The Cryptocurrency Bitcoin

Origins and Definition of the Cryptocurrency Bitcoin

According to ^{Abramova and Böhme (2016)}, cryptocurrencies are innovative, digital instruments with the potential to destroy traditional payment systems that are based on financial intermediation through commercial banks. ^{Ali et al. (2014)} identify Bitcoin as the first and most influential digital currency and define it as "a privately developed, internet-based currency and payment system that requires no intermediaries (like banks) for the processing of payments" (266). Furthermore, they mention that the Bitcoin system is not regulated by any public authority (e. g. a central bank) and its information exchange is based on cryptography in order to ensure a secure processing of financial transactions.

^{Nakamoto (2008)} was the first who introduced the idea of an autonomous, decentralized, and anonymous payment system called Bitcoin in a paper titled "Bitcoin: A Peer-to-Peer Electronic Cash System." According to ^{Bonneau et al. (2015)}, Bitcoin's genesis block was mined in January 2009 and the first transaction based on this currency was realized in 2010. Although Bitcoin appears to be a revolutionary and innovative instrument, introduced just about 10 years ago, the concept of cryptocurrencies is not new at all. Already in 1983, David Chaum presented his idea of an automated payment system, which offers a high degree of anonymity using techniques of cryptography (^{Chaum, 1983}).

Since then, the idea described above was refined by multiple researchers and practitioners, which led to the emergence of a huge variety of cryptocurrencies existing today. In its list of currently (as of 06/18/2020) existing cryptocurrencies, ^{CoinMarketCap (2020)}, one of the key sources of information on the market, mentions 2,685 different cryptocurrencies around the world. Table 1 presents the 10 most important cryptocurrencies worldwide, based on the mentioned list.

According to Table 1, Bitcoin is by far the most important cryptocurrency worldwide with a market capitalization of more than USD 173 billion. At this point, market capitalization is simply the amount of circulating coins multiplied by the current market price of each coin. As evidenced by data included in the table, the differences between Bitcoin and Ethereum as the 2^nd, as well as Tether as the 3^rd most important cryptocurrencies are impressive. Comparing the value of the top cryptocurrencies with the total market capitalization of all the 2,685 cryptocurrencies (USD 266,469,751,315) listed on ^{CoinMarketCap (2020)}, it can be concluded that the global cryptocurrency market is highly concentrated, given that the portion of Bitcoin on the total market capitalization is currently almost 65%, and the top 10 cryptocurrencies, combined, reach almost 88% of the total cryptocurrency market.

Figure 1 shows daily Bitcoin price data for the period 10/01/2013 to 05/31/2020, obtained from cryptocurrency information provider ^{CoinDesk (2020a)}. The Bitcoin Price Index of CoinDesk represents an average of Bitcoin prices across leading global Bitcoin exchanges (^{CoinDesk, 2020b}). As can be seen in the figure, the database started with a value of USD 123.26 (10/01/2013) and reached its all-time high on 12/18/2017 with a price of USD 19,395.84. As of 05/31/2020, the Bitcoin price quotes at USD 9,437.96.

Source: ^{CoinDesk (2020a)}.

Figure 1 CoinDesk Bitcoin Price Index on a Daily Basis for the Period 10/2013-05/2020 

Definition and Characteristics

There exist numerous definitions of an asset price bubble. For example, according to ^{Kindleberger and Aliber (2005)}, an asset price bubble can be defined as a phenomenon in financial markets, which is based on speculation and where the market price of an asset first sharply increases and then collapses. ^{Agosto and Cafferata (2020)} also differentiate between these two main phases of a financial bubble: expansion of the bubble and crash. These authors define asset price bubbles as extremely rapid accelerations of an asset's market price-from a statistical perspective, they are usually referred to as explosive behaviors-, followed by drastic market price drops. Additionally, ^{Jarrow et al. (2010)} describe an asset price bubble as a considerable difference between the market price of an asset and its fundamental value. At this point, an asset's market price can be defined as the visible price for which the asset is exchanged between its buyers and sellers and depends solely on the factors of current demand and supply. On the other hand, the fundamental value (also known as fair or intrinsic value) is the result of a sophisticated analysis (fundamental analysis), which determines the present value of the asset's future cash flows. In other words, the fundamental value is what the asset should cost if its market valuation was fair.

