Bitcoin
Research on the possible bubble in 2011.
Abstract
Motivated by the 2011 Bitcoin price trajectory, this thesis investigates whether rapidly growing investment activities have caused a new bubble. Moreover, finding possible explanations for the rapid growth in volume and increasing popularity of the Bitcoin. In order to conclude if the Bitcoin did experience a bubble in 2011, the Chow-breakpoint test is applied for different periods to look for abnormal price behaviour compared to the S&P 500. In addition, P/E ratios and standard deviations are calculated which could indicate a possible bubble.
Name: Olivier Dekker Student-number: 6122795
Programme: Economics & Business Track: Finance & Organization Supervisor: Natalya Martynova Date: February 22 2014
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Table of Contents
1. Introduction...P.3 2. Literature Review………...P.5 2.1 Macro Economic and Psychological Factors that affect the Bitcoin...P.5 2.2 Bubble Theory Literature...P.6 2.3 Recent Empiric Research on Bubbles...P.8 3. Research Method...P.11
3.1 Event Study...P.11 3.2 Data...P.13 3.3 Hypotheses and Empiric Research Method...P.14 4. Empiric Results...P.16 4.1 Identifying the Bitcoin Bubble...P.16 4.2 Identifying the Signals...P.22 4.3 Analysing the Results...P.25 5. Conclusion...P.26 5.1 Conclusion Research...P.26 5.2 Discussion...P.27 5.3 Recommendations...P.28 6. Bibliography...P.29
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1. Introduction
Kindleberger & Aliber (2005) describe a bubble as a sharp rise in price of an asset or a range of assets in a continuous process, with the initial rise generating expectations of further rises and attracting new buyers, generally speculators, interested in profits from trading in the asset rather than its use as earning capacity. Komáromi (2006) defines rational and speculative bubbles. A rational bubble occurs when a share price is higher than the fundamental value of the underlying asset, but rational expectations of investors may justify such a high price. It is also possible that the gap between the share price and the fundamental value grows to big, which means that the future cash flows do not justify the current price. This is called a speculative bubble. Technological revolutions tend to be accompanied by bubbles in the stock prices of innovative firms who operate in young markets. New technologies, like the Bitcoin, are characterized by high uncertainty about their future sustainability and productivity. Pastor & Veronesi (2009) show that over time, this uncertainty can cause bubbles. If the agent learns that the technology is sustainable and can possibly generate profits, he adopts it on a large scale creating a technological revolution. An example of such a bubble created by a technological revolution is the dotcom-bubble that experienced a burst in March 2000.
Grinberg (2011) describes the Bitcoin as “a digital, decentralized, partially anonymous currency, not backed by any government or other legal entity, and not redeemable for gold or other commodity”. Or, in the words of the founder(s) Nakamoto (2008), the Bitcoin is a purely peer-to-peer version of electronic cash that allows payments to be sent directly from one party to another without going trough a financial institution. The Bitcoin trading volume is growing for a number of reasons. First, Bitcoins are highly liquid. That means that they have low transaction costs and can be used to send payments quickly across the Internet. Second, Bitcoins are used anonymously which is new compared to existing ways of payment and possibly contributes to the growth.
Investigation on the Bitcoin price trajectory is important because characteristics point out that it has potential to become the next major way of payment. The Bitcoincharts website (2014) shows that the total market capitalization grew over 7 billion dollars (7.281.139.964 USD) in 3.5 years. However, the Bitcoin has a volatile price and is conceived as risky. Research on a possible bubble in 2011
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not only makes a contribution to the price information of the Bitcoin but also in field of risk assessment of new digital currencies.
Since 2010, the price of a Bitcoin raised from a level of $0.05 in July 2010 to $31.86 in June 2011, before falling substantially to $2.28 in October 2011. This means that the price rose by 63.620% from July 2010 till June 2011. Moreover, the price declined with 94.84% in a period of June 2011 till October 2011. In Shiller (2001) a raising price trajectory could increase investor enthusiasm, which can increase demand and further increase the price; creating a bubble. Stocks that did well in the past continue to do well in the future. This observation is called momentum. The graph below shows that the possible bubble in June 2011, also shows a peak in momentum in the same time period.
Momentum indicator compared to the volume and price graph for the year 2011 on MT. Gox USD exchange market. Source: Bitcoincharts website (2014)
So far, the possibility that the Bitcoin currency may exhibit a bubble in 2011 has attracted little attention in the academic literature. No final conclusion has been reached due to the novelty of the subject. This thesis aims to make a contribution to economic science by showing evidence for a bubble in 2011 due to applying econometric and statistical methods. Moreover, hopefully this thesis is able to offer insights in the macro economic and psychological factors that contributed to the explosive growth in the volume and price of the Bitcoin.
This research is organized as follows. In section 2, the relevant literature about bubbles is discussed. Section 3 explains the methods that will be used to identify the bubble. In section 4 the model is being presented and explained in more detail. Section 5 will conclude and offer some suggestions for possible further research.
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2. Literature Review
2.1 Macro Economic and Psychological Factors that affect the Bitcoin
The recent world financial crisis is characterized by crashing real estate and stock market downfalls as well ass bank failures. At the same time the Federal Reserve (2013) and European Central Bank (2014) websites show that interest rates on bank deposits in Europe and the US were kept on a very low level to stimulate investments. At the beginning of the financial crisis in 2008, the fixed interest rate set by the European Central Bank was 3.75%. When the crisis continued the fixed interest rate set by the European Central Bank became lower. To illustrate, on November 13th 2013, the fixed interest rate was 0.25%. Related to this, central banks have carried out an expansive monetary policy to solve the financial problems of banks and governments, but simultaneously increasing inflation expectations.
