Bubble analysis on the cryptocurrency market

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Bubble Analysis on the Cryptocurrency Market

Master Thesis Quantitative Finance

University of Amsterdam Name: Sebastiaan de Vries Student number: 10666168 Thesis Supervisor: Florian Peters Date: July 1, 2018

Abstract

In this research, the cryptocurrency market is examined on explosive price behavior by several augmented Dickey-Fuller tests. Additionally, significant evidence on bubble elements is timestamped and compared to the Dotcom bubble. Subsequently, the results are tested on presumable causes regarding different bubble theories from existing literature on extrapolation and disagreement effects. Evidence is found for an opposite extrapolation effect and a disagreement effect.

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Statement of Originality

This document is written by Student Sebastiaan de Vries, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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1. Introduction

It has only been over a decade since Satoshi Nakamoto (2008) composed the underlying blockchain technology which was first used for the encryption of Bitcoin. In the years after this invention, new cryptocurrencies appeared rapidly and therefore created a whole new digital asset market. Due to criminal purposes and a lack of safety among several exchanges, these blockchain assets have been a source of public debate and moreover price speculation.

The cryptocurrency market is emerging towards a globally used investment instrument as daily trading volumes are reaching the same values as the New York Stock Exchange1. Despite uncertain price movements in the market, the amount of Bitcoin investors is still growing with over 25 million certified online wallets2. On top of that, Bitcoin’s market capitalization currently only represents 45% of the total market value3.

Along with the rising numbers of stakeholders grows the risk of a sudden collapse driven by an enormous market return of 3387% in 20173. But do the digital assets have any fundamental value since most of them are a medium of exchange instead of a share in a firm? Furthermore, crypto assets are hardly regulated by governments and are therefore prone to pump-and-dump schemes, Initial Coin Offering (ICO) scams and theft of digital wallets. In this study, the cryptocurrency market is examined to check whether asset prices contain bubble elements over time.

In order to investigate the potential investment risk, this paper concentrates thoroughly on bubble analysis of the cryptocurrency market via unit root testing proposed by Philips et al. (2015). Daily trading volumes are tested with the extrapolation theory proposed by Barberis et al. (2016) that states that investors purchase assets with high past returns with the expectation that the prices will continue to rise in the future. Besides this, the results are put into perspective by comparing the latter asset class to the NASDAQ Computer Index, since they share characteristics in fast-growing technology and explosive price behavior in late 1999. Along

1_{Business Insider reported a $50 billion daily trading volume which is close to the trading average of the}

NYSE. Source: http://uk.businessinsider.com/daily-cryptocurrency-volumes-vs-stock-market-volumes-2017-12

2_{Amount of digital wallets of Bitcoin worldwide over time. Source:}

https://blockchain.info/charts/my-wallet-n-users?timespan=all

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5 with empirical and quantitative testing, the price movement of the cryptocurrency market will be analyzed by existing papers on investor sentiment, market regulation, and extrapolation.

As aforementioned, there have been several papers about financial bubble analysis. However, this research complements prior financial bubble literature because it involves a new digital asset market that is globally accessible at any time and has minor regulation at the moment. This study is beneficial for stakeholders and potential investors who are seeking for a market risk analysis of the cryptocurrency market since there are few existing publications about this particular alternative asset group.

The results of the Dickey-Fuller unit root tests in this study show that there is more significant evidence for multiple bubble periods in the cryptocurrency market compared to the NASDAQ Computer index. Furthermore, the time length of the bubble build up and collapse phases are shorter in the cryptocurrency market. For both markets, there is stronger evidence in the models where trend variables are excluded. Besides this, the window extension of the augmented Dickey-Fuller tests results in even more significant proof of price bubble elements. Additional analysis on probable causes for the large amount of price bubble elements, such as extrapolation and disagreement effects, lead to counterintuitive results. Where extrapolation follows an upward trend in prices due to past returns, the cryptocurrency market has significant evidence for negative returns based on yesterday returns. Firstly, it was believed that there should be large extrapolation effects due to low entry barriers for the cryptocurrency market. Despite these findings, there is a low level of goodness of fit meaning that the model could suffer from specification bias because important predictors are missing.

Tests for price disagreement effects, where current trading volume is rising due to past returns, resulted in relatively low significant effects. However, there is large evidence for lower current trading volumes when future returns are rising. This effect could be established by fundamental traders that are expecting near future returns and therefore keep their assets today to sell them in the next couple of days to speculators. The regression could suffer from simultaneous causality since high volumes could cause future returns because of improved asset visibility. Although disagreement effects were hypothesized by short selling restrictions, these effects are hardly noticeable in the cryptocurrency market.

The further outline of this paper consists of a literature review, in which fundamental theories are explained to make adequate assumptions and hypotheses for this research. Afterwards, the methodology is stated with a data section about where the data is obtained from and which parameters are used to perform the different tests. Subsequently, the research

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6 method is elaborated to define several tests to investigate the research question. In the following chapter the empirical results are presented with descriptive statistics and figures. The concluding part of this paper will discuss the outcomes of the tests and afterwards are compared with the results of the NASDAQ Computer Index. Finally, potential research limitations are debated for improved future examinations.