In their definition of an asset price bubble, ^{Blanchard and Watson (1982)} include a reference to its cause. They state that a financial bubble is a movement in the market price of an asset that is not justified by fundamental news. Thus, according to these authors, a bubble is caused by factors different from fundamental information (fundamental information refers to information that changes the fundamental value of an asset). According to the efficient market hypothesis (^{Fama, 1970}, 1991; ^{Jensen, 1978})-still one of the dominating theories in financial literature nowadays-, only this type of information drives market prices.

In fact, the efficient market hypothesis interprets financial bubbles as inefficiencies, i.e. differences between the market price of a financial asset and its fundamental value, which (according to the theory) are not possible given that capital markets operate efficiently due to a perfect arbitrage process realized by perfectly rational market participants (^{Barberis & Thaler, 2002}). Therefore, in the efficient market hypothesis, market prices and fundamental values are equal and asset price bubbles cannot emerge. Nevertheless, real asset markets can be characterized by market imperfections and limited arbitrage, which simply do not permit an adequate, stabilizing arbitrage (^{Abreu & Brunnermeier, 2002}; ^{Shleifer & Vishny, 1997}).

Therefore, numerous historical examples of asset price bubbles exist within different types of markets, including, for example, stocks, bonds, real estate, crude oil, and even tulip bulbs. There is a multitude of theoretical approaches with reference to the explanation of asset price bubbles. Generally, financial literature establishes a difference between rational and irrational bubbles. On the one hand, rational financial bubbles are in line with the rational (benefit maximizing) investment behavior of market participants. This category of asset price bubbles encompasses theories such as stochastic bubbles (^{Blanchard, 1979}), intrinsic bubbles (^{Froot & Obstfeld, 1991}), information bubbles (^{Allen & Gale, 2000}; ^{Allen & Gorton, 1993}), as well as a super-exponential rational model of bubbles (^{Sornette & Andersen, 2002}).

On the other hand, irrational bubbles contradict rational investment behaviors. Under this category fall, for example, theories that define financial bubbles as fashions and fads (^{Camerer, 1989}; ^{Shiller, 1988}). Furthermore, nowadays, behavioral finance approaches provide very promising and convincing irrational explanations for asset price bubbles. One of the most important and influential behavioral approaches is the positive feedback theory of bubbles of Nobel laureate Robert J. Shiller (2005, 2015).

Central to this theory is a feedback mechanism that provokes both the expansion and crash of the bubble. According to the author, in the expansion phase, an exponentially growing demand results in exponentially growing market prices of the asset, while in the crash phase an exponentially growing supply leads to falling market prices. With respect to this feedback mechanism, ^{Shiller (2015)} uses the medical term epidemic in order to express the importance of social interactions between market participants, which underlie the described demand and supply processes during a financial bubble.

Regarding the positive feedback theory of ^{Shiller (2005)}, ^{Demmler (2017)} enumerates a variety of behavioral anomalies (for instance, investor sentiment, herding, selective awareness, biased self-attribution, overconfidence, etc.) that form the psychological basis for an irrational investment behavior, which consequently leads to the speculative process called financial bubble. Similarly, ^{Akerlof and Shiller (2009)} put instinctive investment behaviors forward as a subject of discussion within financial decision-making processes and speculative phenomena like asset price bubbles.

The South Sea Bubble as an Example of a Historical Asset Price Bubble

Since 1637, the year of the first registered asset price bubble (tulipmania) in the Netherlands (^{Garber, 1989}), numerous examples of financial bubbles have been seen on the international financial markets until today. Among these historical financial bubbles, ^{Demmler (2017)} mentions, for example, the asset price bubble of the roaring twenties of the twentieth century on the US stock market, which principally affected stocks of the then innovative sectors of media, telephone, electronics, aerospace, power supply, and chemical industry. As another mayor example of a historical asset price bubble, the New Economy (internet, telecommunications, and biotechnology) bubble at the turn of the millennium on the US, British, French, and German stock markets can be highlighted (^{Brunnermeier & Nagel, 2004}). Finally, the more recent subprime bubble (^{Brunnermeier, 2009}) on the US housing market should be mentioned here, which resulted in worldwide recessional tendencies at the beginning of 2007.

