 0.900, 0.920, and 0.950, respectively, and are selected based on the dynamics of the indicator. • Close long position: in the case of BTC, when SOPR is above 1.010 (SOPR 1), 1.008 (SOPR 2), and 1.005 (SOPR 3). In the case of ETH, the threshold values are 1.100, 1.080, and 1.050, respectively, and are selected based on the dynamics of the indicator. Then, all long positions are closing. • There are no short positions in the strategy – only long. The strategy based on the PAP indicator consists of the following assumptions: • Open long position: whenever PAP is below 50% (PAP 1), 52% (PAP 2), and 55% (PAP 3). • Close long position: when PAP is above 95% (PAP 1), 93% (PAP 2), and 90% (PAP 3). Then, all long positions are closing. • There are no short positions in the strategy – only long. Strategies based on structural ratios (the so-called active strategies) are further compared with the passive “buy-and-hold” strategy for BTC and ETH. No transaction cost is considered in both active or passive strategies. 4.2 Performance measurement Based on the analyzed time series, the annualized log returns for active strategies are calculated as follows:  =    1, Sell i Buy P R ln TP (7) where T is the time of investment in years, and Sell P and Buy P relate to the prices of a cryptocurrency when an investor should close or open a position, according to rules for the strategies described in Section 4.1. The mean and volatility of returns are calculated as follows: Bitcoin and Ethereum market efficiency 365 Fama, E.F. (1970), Efficient capital markets: a review of theory and empirical work, The Journal of Finance, Vol. 25, No. 2, pp.383–417, https://doi.org/10.2307/2325486. 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NUPL strategies: performance and testing results for the period 2015–2019 BTC ETH B&H NUPL 1 NUPL 2 NUPL 3 B&H NUPL 1 NUPL 2 NUPL 3 Min −1.79 1.13 0.96 0.91 −2.47 1.77 1.58 1.40 Max 3.22 4.02 4.88 5.48 4.93 20.72 27.44 27.44 Median 0.85 2.00 1.96 1.85 1.21 5.57 5.27 5.34 Mean 0.84 2.18 2.19 2.18 1.18 7.02 6.65 6.67 St. dev. 1.01 0.79 1.04 1.16 1.89 4.54 4.66 4.93 Sharpe ratio 0.83 2.76 2.10 1.88 0.62 1.54 1.43 1.35 N210 214 217 205 213 227 Success rate 100% 100% 100% 100% 100% 100% p-value (one-sided test for two means) 0.03** 0.06* 0.14 0.01** <0.01*** <0.01*** p-value (one-sided test for two Sharpe ratios) 0.07* 0.15 0.24 0.07* 0.01** 0.03** Source: own calculations based on the Glassnode data. Notes: The success rate of an active strategy is defined as the percentage of cases where the annualized return on the active strategy is greater than the mean return on the passive strategy. Estimates significant at the significance levels of 0.01, 0.05, and 0.10 are denoted by three (***), two (**), and one (*) asterisk, respectively. B&H, buy-and-hold; BTC, Bitcoin; ETH, Ethereum; NUPL, net unrealized profit/loss. Table A2. SOPR strategies: performance and testing results for the period 2015–2019 BTC ETH B&H SOPR 1 SOPR 2 SOPR 3 B&H SOPR 1 SOPR 2 SOPR 3 Min −1.79 −22.33 −43.39 −43.39 −2.47 −11.18 −11.18 −33.09 Max 3.22 55.20 55.20 55.20 4.93 18.03 18.03 63.59 Median 0.85 1.13 0.80 0.90 1.21 2.18 2.15 1.29 Mean 0.84 2.96 2.13 2.06 1.18 1.93 1.77 1.55 St. dev. 1.01 7.73 8.74 8.51 1.89 4.18 4.36 7.28 Sharpe ratio 0.83 0.38 0.24 0.24 0.62 0.46 0.41 0.21 N172 207 288 233 271 412 Success rate 54.65% 49.28% 50.69% 66.67% 64.58% 51.70% p-value (one-sided test for two means) 0.03** 0.10 0.06* 0.25 0.27 0.39 p-value (one-sided test for two Sharpe ratios) 0.35 0.14 0.03** 0.27 