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2. Literature Review

2.1 Cryptocurrency Assets

At the beginning of the eighteenth century commodity-backed currencies were introduced. This is a monetary system in which a central authority issues money that is pegged to an underlying asset, mostly gold. After the collapse of the Bretton Woods system in 1973, currencies were no longer backed but solely traded on trust in the central authority (Bartov et al., 1996).

Satoshi Nakamoto (2008) introduced a decentralized currency system in which financial institutions do not serve a role. The author claimed that the current fiat system suffers from several weaknesses including reversible transactions, excessive transaction costs, and the limited transaction size banks are able to process. Instead of trust in a central authority, he proposed an electronic payment system based on cryptographic proof. A public blockchain ledger serves as a transaction proof controlled by several nodes. These nodes get compensated for processing a validation of a transaction. According to this decentralized distributed ledger framework Bitcoin was created in 2009 and forms the basis for every other cryptocurrency created to date.

The European Central Bank (2012) classifies these assets as unregulated virtual currencies, mostly controlled and issued by developers. These currencies would encourage drug dealing, money laundering and tax evasion due to its high degree of anonymity. Controversially, the International Monetary Fund (2018) claims that the distributed ledger technology could lead to more efficient market infrastructures. However, they also state that cryptocurrencies are still far from achieving the three basic functions of money. Nowadays there is a lack of merchants who accept cryptocurrencies as a medium of exchange, and they are exposed to high volatility and therefore an unreliable measure of payments.

Despite these reluctant views on cryptocurrencies, the U.S. Security and Exchange Commission (2017) published a statement about the regulatory treatment of these digital assets. Chairman Joe Clayton declared that every single cryptocurrency is subject to the security laws since the assets incorporate features that emphasize for potential profits of the firm. However, there is a clear distinction between the economic dynamics of cryptocurrencies. Tokens are assets that provide access to a company’s platform or service and could give holders any form of ownership and voting rights. Due to a fixed token supply the price of these assets is able to appreciate. On the other hand, coins are assets that are mainly used as a medium of exchange.

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8 The valuation of these coins depend heavily on speculation about transaction costs and speed. In this study both asset classes are investigated on price bubble elements.

2.1.1 Initial Coin Offering

Similar to an initial public offering (IPO) organized by an underwriter, cryptocurrency firms raise funds by an initial coin offering (ICO). Adhami et al. (2018) state that the main difference between the latter two is that ICOs are still subjected to fewer regulations in most countries. Traditional companies must issue a prospectus that is approved by the local market authority before investors are able to exchange funds for securities. While ICOs typically only require a disclosure of the token sale terms or a whitepaper before the initiation of the capital raising. The following figure illustrates how cautious governments are with their legislation towards ICOs.

Figure 1

Levels of national regulation on initial coin offerings worldwide4

Despite this negative attitude, investors seem to get more attracted to ICO capital raising. The question is whether this phenomenon is a better and easier way to globally raise funds or a risky method without much legal backing and security. Through the past years

4_{PwC’s global compass for treatment of ICOs worldwide at 6 June 2018. Source:}

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9 blockchain projects have preferred this capital raising method against seeding rounds with venture capitalists.

Figure 2

Cumulative initial public offering capital and venture capital raised quarterly worldwide in U.S. Dollars5

The uncertain legislation about this capital raising method could play a prominent role in the price fluctuation in the entire cryptocurrency markets because of legal systematic risk. A similar pattern was illustrated by Ritter and Welch (2002, p. 1796) during the rise of internet firms at the end of the last century. In the 1980s there was a modest IPO activity of about $8 billion per year, which doubled during the early 1990s. In the last two years of the Dotcom bubble IPO proceedings rose to $65 billion per year. Research of Ljungqvist and Wilhelm (2003) states that internet related companies accounted for 57.4% of the total IPOs in 1999, whereas it was only 2.9% in 1996. This phenomenon could be a financial bubble indicator for both markets.

5_{Ernest & Young research report about initial coin offerings. Source:}

http://www.ey.com/Publication/vwLUAssets/ey-research-initial-coin-offerings-icos/$File/ey-research-initial-coin-offerings-icos.pdf

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2.1.2 Market Regulation

The price instability of these alternative investments can be explained by the lack of a legal framework. The European Central Bank (2012) declared that there is not a clear definition of rights and obligations for the stakeholder parties within the cryptocurrency market. Furthermore, it is hard to determine a trading location since the data on the blockchain is encrypted and untraceable. The latter has consequences for central banks and authorities who are attempting to install a legal framework.