In addition to the low returns people get on their bank deposits, some banks were declared bankrupt or nationalised during the crisis. The most notorious example is Lehman Brothers who declared bankruptcy on September 13th 2008 and gave the starting sing for the financial crisis and distrust among banks. Moreover, the financial crisis also had psychological consequences that affected the consumer’s trust in banks. To illustrate, Wood & Berg (2011) investigated U.S. consumer trust in banks in October 2010 and showed that consumer trust fell to an all time low of 18%. That is lower than its level at the height of the global financial collapse in 2008.
With stock markets plummeting, interest rates on save deposits extremely low and the fear that banks will go bankrupt, it is assumable that investors turn to other investment opportunities. In these circumstances investors are seeking to add uncorrelated assets to their investment portfolio, which may have lead them to the Bitcoin. Grinberg (2011) shows that the Bitcoin is not directly influenced by any central bank or government regulations. This makes the Bitcoin an investment option that is not directly influenced by interest rates and inflation. But the lack of information and influence by a government could also be a problem. Caginalp et al. (2001) show that bubbles often arise in the case of poor availability of information. In Nakamoto (2008) the “mining” of the Bitcoin is described, but is hard to understand and accessible information is scarce. Moreover, it’s difficult to determine the fundamental value of the Bitcoin. The lack of information causes investors to trust on their intuitive judgements and they appear to be important in determining the
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direction of the market. There are numerous factors, like the media who can influence the human judgement and therefore the momentum. However, this thesis focuses on econometric and statistical methods to research whether the Bitcoin did experience bubble in 2011. So no further attention is given to the possible psychological causes of a speculative bubble. Meanwhile, it should be noticed that the Bitcoin made its advance when the trust in banks was at an all time low in 2010.
2.2 Bubble Theory Literature
Before assessing existing literature, it is important to start at the beginning and know how the economic phenomenon got its name. According to Faber (2011) bubbles have been around since the existence of stocks in the 17th century. The term “bubble” originates from the South Sea Bubble of 1711-1720. In that time trading in South Sea Company stock increased and a growing number of joint stock companies were launched on the London Exchange. The new stock issuances were called “bubbles” at the time. The British parliament passed the “bubble act” on June 9, 1720, which prohibited the existence of any joint-stock company not authorized by a royal charter. The South Sea Company had been granted a royal charter and it attributed to the bubble by making South Sea Company shares more valuable. In July 1720, insiders knew that the company’s earnings would not be as high as the many people thought and the management began quietly selling the stock at the height of the market. South Sea Shares began a rapid downfall. Many companies who invested in the South sea Company with borrowed money where effected. As prices fell, investors where forced to sell even more shares, computing one of the first bubbles.
Since south sea bubble no theories have been produced that are still relevant up on this time, until the 1960’s. At that time scientists doubted whether market forces could ensure that bubbles did arise or not. An important question was if bubbles could exist on the long term or if bubbles must eventually be broken. Focussing on models where individuals have rational expectations and no uncertainty; Hahn (1966), Samuelson (1967) and Shell & Stiglitz (1967) argued that in the absence of a complete set of futures markets, extending infinitely into the future, no market force could ensure that the economy would not set off on a path with a bubble. The idea behind the research in the 1960’s is that if the agent lives forever, a possible investment strategy is to buy and hold forever. This produces a gain equal to the expected discounted value off all future cashflows, the fundamental value. If the
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market price is less than the fundamental value, the agent can increase his gain by buying and holding forever. But in Flood & Hodrick (1990) the increase in demand would increase the price, which eliminates the bubble. In other words if the asset price increased slower than the discount factor, eventually the terminal price became unimportant as viewed from today. Under such presumptions, the value of the asset had to be just equal to the discounted value of the generated returns, and no bubbles could exist.
The debate on he existence of bubbles took a turn in the 1970’s. Economic game theory was applied and concepts as complete information and Bayesian games were introduced. Even if or when it can be shown that bubbles will eventually burst, investors are aware of the bubbles due to complete information that will cause it to burst. In Stiglitz (1990) if the bubble is expected to burst in 1970, the bubble will burst in 1969 because no one wants to pay a high price in the year 1970. However, Shleifer & Summers (1986) argue that as long as there is uncertainty about whether the bubble exist and when the bubble is going to burst, next to the assumption that investors are short lived and risk-averse, markets will not be fully arbitraged and bubbles should not be completely eliminated.
Trying to empirically show that a bubble exist Blanchard & Watson (1982) test for a gold bubble, using fundamental value in addition to conducting runs and tail tests. They assume that crashes will produce large outliers so that the distribution of the observations will have fat tails. The conclusion is that empirical evidence shows that the gold price between 1975 and 1981 violated the variance bounds. In addition, De Grauwe & Grimaldi (2004) define a more precise definition of the bubble, stating a deviation of the exchange rate from its fundamental value by more than three times the standard deviation of the fundamental variable for a significant interval of time. The interval is set equal to 20 periods. However, by only looking at the variance and tails does not allow for significant detection of bubbles.
Aware of this critique Diba & Grossman (1984) investigate fluctuations in the gold price between 1975 and 1983. A model of the relative price of gold is used. The theoretical model consists of a single equation that specifies the relative price of gold that satisfies a condition of equality between the value of existing stock of gold and the portfolio demand for gold. The evidence is consistent with the conclusion that the relative price of gold corresponds to market fundamentals and that the price movements are not caused by rational bubbles.
