This is a self-archived – parallel published version of this article in the publication archive of the University of Vaasa. It might differ from the original. Predicting cryptocurrency defaults Author(s): Grobys, Klaus; Sapkota, Niranjan Title: Predicting cryptocurrency defaults Year: 2020 Version: Accepted manuscript Copyright © 2020 Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Applied Economics Letters on 03 May 2020, available online: http://www.tandfonline.com/10.1080/00036846.2020.1752903 Please cite the original version: Grobys, K. & Sapkota, N. (2020). Predicting cryptocurrency defaults. Applied Economics 52(46), 5060-5076. https://doi.org/10.1080/00036846.2020.1752903 1 Predicting Cryptocurrency Defaults Klaus Grobys ªˢ, Niranjan Sapkota ªˢ* a University of Vaasa, School of Accounting and Finance Abstract We examine all available 146 Proof-of-Work based cryptocurrencies that started trading prior to the end of 2014 and track their performance until December 2018. We find that about 60% of those cryptocurrencies were eventually in default. The substantial sums of money involved mean those bankruptcies will have an enormous societal impact. Employing cryptocurrency- specific data, we estimate a model based on linear discriminant analysis to predict such defaults. Our model is capable of explaining 87% of cryptocurrency bankruptcies after only one month of trading and could serve as a screening tool for investors keen to boost overall portfolio performance and avoid investing in unreliable cryptocurrencies. JEL Classification: G12, G14 Key Words: Cryptocurrency, Bitcoin, Bankruptcy, Default, Credit risk * Correspondence to: K. Grobys (A. Prof. of Finance) Department of Accounting and Finance, University of Vaasa, Wolffintie 34, 65200 Vaasa, Finland E-mail: klaus.grobys@uva.fi N. Sapkota (Ph.D. Student in Finance) Department of Accounting and Finance, University of Vaasa, Wolffintie 34, 65200 Vaasa, Finland Email: niranjan.sapkota@uva.fi ˢ We would like to thank Simon Moore for a lively, interesting, and detailed discussion of our paper in the U.S. Business Magazine Forbes entitled “How To Tell If Your Cryptocurrency Will Go Bust” on May 28, 2019 . Moreover, valuable comments were received from participants of the 2019 Graduate School Seminar at the University of Vaasa. We also received valuable comments from the 2019 Aalto University Graduate School of Finance Workshop at the University of Jyväskyla. In particular, we would like to thank Mika Veihekoski for an encouraging discussion and helpful comments. Furthermore, we are grateful for having received valuable comments from the 2019 Economics & Finance Seminar at Hanken School of Economics. Especially we would like to thank Timo Korkeamäki, Kenneth Högholm and Emilia Vähämaa for useful comments. Moreover, we received interesting comments from the participants from the 2019 Blockchain Seminar at the University of Vaasa. We would like to thank Robert Faff and the participants of the FINANCE, PROPERTY, TECHNOLOGY, AND THE ECONOMY CONFERENCE 2019, University of South Australia. Finally, we would like to thank an anonymous reviewer for helpful comments. 2 1. Introduction Facing the zeitgeist of digitalization, Bill Gates stated that “the future of money is digital currency.”1 Since the advent of Bitcoin—the first cryptocurrency traded—the number of cryptocurrencies has increased exponentially and there are now over 2,000 cryptocurrencies traded on over 16,000 markets around the world. The main advantages of cryptocurrencies are transparency and 24-hour accessibility. Transactions of cryptocurrencies are all recorded on the open public ledger called the blockchain. This decentralized mechanism gives cryptocurrencies an unparalleled transparency. The technology behind the blockchain is revolutionary, but understanding it is challenging, especially for people without a technical background. In contrast to traditional investments, cryptocurrencies carry different risks. For instance, Rauchs and Hileman (2017) reports that the chance of cryptocurrency exchanges being hacked is 74 ̶ 79%. Taking the legal perspective, Kethineni and Cao (2019) argue that cryptocurrencies became the currency of choice for many drug dealers and extortionists because of the opportunities to hide behind the presumed privacy and anonymity. Maume (2019), who explores Initial Coin Offerings (ICO), highlights that the potential lack of regulation and enforcement is particularly tempting for scammers and other miscreants. In contrast to traditional currency markets, cryptocurrency markets also involve credit risk: As a stylized fact, among all the cryptocurrencies launched prior to December 31 2014, 59% went in default by the end of 2018, and the reasons for defaults are manifold.2 As of February 2019, the overall market capitalization in the digital asset market is more than USD 120 billion with Bitcoin dominating slightly with more than 50%.3 In this regard, Fry and Cheah (2016, p.350) highlight that “from an economic perspective the sums of money involved are substantial,” and accordingly, the societal impact of losses due to defaults in the digital asset market may be enormous. Howell, Niessner and Yermack (2019, p.1) define three types of digital assets which are often referred to as coins. Specifically, the first type of digital asset is defined as a general-purpose medium of exchange and store of value cryptocurrency, such as Bitcoin. The second type of digital asset is a security token, which represents a conventional security that is recorded and exchanged on a blockchain to 1 The Bloomberg interview took place on October 2, 2014. 2 The dead coin tracking website coinopsy.com lists the following as the main reasons for default: abandoned, abandoned/website, abandoned/volume, abandoned/buyback, abandoned/scam, scam, scam project/virus, joke, no exchanges/struggling, failed fork, failed/pre-mine no/low trade volume, pump and dump, and crashed (see https://www.coinopsy.com/dead-coins/). 3 See https://coinmarketcap.com (accessed on 15 February 2019, 11:00 EST). 3 reduce transaction costs and create a record of ownership, whereas the third type of digital assets is a utility token, which gives its holder consumptive rights to access a product or service. In Tables 1 and 2, we provide a demographic overview of new and bankrupt cryptocurrencies in different years. Note: This table reports the numbers of new, bankrupt, and total cryptocurrencies during each year from April 2013 till April 2019. It is generated using the historical snapshot available at coinmarketcap.com. Table 2. Life Span of default cryptocurrencies including tokens Default Year 2014 2015 2016 2017 2018 Jan-Apr 2019 Total Number of default cryptocurrencies Y ea r of is su an ce Before Apr 28, 2013 0 0 0 0 1 0 1 Mar-Dec 2013 2 1 17 3 11 4 38 2014 149 133 34 58 13 387* 2015 213 56 98 20 387 2016 120 174 26 320 2017 401 72 473 2018 172 172 Total number of default cryptocurrencies 2 150 363 213 743 307 1778 Note: This table reports the numbers of bankrupt cryptocurrencies with their specific year of issuance and year of bankruptcy. It is generated using the historical snapshot available at coinmarketcap.com. *It includes all cryptocurrencies and tokens using different consensus mechanisms. Out of which 86 cryptocurrencies that we used for our analysis are based on PoW consensus protocols. Table 1. Population of cryptocurrencies including tokens Year Before Apr 28, 2013 Mar- Dec 2013 2014 2015 2016 2017 2018 2019 New cryptocurrencies 7 60 452 207 298 800 1187 168 Default cryptocurrencies 0 0 2 150 363 213 743 307 Total cryptocurrencies 7 67 517 577 663 1353 2073 2147 4 Figure 1 shows that the numbers of default cryptocurrencies are increasing in comparison to the new cryptocurrencies added to the digital finance world after 2018. Specifically, we find that as of April 2019 there are altogether 1778 defaulted coins, however, 2147 coins are still in the digital asset market.4 Fig. 1. Demography of cryptocurrencies (Apr 2013 – Apr 2019) Note: This figure shows the evolutions of new, default and total cryptocurrencies. Cryptocurrencies correspond to all three types of digital assets as defined in Howell, Niessner and Yermack (2019, p.1) where the first type is defined as a general-purpose medium of exchange and store of value cryptocurrency, such as Bitcoin. The second type of cryptocurrencies is a security token, which represents a conventional security that is recorded and exchanged on a blockchain to reduce transaction costs and create a record of ownership, whereas the third type of cryptocurrencies is a utility token, which gives its holder consumptive rights to access a product or service. It should not be surprising that in a zero-interest regime even the asset management industry pays ever more attention to digital assets as an investment alternative. Given the likelihood of digital assets ending up in default, it is surprising that there is no paper available exploring the extent to which a default of a digital asset is forecastable. This current paper fills this important gap in the new age of digital finance literature. 