Digital cryptocurrency exchanges do not have to comply with certain trading laws in contrary with regular stock markets. Therefore, the cryptocurrency markets are exposed to market manipulation and inefficiencies such as pump-and-dump schemes. In this case a perpetrator purchases a certain asset and afterwards spreads false information to drift the price upwards. Finally, the agent liquidates the long position to gain a profit (Kyle & Viswanathan, 2008, p. 276). The authors conclude that this affects market efficiency as it becomes more difficult to obtain trading profits with the available information and subsequently market volatility rises. Hence, the lack of a legal framework has a great impact on price movements in the market and possibly supports generating bubble elements.

2.2 Financial Bubble Indicators

Financial bubbles have been part of the global economy since 1720 according to Frehen et al. (2012). There is still uncertainty about the causes of this phenomenon, except for the fact that technological revolutions are frequently involved. Pastor and Veronesi (2005) investigated price movements concerning railroad and internet technologies and find out that bubbles in stock prices are typically present in highly uncertain technology and fast adoption. These characteristics share great similarities with aspects of the cryptocurrency market. The worldwide adoption of this technology is still questionable whereas investors have been using the assets to speculate about the potential of this underlying blockchain technology. This theorem does not suggest that a financial bubble involves irrationality, but the uncertainty of the future integration of the new technology and the expected cash flows of the underlying.

On the contrary, Shiller (2000, p. 12) forms the idea of a speculative bubble where temporary high prices are set by investor’s optimism rather than by fundamental asset valuation. Another interesting theory that is applicable to the cryptocurrency market was researched by Ofek and Richardson (2003). They found evidence in data concerning the

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11 Dotcom bubble that short sale restrictions forced the pessimistic investors out of the market, while optimistic traders kept driving up the stock prices. In the cryptocurrency market there are only a few options to short sell certain assets. This could be seen as a trading restriction causing an upward bias of the asset valuation. In the following paragraph a behavioral aspect of financial bubbles is elaborated that could influence the cryptocurrency market.

2.2.1 Extrapolation

An example of a psychological cause generating bubble elements is extrapolation. Barberis et al. (1998) introduced a model to test under- or overreaction to company or market-related news. Although by assuming that earnings are a random walk, evidence was found that investors could think that an upward price trend continuously holds and therefore extrapolate past performance too far into the future. Greenwood and Shleifer (2013) examined the extrapolation during the Dotcom bubble. They have first tested the investor’s optimism with a Gallup survey that measures investors expectation with respect to the market. Afterwards they compare it with 12 months lagged returns. The results show a high positive correlation between current investor expectations and past stock market returns.

Additionally, Barberis et al. (2016, p. 4) describe their extrapolation model as a three-stage cycle. At first, positive cash flow news drives the stock price up. Afterwards, extrapolators enter the market to purchase the risky assets from fundamental traders. Secondly, fundamental traders exit the market because of overvaluation of the assets. Ultimately, when positive news decreases, the extrapolator’s optimism reduces with a price collapse as a result.

In case of the cryptocurrency market this effect could have an enormous impact considering a larger (positive) news distribution compared to for instance the Dotcom bubble with the adoption of the internet. On top of that, entry barriers are lower for extrapolators since markets are globally accessible and do not require minimum investment fees.

2.2.2 Trading Volume

Apart from investors sentiment, the magnitude of a financial bubble could be measured by looking at daily trading volumes. The environment is based on a short selling restricted disagreement bubble. In this model agents purchase assets at a price that is higher than their own valuation under the assumption that in the future they will find a buyer that is willing to pay even more (Scheinkman & Xiong, 2003). Empirical results of Barberis et al. (2016, p. 5)

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12 show that in the Dotcom bubble daily trading volume is strongly predicted by high past returns. The authors state that overpricing leads to endogenously higher disagreement and therefore daily volumes are rising. Furthermore, they have discovered that as the bubble evolves the fraction of speculative investors grows in respect to fundamental investors.

On the contrary, Gervais et al. (2001) investigated trading volume spikes in relation to the evolution of stock prices. They found that stocks that are experiencing high trading volumes over a day or week tend to have large price increases over the course of a month. This is in line with their hypothesis that higher trading activity creates more visibility for a certain stock and therefore increases the demand and price of the underlying. This is contradictive to the efficient market hypothesis that states that trading volume should not have any predictive power about future stock prices. Due to a high fluctuation in daily trading volume on the cryptocurrency market this could be a benchmark to measure excessive returns. In the following graph, there is evidence for the volatility in daily trading volumes on the cryptocurrency market.