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Obstfeld (1996) uses game theory to model currency crises with self-fulfilling features. The game consists of two private holders that have domestic currency who can hold or sell. In addition, the government can fix its currency exchange rate depending on its reserves. Their conclusion is that speculative attacks differ among themselves by showing pre-crises changes in variables such as fiscal differences and unemployment rates. Moreover, Abreu & Brunnermeier (2003) show that selling pressure only burst the bubble when a sufficient number of arbitrageurs have sold out. This means that a permanent shift in price levels requires a coordinated attack. Since crises are often due to a bubble burst, like the subprime mortgage bubble in 2007, in combination with currency policy this should be interesting literature. However, this model cannot be applied on the Bitcoin, because the Bitcoin is not affected by government reserve policies. Moreover, the Bitcoin is anonymously used which makes a coordinated attack impossible.
The literature shows that there are different opinions about the existence and formation of bubbles. In this thesis it is assumed that bubbles do exist. Komáromi (2006) explains what conditions are needed to define a stock market boom as bubble. First there is an initial rise in price and expectations that the price will rise even more. The second condition states that high expectations lead to more demand for shares this leads to a growth in volume. The third condition yields that investors do not buy to receive dividends, but to speculate on a rise in the price. At some point the investor behaviour changes and they start leaving the market. The fourth condition yields a sudden or gradually price decline, not triggered by fundamental news but due to the change of investor behaviour. The fifth and last condition is that the collapsing prices have macro-economic effects, positive or negative. But since the Bitcoin is relatively new and impact on the economy is unknown, this condition is relaxed. In the conclusion these conditions are evaluated.
2.3 Recent Empiric Research on Bubbles
Since research that used game theory to prove bubbles in the past is hard to apply on the Bitcoin, the focus is on econometric and statistical testing for economic bubbles using stocks as benchmark. But before continuing on these methods, there needs to be a clear description of what the Bitcoin is in terms of investment, regulation and why the Bitcoin is comparable to stocks.
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When the Bitcoin was launched in 2010, Nakamoto (2008) described it as a means of currency or commodity. However, according to an article in Up & Right (2013) the Bitcoin is mainly seen by investors as an investment option to generate profits. Grinbergen (2011) proved that the Bitcoin should be seen as a security in the U.S. because it falls within the broad description of an “investment contract” which is described in the Securities Act of 1933. In Hazen (2009) the Supreme Court of the U.S. has interpreted something to be an “investment contract”, and so a “security” if it is a contract transaction or scheme whereby a person first, invest money, second, in a common enterprise, third, is led to expect profits and fourth, solely from the efforts of the promoter or a third party. So a security is a financial instrument that represents some type of financial value, like a stock. Given this description, the Bitcoin shows signs of a stock. Moreover, Coindesk (2014) and FinExtra (2013) published articles that show Germany, Sweden and Norway already declared the Bitcoin as asset or security. Given these facts, this thesis will assume the Bitcoin is to be compared to a stock. The Mt. Gox USD exchange market acts as field of research and the focus is on comparable bubble research on US stock markets. By looking at the Bitcoin as a security, several empiric methods that are applied in stock-bubble-research can be applied on the Bitcoin.
Corsi & Sornette (2011) provide a reduced form model for the Miniskian dynamics of liquidity and asset prices in terms of so called financial accelerator mechanism. In other words, credit creation is driven by the market value of the financial assets that are used as collateral in the bank loans. The financial accelerator dynamics are implemented in a macro economic model that shows that the cycle of booms and bursts of stocks using the S&P 500 besides liquidity determines economic recessions in the form of increasing default rates and decreasing GDP.
Bakshi & Wu (2006) investigate whether the rise and fall of the Nasdaq and the bursting of the dot-com bubble can be linked to changes in the return risk and whether investors are driven by irrational behaviour. Using an empirical model, they conclude that volatility increased with the Nasdaq index and that volatility stayed high even after the bubble burst.
Due to recent progress in the characterization of asset bubbles, new methods were introduced based on the assets price volatility. Jarrow et al. (2011) show that bubbles characterized in frictionless, competitive and continuously trading economies, using an arbitrage free pricing technology. According to Jarrow et al.
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(2011) there are three types of asset price bubbles possible. Two of these types exist only in infinite horizon economies. The third type exists in finite horizon settings, which is most relevant to actual market experiences. The asset price model consists of a standard stochastic differential equation driven by a Brownian motion. If the asset price volatility is large enough, then a bubble exists. The methodology is illustrated using data from the dotcom-bubble-period during 1998-2001. The results show that in one case a bubble is confirmed and the other case lacks a confirmed bubble. The final conclusion is that the test is inconclusive, so more research has to be done. It does seem increasingly important to use volatility in identifying bubbles.
David & Veronesi (2008) have developed a methodology for understanding the fluctuations and predictability of volatilities and co-variances of asset returns. They use the GARCH model, which shows that volatilities of asset returns are highly persistent. This thesis will try to show there was a Bitcoin bubble in 2011, so the empirical research is done ex-post. However, research like David & Veronesi made a contribution to the field of showing a bubble ex-ante.
Pastor & Veronesi (2008) have developed a model that focuses on how technological revolutions affect stock prices. A general equilibrium model shows which stock prices of innovative firms exhibit bubbles during technological revolutions. They find empirical support by looking at the market to book ratio and the market beta. Pastor & Veronsesi (2008) predicted that market beta should increase sharply before the end of the technological revolution. The research proved that there was a bubble in 1830-1861 (railroad-bubble) and in 1992-2005 (dotcom-bubble). However, the Pastor and Veronesi (2008) model would need modifications if it were to be used on the Bitcoin. At this moment the Bitcoin is not widely adopted and we cannot speak of a technological revolution (yet).