4 Note that Howell, Niessner and Yermack (2019, p.1) define three types of coins, Figure 1 accounts for the whole universe of digital assets. For instance, as of 2014, 146 out of 517 coins were cryptocurrencies that have the Proof-of-Work consensus protocol which are subject of examination in this study. 0 500 1000 1500 2000 2500 Apr 2013 Dec 2013 2014 2015 2016 2017 2018 Apr 2019 Total Cryptocurrencies New Cryptocurrencies Default Cryptocurrencies 5 In our paper, we exclusively focus on the first category of digital asset defined as cryptocurrencies. As this type of digital asset is considered general-purpose medium of exchange, it is an alternative to traditional currency. We start our analysis by exploring which cryptocurrency-specific variables are accessible to the naïve investor. As we are interested in forecasting potential cryptocurrency defaults at an early stage, we focus on variables that are a part of the information set of the investor at most one month after a cryptocurrency started trading. Accordingly, we downloaded data for all cryptocurrencies launched before 2015 and followed those cryptocurrencies until the end of 2018.5 Specifically, our data set consists of 146 cryptocurrencies, of which 86 went bankrupt before the end of 2018. We divided our dataset into two subsamples: The first subsample contains data on those cryptocurrencies that went into default and the second subsample contains the data of those cryptocurrencies that functioned until the end of our sample period. To analyze which of our variables have discriminative power, we then test which of the mean differences of our cryptocurrency- specific variables for our two subsamples were statistically significant. We made use of those variables that exhibited significant differences in sample means in a multiple linear discriminant model. We compared the estimated bankruptcies with the actual numbers. Moreover, we applied bootstrapping techniques to investigate the robustness of our model involving Type-I and Type-II errors. Our paper contributes to the new strand of digital finance literature exploring cryptocurrencies. Recent literature investigates the volatility of cryptocurrencies (Katisiampa, 2017; Balcilar, Bouri, Gupta, and Roubaud, 2017; Osterrieder and Lorenz, 2017; Ardia, Bluteau, and Rüede, 2018; Baur and Dimpfl, 2018; Borri, 2019), price spillovers between cryptocurrencies (Fry and Cheah, 2016), predictability of cryptocurrency time series (Catania, Grassi and Ravazzolo, 2019; Lahmiri and Bekiros, 2019; Omane-Adjepong, Alagidede and Akosah, 2019; Shen, Urquhart, and Wang, 2019), cryptocurrencies as investment assets (Urquhart 2016; Dyhrberg, 2016; Dwyer, 2015), and speculative bubbles in the cryptocurrency market (Cheah and Fry, 2015; Chaim and Laurini, 2019; Li, Tao, Su, and Lobont, 2019). Even though empirical evidence shows that the majority of cryptocurrencies 5 It is also noteworthy that cryptocurrencies exhibit different types of consensus protocols to verify transactions such as Proof-of-Work, Proof-of-Stake or a mixture of both which is often referred to as Hybrid. Before 2015, however, there were only few cryptocurrencies issued that were implemented using the Proof of Stake (PoS) mechanism. PoS was first introduced by Sunny King and Scott Nadal in 2012 and later in 2013 Sunny King created the first cryptocurrency Peercoin (PPC) implementing the PoS protocol. PoS is created to solve the high energy consumption problem of Bitcoin which uses the Proof-of-Work mechanism. In order to keep our sample homogenous, we exclude those cryptocurrencies using a PoS mechanism from our sample. 6 go into default, there is no paper available on the predictability of such cryptocurrency bankruptcy. Being able to forecast potential cryptocurrency defaults is important because the sums of money involved are substantial (Fry and Cheah, 2016). This paper fills this important gap in the literature while also complementing the large body of literature exploring the predictability of commercial bankruptcy. The publication of Altman’s (1968) z-score model for predicting bankruptcy among manufacturing firms in the U.S.A, led to a wealth of research (Satish and Janakiram, 2011; Wang and Campbell, 2010; Lugovskaya, 2010), and Altman (2018) has recently provided an excellent overview of the relevant literature. Moreover, Cheah and Fry (2015) and Osterrieder and Lorenz (2017) express concern that academic research on cryptocurrency is often focused on the legality of cryptocurrencies (Kethineni and Cao, 2019; Maume, 2019) rather than offering a comprehensive analysis of their statistical or financial aspects. Therefore, our paper contributes to the finance literature by adding a new perspective, credit risk. Finally, and from a more practical point of view, our paper also supports the finance industry by proposing a model that could be used for investment decisions. For instance, new digital asset management could use our model to determine which cryptocurrencies should be treated with caution owing to a high probability of default. The results of this research show that bankruptcies among cryptocurrencies are predictable. Specifically, our model shows that we can predict 75 out of 86 cryptocurrency defaults. Employing 5000 bootstrap replications shows that the confidence interval for the point estimate indicating default does not overlap with the point estimate for the Type-I error. This shows that the discriminative power of our model is significant. Our results are in line with the literature on predicting firm bankruptcy (Altman, 1968, 1983, 2000, 2002; Altman, Haldeman, and Narayanan, 1977; Altman, Hartzell and Peck, 1995; Lugovskaya, 2010). Surprisingly, our model is not suitable for predicting the fate of functioning cryptocurrencies unlike Altman’s (1968) z-score model or Altman, Haldeman, and Narayanan’s (1977) ZETA model. We strongly encourage future research to elaborate on this issue. The paper is organized as follows: The next section presents the empirical framework, including the model setup and robustness checks and the last section concludes. 