Figure 3

Percent change on daily trading volumes in the top 100 market cap ranked cryptocurrencies

-200% -150% -100% -50% 0% 50% 100% 150% 200% 250% M ay -1 3 Ju l-1 3 S ep -1 3 N o v -1 3 Ja n -1 4 M ar-1 4 M ay -1 4 Ju l-1 4 S ep -1 4 No v -1 4 Ja n -1 5 M ar-1 5 M ay -1 5 Ju l-1 5 S ep -1 5 No v -1 5 Ja n -1 6 M ar-1 6 M ay -1 6 Ju l-1 6 S ep -1 6 No v -1 6 Ja n -1 7 M ar-1 7 M ay -1 7 Ju l-1 7 Sep-1 7 No v -1 7 Ja n -1 8 M ar-1 8

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2.3 Hypothesis

Based on the information given in prior literature there is a large chance to find bubble elements in the cryptocurrency market price over time. Theoretical assumptions regarding technological revolutions and valuation uncertainty perfectly fit the current market conditions. Apart from that, short sell restrictions hold back pessimistic investors from betting against the market, which means prices are set by the greatest optimists and form an upward bias of asset prices.

Besides the asset characteristics, global legislation is still under construction which has a great impact on price fluctuation when new public information becomes available. On top of that, large investment agents are possibly manipulating the prices with pump-and-dump schemes to make profits. The latter fact accelerates price volatility and bubble elements in the asset prices. Cryptocurrency markets are globally accessible without entry barriers for extrapolators to push prices even more.

Compared to the Dotcom bubble, the cryptocurrency market could contain even higher magnitudes of bubble elements in the prices since this is a new asset class with more speculation involved in terms of technological adoption.

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3. Data

In this section there is an elaboration about how the data is retrieved to investigate price bubble elements in the Dotcom bubble and cryptocurrency market. Afterwards, descriptive statistics of both asset markets are given to give further insights into the data that is used in this study.

In order to create a representative view upon price movements in the cryptocurrency market, assets must be tracked that are liquid and are marginally exposed to transaction costs. These factors could cause price premiums in some assets and therefore affect the market index. Therefore, only the currencies on Coinmarketcap6 that are part of the daily top 100 market capitalization are included for every single day. Under the assumption that these assets have the highest daily trading volumes and are widely available on numerous exchanges. To obtain the most information about the price movements of the emerging blockchain technology the widest timeframe possible is taken from the index beginning from the 28th of April 2013 until the 31st of March 2018. Apart from daily closing prices, daily trading volumes in U.S. Dollars are retrieved. Daily market capitalizations per currency are used to filter the database.

Additionally, to put the results of the cryptocurrency market in perspective, a similar emerging market will be tested. The market that will be investigated is the NASDAQ Computer index because it is the most recent internet technological bubble and therefore suitable for comparisons. The adjusted close price data from the index is taken from the first trading day at 31st_{of March 1995 until 31}st_{of December 2004. This timeframe is chosen to identify the} patterns in price movements ex-ante and ex-post the index collapse. The following table represents a summary of statistics of the data in this research.

Table 1

Summary of statistics

Entities Observations Median Mean Std. Dev. Min Max Source

Cryptocurrency Return 523 1798 0.30% 0.28% 4.46% -27.77% 36.71% Coinmarketcap Cryptocurrency Volume Change 523 1555 -1.92% 0.31% 39.63% -154.71% 202.39% Coinmarketcap NASDAQ Computer Return 79 2545 0.02% 0.07% 2.30% -9.48% 13.24% Datastream

4. Methodology

6_{All historical data is fetched from https://coinmarketcap.com/ by using a RStudio library obtained from Jesse}

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15 In this section the various research methods to measure divergent prices are thoroughly discussed. First of all, the theory is elaborated on fundamental asset pricing and price bubble elements. Secondly, possible causes for price bubble elements in the cryptocurrency market are examined by two regressions. The extrapolation effect is examined by regressing past lags of daily returns on current returns. The disagreement effect is tested by regressing forward and past lags of returns on the current trading volumes.

4.1 Identifying Bubbles

Over the past decades there have been developed a lot of models to detect financial bubbles. Although these models are all different, the fundamentals for every approach are built on the present value theory according to Kräussl et al. (2016):

𝑃_𝑡 = 1

1 + 𝑅𝐸𝑡(𝑃𝑡+1+ 𝜓𝑡+1)

This means that the current price of an asset equals the discounted future price with ψt+1 a

dividend yield over time. The theory also states that when t + n is far away in the future ψ and

R are the only dependent variables determining the price of an asset:

𝑃_𝑡∗= 𝐸_𝑡[Σ_𝑖=1𝑛 1

1 + 𝑅(𝜓𝑡+𝑛)]

Here the price of the underlying asset only contains fundamental value elements. Different to stocks, cryptocurrency assets do not always pay dividend depending on the structure of the blockchain. The latter could result in more uncertainty in pricing the underlying assets. If the last equation does not hold and the actual price is higher there is an existing bubble element.

𝐵𝑡 = 𝑃𝑡− 𝑃𝑡∗

Philips et al. (2011) introduced a method to test time series on the presence of exuberance in asset prices with a Dickey-Fuller test. However, the standard Dickey-Fuller regression takes only the first lag into account.