The present article has a special interest in yet another historical financial bubble, which will be part of the statistical analysis. Hence, this specific bubble should be presented in more depth. 300 years ago, in 1720, an asset price bubble appeared on the English stock market, known as the South Sea Bubble since it occurred primarily in shares of the South Sea Company, a trading company and financing firm of the English government at the moment. However, this bubble was not limited to this single enterprise as it spread to numerous other newly founded firms that became known as "bubble companies" (^{Frehen et al., 2009}).

As can be seen in Figure 2, the entire financial bubble only lasted about one year. At the beginning of 1720, the South Sea Company stock quoted at 128 pounds; the maximum market price was reached at the end of June with 950 pounds. Until the end of the year, the asset price bubble was eliminated again as the Company's market price fell back to 200 pounds. Figure 2 clearly shows the typical phases (expansion and crash) of an asset price bubble. ^{Garber (1990)} estimates that before the beginning of the crash of the South Sea Bubble, the South Sea Company was about 5 times overvalued in comparison to its fundamental value.

Source: European State Finance Database (2020).

Figure 2 Historical Prices of the South Sea Company from 01/01/1720 to 12/23/1720 

Bitcoin and Asset Price Bubbles

During the last years, the topic "Bitcoin and asset price bubbles" has been analyzed by a growing number of scientific research studies. For example, ^{Grinberg (2011)} indicates the possibility that the Bitcoin network could be vulnerable to speculative movements, similar, for example, to asset price bubbles. Regarding the fundamental value of the cryptocurrency Bitcoin, ^{Weidmann (2018)} is convinced that it does not have an intrinsic value. In line with this argument, ^{Cheah and Fry (2015)} also calculate the fundamental value of Bitcoin with 0. Consequently, every positive market price of Bitcoin would fulfill the direct definition of an asset price bubble. Nevertheless, in general, scientific approaches to determine the fundamental value of cryptocurrencies are (still) limited (^{Chen & Hafner, 2019}).

In general, ^{Chen and Hafner (2019)} believe that cryptocurrencies could be more vulnerable to financial bubbles than, for example, stock markets. They consider that within cryptocurrency markets, compared to stock markets, a necessary stabilizing process that aligns potentially differing market prices and fundamental values is more difficult due to greater effects of existing limits of arbitrage (e.g., lack of short-sale instruments) and market imperfections (e.g., limited fundamental information).

In another research study, ^{Phillips and Gorse (2018a)}, after analyzing four cryptocurrencies including Bitcoin, came to the conclusion that cryptocurrencies in general are vulnerable to speculative investment behavior and bubble-like price growth in case of increasing interest levels of market participants. Furthermore, ^{Phillips and Gorse (2018b)}, using social media and trading volume data, show that financial bubbles in cryptocurrencies can be predicted by epidemic modelling. Moreover, and in line with ^{Shiller (2015)}, they provide empirical evidence that asset price bubbles mirror the social epidemic-like spread of an investment idea among market participants.

In a similar result to ^{Phillips and Gorse (2018b)}, ^{Garcia et al. (2014)} point out the existence of self-reinforcing positive feedback processes between the volume of Twitter messages and Bitcoin prices. Additionally, ^{Chen and Hafner (2019)} present empirical evidence for multiple bubble periods in cryptocurrency market prices and find an explanation in exuberant investor sentiment movements. ^{Eom et al. (2019)} also emphasize the high dependency of Bitcoin market price behavior on investor sentiment and, as a consequence, the vulnerability of Bitcoin to financial bubble tendencies.