7 2. Empirical framework 2.1. Multiple Linear Discriminant Analysis Our analysis is supported by data from the various sources.6 Each cryptocurrency has certain characteristics related to its history, specification, trading activities, reward, privacy, and scaling among others. Table A.1 in the appendix shows the categorized specification details of cryptocurrencies. We downloaded all cryptocurrencies that incorporated the Proof-of- Work (PoW)7 mechanism and started trading between 2010 and the end of 2014 and considered a data period of four years ahead.8 In total, we retrieved 146 cryptocurrencies, of which 86 went into default in the sample period and 60 continued functioning. We define a cryptocurrency as being in a ‘default state’ when the cryptocurrency stopped trading, that is, there is no more evidence of any trading.9 Altman (2010, pp.4–5) emphasizes the importance of ratio analysis as an empirical tool in assessing the performance of business enterprises. Identifying variables that exhibit discriminative power is ultimately an empirical question. Therefore, the first step in our analysis was to explore variables that potentially discriminate between cryptocurrencies that ended up in default and those that remained functioning. Moreover, we wanted to account for variables that only the investor has access to at most one month after starting trading that support a decision on whether to invest in the relevant cryptocurrency at an early stage. Table A.2 in the appendix records 20 cryptocurrency- specific variables that exhibit information that could be utilized. Unfortunately, some information was not available for some now defunct cryptocurrencies. There are many cryptocurrencies that are pre-mined before being offered to the public. Pre-mining has some advantages like rewarding the developers or creating a balanced distribution of coins (e.g., units of a cryptocurrency) between developers and traders. However, a larger number of pre-mined coins could be a negative indication, as when the developer has a large percentage of available coins and could therefore opt to leverage the 6 We used the following sources: mapofcoins.com (name of cryptocurrency, categorization of ‘running’ and ‘defunct’), coinmarketcap.com (historical price data), deadcoins.com (confirmation of categorization as ‘defunct’), coinopsy.com/dead-coins (life span and founder information of dead coins), bitcointalk.org (announcement date and other technical specifications), and personal websites of coins for gathering any missing data. 7 PoW is the very first consensus algorithm in decentralized public blockchain where miners solve complex cryptographic puzzles to add a block to the blockchain in exchange for coin as rewards. 8 We downloaded price history from the coinmarketcap.com. The earliest data provided by this website starts on 28 April 2013. Though Bitcoin (BTC), Litecoin (LTC), Namecoin (NMC), Terracoin (TRC), Devcoin (DVC) and, Novacoin (NVC) started trading before this date. To have uniformity and consistency across our data set, however, we set 28 April 2013 as the first day of trade for the above mentioned coins. 9 There are a few cryptocurrencies in the list of functioning cryptocurrencies in coinmarketcap.com even though these cryptocurrencies do not exhibit any trading activities. In our data set, we adjusted for these errors. 8 price before selling quickly. Cryptocurrencies exhibiting higher levels of pre-mining are under constant attack and carry a high manipulation risk10. Therefore, investors are generally concerned about whether a particular cryptocurrency is pre-mined or not (which we account for by using a simple binary dummy variable), and also the fractions of pre-mined coins (it measures the extent to which the developers retain control over that particular cryptocurrency if the total coins are mined as the Pre-mined-to-Total-Coins-Ratio (PMTTCR)). Moreover, we accounted for block time, Day-1 return, Week-1 return, and Month-1 return after the respective cryptocurrency started trading. For instance, a positive return in the initial trading period could indicate the popularity of a particular cryptocurrency. We also compounded the corresponding time-congruent volatilities (Day-1, Week-1, and Month-1) simply as the corresponding squared return. Instead of interpreting each variable in isolation, our variables should be considered in the respective context. For instance, a slightly negative first day trading return with a low volatility in association with a high monthly volatility could indicate that the cryptocurrency did not attract attention following the announcement owing to a lack of social promotion, but the cryptocurrency could be subject to excessive speculation within the first month after trading. Generally, assets that are subject to excessive speculation may end up in trouble—or in default—at a later stage. Furthermore, reward per block shows the level of coin supply during that particular block interval. We include Minimum-Reward-To- Total-Coin-Ratio (MTTCR) as a common comparative tool to measure the minimum level of controlled supply among the cryptocurrencies in our sample. Our model includes both an individual and a comparative level of minimum controlled supply. Finally, we also coded dummy variables for identifying both the cryptocurrency-specific algorithm and whether the cryptocurrency has a known founder.11 We report the descriptive statistics of our selected variables in Table A.3 in the appendix. Moreover, Table 3 reflects the variable means and the results of testing the difference in means for significance. We used a simple two-sample t-test to test the difference in sample means (Snedecor and Cochran, 1989). The sample differences of minimum reward, Day-1 and Month-1 returns, Day-1 volatility, and PMTTCR are statistically significant on at least a 5% level (see Table 3). Moreover, the Month-1 volatility is at least marginally significant on a 10% level. Interestingly, we also find that among functioning cryptocurrencies, 58% of the founders remain anonymous, whereas among bankrupt 10 See https://cryptodaily.co.uk/2018/08/premined-coins-like-xrp-trx-xlm-and-neo-are-causing-problems-for- index-funds (published on August 29, 2018). 11 We categorized algorithms into three types; ‘SHA’ (Secure Hash Algorithm), ‘Scrypt’, and ‘others’. ‘Others’ contains all other algorithms besides SHA and Scrypt family algorithms. 9 cryptocurrencies that figure rises to 79%. For a 95% confidence interval, the critical values for the binary-distributed variable known founder in the sample of functioning cryptocurrencies is between 0.50 and 0.66, implying that the sample of bankrupt cryptocurrencies exhibits a significantly higher probability of the founder being anonymous, given a 5% significance level. Moreover, for a 95% confidence interval, the critical value for the binary-distributed variable scrypt algorithm in the sample of functioning cryptocurrencies is between 0.52 and 0.68. As the sample average in the default sample is 0.80, we can reject the null hypothesis that the sample means are equal, implying that those cryptocurrencies that ended up in default exhibit this specific algorithm more frequently. More precisely, the definitions of our variables are as following: 𝑅𝑒𝑡_𝐷1௧ = (஽௔௬భ஼௟௢௦௘)೟ି(஽௔௬భை௣௘௡)೟ (஽௔௬భை௣௘௡)೟ , where 𝑅𝑒𝑡_𝐷1௧ denotes the first day’s return of cryptocurrency t, (𝐷𝑎𝑦ଵ𝐶𝑙𝑜𝑠𝑒)௧ denotes the first day’s closing price of cryptocurrency t, and (𝐷𝑎𝑦ଵ𝑂𝑝𝑒𝑛)௧ denotes the first day’s opening price of cryptocurrency t. 𝑅𝑒𝑡_𝑊1௧ = (஽௔௬ళ஼௟௢௦௘)೟ି(஽௔௬భை௣௘௡)೟ (஽௔௬భை௣௘௡)೟ , where 𝑅𝑒𝑡_𝑊1௧ denotes the first week’s return of cryptocurrency t, (𝐷𝑎𝑦଻𝐶𝑙𝑜𝑠𝑒)௧ denotes the closing price after the seventh day of cryptocurrency t, and (𝐷𝑎𝑦ଵ𝑂𝑝𝑒𝑛)௧ denotes the first day’s opening price of the cryptocurrency t. 𝑅𝑒𝑡_𝑀1௧ = (஽௔௬యబ஼௟௢௦௘)೟ି(஽௔௬భை௣௘௡)೟ (஽௔௬భை௣௘௡)೟ , where 𝑅𝑒𝑡_𝑀1௧ denotes the first month’s return of the cryptocurrency t, (𝐷𝑎𝑦ଷ଴𝐶𝑙𝑜𝑠𝑒)௧ denotes the closing price of cryptocurrency t after 30 trading days, and (𝐷𝑎𝑦ଵ𝑂𝑝𝑒𝑛)௧ denotes the first day’s opening price of cryptocurrency t. 𝑉𝑜𝑙_𝐷1௧ = (𝑅𝑒𝑡_𝐷1௧)ଶ, where 𝑉𝑜𝑙_𝐷1௧ denotes the first day’s volatility of cryptocurrency t, and 𝑅𝑒𝑡_𝐷1௧ denotes the first day’s return of cryptocurrency t. 10 𝑉𝑜𝑙_𝑊1௧ = (𝑅𝑒𝑡_𝑊1௧)ଶ, where 𝑉𝑜𝑙_𝑊1௧ denotes the first week’s volatility of cryptocurrency t, and 𝑅𝑒𝑡_𝑊1௧ denotes the first week’s return of cryptocurrency t. 