𝑦_𝑡 = 𝛽𝑦_𝑡−1+ 𝑢_𝑡

To test whether yt follows a random walk and therefore is non-stationary Dickey and Fuller

(1979) presented the following hypotheses:

𝐻₀: 𝛽 = 1 𝐻₁: 𝛽 > 1

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16 In real practice prices do not only depend on the price of yesterday and thus a higher order autoregressive dynamic needs to be introduced. The amount number of lags to be included in the regression equation depends on which historical price will not provide any relevant information in predicting the price of today. This is called an augmented Dickey-Fuller regression.

∆𝑦_𝑡 = 𝛽_𝑦_𝑡−1+ ∑ 𝜙_𝑖∆𝑦_𝑡−𝑖 𝑝

𝑖=1

+ 𝑢_𝑡

In the following Dickey-Fuller tests for the cryptocurrency and NASDAQ Computer market the number of lags is determined by the Akaike Information Criterion (Akaike, 1974).

𝐴𝐼𝐶 = 𝑛 ∗ log (𝑅𝑆𝑆

𝑛 ) + 2𝑘

The measure uses the residual sum of squares for every possible model and divides this number by the total amount of observations. Ultimately, the model is corrected by two times the amount of parameters because the goodness of fit always increases by adding an extra factor. The model that results in the lowest AIC value fits best and is used in the research.

Evans (1991) criticized the latter unit root methodology because the author found that explosive behavior often happens in small time periods. Therefore, it is hard to measure such collapsing bubbles because over time the price movement seems non-stationary.

Phillips et al. (2011) attempt to develop a more accurate measure and use a recursive supremum augmented Dickey-Fuller test, in which the test statistic is calculated for every forward recursive sample. In the first sample it contains only the first observation until the p lag observation. The sample extends by one observation at the time and recalculates a new test statistic. In addition to this, a rolling window test was realized to test every window in the timeframe. A few years later Phillips et al. (2015) presented a generalized supremum rolling window test where the largest test statistics in a double recursion are shown over time for all feasible ranges.

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Figure 4

Visual construction of the different Dickey-Fuller tests7

All the Dickey-Fuller regressions stated above are used to detect explosive bubble element on the cryptocurrency and NASDAQ Computer market. Subsequently, the results are analyzed and discussed on which model fits the time series best.

4.2 Bubble Theory Investigation

Besides the investigation of explosive price behavior, extrapolation within the cryptocurrency market will be reviewed. Previously mentioned theories suggest that positive returns will cause a continuous upward trend in price for the following days. These investors are overreacting a positive news impact on the underlying asset and diverge from the fundamental value theory. To observe this possible outcome, a panel data lagged auto regression is constructed and validated by a Student’s t-test to check if this effect is significant. The maximum number of lags in the regression is restricted to 7 days because it is believed that the extrapolation effect holds for only a week. The regression model looks as follows:

𝑅𝑖,𝑡 = 𝛽0+ 𝛽1+ 𝑅𝑖,𝑡−1+ 𝑅𝑖,𝑡−2+ 𝑅𝑖,𝑡−3+ 𝑅𝑖,𝑡−4+ 𝑅𝑖,𝑡−5+ 𝑅𝑖,𝑡−6+ 𝑅𝑖,𝑡−7+ 𝑢𝑖

7_{Property of the images belongs to the Bank of Isreal. Source:}

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18 Apart from the formulation above, there will be additional regressions including time fixed effects and cryptocurrency entity effects. If there is a strong and significant lag effect on returns, there is evidence found for extrapolation.

Finally, there will be a test for past or future returns causing higher daily trading volumes. As stated in the literature review, there is both evidence for an increase in trading volume before and after a return increase. Therefore, a panel data regression is set up to check for the effect of future and past returns on the current daily trading volume.

ln (𝑉𝑜𝑙𝑢𝑚𝑒_𝑖,𝑡) = 𝛽₀+ 𝑅_𝑖,𝑡+1+ 𝑅_𝑖,𝑡+2+ 𝑅_𝑖,𝑡+3+ 𝑅_{𝑖,𝑡−1}+ 𝑅_{𝑖,𝑡−2}+ 𝑅_{𝑖,𝑡−3}+ 𝑢_𝑖

Significant results for the forward lags would be in line with the study of Gervais et al. (2001) that suggests that due to visibility of assets, future returns will be higher. On the other hand, when the past lags are significant this would confirm the findings by Barberis et al. (2016). Additionally, the latter regression is extended by time fixed effects and cryptocurrency entity effects.

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5. Empirical Results

5.1 Explosive Price Behavior

In this subsection prior discussed Dickey-Fuller test results are specified with market capitalization regarding the cryptocurrency and NASDAQ Computer market. Initially, all the outcomes for both markets are discussed and related to theories that are stated in the literature review. Afterwards, these are followed by a thorough comparison analysis between the two price movements. The test windows of the advanced Dickey-Fuller tests for both markets are set to 30 trading days to check for monthly effects. A larger window would be prone to a generalization of the model because bubbles are happening in small time frames and thus the evidence would be less significant.

