Evolution of Bitcoin Dynamics

The recent progression of Bitcoin price attracted investors&rsquo; interest but also raised the question of a possible bubble. In most research articles Bitcoin price determinants are reviewed on short periods of time until 2015. In this paper, Bitcoin price dynamics are studied on a longer period from 2011 to 2017 focusing on the past year when its price saw a rapid growth. Long-term relationship between Bitcoin price and fundamental sources are studied using econometric tests. Overall, results indicate that Bitcoin does not have a strong correlation with any fundamental factors but investors&rsquo; interest. During the past couple of years, public interest increased towards Bitcoin. This attention entertained by media surged even more from the beginning of 2017 with the rapid growth of Bitcoin price. In one year, Bitcoin saw its price plummet and reach 10 times its value going from 1 000 dollars to more than 11 000 dollars in the end of 2017 before losing value in April 2018. Headlines published in newspapers convey not only positive and encouraging messages on the future of the cryptocurrency but also extremely alarming ones. Public opinion regarding Bitcoin is quite controversial. When some raise awareness about the cryptocurrency, others sing its praises. Many believe that Bitcoin is a speculative asset and explain its fast appreciation by the fact it is caught in a bubble. It is usually compared to the Tulip mania from the XVII century or to the web bubble from early 2000s. Fran&ccedil;ois Villeroy de Galhau, governor of the Bank of France, explained during his Peking conference in December 2017 that according to him Bitcoin is not a currency and is not comparable to any economic asset class making it a speculative asset. Randal Quarles, a member of the Board of Governors of the Federal Reserve System, also warned about the dangers of investing in Bitcoin. He explained that it is not the responsibility of any institution and in case of a financial crisis it would be a threat to the financial stability. On the other side, many defend the potential of Bitcoin and argue how it is going to change not only the whole financial system but also many other fields. One of the first financial institutions that showed interest in Bitcoin is Goldman Sachs, which declared being interested in creating a desk to trade it. Another example is Jamie Dimon, the CEO of JP Morgan, who called it a &laquo; scam &raquo; in September 2017 before changing his mind when he announced thinking about offering Bitcoin to its institutional clients. Furthermore, exchanges such as The Chicago mercantile exchange and The Chicago Board Options Exchange offered future contracts on Bitcoin in mid-December 2017. This on-going debate is due to a lack of understanding of Bitcoin, what it represents and how it works. The aim of this article is to study the determinants of Bitcoin price from 2011 to 2017 when most of the studies focused on shorter periods up to 2015 before the rapid rise of its price and try to understand if it is linked to any economical factor or if it is purely linked to a speculative bubble. How Bitcoin works A Bitcoin transaction is completed after following 5 main steps. First, the transaction is sent to the whole network as a crypted message. Nakamoto (2008) used the concept of asymmetric cryptography on electronic signatures. Every Bitcoin user has two keys: a public one and a private one. The private key is only known by the user whereas the public one is known by the whole network. Therefore, when person A sends Bitcoins to person B, A will crypt the transaction message using his private key and after being publicly announced, the network can decrypt it using person A public key. The aim of this system is to ensure that the transaction was initiated and sent by person A as he is the only one in possession of the private key making it impossible to falsify (step 1). Every user in the network with a central processing is defined as a node. After being publicly announced, new transactions are collected by nodes and stocked in a list. Each list of new transactions constitutes a block to be confirmed. To validate a block, a node has to resolve a complicated mathematical problem using its computer power. The first node to resolve the problem will declare it to the rest of the network, which will automatically synchronise on the new list allowing everyone to share the same chronological list of transactions (step 2). For a block to be confirmed, a node needs to resolve a complicated mathematical problem. To explain in what consists the mathematical problem, the notion of hash has to be clarified first. A hash function allows translating a string of characters with an undefined length to a defined one. By using a hash function, any small change in the input will lead to a big change in the output. Therefore, every node will have to use the list of all new transactions on hold and the identifier of the last block to create a file that will be hashed and finally create a new identifier to the new block. This system is used to protect the database against any change by an attacker. Indeed, if an attacker decides to change any information, it will change the whole identifier and he then will have to change all the following ones since they are all linked. In order to find an identifier that respects the conditions imposed, nodes need to have an important processing power since the resolution of the problem