𝑉𝑜𝑙_𝑀1௧ = (𝑅𝑒𝑡_𝑀1௧)ଶ, where 𝑉𝑜𝑙_𝑀1௧ denotes the first month’s volatility of cryptocurrency t, and 𝑅𝑒𝑡_𝑀1௧ denotes the first month’s return of cryptocurrency t. Moreover, PMTTCR (Pre-Mined-To-Total-Coins-Ratio) indicates the fraction of coins that are allocated to the developers in relation to the total coins in circulation, given that a cryptocurrency is fully mined. (Note that developers with a large portion of coins in stake can manipulate the market with a so-called pump-and-dump strategy. Note also that if a large proportion of a cryptocurrency is pre-mined, this cryptocurrency could be subject to potential scam.) Further, 𝑃𝑀𝑇𝑇𝐶𝑅௧ = (ே௎ெ஻ாோ ைி ௉ோாିெூோ஽ ஼ைூேௌ)೟ (்ை்஺௅ ஼ைூேௌ ௐுாே ி௎௅௅௒ ெூோ஽)೟ , where 𝑃𝑀𝑇𝑇𝐶𝑅௧ denotes the Pre-Mined-To-Total-Coins-Ratio of cryptocurrency t, (𝑁𝑈𝑀𝐵𝐸𝑅 𝑂𝐹 𝑃𝑅𝐸 − 𝑀𝐼𝑁𝐸𝐷 𝐶𝑂𝐼𝑁𝑆)௧ denotes the number of pre-mined coins of cryptocurrency t, and (𝑇𝑂𝑇𝐴𝐿 𝐶𝑂𝐼𝑁𝑆 𝑊𝐻𝐸𝑁 𝐹𝑈𝐿𝐿𝑌 𝑀𝐼𝑁𝐸𝐷)௧ denotes the number of total coins of cryptocurrency t when being fully mined. The number of coins received by miners as a reward per block for any cryptocurrency shows how new coins are generated after every block time interval (which, in turn, varies among cryptocurrencies). Specifically, block time is the time it takes to verify one block. This also indicates how frequently the new coins are generated to reward the miners for verifying the block. Moreover, the coins rewarded for the miners are the new coins supplied to the market. Due to the limited supply of coins (at least for the majority of cryptocurrencies), the reward decreases over time. Minimum reward measures the lowest number of coins as a reward given to the miners. The mining of a cryptocurrency continues only if the rewards cover the mining cost. If the minimum reward is meager such that the mining cost cannot be 11 covered, miners will stop mining and eventually that cryptocurrency is likely to end up in default. Therefore, minimum reward may be an important factor to consider in our current research’s context. On the other hand, MTTCR (Minimum-Reward-to-Total-Coins-Ratio) measures the minimum level of controlled supply until the cryptocurrency is fully mined. Both, too much or too little supply of coins are not beneficial for the crypto economy. Further, 𝑀𝑇𝑇𝐶𝑅௧ = (ெூேூெ௎ெ ோாௐ஺ோ஽ௌ ௉ாோ ஻௅ை஼௄ ா௑஼௅௎஽ூேீ ஻ைே௎ௌ ோாௐ஺ோ஽ௌ)೟ (்ை்஺௅ ஼ைூேௌ ௐுாே ி௎௅௅௒ ெூோ஽)೟ , where 𝑀𝑇𝑇𝐶𝑅௧ denotes the Minimum-Reward-to-Total-Coins-Ratio of cryptocurrency t, (𝑀𝐼𝑁𝐼𝑀𝑈𝑀 𝑅𝐸𝑊𝐴𝑅𝐷𝑆 𝑃𝐸𝑅 𝐵𝐿𝑂𝐶𝐾 𝐸𝑋𝐶𝐿𝑈𝐷𝐼𝑁𝐺 𝐵𝑂𝑁𝑈𝑆 𝑅𝐸𝑊𝐴𝑅𝐷𝑆)௧ denotes the minimum number of coins rewarded for the miners of cryptocurrency t, and (𝑇𝑂𝑇𝐴𝐿 𝐶𝑂𝐼𝑁𝑆 𝑊𝐻𝐸𝑁 𝐹𝑈𝐿𝐿𝑌 𝑀𝐼𝑁𝐸𝐷)௧ denotes the number of total coins of cryptocurrency t, given the cryptocurrency is fully mined. 12 Table 3. Testing the differences-in-means between functioning and default cryptocurrencies Default (D) Functioning (F) Difference (F-D) Minimum Reward 65880.65 3377.064 -62503.6** (-1.97) Block time 160.79 152.92 7.87 (0.30) Ret_D1 0.0403 0.7124 0.6721*** (3.17) Ret_W1 0.2541 0.2849 0.0309 (0.19) Ret_M1 0.2454 0.1197 -0.1257** (-2.31) Vol_D1 3.1776 10.2559 7.0783** (2.43) Vol_W1 2.7361 4.8749 2.1388 (0.93) Vol_M1 0.6147 0.3131 -0.3016* (-1.78) MTTCR 3.2E-05 8.0E-06 -2.4E-05 (-1.57) PMTTCR 0.0152 0.0041 -0.0111** (-2.47) Pre-mined 4.89E+07 6.14E+08 -5.65E+08** (-2.03) Known founder 0.79 0.58 -0.21*** (-8.62) Scrypt algorithm 0.80 0.60 -0.20*** (-8.33) Note: This table reports the differences of the means of our predictor variable candidates between our sample of functioning cryptocurrencies and those that went into default. As potential predictor variable candidates we consider the minimum reward, block time, first day return (Ret_D1), first week return (Ret_W1), first month return (Ret_M1), first day volatility (Vol_D1), first week volatility (Vol_W1), first month volatility (Vol_M1), Minimum-Reward-to-Total-Coins-Ratio (MTTCR), Pre-Mined-To-Total-Coins-Ratio (PMTTCR), and pre- mined coins (pre-mined). Our data set consists of all cryptocurrencies that incorporated the Proof-of-Work mechanism and started trading prior to December 31, 2014. We followed those cryptocurrencies until the end of 2018. We retrieved 146 cryptocurrencies, of which 86 went into default (D) in the sample period and 60 remained functioning (F). (F-D) measures the mean-difference between the functioning and default sample. The corresponding t-statistics are given in parentheses. *Statistically significant on a 10% level. **Statistically significant on a 5% level. ***Statistically significant on a 1% level. Next, we employed Multiple Linear Discriminant Analysis (MLDA) to address our research question. MDLA, which is a type of cluster analysis, has been used to model credit risks. For instance, in his seminal paper, Altman (1968) explored bankruptcy among companies in the 13 manufacturing industry and proposed the z-score to predict the probability that a firm will go bankrupt within two years. That research led to many modifications being applied to predict various types of financial failure (Altman, 1983; 2002; Altman, Hartzell, and Peck, 1995; Altman, Haldeman, and Narayanan, 1977; Altman, Danovi, and Falini, 2013; Altman, and Rijken, 2010). This is the first paper to make use of MLDA to model defaults in the cryptocurrency market. Again, all input variables used in our model were available to the naïve investor within one month after a cryptocurrency started trading. Since there are different methodologies to perform cluster analysis, below we explain how we set up our model. We divided the data into two groups, the default group, and the group that consists of functioning cryptocurrencies. We stacked the data of those two groups into two matrices defined as 𝑿𝟏 and 𝑿𝟐, where 𝑿𝟏 denotes the default group and 𝑿𝟐 denotes the functioning group. Moreover, the matrix 𝑿 defines the whole data set, that is, 𝑿 = ൤𝑿𝟏𝑿𝟐 ൨=൤ [𝒙ଵ,ଵ … 𝒙ଵ,௄] [𝒙ଶ,ଵ … 𝒙ଶ,௄]൨. (1) Let us assume that we consider 𝐾 variables of the cryptocurrency-specific data and let us also assume that we deal with 𝑇ଵ cryptocurrencies that went into default and 𝑇ଶ cryptocurrencies that were functioning during our sample period. For instance in Equation’s (1) notation, 𝒙ଵ,ଵ defines a 𝑇ଵx1 column vector that contains the values for variable 1 for the default sample (e.g., group 1), whereas 𝒙ଵ,௄ defines a 𝑇ଵx1 column vector that contains the values for variable K in the default sample, and so forth. More concretely, 𝒙ଵ,ଵ = ൦ 𝑥ଵ,ଵ 𝑥ଶ,ଵ ⋮ 𝑥 భ்,ଵ ൪, or 𝒙ଵ,௄ = ൦ 𝑥ଵ,௄ 𝑥ଶ,௄ ⋮ 𝑥 భ்,௄ ൪, and analogously 𝒙ଶ,ଵ = ൦ 𝑥 భ்,ଶ 𝑥 భ்ାଵ,ଶ ⋮ 𝑥்,ଶ ൪, or 𝒙ଵ,௄ = ൦ 𝑥 భ்,௄ 𝑥 భ்ାଵ,௄ ⋮ 𝑥்,௄ ൪. Then for the matrices 𝑿𝟏 and 𝑿𝟐, the sample average of each column can be stacked into the 1xK vectors 𝝁ଵ and 𝝁ଶ, given by 𝝁ଵ = [𝒙ഥଵ,ଵ … 𝒙ഥଵ,௄] and 𝝁ଶ = [𝒙ഥଶ,ଵ … 𝒙ഥଶ,௄]. (2) 14 For instance, the element 𝒙ഥଵ,ଵ = ଵ భ் ∑ 𝑥௧,ଵభ்௧ୀଵ defines the sample average of the first cryptocurrency-specific variable of the default group and 𝒙ഥଶ,ଵ = ଵ (்ି భ்) ∑ 𝑥௧,ଶ்௧ୀ భ்ାଵ defines the corresponding sample average of the first cryptocurrency-specific variable of the functioning group. Moreover, the global mean vector 𝝁 stacks the overall sample averages for each column of the matrix 𝑿 into a 1xK row vector. Note that 𝝁 can be simply calculated as 𝝁 = ଵ ் (𝑇ଵ𝝁ଵ + (1 − 𝑇ଵ)𝝁ଶ) = ଵ ் (𝑇ଵ𝝁ଵ + 𝑇ଶ𝝁ଶ) ≡ [𝜇ଵ 𝜇ଶ … 𝜇௄]. (3) Then we calculated the mean-corrected matrices 𝑿𝟏𝟎 and 𝑿𝟐𝟎 defined as 𝑿𝟏𝟎 = ൦ 𝒙ଵ,ଵ − 𝝁 𝒙ଶ,ଵ − 𝝁 ⋮ 𝒙 భ்,ଵ − 𝝁 ൪ and 𝑿𝟐𝟎 = ൦ 𝒙 భ்ାଵ,ଶ − 𝝁 𝒙 భ்ାଶ,ଶ − 𝝁 ⋮ 𝒙்,ଶ − 𝝁 ൪, (4) where obviously 𝑇 − 𝑇ଵ = 𝑇ଶ and given Equation’s (4) notation, 𝒙௧,௜ − 𝝁 defines a 1xK row vector 𝑖 in each respective matrix, 𝑿𝟏 and 𝑿𝟐, subtracted by the global mean vector 𝝁. For instance, 𝒙ଵ,ଵ − 𝝁 = [(𝑥ଵ,ଵ − 𝜇ଵ) (𝑥ଵ,ଶ − 𝜇ଶ) … (𝑥ଵ,௄ − 𝜇௄)], or 𝒙ଶ,ଵ − 𝝁 = [(𝑥ଶ,ଵ − 𝜇ଵ) (𝑥ଶ,ଶ − 𝜇ଶ) … (𝑥ଶ,௄ − 𝜇௄)], for the default group and analogously, 𝒙 భ்ାଵ,ଶ − 𝝁 = ൣ(𝑥 భ்ାଵ,ଵ−𝜇ଵ) (𝑥 భ்ାଵ,ଶ − 𝜇ଶ) … (𝑥 భ்ାଵ,௄ − 𝜇௄)൧, or 𝒙 భ்ାଶ,ଶ − 𝝁 = ൣ(𝑥 భ்ାଶ,ଵ−𝜇ଵ) (𝑥 భ்ାଶ,ଶ − 𝜇ଶ) … (𝑥 భ்ାଶ,௄ − 𝜇௄)൧, for the functioning group respectively. We compounded the corresponding empirical sample covariance matrices as 𝑪𝟏 = 𝑿𝟏 𝟎೅𝑿𝟏 𝟎 భ் and 𝑪𝟐 = 𝑿𝟐 𝟎೅𝑿𝟐 𝟎 మ் , (5) 15 where the dimension of 𝑪𝟏 and 𝑪𝟐 must be the same, that is, KxK as we want to investigate the characteristic-specific differences in cryptocurrencies. Then we employed the estimated sample covariance matrices 𝑪𝟏 and 𝑪𝟐 to calculate the