In the table below results are listed of all Dickey-Fuller tests specified in the methodology. The critical values are based on Monte Carlo simulations derived in EViews statistical software package. Maximum t-statistic values are shown in the table.

Table 2

Right-tailed augmented Dickey-Fuller test results

Cryptocurrency Market NASDAQ Internet Index

Dependent variable: Student's t-statistic Student's t-statistic

Market Capitalization (95% critical value) (95% critical value)

Standard ADF with constant -1.074 -1.863

(-0.032) (-0.044)

Standard ADF with constant and trend -1.801 -1.768

(-0.928) (-0.656)

Rolling ADF with constant 6.552*** 2.539

(-0.012) (-0.023)

Rolling ADF with constant and trend 2.856*** 1.453

(-0.855) (-0.023)

Supremum ADF with constant 19.400*** 3.264

(1.647) (1.802)

Supremum ADF with constant and trend 18.520*** 1.381

(0.759) (1.802)

GSADF with constant 20.934*** 3.265

(2.894) (3.760)

GSADF with constant and trend 20.265*** 1.470

(2.894) (3.760)

Window size 30 30

Total observations 1799 2546

Timeframe 28/04/2013 - 31/03/2018 31/03/1995 - 31/12/2004 * p<0.05, ** p<0.01, *** p<0.001

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20 According to the table, there is significant evidence for price bubble elements over time in the cryptocurrency market. Apart from the standard augmented Dickey-Fuller test, every result confirms the existence of overpricing at least once in the time frame. On the contrary, the NASDAQ Internet Index does not show substantial proof for explosive price behavior. The bubble effect could be lower due to a mismatch in window sizing. If price movements in the NASDAQ Internet Index move more quickly up and down, a single time frame does not capture this fluctuation because the divergence is already corrected. Improvements could be made by testing for different time windows to capture the most volatile time fractions. The most extended augmented Dickey-Fuller model will capture every time window when a window size of 1 trading day is chosen. However, due to computing limitations this was not possible to measure.

By looking at the difference in the test with or without trending, there consecutively is larger evidence for the models without a trend element. Reason for this could be that a part of the return is explained by an up moving price trend instead of only past returns. Therefore, significance falls and results are less significant. Besides this, results are tending to be more significant if the model expands. The enlarged models are checking more time frames and thus have a larger probability of finding extreme values in price behavior.

5.1.1 Timestamping

The prior table only gave perspective on the most extreme values in the entire sample period per executed test. In this subsection there is an overview of the experiment to analyze the time structure of explosive price behavior. For the generalized supremum version of the Dickey-Fuller test a time series graph is drawn of both markets. A comparison between the time series is made to discuss similarities in the markets.

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Figure 5

Generalized Supremum ADF time series

When comparing the market capitalizations of both markets it stands out that the cryptocurrency market experienced a more rapid increase compared to the NASDAQ Computer Index. Only in 2017 the market value rose to more than four times since the start of the year. The NASDAQ Internet Index had a smoother price momentum spread out over approximately four years. Exactly the same trend is applicable to the collapse of the price peak, which seems that there is more uncertainty and overreaction in the cryptocurrency market.

The cryptocurrency market was subject to three severe price eruptions since its existence. Even though the market cap rose the most amount at the end of 2017, the largest price bubble elements were found 6 months earlier. A similar pattern with lower magnitude is visible in the NASDAQ Computer market in the preface of the bubble collapse. A higher level of uncertainty regarding future cash flows and regulation could explain more significant evidence of price bubble elements in the cryptocurrency market. Besides that, prior discussed literature foresees more volatile pricing in times of faster adoption of new technology, which in this case is blockchain technology.

5.2 Extrapolation Regression

Other sources for price bubble elements in the cryptocurrency market could be due to extrapolation combined with short sale constraints. In the table below the effect of past returns

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22 on the current return are measured. In the case of noticeable extrapolation effects, past returns would influence the return of today because expectations of speculators are rising. Short sale restrictions do not give fundamental traders the opportunity to bet against the market and therefore the effect is presumably stronger.

Table 3

Regression for testing extrapolation on the cryptocurrency market

Simple Regression Coin Fixed Effects Time Fixed Effects

Dependent variable: Coeff. Coeff. Coeff.

Return (Std. Err) (Std. Err) (Std. Err)

Return t-1 -0.0085** -0.0169*** -0.0107** (-0.0028) (-0.0039) (-0.0038) Return t-2 0.0045 -0.0042 0.0007 (-0.0037) (-0.0039) (-0.0038) Return t-3 0.0021 -0.0063 0.0000 (-0.0022) (-0.004) (-0.0038) Return t-4 0.0189 0.0112 0.0185*** (-0.0125) (-0.0133) (-0.0039) Return t-5 0.0004** -0.0001 0.0000 (-0.0001) (-0.0004) (-0.0009) Return t-6 0.0003 -0.0002 0.0002 (-0.0005) (-0.0005) (-0.0009) Return t-7 0.0000 -0.0004 0.0000 (-0.0001) (-0.0004) (-0.0009) Constant 0.0278*** 0.0287*** 0.0281*** (-0.0033) (-0.0002) (-0.0033)