Examining harmful speculative movements and explosive behaviors within time series of Bitcoin market prices, ^{Bianchetti et al. (2018)} demonstrate strong bubble tendencies in Bitcoin market prices during 2017, reaching a maximum in December; a result confirmed by studies of ^{Agosto and Cafferata (2020)} and ^{Geuder et al. (2019)}, who as well find financial bubbles in Bitcoin and other cryptocurrencies especially in late 2017. On the other hand, there are studies that speak against bubble processes in Bitcoin market prices in 2017. For example, in their analysis of daily and high-frequency Bitcoin market prices, ^{Chaim and Laurini (2019)} find evidence for a Bitcoin bubble during the years 2013 and 2014, but not for late 2017. Furthermore, ^{Fry (2018)} urges to be cautious with preliminary conclusions about financial bubbles in cryptocurrency markets given that, as he demonstrates, dramatic booms and busts cycles can occur even in the absence of bubbles due to liquidity risks.

Data Analysis

This document uses BTC and SSC daily price data spanning nearly two years (one year before and one year after the maximum price date). Estimations were made using Stata 13. BTC price data go from 12/18/2016 to 12/18/2018 and were obtained from Coindesk (2020a). SSC prices were obtained from the European State Finance Database (2020) and go from 07/01/1719 to 07/12/1721. As it is evident from Figures 1 and 4, data used for each financial asset show the typical sharp rise and decline of prices, which is characteristic of a financial bubble.

The returns of each financial asset are obtained as the percentage of daily log-price differences: r _t = [ln(P_t) _ ln(P_t-1)] x 100. Figure 3 displays respective returns, as well as maximum price dates (MPD) marked with a red vertical line: 12/18/2017 for BTC and 06/30/1720 for SSC.

Source: authors' elaboration.

Figure 3 Log Returns of Bitcoin and South Sea Company Market Prices 

Figure 3 suggests that the two series are stationary around zero, so a less-than-unity AR(1) coefficient could be expected. The figure indicates that SSC is the asset with greater volatility (minimum return close to 50% negative and maximum return close to 44% near 09/28/1720). Moreover, Figure 3 also shows that the greatest volatility in returns happened after MPD for SSC (06/30/1720), whereas for BTC the picture is not that clear. The maximum positive return of BTC occurred before MPD (close to 23% on 07/21/2017), while in the case of SSC it was after MPD (close to 44% near 09/28/1720). Interestingly, both assets display a return greater than 20% within five months before MPD (starting on 07/21/2017 for BTC and on 03/16/1720 for SSC), and both assets have negative returns greater than 20% within three months after MPD (01/17/2018 and 02/06/2018 for BTC; 09/28/1720 for SSC).

Table 2 shows return distributions and exhibits several similarities between BTC and SSC. Considering the whole sample, BTC and SSC mean returns are positive, though those of BTC are considerably higher. BTC standard deviation is similar to that of SSC in magnitude, suggesting that overall volatility is similar for both assets. The skewness of returns is negative for both assets, so most returns are greater than their mean. The fact that the SSC return mean is close to zero indicates that most of its returns were positive. Moreover, each asset shows similar absolute values for maximum and minimum returns, i.e., close to 22 for BTC (maximum of 22.64 and minimum of -21.57) and greater than 40 for SSC (maximum of 43.83 and minimum of -51.08).

Table 2 also shows that, before MPD, the BTC return mean is positive and relatively large in magnitude, similar to that of SSC. Moreover, in terms of BTC returns, standard deviation is somewhat greater than that of SSC, suggesting that BTC returns were slightly more volatile before MPD. Interestingly, Table 2 demonstrates that BTC and SSC return skewness is positive before MPD, indicating that most daily returns were smaller than their mean during this period. However, after MPD, the return mean, as well as return skewness, were negative for both assets. Additionally, the standard deviation of BTC returns decreased slightly compared to the period before MPD, but that of SSC increased, suggesting that SSC asset returns became more volatile after MPD, contrary to BTC.

According to the discussion of data presented in Figure 3, Table 3 presents evidence that none of the asset returns follow a unit root process during the whole sample period, nor after MPD. Only SSC shows some evidence of following a unit root before MPD, depending on the information criterion chosen in the ADF test. Also, BTC and SSC returns do not follow a (stable) AR(1) process in the whole sample period, nor after MPD. Only SSC returns exhibit evidence of following a (stable) AR(1) process before MPD. These results support the argument that even though asset returns show volatility, deviations from a long-term value (ρ in equation [1]) do not last forever, and the process returns to equilibrium.