pooled within-group covariance matrix, simply defined as 𝑪(𝑟, 𝑠) and given by 𝑪(𝑟, 𝑠) = ଵ( భ்ା మ்) ∑ 𝑇௜௜∈(ଵ,ଶ) ∙ 𝑪𝒊(𝑟, 𝑠), (6) where 𝑟 = 1, … , 𝐾 and 𝑠 = 1, … , 𝐾. As 𝑟𝑎𝑛𝑘(𝑪) = 𝐾 was satisfied, we then compounded the inverse of 𝑪, defined as 𝑪ିଵ. Moreover, the prior-probability vector, based on the empirical data, can simply be calculated as 𝑷 = ቂ 𝑝ଵ 𝑝ଶቃ = ቎ ቀ భ்( భ்ା మ்)ቁ ቀ మ்( భ்ା మ்)ቁ ቏. (7) Finally, for our 𝑇 cryptocurrencies, we can estimate the discriminant function depending on the default and non-default cluster as 𝑓ଵ,௧ = 𝝁ଵ𝑪ି𝟏𝒙𝒕,𝑲் − 0.5 ∙ 𝝁ଵ𝑪ି𝟏𝝁ଵ் + 𝑙𝑛(𝑝ଵ), and (8.a) 𝑓ଶ,௧ = 𝝁ଶ𝑪ି𝟏𝒙𝒕,𝑲் − 0.5 ∙ 𝝁ଶ𝑪ି𝟏𝝁ଶ் + 𝑙𝑛(𝑝ଶ), (8.b) where 𝒙௧,௄் is the corresponding transposed 1xK vector of characteristics of cryptocurrency t. If 𝑓ଵ,௧ > 𝑓ଶ,௧, cryptocurrency t is predicted to be in the default group, otherwise it is predicted to be in the functioning group. Given the subsamples, we defined 𝑓ଵ,௧ > 𝑓ଶ,௧ as success for the default group and 𝑓ଵ,௧ < 𝑓ଶ,௧ as success for the functioning group meaning that the discriminant model correctly assigned the respective cryptocurrency to its corresponding group. Furthermore, for each group, we coded two vectors of dummy variables denoted as 𝒅ଵ and 𝒅ଶ that have a value of one in case of success and a value of zero otherwise. The prediction accuracy of predicting a cryptocurrency’s default within four years is then simply given by ∑ 𝑑ଵ,௧భ்௧ୀଵ /𝑇ଵ, whereas the Type-I error of this model is 1 − ∑ 𝑑ଵ,௧భ்௧ୀଵ /𝑇ଵ. In the same 16 manner, the prediction accuracy for predicting a cryptocurrency’s continued functioning can be calculated as ∑ 𝑑ଶ,௧మ்௧ୀଵ /𝑇ଶ, while the Type-II error is then given by 1 − ∑ 𝑑ଶ,௧మ்௧ୀଵ /𝑇ଶ. Setting up the empirical model is ultimately an empirical question. After our initial analysis of differences in sample means, we decided to employ the following cardinal variables in our discriminant analysis: Day-1 return, Month-1 return, and the corresponding volatilities, PMTTCR, and minimum reward. We also account for a set of dummy variables for measuring the qualitative variables algorithm, anonymous founder, and pre-mined. Specifically, we employ K=9 predictor variables in our analysis. Since we have 𝑇ଵ = 86 cryptocurrencies that ended up in default and 𝑇ଶ = 60 that remained functioning, our matrices 𝑿𝟏 and 𝑿𝟐 have the dimension 86x12 and 60x12, respectively. Our model operates with 12 instead of nine columns because we employ three dummy variables for indicating the algorithm (scrypt, SHA, or others), one binary dummy variable for indicating whether a cryptocurrency is pre-mined, one dummy variable indicting whether the founder is anonymous, and continuous variables for Day-1 return, Day-1 volatility, Month-1 return, Month-1 volatility, actual amount of pre-mined coins, actual amount of minimum reward, and PMTTCR. The estimated discriminant function is reported in Table A.4. and A.5. in the appendix. Finally, these estimates are used to calculate the results reported in Table 4. For example, from Table A.4. we learn that the discriminant function correctly predicts in 75 out of 86 cryptocurrencies that they are in group 1 because the value of the discriminant function is larger for group1 than for group 2. Consequently, 87.21% of cryptocurrency defaults are predicted correctly. Table 4. Predicting cryptocurrency default Actual Group Predicted group by the Multiple Linear Discriminant Function Default group Functioning group Default group 87.21% 12.79% Functioning group 43.33% 56.67% Note: This table reports the results of our multiple linear discriminant analysis. Our dataset consists of all cryptocurrencies that incorporated the Proof-of-Work mechanism and started trading between 2009 and the end of 2014. We followed up those cryptocurrencies until the end of 2018. We retrieved 146 cryptocurrencies, of which 86 went into default in the sample period and 60 remained functioning. Our model incorporates the following predictor variables: minimum reward, pre-mined, Day-1 return, Month-1 return, Day-1 volatility, 17 Month-1 volatility, and PMTTCR. Moreover, we include a set of dummy variables for indicating ‘algorithm’ and ‘founder anonymity’. Given the data of bankrupt and functioning cryptocurrencies, as reported in Table A.6. that are in either the default group or the functioning group our model is able to correctly predict 87% of the defaults corresponding to a Type-I error of 13%. Our estimates are close to models that predict bankruptcy of enterprises. For instance, the popular multiple discriminant model from Altman (1968) predicted 94% of bankruptcies of U.S. firms in the manufacturing industry. It is important to note, however, that first Altman’s (1968) benchmark model uses recent information on those companies investigated because he employed data from balance sheets that were released about one year before the bankruptcy occurred. Second, he matched that sample of companies that went bankrupt with a sample of matched companies having the same number of firms and the same firm characteristics, whereas our analysis accounts for the whole sample of available cryptocurrencies. Furthermore, we use only information available at an early stage, that is, after one month of trading. Its chosen sample means our model predicts bankruptcy within the next four years, which is very different from Altman’s findings. Even though Altman’s (1968) model performed remarkably well for a one- and two-year period prior to bankruptcy, a robustness check shows that its success rate is only 29% for a four year period.12 Even though our results suggest that our cryptocurrency default prediction model is an accurate forecaster of failure, Table 4 shows that the Type-II error is 43%. This result implies that our model struggles to predict functioning cryptocurrencies. 2.2. Robustness checks Since we only have one sample available, our estimates reported in Table 4 are only point estimates. To investigate how sensitive our model is with respect to resampling and to compound confidence intervals for our estimates, we employed bootstrapping. It seems reasonable to assume that characteristic k of cryptocurrency t is uncorrelated with the characteristic k of cryptocurrency s, that is, 𝑐𝑜𝑣൫𝑥௧,௞, 𝑥௦,௞൯ = 0.13 However, characteristic k of cryptocurrency t is not necessarily uncorrelated with characteristic l, meaning 𝑐𝑜𝑣൫𝑥௧,௞, 𝑥௧,௟൯ ≠ 0. We have ensured this is ex-ante by simply choosing our research set-up because all cryptocurrencies have the same consensus protocol and are therefore 12 The average success rate of Altman’s (1968) model between year one and four prior to bankruptcy is 61%. 13 Note that Altman (1968, p.592) highlights that “there is reason to believe that some of the measurements will have a high degree of correlation or collinearity with each other.” 18 homogenous. However, characteristics of a cryptocurrency could be – at least potentially – correlated with other characteristics of the same cryptocurrency. To account for this issue, we employed a pairs bootstrap as detailed by Godfrey (2009, pp.183 ̶ 185). In doing so, we constructed new data matrices defined as 𝑿ଵ௕ and 𝑿ଶ௕ where each row vector in 𝑿𝟏 and 𝑿𝟐 is randomly resampled with replacement where each row in 𝑿𝟏 and 𝑿𝟐 is drawn with probability 1/𝑇ଵ and 1/𝑇ଶ respectively. We employ 𝐵 = 5000 bootstrap samples and re- estimate the corresponding discriminant functions to estimate the empirical confidence interval. More concretely, for each bootstrap run b, we employ the original data matrix 𝑿𝟏 that has the dimension 86x12, as described in section 2.1. Then we randomly draw with replacement and with probability 1/86=0.0116 a row from matrix 𝑿𝟏 and add that row into matrix 𝑿ଵ௕ to construct a new data matrix. For each run b, this procedure is stopped when all 86 rows in the new data matrix 𝑿ଵ௕ are filled. In the same manner, for each bootstrap run b, we employ the original data matrix 𝑿𝟐 that has the dimension 60x12, as described in section 2.1. Then we randomly draw with replacement and