Continuing on the correlation between volatility and volume to proof bubbles, Pastor & Veronesi (2009) explain why bubbles often accompany technological revolutions. Pastor & Veronesi (2006) extend their 2003 model and calibrate it to match the observed stock valuations at the peak of the Nasdaq bubble. In general the authors argue that the level and volatility of stock prices are positively linked tough firm-specific uncertainty about g.
A number of researches have been conducted on other bubbles. Motivated by the gold price boom during the crisis, Bialkowski et al. (2013) investigates whether gold could function as a safe haven for investors. The research of Bialkowski et al.
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(2013) is comparable to this thesis in a way that it empirically investigates whether rapidly growing investment have caused a new asset bubble. However, empirically advanced methods are used, which will not be used in this thesis. A Markov regime-switching Augmented Dicky Fuller (ADF) test is applied, which tests for detecting explosive behaviour and potential bubbles.
Most of the literature defines a bubble as the difference between the market value and the fundamental value of a security, for example Blanchard & Watson (1982). The fundamental value is hard to calculate because it is based on a set of future cash flows. A more workable tool to identify bubbles is the P/E ratio. The yearly average P/E ratio based on a long period of time is 14% according to Shen (2000). Moreover, Ou & Penman (1989) show that current P/E is mean-reverting and has a small negative correlation to later yield. So the shares with high P/E ratios now, will probably have low or negative yield later on. Looking at P/E ratio’s ex-post, these could indicate a bubble.
With regard to the Bitcoin price boom of 2011, not one study is done to provide empirical evidence for a bubble. However, journalists like Graf (2013) publish articles that discuss the price movements of the Bitcoin and speculate about possible bubbles. To hopefully make an end off some of these discussions about whether the Bitcoin did, or did not experience a bubble in 2011, this thesis will use several empirical methods that are described in the following part.
3. Research Method
3.1 Event Study
In De Jong (2007) an event study is conducted and the research steps are described. In this thesis an event study will also be conducted; the event is focussed on the possible Bitcoin bubble in 2011. The first step of an event study is to identify the event of interest and the timing of the event. To calculate whether the Bitcoin price trajectory, during the event, shows significant differences compared to the period before and after the event, we have to determine the estimation period (T1, T2) and the post-event period (t1, t2). The post-event itself is indicated by t = 0. There is some date uncertainty about when the bubble starts and on which date it ends. There is no clear rule in the literature which formulates a general guideline to determine the exact bubble begin and end date.
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(2010-07-17) (2011-01-17) (2011-04-01) (2011-01-11) (2014-01-17)
The starting date of the bubble is approximately April 1st 2011 because a sharp increase in price is detected. Looking at the monthly percentage change in the price of the Bitcoin, the 1st of April 2011 shows an abnormal growth of 302.56% compared to the previous months of that year. In addition, November 1st 2011 acts as end date of the bubble because it shows the last big downfall concerning the Bitcoin price of 36.83%.
Date Weighted Price Price Change in Percentage
2011-01-01 $0.30 X 2011-02-01 $0.74 146.67% 2011-03-01 $0.95 28.38% 2011-04-01 $078 - 17.89% 2011-05-01 $3.14 302.56% 2011-06-01 $9.21 193.31% 2011-07-01 $15.90 72.64% 2011-08-01 $13.17 - 17.17% 2011-09-01 $8.22 - 37.59% 2011-10-01 $5.05 - 38.56% 2011-11-01 $3.19 - 36.83% 2011-12-01 $3.05 - 4.39%
This table gives an overview of the monthly Bitcoin prices and changes in Percentages of a month compared to the previous month on the Mt. Gox USD exchange market in 2011. Source: Bitcoincharts website (2014)
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Grinberg (2011) explains that the growing demand has resulted in the creation of several exchange markets that provide exchanges between Bitcoin and traditional currencies, including the US Dollar, Yen, Euro and other digital currencies like WebMoney. This thesis focuses on the Mt. Gox USD exchange market because the Bitcoincharts website (2014) shows it is the longest existing US Dollar exchange market for the Bitcoin, starting on July 17th 2010. In addition, the MT. Gox USD is the third largest exchange market overall, based on a volume of 301,867,975.12 USD and also the third largest exchange market based on the US Dollar currency. The largest and second largest exchange markets for the Bitcoin are also based on the US Dollar currency and are consecutively called btce and BitStamp. The reason for not using the btce and BitStamp exchange market is because these exchanges originate from August and September 2011 and therefore do not provide enough data to conduct research on a possible bubble in 2011.
The reason for not choosing the Chinese Yuan as field of research is because the Chinese government still has a big influence on the economy. In an indirect way, it can influence the Chinese Yuan exchange market for the Bitcoin. In an article published by Bloomberg (2013) the influence of the Chinese Government becomes clear on December 5th, 2013; China’s Central Bank banned financial institutions from handling Bitcoin transactions. This action resulted in a downfall of the Chinese Yuan on the Bitcoin exchange markets.
To investigate whether the Bitcoin did experience a bubble in 2011, the price trajectory of the Bitcoin is compared to the price trajectory of stocks. The S&P 500 acts as benchmark for the Bitcoin for a number of reasons. First, both the Mt. Gox and S&P 500 can be expressed in U.S. Dollar. Second, the S&P 500 has the longest historical data series that are easily accessible trough DataStream. Third, the S&P 500 makes a good benchmark for stocks, since it includes the biggest 500 U.S. companies and represent more than 70% of the U.S. stock market in terms of market values.
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The definition of a Bitcoin and the two kinds of bubbles, area of research, the time period of the possible Bitcoin bubble and the data is clear. The next step is to look at the research approach. First the following hypotheses will be investigated:
H1: The price trajectory of a Bitcoin in USD is not significantly different from the price trajectory of stocks during the event period.