Coin Fixed Effects No Yes No

Time Fixed Effects No No Yes

Total observations 155,023 155,023 155,023

Adj. R-squared 0.0002 0.0002 0.0002

* p<0.05, ** p<0.01, *** p<0.001

The table shows that there is no significant evidence for extrapolation from past returns. The only returns that seem to influence current returns are from yesterday. However, the latter indicates a negative effect, which is an opposite extrapolation effect. Taking the R-squared figures into account, the regression does not fit the model very well even with fixed effects included. The result is counter-intuitive compared to the stated hypothesis that extrapolators have low entry barriers to enter the market and have a great impact on the price movement.

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5.3 Trading Volume Regression

In this subsection, return effects on volume are measured to test for price disagreement in the cryptocurrency market. According to previous literature, past and future returns should have significant predicting power for the current trading volumes.

Table 4

Regression for testing disagreement effect on the cryptocurrency market

Simple Regression Coin Fixed Effects Time Fixed Effects

Dependent variable: Coeff. Coeff. Coeff.

log(Volume) (Std. Err) (Std. Err) (Std. Err)

Return t+1 -0.1056*** -0.0500*** -0.1150*** (-0.016) (-0.0088) (-0.0104) Return t+2 -0.1148*** -0.0591*** -0.1191*** (-0.0158) (-0.0087) (-0.0103) Return t+3 -0.0467*** -0.0203*** -0.0392*** (-0.0086) (-0.0047) (-0.0056) Return t-1 0.0044 0.0043** -0.0014 (-0.003) (-0.0016) (-0.0019) Return t-2 0.004 0.0039* -0.0018 (-0.003) (-0.0016) (-0.0019) Return t-3 0.0035 0.0035* -0.0022 (-0.0029) (-0.0016) (-0.0019) Constant 9.8539*** 9.8509*** 9.8545*** (-0.0105) (-0.0057) (-0.0068)

Coin Fixed Effects No Yes No

Time Fixed Effects No No Yes

Total observations 148,985 148,985 148,985

Adj. R-squared 0.001 0.001 0.002

* p<0.05, ** p<0.01, *** p<0.001

The results in all the regressions indicate that future returns have a significant negative impact on current trading volume. Although past returns are not significant in every regression, they seem to have a positive impact on the current trading volume. This is in line with the stated disagreement hypothesis, where fundamental traders have a stronger incentive to sell the assets and therefore volume rises.

Additionally, forward lagged returns have a negative impact on current trading volume which could mean that fundamental traders tend to hold assets when they expect returns in the near future. The regression might be prone to simultaneous causality since high volumes could cause future returns due to the visibility effect. Moreover, the regression seems to misfit the model taking the adjusted R-squared values into account.

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6. Conclusion

In this study the objective was to research whether there are perceptible bubble elements in the cryptocurrency market over time. In extension to this, several bubble theories were investigated to find out possible causes for this new asset market. Additionally, this research benchmarks the explosive price movements to the Dotcom bubble to put the results in perspective.

First of all, there is great evidence for explosive bubble behavior over time in the cryptocurrency market. The largest price anomalies according to the augmented Dickey-Fuller tests are most noticeable at the end of 2013 and through 2017. When comparing these results with the NASDAQ Internet Index, there is much more evidence in the cryptocurrency market in certain timeframes. Another discrepancy between these markets is the build-up to the collapse. The cryptocurrency market bubbles occurred in short time frames whereas the NASDAQ Internet market bubble was loading for two years before the prices fell. Reasons for this could be due to different types of uncertainty regarding market regulation, exchange security, and initial coin offerings bans. Furthermore, fast global adoption in combination with widespread public information channels has an impact on the duration of the bubble. The outcome corresponds with the stated hypothesis based on prior literature about bubble characteristics.

Further analysis about extrapolation effects showed that there is a minor significant influence of past returns on the current returns on the cryptocurrency market, except for the returns of yesterday. However, this is an opposite extrapolation effect because these returns have a negative impact on the current returns. This test could be improved by searching for intraday extrapolation by regressing intraday trading returns. It is possible that over time these effects happen in a shorter time span than before due to the faster access to trading information. Due to short selling restrictions in the cryptocurrency market it was expected that there is a measurable disagreement effect. In this theory fundamental traders will have greater incentive to sell assets when prices exceed their fundamental asset valuation. There is some information that confirms this concept for past returns. The largest evidence is found on decreasing current volumes due to future returns. A possible explanation could be that fundamental traders hold assets in expectation that in the near future asset prices will rise and have the possibility to sell it to extrapolators.