with probability 1/60=0.0167 a row from matrix 𝑿𝟐 and add that row into matrix 𝑿ଶ௕ to construct a new data matrix. For each run b, this procedure is stopped when all 60 rows in the new data matrix 𝑿ଶ௕ are filled. These new data matrices are used to run the linear discriminant analysis described in section 2.1 for each bootstrap iteration 𝑏 = 1, … ,5000. The corresponding point estimates are stored in vector. These vectors are sorted in an increasing order. Then, the 125th observation gives us the value of the lower bound and the 4875th observation gives us the upper bound of our confidence interval covering 95% probability. The results of our analysis can be found in Table 5. Using bootstrapping, the 95% confidence interval for our point estimate concerning successfully predicting cryptocurrency default is between 83.72% and 89.53% again suggesting a high level of accuracy. However, the 95% confidence interval for the Type-II error ranges between 41.67% and 53.33%. Assuming that the point estimate for the Type-II error is distributed as 𝑁(𝜇ଵ, 𝜎) with 𝜇ଵ = 47.50 and 𝜎 = 2.97, and that the corresponding point estimate for the correctly predicted functioning cryptocurrencies is distributed as 𝑁(𝜇ଶ, 𝜎) with 𝜇ଶ = 52.50, 60.99% of the confidence intervals are overlapping.14 This result implies that our model overpredicts defaults in the sample of functioning cryptocurrencies. 14Note, 𝜇ଵ = (ସଵ.଺଻ାହଷ.ଷଷ) ଶ = 47.50, 𝜎 = (ହଷ.ଷଷିସ଻.ହ଴) ଵ.ଽ଺ = (ହ଼.ଷଷିହଶ.ହ଴) ଵ.ଽ଺ = 2.9745, 𝜇ଶ = (ସ଺.଺଻ାହ .ଷଷ) ଶ = 52.50. 19 Table 5. Estimated confidence intervals using bootstrapping Actual Group Predicted group by the Multiple Linear Discriminant Function Default group Functioning group Default group [83.72%; 89.53%] [10.47%; 16.28%] Functioning group [41.67%; 53.33%] [46.67%; 58.33%] Note: This table reports the results of 𝐵 = 5000 bootstrap replications using a pairs bootstrap. We constructed new data matrices by random resampling with replacement using a probability of 1/𝑇ଵ for the subsample of default cryptocurrencies and a probability of 1/𝑇ଶ for the subsample of functioning cryptocurrencies. Then we re-estimated our model 𝐵 times and sorted the estimated probabilities in an increasing order. The 125th observation gives us the value of the lower bound and the 4875th observation gives us the upper bound of our confidence interval covering 95% probability. It is important to note that the new digital financial markets evolve fast over time. For instance, during 2016 few cryptocurrencies were launched implementing SHA algorithms.15 Moreover, we would like to stress that new cryptocurrencies are applying more advanced algorithms and security mechanisms; there are only few new cryptocurrencies implementing the SHA hashing algorithms and PoW mechanism because these methods have slower speeds and higher energy consumption. Moreover, as technology advances so too does the blockchain. The most common algorithms for the cryptocurrencies issued before 2015 were SHA and Scrypt, but new cryptocurrency algorithms like X11–X17 were created specifically for Graphical Processing Unit (GPU) mining and provide good profit levels to the Portable Instant Mining Platform (PiMP) community since the rise of large Application-Specific Integrated Circuits (ASICs) for Scrypt. Table A.7. in the appendix provides a brief overview of those new algorithms X11–X17. New research needs to account for technological changes associated with cryptocurrencies. In the same way like Altman (1968) proposed in his seminal paper a model that had the ability to predict bankruptcies for firms in a specific industry in the U.S. (e.g., manufacturing industry), our paper takes the first step in exploring predictable patterns in defaults in new emerging digital financial markets. Expecting that we could propose a universal model being capable of predicting defaults across different categories of digital 15 See footnote 8. 20 asset would be an illusion. As pointed out in Howell, Niessner and Yermack (2019) there are three types of digital assets. While cryptocurrencies that are defined as “general-purpose medium of exchange and store of value cryptocurrency” can be considered as alternative to traditional fiat currency, utility tokens or security tokens have a very different purpose, which is financing business projects. Due to their nature, those digital assets have very different characteristics compared to cryptocurrencies. While our paper specifically governs cryptocurrencies that incorporate the PoW consensus protocol – which obviously was the dominant consensus protocol in our sample of investigation – future research is needed to explore the predictability of defaults for either cryptocurrencies that follow other consensus protocols (e.g., Proof-of-Stake or Hybrid), or other types of digital currencies, such as tokens issued in Initial Coin Offerings. Moreover, the research methodology of our paper is related to the literature applying MLDA to predict various types of financial failure (e.g., Altman, 1968; Altman, 1983; 2002; Altman, Hartzell, and Peck, 1995; Altman, Haldeman, and Narayanan, 1977; Altman, Danovi, and Falini, 2013; Altman, and Rijken, 2010). However, there are other strands of literature dealing with analyzing credit risks and employ methodologies such as Probit/Logit models. Future research is encouraged to investigate the predictability of defaults using other methodologies than MLDA also. 3. Conclusion In this age of digital finance, investors can now choose from more than 2,000 cryptocurrencies to invest in. Among cryptocurrencies that started trading prior to December 2014, we found 59% went bankrupt by the end of 2018. This paper proposes a model to predict cryptocurrency default. We downloaded data for all cryptocurrencies launched between January 2009 and December 2014 and established if they went bankrupt by December 2018. We explored almost two dozen cryptocurrency-specific variable candidates that might serve as predictor variables. From those variables, we only used data for the model setup available to the naïve investor one month after a new cryptocurrency started trading. For each of the selected variables, we estimated the sample means for both the default sample and the functioning sample. Our model correctly predicts 75 of 86 bankruptcies (87%). Employing bootstrapping established that the estimates are statistically significant. Notably, the new digital asset markets are subject to technological changes: For instance, many 21 cryptocurrencies issued after 2015 adopted the PoS (minting) consensus mechanism due to greater energy consumption of PoW (mining). Other major changes that we identified are among others that new cryptocurrencies adopt more efficient and profitable algorithms like X11, X12, and X17 over previously popular algorithms like SHA and Scrypt. Therefore, future research on such technological changes is warranted. Nevertheless, our proposed model could be employed in the asset management industry, for instance, as a screening tool for investment decision making. A rational investor would avoid investing in digital assets exhibiting overly high default risks. Portfolios that pre-condition the set of digital assets on those cryptocurrencies that are not predicted as at risk of bankruptcy might generate a better risk-return profile for investors. 22 References Altman, E., 1968. Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. Journal of Finance 23, 189–209. Altman, E. I., Haldeman, R.G. and Narayanan, P. 1977. ZETA Analysis: A New Model to Identify Bankruptcy Risk of Corporations. Journal of Banking and Finance 129-54. Altman, E. 2000, Predicting Financial Distress of Companies: Revisiting the Z-score and Zeta Models, New York University Working Paper. Altman, E.1983. Corporate Financial Distress. New York: Wiley Interscience. Altman E., 2002. Revisiting Credit Scoring Models in a Basel 2 Environment. Salomon Center for the Study of Financial Institutions 2, 2-37. Altman, E., Hartzell, J. and Peck, M., 1995. Emerging Markets Corporate Bonds: A Scoring System. New York: Wiley and Sons. Altman, E.I, Danovi, A. and Falini, A., 2013. Z-Score Models' Application to Italian Companies Subject to Extraordinary Administration. Journal of Applied Finance 23, 128-137. Altman, E.I. and Rijken, H., 2010. Assessing Sovereign Debt Default Risk: A Bottom-up Approach. Journal of Applied Corporate Finance 41, 1-30. Altman, E.I., 2018. Applications of Distress Prediction Models: What Have We Learnt After 50 Years from the Z-Score Models? International Journal of Financial Studies 6, 1-15. Ardia, D., K. Bluteau, and M. Rüede, 2018. Regime changes in Bitcoin GARCH volatility dynamics, Finance Research Letters 29, 266-271. Baur, D.G., and T. Dimpfl, 2018. Asymmetric volatility in cryptocurrencies. Economics Letters 173, 148-151. Borri, N., 2019. Conditional tail-risk in cryptocurrency markets. Journal of Empirical Finance 50, 1-19. Catania, L., Grassi, S. and F. Ravazzolo, 2019. Forecasting cryptocurrencies under model and parameter instability. International Journal of Forecasting 35, 485-501. Chaim, P., and M.P. Laurini, 2019. Is Bitcoin a bubble? Physica A: Statistical Mechanics and its Applications 517, 222-232. Cheah, E.T. and Fry, J., 2015. Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin. Economics Letters 130, 32-36. Dwyer, G.P., 2015. The economics of Bitcoin and similar private digital currencies. Journal of Financial Stability 17, 81-91. 23 Dyhrberg, A.H., 2016. Hedging capabilities of Bitcoin. Is it the virtual gold?. Finance Research Letters 16, 139-144. Fry, J. and Cheah, E.T., 2016. Negative bubbles and shocks in Cryptocurrency markets. International Review of Financial Analysis 47, 343-352. Godfrey, L., 2009. Bootstrap Test for Regression Models. Palgrave MacMillan, New York. Howell, S.T., Niessner, M., and Yermack, D. 2019. Initial Coin Offerings: Financing Growth with Cryptocurreny Token Sales. Working paper, Leonard N. Stern School of Business. Katsiampa, P., 2017. Volatility estimation for Bitcoin: A comparison of GARCH models. Economics Letters 158, 3-6. Kethineni, S., and Y. Cao, 2019. The Rise in Popularity of Cryptocurrency and Associated Criminal Activity. International Criminal Justice Review, forthcoming. Lahmiri, S., and S. Bekiros, 2019. Cryptocurrency forecasting with deep learning chaotic neural networks. Chaos, Solutions and Fractals 118, 35-40. Li, J. and Rahgozar, R., 2012. Application of the Z -Score Model with Consideration of Total Assets Volatility in Predicting Corporate Financial Failures from 2000-2010. Journal of Accounting and Finance 12, 11-19. Li, Z.-Z., Tao, R., Su, C.-W., and O.-R. Lobont, 2019. Does Bitcoin bubble burst? Quality and Quantity 53, 91-105. Maume, P., 2019. Initial Coin Offerings and EU Prospectus Disclosure. European Business Law Review, forthcoming. Omane-Adjepong, M., Alagidede, P., and N.K. Akosah, 2019. Wavelet time-scale persistence analysis of cryptocurrency market returns and volatility. Physica A: Statistical Mechanics and its Applications 514, 105-120. Osterrieder, J. and Lorenz, J., 2017. A statistical risk assessment of Bitcoin and its extreme tail behavior. Annals of Financial Economics 12, 1750003. Satish, Y.M. and B. Janakiram, 2011. Turnaround Strategy Using Altman Model as a Tool in Solar Water Heater Industry in Karnataka. International Journal of Business and Management 6, 199-206. Snedecor, G. W. and Cochran, W. G. (1989). Statistical Methods. Eighth Edition, Iowa State University Press. Shen, D., Urquhart, A., and P. Wang, 2019. Does twitter predict Bitcoin? Economics Letters 174, 118-122. Urquhart, A., 2016. The inefficiency of Bitcoin. Economics Letters 148, 80-82. 24 Appendix Table A.1. Cryptocurrency characteristics Category Details Resource and history Website, announcement, whitepaper, block explorer, github, etc. Coin specifications Coin name, type, founder(s), contributor(s), block time, security mechanism, algorithm, staking maturity, block size, launch type, etc. Daily trading, supply and distribution rank, market cap, price ($), price (BTC), volume(24h), market Dominance (Volume, Value), Supply (Max, Total, Circulating), etc. Economics Block reward, inflation, fees recipient, funding model, etc. Privacy Cryptographic privacy, sender privacy, recipient privacy, hidden transaction amount, transaction link broken, balances visible, anonymous holdings, network trust required, quantum-proof privacy, trusted setup, auditable supply, mobile privacy, etc. Features and scaling Instant send, protocol level, governance, voters, multi-signature support, scaling model, transparent transaction size (bytes), private transaction size (bytes), most throughput in a block, prunable blockchain, etc. Wallets Ledger, trezor, coinomi, jaxx, native mobile wallet binaries for all major OS, webwallet, etc. Network and masternodes Largest miner or pool, entities controlling, staking supply, public nodes, masternodes, masternode cost (coin), masternode cost ($), etc. Community Percentage of active users, number of subscribers, facebook likes, Twitter followers, Alexa rank, Google/Bing searches, etc. Note: This table provides an overview of different features and characteristics of a cryptocurrency. (Source: https://news.bitcoin.com) 25 Table A.2. Potential cryptocurrency-specific variables for the model Potential categorical variable candidates 1.Security mechanism PoW/PoS/Hybrid/Others 2.Launch type* Standard/ICO/Fork/Coinswap/others 3.Algorithms SHA/Scrypt/others 4.Funding model* ICO/donations/founders/others Potential Binary Variable Candidates 5. Pre-mined, 6.Privacy choice*, 7.Sender privacy*, 8.Recipient Privacy*, 9.Network trust required*, 10. Multi-signature Support*, 11.Founder anonymity YES/NO Potential Continuous Variable Candidates 12. Block time, 13.Block reward, 14.Block size*, 15.Pre-mined ratio, 16.Total coins, 17. Volume*, 18.Return, 19.Volatility, 20. Reward percentage Note: This table provides an overview of different quantifiable (continuous/categorical/binary) cryptocurrency- specific variables that could potentially be used to develop a model. Our model incorporates 9 variables from the 20 candidates. The remaining variables were excluded owing to the non-accessibility of websites for many dead coins highlighted with an asterisk (*). 26 Table A.3. Descriptive statistics of functioning and bankrupt cryptocurrencies Panel A. Descriptive statistics of the functioning sample N Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis Jarque-Bera PMTTCR 60 0.0041 0.0000 0.0842 0.0000 0.0153 4.5660 23.2754 1236.2090 MTTCR 60 0.0000 0.0000 0.0004 0.0000 0.0000 7.3888 56.3109 7651.0780 Ret_D1 60 0.7124 -0.3779 18.3576 -0.9655 3.1486 3.7353 18.8502 767.6010 Ret_W1 60 0.2849 -0.0753 16.2296 -0.8501 2.2079 6.4717 46.9459 5246.9390 Ret_M1 60 0.1197 0.0000 2.6973 -0.7500 0.5512 2.6563 11.9317 269.9996 Vol_D1 60 10.2559 0.4855 337.0018 0.0000 45.5486 6.4127 45.7924 4989.2090 Vol_W1 60 4.8749 0.0694 263.4009 0.0000 33.9713 7.5306 57.8118 8077.9110 Vol_M1 60 0.3131 0.0116 7.2756 0.0000 1.1050 5.0058 29.2786 1976.9990 Block time 60 152.9167 60.0000 600.0000 5.0000 185.9005 1.7929 4.6947 39.3247 Minimum reward 60 3377.0640 50.0000 100000.0000 0.0000 14473.7900 5.6653 36.1092 3061.5140 Pre-mined 60 6.1400E+08 0.0000E+00 3.6800E+10 0.0000E+00 4.7500E+09 7.5509E+00 5.8017E+01 8.1373E+03 Total coins 60 2.9500E+10 8.4000E+07 5.0000E+11 4.2000E+01 1.0000E+11 3.8711E+00 1.6909E+01 6.3351E+02 Panel B. Descriptive statistics of the default sample PMTTCR 86 0.0152 0.0000 0.5000 0.0000 0.0754 6.1213 39.2322 5241.1920 MTTCR 86 0.0000 0.0000 0.0024 0.0000 0.0003 9.0733 83.5495 24429.4600 Ret_D1 86 0.0403 -0.4245 13.4928 -0.9815 1.7926 5.4962 39.2686 5146.5500 Ret_W1 86 0.2541 -0.0911 13.4928 -0.9827 1.6441 6.3551 50.4816 8657.5260 Ret_M1 86 0.2454 0.0405 4.6154 -0.4512 0.7490 3.7423 18.5781 1070.3270 Vol_D1 86 3.1776 0.3235 182.0544 0.0000 19.8910 8.6488 77.9195 21185.1800 Vol_W1 86 2.7361 0.1414 182.0544 0.0000 19.6609 8.9798 82.3686 23728.5600 Vol_M1 86 0.6147 0.0152 21.3018 0.0000 2.6716 6.1461 44.6106 6745.7830 Block time 86 160.7907 60.0000 3600.0000 10.0000 407.9158 7.2223 60.3602 12537.5000 Minimum reward 86 65880.6500 50.0000 5000000.0000 0.2500 541325.8000 8.9668 82.1671 23610.7400 Pre-mined 86 4.8800E+07 0.0000E+00 1.8200E+09 0.0000E+00 2.3400E+08 6.1705E+00 4.3285E+01 6.3612E+03 Total coins 86 1.4000E+10 1.0000E+08 5.5000E+11 3.2000E+04 6.3300E+10 7.3333E+00 6.1404E+01 1.2994E+04 Note: This table reports the descriptive statistics for the following 12 variables: Pre-Mined-To-Total-Coin-Ratio (PMTTCR), Minimum-Reward-To-Total-Coin-Ratio (MTTCR), first day return (Ret_D1), first week return (Ret_W1), first month return (Ret_M1), first day volatility (Vol_D1), first week volatility (Vol_W1), first month volatility (Vol_M1), block time (in seconds), minimum reward for the miners per block (minimum reward), number of coins mined before issued to the public (pre-mined), and the total number of coins of the Cryptocurrency (total coins). The figures are reported for both, the running sample (Panel A) and the default sample (Panel B). 