0.28 0.35 Source: own calculations based on the Glassnode data. Notes: The success rate of an active strategy is defined as the percentage of cases where the annualized return on the active strategy is greater than the mean return on the passive strategy. Estimates significant at the significance levels of 0.05 and 0.10 are denoted by two (**) and one (*) asterisk, respectively. B&H, buy-and-hold; BTC, Bitcoin; ETH, Ethereum; SOPR, spent output profit ratio. Bitcoin and Ethereum market efficiency 369 Table A3. PAP strategies: performance and testing results for the period 2015–2019 BTC ETH B&H PAP 1 PAP 2 PAP 3 B&H PAP 1 PAP 2 PAP 3 Min −1.79 0.52 1.00 0.69 −2.47 0.41 0.40 0.38 Max 3.22 1.50 3.69 3.91 4.93 14.18 26.56 26.56 Median 0.85 0.81 2.06 1.91 1.21 3.46 3.58 3.45 Mean 0.84 0.99 2.03 1.90 1.18 3.98 4.28 4.41 St. dev. 1.01 0.33 0.74 0.80 1.89 2.91 3.37 3.32 Sharpe ratio 0.83 2.97 2.74 2.38 0.62 1.37 1.27 1.33 N125 150 181 326 337 363 Success rate 38.40% 100% 97.25% 82.82% 84.57% 90.64% p-value (one-sided test for two means) 0.39 0.12 0.15 <0.01*** <0.01*** <0.01*** p-value (one-sided test for two Sharpe ratios) 0.04** 0.08* 0.14 0.05* 0.14 0.02** Source: own calculations based on the Glassnode data. Notes: The success rate of an active strategy is defined as the percentage of cases where the annualized return on the active strategy is greater than the mean return on the passive strategy. Estimates significant at the significance levels of 0.01, 0.05, and 0.10 are denoted by three (***), two (**), and one (*) asterisk, respectively. B&H, buy-and-hold; BTC, Bitcoin; ETH, Ethereum; PAP, percent of addresses in profit. Table A4. NUPL strategies: performance in the COVID-19 period (2020–2022) BTC ETH B&H NUPL 1 NUPL 2 NUPL 3 B&H NUPL 1 NUPL 2 NUPL 3 Min 1.24 1.38 1.83 3.90 −1.18 1.49 1.36 1.14 Max 2.47 1.59 2.18 4.87 3.11 3.21 5.10 14.84 Median 1.14 1.50 2.05 4.62 1.92 2.63 2.70 2.77 Mean 0.64 1.50 2.02 4.50 1.18 2.43 2.52 3.00 St. dev. 1.01 0.07 0.13 0.32 1.26 0.56 0.67 2.01 Sharpe ratio 0.63 20.91 15.18 13.95 0.94 4.34 3.75 1.49 N7 8 9 103 121 158 Success rate 100% 100% 100% 100% 100% 98.10% Source: own calculations based on the Glassnode data. B&H, buy-and-hold; BTC, Bitcoin; ETH, Ethereum; NUPL, net unrealized profit/loss. Table A5. SOPR strategies: performance in the COVID-19 period (2020–2022) BTC ETH B&H SOPR 1 SOPR 2 SOPR 3 B&H SOPR 1 SOPR 2 SOPR 3 Min 1.24 -4.77 -6.00 -6.00 -1.18 -4.14 -4.14 -21.67 Max 2.47 39.65 39.65 39.65 3.11 13.00 37.21 37.21 Median 1.14 4.40 2.99 -0.22 1.92 1.95 2.09 1.47 Mean 0.64 5.18 5.25 2.58 1.18 1.76 2.54 2.30 St. dev. 1.01 9.17 9.91 7.31 1.26 4.02 6.44 7.58 Sharpe ratio 0.63 0.57 0.53 0.35 0.94 0.44 0.39 0.30 N28 39 114 48 49 98 Success rate 57.14% 62.16% 33.33% 52.08% 55.10% 50% Source: own calculations based on the Glassnode data. B&H, buy-and-hold; BTC, Bitcoin; ETH, Ethereum; SOPR, spent output profit ratio. 370 B. Łęt et al. Table A6. PAP strategies: performance in the COVID-19 period (2020–2022) BTC ETH B&H PAP 1 PAP 2 PAP 3 B&H PAP 1 PAP 2 PAP 3 Min 1.24 1.74 1.59 1.44 −1.18 1.62 1.31 1.09 Max 2.47 2.27 2.19 2.18 3.11 2.93 2.58 2.43 Median 1.14 2.00 1.85 1.69 1.92 2.35 2.02 1.92 Mean 0.64 2.00 1.85 1.77 1.18 2.24 1.93 1.81 St. dev. 1.01 0.19 0.21 0.23 1.26 0.35 0.33 0.35 Sharpe ratio 0.63 10.56 9.01 7.74 0.94 6.42 5.87 5.18 N13 17 22 136 151 174 Success rate 100% 100% 100% 100% 100% 94.83% Source: own calculations based on the Glassnode data. B&H, buy-and-hold; BTC, Bitcoin; ETH, Ethereum; PAP, percent of addresses in profit.