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25 Following the determination of clear explosive price behavior on the cryptocurrency market, some model extensions could be made to construct even more insightful results. An augmented Dickey-Fuller test with a distinction between the two cryptocurrency types, coin and token, could have other price movements and volatility due to different dividend and valuation dynamics. Testing on a smaller window size could identify new explosive price effects within a smaller timeframe. Additionally, the extrapolation and disagreement effects could be larger within bubble periods. By using the timestamps of the augmented Dickey-Fuller tests, regressions could be run more specifically in these time periods to check for the effects.

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References

Adhami, S., Giudici, G., Martinazzi, S. (2018). Why Do Business Go Crypto? An Empirical Analysis of Initial Coin Offerings. Journal of Economics and Business

Akaike, H. (1974). A New Look at the Statistical Model Identification. IEEE Transactions on

Automatic Control, 19(6), pp. 716–723.

Barberis, N., Greenwood, R., Jin, L., Shleifer, A. (2016). Extrapolation and Bubbles. (NBER Working Paper No. 21944). Retrieved from National Bureau of Economic Research website: http://www.nber.org/papers/w21944

Barberis, N., Shleifer, A., Vishny, R. (1998). A model of investor sentiment. Journal of

Financial Economics, 49, pp. 307-343

Bartov, E., Bodnar, G. M., Kaul, A. (1996). Exchange rate variability and the riskiness of U.S. multinational firms: Evidence from the breakdown of the Bretton Woods system.

Journal of Financial Economics, 42(1), pp. 105-132

Dickey, D. A., Fuller, W. A. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, 74(366), pp. 427-431

Evans, G. W. (1991). Pitfalls in Testing for Explosive Bubbles in Asset Prices. The American

Economic Review, 81(4), pp. 922-930

European Central Bank (2012). Virtual Currency Schemes. Retrieved from: https://www.ecb.europa.eu/pub/pdf/other/virtualcurrencyschemes201210en.pdf Frehen, R., Goetzmann, W. N., Rouwenhorst, K. G. (2013). New Evidence on the First

Financial Bubble. Journal of Financial Economics, 108(3), pp. 585-607

Friedman, M. (1951). Commodity-Reserve Currency. Journal of Political Economy, 59(3), pp. 203-232

Gervais, S., Kaniel, R., Mingelgrin, D. H. (2001). The High-Volume Return Premium. Journal

of Finance, 56(3), pp. 877-919

Greenwood, R., Shleifer, A. (2013). Expectations of Returns and Expected Returns. (NBER Working Paper No. 18686). Retrieved from National Bureau of Economic Research website: http://www.nber.org/papers/w18686

Hong, H., Stein, J. C. (1999). A Unified Theory of Underreaction, Momentum Trading, and Overreacting in Asset Markets. The Journal of Finance, 54(6), pp. 2143-2184

(27)

27 Hyung, J. L., Phillips, P. C. B. (2016). Asset pricing with financial bubble risk. Journal of

Empirical Finance, 36(B), pp. 590-622

International Monetary Fund. (2018). Global Financial Stability Report. Retrieved from: https://www.imf.org/en/Publications/GFSR/Issues/2018/04/02/Global-Financial-Stability-Report-April-2018

Kräussl, R., Lehnert, T., Martelin, N. (2016). Is there a bubble in the art market? Journal of

Empirical Finance, 35, pp. 99-109

Kyle, A. S., Viswanathan, S. (2008). How to Define Illegal Price Manipulation. American

Economic Review, 98(2), pp. 274-279

Ljungqvist, A., Wilhelm Jr., W. J. (2003). IPO Pricing in the Dot-com Bubble. Journal of

Finance, 58(2), pp. 723-752

Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System. Retrieved from: https://bitcoin.org/bitcoin.pdf

Ofek, E., Richardson, M. (2003). DotCom Mania: The Rise and Fall of Internet Stock Prices.

Journal of Finance, 58(3), pp. 1113-1137

Pastor, L., Veronesi, P. (2005). Technological Revolutions and Stock Prices. (NBER Working Paper No. 11876). Retrieved from National Bureau of Economic Research website: http://www.nber.org/papers/w11876

Phillips, P. C. B., Wu, Y., Yu, J. (2011). Explosive Behavior in the 1990s NASDAQ: When Did Exuberance Escalate Asset Values? International Economic Review, 52(1), pp. 200-226

Phillips, P. C. B., Shi, S., Yu, J. (2015). Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P500. International Economic Review, 56(4), pp. 1043-1077

Ritter, J. R., Welch, I. (2002). A Review of IPO Activity, Pricing, and Allocations. Journal of

Finance, 57(4), pp. 1795-1828

Scheinkman, J., Xiong, W. (2003). Overconfidence and Speculative Bubbles. Journal of

Political Economy, 111(6), pp. 1183-1219.

Shiller, R. J. (2000). Irrational Exuberance. Princeton, New Jersey: Princeton University Press. U.S. Securities and Exchange Commission (2017). Statement on Cryptocurrencies and Initial Coin Offerings. Retrieved from website: https://www.sec.gov/news/public-statement/statement-clayton-2017-12-11

Bubble analysis on the cryptocurrency market