This graph shows the price of a Bitcoin on percentage scale. The peak in June is clearly visible. Source: Bitcoincharts website (2014)
• H2a: the peak in Bitcoin price in June 2011 is parallel to the peak in stocks • H2b: the fall of Bitcoin price from June 10th 2011 till October 31st is parallel to
a fall in stock prices.
These hypotheses must identify the existence of the Bitcoin bubble. H1 proves whether there was a significant difference between the price trajectory of Bitcoins and the S&P 500 stock market index.
If the peak and fall of Bitcoin prices are similar to that of other stocks, it is possible that the Bitcoin bubble is part of an overall high in the stock market. The expectation is that there is a significant difference between Bitcoin and stock price trajectories due to a steep increase in the event period of the Bitcoin price. To specify the bubble, the H1 is divided in more hypotheses (H2a and H2b).
If the Bitcoin bubble is identified, the next step is to find possible bubble indicators. As discussed before, to calculate fundamental value is mathematically too advanced, but high P/E ratios could function as indicator for a bubble according to Ou
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& Penman (1989). A high P/E ratio indicates that long-term buyers become scarcer and short-term investors will grow in numbers. Moreover, high P/E ratios means that the Bitcoin should have a low fundamental value, which could lead to declining prices if the price is higher than the fundamental value. To test this, the following hypothesis is investigated.
H3: The average yearly P/E ratio of the Bitcoin during the possible bubble period is significantly different from the average yearly S&P 500 P/E ratio of 24.12%.
The average yearly S&P 500 P/E ratio of 24.12% is calculated over the last 25 years, starting in 1989. The data to calculate the average S&P 500 P/E ratio is collected from the Multpl website (2014). A period of the last 25 years is taken because this period covers the recent market changes, for example the introduction of the Internet. Moreover, a period of 25 years equalizes economic high and low conjuncture. In addition the average yearly S&P 500 P/E ratio of 18.68% is calculated over the last 50 years, starting in 1964. The 50-year period P/E ratio acts as a test of robustness. The expectation is that evidence will show that the P/E ratio of the Mt. Gox USD exchange market was significantly high compared to the S&P 500 index during the Bitcoin bubble due to the steep increase in the Bitcoin price. This may lead to a rejection of the hypothesis.
To complement the research, another bubble identification method will be applied. Pastor & Veronesi (2009) point out that systematic risk or volatility rises due to new technologies and signal for bubble like patterns. Again the S&P 500 will act as a benchmark for the Bitcoin USD. The following hypothesis can be drawn from this literature.
H4: The volatility of Bitcoin USD during the bubble period is three times as high compared to the estimation period.
In addition to the P/E ratios and the volatility bubble indicators, the correlation between the oil prices and the Bitcoin currency is calculated. If the prediction that macro economic factors like low interest rates, consumer distrust in banks and government monetary policies cause decreasing investments in stocks and save deposits next to increasing investments in the Bitcoin, the correlation between the
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Bitcoin and oil prices should be negative. Oil prices is an internationally traded commodity and acts as a world wide economy indicator. The oil price data is collected from investing website (2014). A declining oil price indicates economic downfall and a growth in alternative investments like the Bitcoin are expected. H5: Bitcoin USD prices and the oil prices are negatively correlated.
All hypotheses will be tested in Eviews. The data will be analyzed and formally tested using the appropriate tests. The tests will be performed at a 5% significance level. The data will be summed to weekly returns and volumes. The data and results are illustrated by graphs.
4. Empirical Results
4.1 Identifying the Bitcoin Bubble
For the first hypothesis the price trajectories of the Bitcoin and S&P 500 are compared and tested for a significant difference. First the weekly prices are compared in period 2010-01-17 till 2014-01-17. The total number of observations is 186. So in total, the data consists of 186 weekly weighted prices. Observation 1 (2010-07-17) till observation 40 (2011-04-01) functions as the period before the possible bubble. Observation 40 till 76 (2011-11-01) functions as the possible bubble event. Observation 76 till 186 (2014-01-17) functions as the period after the event. To illustrate the weekly weighted price trajectories of the Bitcoin and S&P 500 the prices are plotted in graph 1.
Graph 1 0 400 800 1,200 1,600 2,000 25 50 75 100 125 150 175
W eighted average price Bitcoin W eighted average price S&P 500
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Graph 1 shows that the Bitcoin and S&P 500 first follow a steady similar path. However, the Bitcoin has higher price fluctuations during the post event period compared to the S&P 500, especially from 2012-06-25 (t=110) till 2014-01-17 (t=186). This could be explained by the fact that the S&P 500 consists of the 500 biggest stocks in the U.S, so the larger number of stocks and observations gives a mean and variance which are less sensitive to price changes compared to a single stock like the Bitcoin. To give a clearer picture of the price trajectory, both the weekly weighted prices of S&P 500 and the Bitcoin are plotted separately in graph 2 and 3.
Graph 2
The event period 2011-04-01 till 2011-11-01 (t=40 – 76) shows a very small peak in the price compared to the period after the possible bubble event. However, this does not imply that the bubble event period did not experience a bubble. It could be possible that the possible bubble in 2011 is followed by another bigger bubble in 2013. 0 200 400 600 800 1,000 1,200 25 50 75 100 125 150 175
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Graph 3
The S&P 500 weekly weighted prices show an upward slope, but far more gradually than the weekly weighted Bitcoin prices. Furthermore, the average weighted price of the Bitcoin calculated over the whole estimation period 2010-07-17 till 2014-01-17 is $81.62, with a standard deviation of $207.46. In addition, the average weighted price of the S&P 500 is $1400.73, with a standard deviation of $194.82. The relatively high standard deviation of the Bitcoin implies a high level of uncertainty.