A deeper analysis of return volatility is shown in Table 4, which presents the estimation of equations [2]. The insignificant ρ coefficients in the mean equation show that none of the asset returns follow a stable AR(1) process in any period analyzed when volatility is estimated along with the AR(1) equation. Considering the whole sample period, the insignificant constant coefficients suggest that the long-term expected value of returns moves close to zero. Furthermore, BTC has the highest δ, so BTC returns present the greatest general volatility. Also, both asset returns present a positive ARCH coefficient (α), so past innovations have a positive effect on current volatility. For BTC, a is relatively small compared to SSC, so SSC past innovations have a greater positive effect on current volatility. Moreover, only BTC returns display a statistically significant negative TARCH coefficient ( ү ), meaning that a positive shock has a smaller effect on BTC return volatility than a negative shock. For SSC returns, on the other side, a positive or negative shock has the same effect on volatility. Finally, GARCH coefficients (β) are similar for both assets considering the whole sample period, as well as before and after MPD. Hence, past volatility has nearly the same effect on current volatility for BTC and SSC.

Regarding the subsample before MPD, Table 4 also displays significant constant coefficients, suggesting that the long-term expected value of returns moved close to a positive value for BTC, but to a negative value for SSC. Again, both asset returns show positive ARCH coefficients, so past innovations have a positive effect on volatility. Within this subperiod, for BTC, α is higher than that of SSC. Before MPD, SSC returns were the only ones displaying a statistically significant negative TARCH coefficient ( ү ), meaning that, for SSC, a positive shock had a smaller effect on volatility than a negative shock. On the other hand, for BTC, a positive or negative shock had the same effect on volatility.

When analyzing the subsample after MPD, only SSC's constant coefficient was significant, but negative, indicating that the long-term expected value of SSC returns moved close to a negative value. For BTC, δ is not significant after MPD, contrary to what was found considering the whole sample period (i.e., BTC volatility was significantly smaller). Both asset returns still show a positive ARCH coefficient, though for BTC, it is not significant at a 95% level, indicating that past innovations did not have a positive effect on BTC return volatility. Moreover, both assets present a relatively large and significant TARCH coefficient, though this was positive for BTC and negative for SSC. Therefore, after MPD, a positive shock had a greater effect on volatility than a negative shock for BTC, and vice versa for SSC. This suggests that, after MPD, investors reacted more after falls in SSC returns.

Table 5 demonstrates that asset statistics reject the SADF and GSADF null at a 99% level. Hence, there is evidence that both BTC and SSC experienced bubble behavior. In order to identify the dates when BTC and SSC prices had a mildly explosive behavior, Figure 4 shows the SADF test recursions. It is clear that the SADF test statistics for both assets reach their highest values close to MPD. Also, it is interesting to note that SADF test recursions reject the null generally during episodes of greater return volatility. For instance, when BTC returns reached their lowest value before MPD (close to -18% on 09/14/2017 as shown in Figure 3), the SADF test statistic started to increase until it reached its maximum value. Similarly, when SSC returns reached their greatest value before MPD (over 20% on 03/16/1720 as shown in Figure 3), the SADF test statistic started to increase until it reached its maximum value.

Source: authors' elaboration.

Figure 4 SADF Sequence 

The SADF test recursions displayed in Figure 4 suggest that there are at least two periods where the SADF statistics for BTC and SSC reject the null, confirming the presence of financial bubbles, as discussed in the results of Table 5. However, ^{Phillips et al. (2015)} argue that if there is more than one episode of exuberance, the SADF test is not consistent. Therefore, the GSADF test is carried out.

Source: authors' elaboration.

Figure 5 GSADF Sequence 

Figure 5 evidences several explosive moments of BTC and SSC returns, which implies that the assets exhibit more than one financial bubble. For SSC, the GSADF statistic rejects the null at a 99% level in several moments in 1720, including near 01/01, 03/16, 05/28, 06/30 (MPD), and 09/28. For BTC, the GSADF statistic rejects the null at a 99% level in 2017 around 05/21, between 07/21 and 09/14, and around 12/18 (MPD). As discussed before, these dates coincide with periods of greater return volatility in both assets.