27 Table A.4. Discriminant function for the default group t Predicted group 1 Predicted group 2 t Predicted group 1 Predicted group 2 1 27.3805 27.7258 44 24.5862 23.9807 2 25.7955 26.5482 45 25.1247 24.3461 3 29.1404 28.5218 46 23.6011 24.0290 4 28.5050 28.3511 47 23.7185 24.0802 5 28.4949 28.3009 48 26.6271 27.7649 6 26.7095 25.0682 49 23.6858 24.0478 7 29.0677 29.6769 50 22.7344 22.5435 8 27.3892 27.7573 51 24.1190 23.7822 9 28.7611 28.5356 52 24.6971 24.2462 10 23.3757 22.8601 53 25.1351 24.5761 11 26.2717 23.9860 54 24.8930 24.4421 12 -24.1924 -24.2417 55 23.4671 23.1464 13 24.5396 23.8052 56 25.5403 24.3222 14 25.0503 24.3044 57 25.0424 23.9827 15 25.2780 24.4149 58 27.0499 25.4708 16 28.3193 28.2433 59 29.1556 28.5972 17 28.7954 28.5569 60 25.4615 24.2150 18 27.1257 25.3986 61 25.7609 24.4991 19 27.4460 25.7223 62 25.6308 24.3650 20 24.9086 23.8277 63 25.5393 24.4207 21 28.8249 28.2669 64 24.8019 23.8088 22 24.3948 23.4981 65 26.0950 24.7936 23 25.5785 24.3492 66 24.2334 23.3495 24 24.5392 23.7033 67 25.4390 24.2220 25 25.5527 24.3702 68 25.3581 24.1425 26 25.2765 24.4344 69 25.9102 24.6305 27 25.1694 24.2734 70 26.1701 24.7816 28 27.1309 24.7269 71 23.4963 23.2327 29 25.4649 24.5927 72 25.0475 24.2988 30 25.4501 24.6327 73 24.6484 23.9325 31 24.4508 24.0105 74 25.4414 24.5399 32 26.4005 25.3303 75 25.3188 24.4492 33 25.0495 24.2478 76 26.1223 25.0992 34 25.7881 24.8164 77 24.1029 25.0230 35 24.8941 24.1895 78 24.9693 24.2222 36 28.7836 28.5683 79 25.9494 24.9470 37 27.7893 27.7997 80 24.8711 24.0899 38 25.4256 24.4933 81 25.8052 24.8806 39 24.8828 24.1603 82 23.0776 22.8346 40 23.6977 23.4344 83 24.9735 23.4067 41 28.5788 28.3744 84 24.4830 23.9345 42 28.5522 28.3965 85 24.4737 23.8478 43 28.6334 28.1262 86 24.1142 24.5685 Note: This table reports the values for the discriminant function (Equation 8.a) for the default group (e.g., group 1). 28 Table A.5. Discriminant function for the functioning group t Predicted group 1 Predicted group 2 t Predicted group 1 Predicted group 2 1 27.82065 27.73309 31 23.81871 23.66742 2 28.21115 28.06119 32 22.69601 22.69963 3 27.56446 27.8617 33 25.47647 24.56926 4 24.88217 26.79222 34 26.46251 27.41852 5 24.18907 23.8235 35 24.05865 24.03279 6 27.64701 27.89729 36 23.55639 23.60259 7 28.47438 28.74628 37 26.2968 27.56041 8 28.23995 28.78224 38 26.63752 27.78143 9 28.43512 28.02157 39 23.94774 24.32457 10 27.85306 27.72618 40 27.08734 28.17422 11 24.93163 23.89347 41 26.38169 27.58451 12 25.24417 24.02586 42 26.65863 27.79309 13 24.07879 23.36516 43 26.46865 27.67717 14 25.39226 24.0771 44 21.97226 22.86871 15 25.19025 24.36664 45 28.81073 29.50451 16 31.00211 30.156 46 24.47789 24.03402 17 24.91486 24.19066 47 24.29782 25.81669 18 25.57118 24.62532 48 25.75796 24.53365 19 26.27598 25.23614 49 26.17337 25.1366 20 25.00121 24.35303 50 28.75249 28.56327 21 28.64485 28.4349 51 24.91487 24.19067 22 26.96299 27.15382 52 25.01501 24.15877 23 24.91487 24.19067 53 25.19886 24.33645 24 24.4346 23.66766 54 24.09113 24.42255 25 26.47026 26.85933 55 23.3386 23.74375 26 26.01675 25.00639 56 -23.2155 -22.1288 27 22.73395 23.34834 57 28.3670 28.27678 28 24.55047 23.99539 58 24.27292 23.87617 29 25.37536 24.50556 59 25.17099 24.26115 30 22.85169 23.04122 60 -22.6525 -21.7619 Note: This table reports the values for the discriminant function (Equation 8.b) for the functioning group (e.g., group 2). 29 Table A.6. Name and symbol of cryptocurrencies used for the study Panel A. Name and symbol of running cryptocurrencies S.No. Cryptocurrency Symbol S.No. Cryptocurrency Symbol S.No. Cryptocurrency Symbol S.No. Cryptocurrency Symbol S.No. Cryptocurrency Symbol 1 Blakecoin BLC 13 Fedoracoin TIPS 25 Reddcoin RDD 37 Bitcoin BTC 49 SmartCoin SMC 2 Maxcoin MAX 14 Novacoin NVC 26 NobleCoin NOBL 38 Peercoin PPC 50 Gridcoin GRC 3 Zurcoin ZUR 15 Spots SPT 27 Mooncoin MOON 39 Zetacoin ZET 51 Lucky7Coin LK7 4 DimeCoin DIME 16 Diamond DMD 28 Phoenixcoin PXC 40 Unobtanium UNO 52 42coin 42C 5 Quark QRK 17 Royalcoin RYC 29 Fastcoin FST 41 Bytecoin BCN 53 Goldcoin GLD 6 Animecoin ANI 18 Worldcoin WDC 30 Argentum ARG 42 Terracoin TRC 54 Huntercoin HUC 7 Primecoin XPM 19 Mincoin MNC 31 Florincoin FLO 43 Namecoin NMC 55 Curecoin CURE 8 Vertcoin VTC 20 Megacoin MEC 32 Annoncoin ANC 44 Tekcoin TEK 56 Stellar XLM 9 Litecoin LTC 21 Feathercoin FTC 33 Grandcoin GDC 45 Skeincoin SKC 57 Trollcoin TROLL 10 Bullion CBX 22 Dogecoin DOGE 34 Supercoin SUPER 46 CDNcoin CDN 58 SecureCoin SRC 11 Communitycoin COMM 23 Galaxycoin GLX 35 Betacoin BET 47 Bela Coin BELA 59 Marscoin MARS 12 Emerald EMD 24 BitBar BTB 36 iXcoin IXC 48 Redcoin RED 60 Pandacoin PND Panel B. Name and symbol of default cryptocurrencies S.No. Cryptocurrency Symbol S.No. Cryptocurrency Symbol S.No. Cryptocurrency Symbol S.No. Cryptocurrency Symbol S.No. Cryptocurrency Symbol 1 Datacoin DTC 18 Sexcoin SXC 35 Doubloons DBL 52 Metiscoin MTS 69 Cagecoin CAGE 2 Tagcoin TAG 19 Xivra XIV 36 CHNCoin CNC 53 Unioncoin UNC 70 Electric VOLT 3 Nyancoin NYAN 20 Extremecoin EXC 37 Globalcoin GLC 54 Frozencoin FZ 71 Bottlecaps CAP 4 Paycoin XPY 21 Americancoin AMC 38 Krugercoin KGC 55 KingdomCoin KING 72 Neocoin NEC 5 Infinitecoin IFC 22 Lottocoin LOTTO 39 Franko FRK 56 Memecoin MEM 73 Bitgem BTG 6 Qubitcoin Q2C 23 Graincoin GRA 40 Netcoin NET 57 Solcoin SOL 74 Lebowskis LBW 7 Freicoin FRC 24 Xencoin XNC 41 BBQcoin BQC 58 Hypercoin HYC 75 Growthcoin GRW 8 AllAgesCoin AAC 25 Batcoin BAT 42 Catcoin CAT 59 Craftcoin CRC 76 Prospercoin PRC 9 Joincoin J 26 Junkcoin JKC 43 Memorycoin MMC 60 Nanotoken NAN 77 Hobbitcoin HBC 10 Cthulhu Offerings OFF 27 StarCoin STR 44 Luckycoin LKY 61 GIL GIL 78 Hotcoin HTC 11 Colossuscoin COL 28 Zenithcoin ZTC 45 Yacoin YAC 62 Usecoin USE 79 Lovecoin LOVE 12 Particle PRT 29 HoboNickels HBN 46 AsicCoin ASC 63 AlphaCoin ALF 80 Bells BEL 13 Pennies CENT 30 Philosopherstone PHS 47 Tigercoin TGC 64 Richcoin RCH 81 Zeuscoin ZEU 14 Qqcoin QQC 31 CACHeCoin CACH 48 Devcoin DVC 65 Zedcoin ZED 82 ELACoin ELC 15 Applecoin APC 32 Microcoin MRC 49 Teacoin TEA 66 Stablecoin SBC 83 EzCoin EZC 16 ZcCoin ZCC 33 Kittehcoin MEOW 50 Copperlark CLR 67 Socialcoin SOC 84 Noirbits NRB 17 Onecoin ONE 34 Gamecoin GME 51 Chaincoin CHC 68 ElephantCoin ELP 85 Nibble NBL 86 Globe GLB Note: This table reports the name and symbol of cryptocurrencies with PoW consensus protocol issued prior to the end of year 2014. These cryptocurrencies were tracked till the end of year 2018 and categorized them into running (Panel A) and default (Panel B) samples. 30 Table A.7. Algorithms X11. X13. X14. X15. and X17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Blake BMW Groestl JH Keccak Skein Luffa Cubehash Shavite SIMD Echo X11 Hamsi Fugue X13 Shabal X14 Whirlpool X15 Loselose Djb2 X17 Note: This table shows the chain of different hashing algorithms X11. X13. X14. X15. and X17 with their sub-algorithms (Source: getpimp.org)