Weighted Price Bitcoin Weighted Price S&P 500
Mean 81.62 1400.73
Std. Dev. 207.46 194.82
Table 1
A regression is conducted: the weighted price of the Bitcoin is regressed on a constant and the weighted price of the S&P 500. Table 2 shows that the p-value is 0.0000. The conclusion drawn from this p-value is that the relation between the weighted price of the Bitcoin and the weighted price of the S&P 500 is significant given a significance level of 5%. 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 25 50 75 100 125 150 175
! *)! Dependant Variable:
Weighted Price Bitcoin
Coefficient Std. Error T-statistic
Constant - 945.84* 140.20 - 6.75
Weighted Price S&P 500 0.73* 0.11 6.90
Table 2
To formally test H1, the Chow-Break-Test is used. The Chow-breakpoint test splits the Bitcoin and S&P 500 sample in three parts. The beta’s are compared as follows: :!!!"#$%"& ! ! ! !!!!!!!"". The regression equation is first estimated for each
individual subsample (before, during and after the bubble period), whereafter the regression equation is estimated based on the whole sample.
The Chow-Break test compares the betas that are estimated by the regressions.
The resulting F-statistic will tell us to reject
!!!!!!"#$%&#$'( ! !!"#$% ! !!!!"#!!"#$%!, when a large value for the F-statistic is obtained. To test this, the total number of observations of the Bitcoin and S&P 500 is divided in three groups: (t=0,39), meaning testing the period of July 2010 till April 2011. Next (t=40,76) meaning testing period April 2011 till November 2011 and (t=77,186) meaning testing period November 2011 till January 2014. To test for a possible bubble, multiple periods are tested to specify the bubble event period. The first Chow-breakpoint test focuses on period 2010-07-17 till 2011-04-01 and is compared to period 2011-04-08 till 2014-01-17. So observations (t=0,40) and (t=41,186) are tested. The results are presented in table 3.
Beakpoint Test: 2011-04-01 or (t=40)
F-statistic 3.14
Prob. F(2,182) 0.0457
Table 3
There is evidence to assume that April 1st 2011 or (t=40) could be the starting point of the bubble because it is a breakpoint, given the p-value of 0.0457 which is enough to reject H0 at a significance level of 5%. While this is already convincing evidence for a structural break, further research has shown that other parts of the sample will result in even more convincing values of the F-statistic.
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Next, the Chow-breakpoint test focuses on the end of the bubble event period. Period 2010-07-17 till 2011-12-01 is compared to 2011-12-08 till 2014-01-17. So observations (t=0,80) and (t=81,186) are tested. The results are presented in table 4. Breakpoint Test: 2011-12-01 or (t=80)
F-statistic 8.14
Prob. F(2,182) 0.0004
Table 4
This table shows more convincing evidence of a breakpoint with a p-value of 0.0004. So the H0, that there will be no breakpoint on December 1st 2011 or t=80,can be rejected given a significance level of 5%.
To look for a possible other bubble, different periods are tested for breakpoints. Period 2010-07-17 till 2013-02-11 is compared to 2013-02-18 till 2014-01-17. So observations (t=0,144) and (t=145,186) are tested. Moreover, a test is done on the period 2011-10-17 till 2013-02-11, so observations (t=60,144) are tested. The results are presented in the tables 5 and 6.
Breakpoint Test: 2013-02-11 or (t=144) F-statistic 36.51 Prob. F(2,182) 0.0000 Table 5 Breakpoint Test: 2011-10-17 till 2013-02-11 or (t=60,144) F-statistic 18.05 Prob. F(4,180) 0.0000 Table 6
These results show that breakpoints in the Bitcoin Mt. Gox exchange market not only occurred in 2011 compared to the S&P 500, but also in 2013. This could indicate that the Bitcoin experienced at least one other bubble given a p-value of 0.0000 with a significance level of 5%.
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In conclusion, given all the results of the Chow-breakpoint test, there is evidence for breakpoints that indicate bubbles. Now the focus is on the specific possible bubble period 2011-04-01 till 2011-11-01, so observations (t=40,76) are tested. The results are presented in the table 7.
Beakpoint Test: 2011-04-01 till 2011-11-01 or (t=40,76) F-statistic 3.49 Prob. F(4,180) 0.0090 Table 7
These results show that there was a breaking point in the period 04-01 till 2011-11-01 with a p-value of 0.0090. So H0 is rejected given a significance level of 5%. In conclusion, the price trajectory of the Bitcoin is significantly different from stocks during the event period and the Bitcoin rise in price is not part of an overall effect in the stock market.
If H1 is accepted a bubble is identified. H2 can specify the peak of the bubble.
For more precise tests on H2, the number of observations is narrowed to 131. It follows that the year 2013 and 2014 are left out because these show large price swings compared to 2010/2011/2012 and the focus of this thesis is most and foremost on the bubble in 2011. The Chow-breakpoint test is conducted to test for a difference of Bitcoin prices in June and in the period July-November compared to the S&P 500 index. First period 2011-06-01 till 2011-06-30, so observations (t=56,59) are tested. The results are presented in table 8.
Breakpoint Test:
2011-06-01 till 2011-06-30 or (t=56,59)
F-statistic 6.06
Prob. F(4,125) 0.0001
Table 8
Second, period 2011-07-01 till 2011-11-01, so observations (t=60,76) are tested. The results are presented in table 9.
! ""! Breakpoint Test: 2011-07-01 till 2011-11-01 or (t=60,76) F-statistic 15.95 Prob. F(4,125) 0.0000 Table 9
These results show that H2 is rejected, so the Bitcoin price trajectory differs from the S&P 500 in June and in the period July-November compared to the S&P 500 index. The breakpoint test for the June period gives a p-value of 0.0001. In addition, the breakpoint test for the period July-November gives a p-value of 0.0000. Given a significance level of 5% both H2a and H2b are rejected and a breakpoint is proved. 4.2 Identifying the Signals
The P/E ratio and standard deviation could function as indicators for a bubble. High P/E ratios means that the Bitcoin has a low fundamental value, which could lead to prices declines if the price is higher than the fundamental value. The weekly P/E ratios of the Bitcoin and S&P 500 are calculated in the following way:!! !!! !! ! !!!!!!! . In other words, the price is divided by the weekly average earnings per share (EPS).
This thesis focuses on weighted weekly returns, so the S&P 500 yearly average P/E ratio has to be converted to weekly P/E ratio before compared to the Bitcoin. The S&P 500 average P/E ratio per year = 24.12%, so the average weekly P/E ratio = 1.2412^(1/52) = 0.42%. Looking at the Bitcoin P/E ratio in table 10, it shows that the average weekly P/E ratio over the year 2011 is 0.44% with a standard deviation of 47.28. As stated before, the Bitcoin’s high standard deviation implies a high level of uncertainty.
P/E Ratio Bitcoin
Mean 0.44
Std. Dev. 47.28
Table 10
The earnings per share are expressed as the weekly rise in average price of the Bitcoin or S&P 500. As stated before, the S&P 500 weekly P/E ratio is 0.42% per week. To
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formally test H3 a t-test is used. The nul hypothesis is: the P/E ratios of Bitcoin during the possible Bitcoin bubble are not significantly different from the weekly P/E ratio of 0.42%.
Graph 4
The t-test is conducted with (35+185-2) 218 degrees of freedom. [(0.44-0.42)/47.28] = 0.0004. The nul hypothesis is rejected if t is equal to or bigger than 1.96. Moreover, the nul hypothesis is rejected if t is equal to or smaller than -1.96 given is significance level of 5%. Given the t-value of 0.0004, there is not enough evidence to reject the nul hypothesis. So the P/E ratio of the Bitcoin is not significantly higher compared to the weekly S&P 500 P/E ratio calculated over the last 25 years.
For robustness another t-test is conducted using the S&P 500 weekly P/E ratio calculated over the last 50 years. On average, the yearlt P/E ratio of the S&P 500 is 18.68%. So the average weekly P/E ratio of the S&P 500 = 1.1868^(1/52) = 0.33%. Looking at the Bitcoin P/E ratio in table 9, it shows that the average weekly P/E ratio over the year 2011 is 0.44% with a standard deviation of 47.28. The t-test is conducted with (35+185-2) 218 degrees of freedom. [(0.44-0.33)/47.28] = 0.0023. Given the t-value of 0.0023, there is not enough evidence to reject the nul hypothesis. So the P/E ratio of the Bitcoin is also not significantly higher compared to the weekly S&P 500 P/E ratio calculated over the last 50 years.
-240 -200 -160 -120 -80 -40 0 40 80 120 5 10 15 20 25 30 35 Constant rate 0,42 Price earnings Bitcoin
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To complement the research, another bubble identification method will be applied. Pastor and Veronesi (2009) point out that systematic risk or volatility rises due to new technologies signal for bubble like patterns. De Grauwe and Grimaldi (2004) came up with a strict rule using standard deviation as a bubble identification method. So to formally test H4, the standard deviation of the S&P 500 covering the data period is compared to the standard deviation of the the Bitcoin during the bubble event period. The nul hypothesis is: the volatility of Bitcoin USD during the bubble period is not three times as high compared to the estimation period. The results are presented in the table 11.
Weighted Price Bitcoin
Mean 707.11
Std. Dev. 548.79
Table 11
The standard deviation of the Bitcoin price is measured in the bubble event period and results in $548.79, while the standard deviation of the S&P price (table 1) is $194.82. Using the S&P 500 as benchmark, it is possible to calculate how much the standard deviation of the Bitcoin price differs compared to the S&P 500.
$548.79/194.82 = 2.8 times. Since the volatility of Bitcoin USD during the bubble period is less than three times as high compared to the estimation period, the nul hypothesis is not rejected.
To formally test H5, the correlation between the weighted oil prices and Bitcoin is calculated. The nul hypothesis is formulated as follows: the Bitcoin USD and the oil prices are not negatively correlated. The correlation is presented in the table 12.
Weighted Oil Price Weighted Price Bitcoin
Weighted Oil Price 1 - 0.0414
Weighted Price Bitcoin - 0.0414 1
Table 12
The correlation between the oil prices and Bitcoin is – 0.0414. So the oil prices, that function as benchmark for the worldwide economic condition and the Bitcoin prices
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are negatively correlated and the nul hypothesis is rejected. This result is according to the prediction that the nul hypothesis would be rejected and that the weighted prices were negatively related. Investors were expected to see the Bitcoin as an alternative investment option like gold, meaning that when the economy experiences a downfall, investors get nervous and store their money on a save deposit or invest in alternative investment options like the Bitcoin. Moreover, the negative news about banks, low interest rates and downfall of the stock market described in part 2.1 should result in a negative relation between the stock market and Bitcoin. Hence, negative economic news should be reflected in the oil price and decrease demand for stocks, lowering the stock price, while pushing up the demand and price for alternative like the Bitcoin. Momentum could increase the demand for Bitcoins and lowering the demand for Stocks. However, it should be mentioned that the correlation is close to zero which results in a weak correlation. The weak correlation shows that investment in Bitcoins and stocks do not necessarily cancel each other out.
4.3 Analysing the Results
The results are divided in the bubble identification section yielding H1 and H2. The second section consists of the possible bubble indicators yielding H3, H4 and H4. For the first section the Chow-breakpoint test shows that the price trajectory significantly differs compared to the S&P 500 price trajectory. Both the Bitcion and the S&P 500 follow a similar steady price path in the beginning measured from July 2010 till April 2011. From that point in time a significant breakpoint is proven which acts as the starting point of the bubble event. Therefore, a bubble is identified. The price trajectory of the Bitcoin most significantly differs from the S&P 500 in the period June till November. More Chow-breakpoint tests were conducted that implies the possibility for at least one more bubble in 2013, but no further attention is given to that event since this thesis focuses on the bubble in 2011.
The second section of the results looks at possible indicators for the bubble. The first indicator is the P/E ratio. P/E ratios are considered a valuable measure to predict long-term performance. Companies with high P/E ratios now, tend to have low or negative yield later on. The calculations did not showed an on average higher P/E ratio for the Bitcoin than for the S&P 500, given the t-value of 0.0004. This finding is surprising; a higher P/E ratio was expected for the Bitcoin given a high price followed by a downfall in the price.
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The following indicator is based on the standard deviation. The standard deviation of the Bitcoin during the bubble period was 2.8 times higher as the standard deviation of the S&P 500 during the whole research period, from 2010 till 2014. This signals that the Bitcoin price does not have a variance big enough to indicate a bubble.
In addition to the bubble indicator research, the correlation of the Bitcoin and oil prices was calculated. Due to the macro economic environment, which yields the crisis and downfall of stock, the expectation was that people were investing less in stock when the oil prices go down. This yields that when the economy could has the tendency to go down, people will invest more in alternatives like Bitcoin, resulting in a negative correlation. This negative correlation yields that the tendency of the Bitcoin market is a weak reversed tendency of the economy given the negative correlation close to zero.
All these findings together show that the Bitcoin investors did faced a bubble in 2011 but the indicators are not detected. The investor who did not sell his Bitcoins at the peak in June 2011 should not be sorry since the current price is now in January 2014 is higher than it was at the height of the bubble in 2011.
5. Conclusion
5.1 Conclusion Research
This research focused on the Bitcoin bubble in the period during April 2011 till November 2011. The first and second part of the paper discussed the theoretical background of bubbles. A bubble yield an initial rise in price will cause expectations to rise and that the price will rise even more. Moreover, high expectations lead to more demand for shares this leads to a growth in volume. At some point the investor behaviour changes and they start leaving the market. Therefore a sudden or gradually price decline could arise, not triggered by fundamental news but due to the change of investor behaviour. The collapsing of prices could have macro-economic effects, positive or negative. The Bitcoin follows this bubble path with a sudden price decline. However, the downfall of the Bitcoin does not have macro economic effects, since the Bitcoin is not seen as a big technological revolution (yet). Its impact on the overall economy should not be significant.
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In the third part of this thesis, several hypotheses are introduced yields to test for a possible bubble. Moreover, several hypotheses are introduced to test for the bubble indicators. In addition, the methodology is explained. In the fourth part the results of the tests are presented and it becomes cleat that the Bitcoin did experience a bubble in 2011. An unexpected result was that the indicators for a bubble were not significant. The P/E ratios of the S&P 500 and the Bitcoin did not significantly differ. Moreover, the price variance of the Bitcoin was not big enough to indicate for a bubble. Given the weak negative correlation between the oil prices and the Bitcoin, it appears to be that Bitcoin prices, which reflect the demand for Bitcoins, are not led by macro economic circumstances. In addition, evidence is found that proves at least one more bubble in 2013.
Concluding, this research underlined the importance of financial measures like the Chow-Break test. Furthermore a bubble is revealed in the Mt. Gox Bitcoin (USD) exchange market using the S&P 500 as benchmark. This thesis contributes to a better understanding of bubbles in the field of new electronic currencies. The finding of the bubble shows a delicate market and makes it even more important to conduct more research on electronic currencies.
5.2 Discussion
A point of discussion is the lacking of the calculation of the fundamental value. The calculation of the fundamental value is mathematically to advanced. Moreover, it is doubted whether the Bitcoin has a fundamental value that can be calculated. A bubble is defined as the difference between the market value and the fundamental value. However, the Bitcoin is not comparable to something tangible like a house. The fundamental value of a house is represented by the actual cost to own and maintain the house. However, the Bitcoin is a digital currency without a tangible value what so ever.
The way investor’s value the Bitcoin is comparable to art. Price is determined by what somebody thinks its worth. In contrary to the Bitcoin, art is also tangible. The fundamental value of the Bitcoin is a subject of discussion and could be due to lack of information about the cost have creating one called mining. In addition, the variance of the growth factor could also add to the difficulty of fundamental price determination. More accessible information about how the Bitcoin is mined and a
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more stable growth could solve the discussion about the fundamental value of the Bitcoin.
5.3 Recommendations
For further researches a couple of recommendations can be made. First, as described in part 2.1, momentum and investor judgement have a certain amount of influence on the price trajectory. However, how many investors combined could really alter the direction of the Bitcoin price trajectory is unknown. The total number of Bitcoins is already determined and about half of the total Bitcoins are mined. So the influence of a single investor on the price becomes smaller if he does not buy or “mine” more Bitcoins.
Next, there is discussion about what the Bitcoin really is regarding a currency or asset. Some countries accepted the Bitcoin as asset and other countries see it as a currency. Further research in the field of economic law should give a final conclusion of which economic classification the Bitcoin refers to.
Finally, as described in part 5.2, research has to be done on the fundamental value of the Bitcoin. In addition, the possible bigger Bitcoin bubble in 2013 could be a subject of investigation.
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