consists on trying several inputs until a correct output is found. The part of the input that needs to be found is called a nonce. Thus, a nonce is added to the block until a hash that respects the conditions is found. The conditions are defined so that the network will take in average 10 minutes to find the solution. Therefore, the more the network develops and technology evolves, the more the conditions become difficult (step 3). Once the nonce is found by a node, the block is distributed to all nodes before it is confirmed and added to the blockchain. In order for the block to be confirmed, the majority of nodes have to vote to accept or deny the block. Every central processing unit is equivalent to a right to vote. A node will vote to accept the block only if the list of transaction is valid and there is no double spending problem. This system minimises the risk of fraud since to fail the system an attacker needs to first successfully change all the identifier of the present and all future blocks but also obtain the vote of the majority of the system. To obtain the vote of the majority, he will need to own or to get associated with half of the voters, which is quite improbable and difficult to realise. The more transactions are executed, the more the blockchain is long and the more difficult it is to attack the system (step 4). After receiving a majority of positive votes, the block is confirmed, dated and added to the blockchain. The counterparty B receives his Bitcoins (step 5). Different factors influencing Bitcoin price Findings from previous studies focused on four main factors to explain the evolution of Bitcoin price: economic drivers, social media, hedging properties of Bitcoin and technological factors. Kristoufek (2015) focused on two economic theories and tried to see if what was applicable to a fiat currency would be applicable to the cryptocurrency. He used a Morelet Wavelets method from 2011 to 2014 and observed a positive correlation between the Bitcoin price index and trade vs. transaction volume ratio and came up with the conclusion that the Quantity Theory of Money is applicable to Bitcoin. According to this theory the more money is in circulation, the more the price level of goods increases. Another theory tested is The Law of One Price (LOOP). According to this theory, any good or asset traded on different exchanges should have the same price. If it were not the case, then an arbitrageur would buy the asset at the lowest price and sell it in another market at a higher price making profit from this operation. The arbitrage opportunities would continue until the price of the market converges to the right price. Kristoufek tested the relationship between the average price level of a trade and Bitcoin price searching for causality from the first one to the second one. He concluded that Bitcoin behaviour follows this theory as he observed a negative relationship between the two variables with the average price level being the lead on the long run. Other studies focused on the possible hedging and safe-heaven properties of Bitcoin to understand how it could drive its price. Bouri, Molnar, Azzi, Roubaud and Hagfors (2017) analysed the correlation between Bitcoin and other financial assets on different time horizon: daily and weekly. They used an Engle Bivariate DCC model from 2011 to 2015. According to the sign of the correlation, Bitcoin can be considered as a safe-heaven, a diversifier or a hedger. If Bitcoin is positively correlated with another asset on average then it is a diversifier. It is considered as a hedger if it is negatively correlated with another asset on average and a safe heaven if the negative correlation is observed in times of stress. The results observed through this study are different according to the time horizon. By using daily data, the authors observed that Bitcoin cannot be considered as a safe heaven but as a diversifier. It is however a strong hedge against commodities and movements in Japanese and Asian Pacific stocks. Regarding the weekly analysis, the authors argued that Bitcoin is a strong hedge and safe heaven against movement in Chinese stocks. Dyhrberg (2016) stated that because of its specific nature between a commodity and a currency, Bitcoin has some hedging properties. By using a Garch model from 2010 to 2015 the author observed that Bitcoin and gold share similar volatility of their returns, those being more affected by the demand than by temporary shocks. Similarly to gold, the volatility of Bitcoin returns decreases when a high volatility is observed either on USD/GBP or on the FTSE index. Dyhrberg (2016) concluded Bitcoin has the same hedging properties as gold. He also observed that Bitcoin reacts the same way as USD/GBP to an increase in Fed funds rates. Therefore, it also has medium of exchange properties. Contrarily to the previous results, Kristoufek (2015) argued that Bitcoin is not a safe-heaven. Kristoufek tested the correlation between Bitcoin, and both gold price in Swiss Francs (CHF) and the Financial Stress Index (FSI). The results show that there is no statistically significant positive correlation between Bitcoin and FSI. Another factor that was studied is investors&rsquo; sentiment through social media. Kristoufek (2015) studied the correlation and the lead between Bitcoin price and both Google and Wikipedia search queries for the word &ldquo;Bitcoin&rdquo; using a Morelet Wavelets methodology. A positive correlation has been observed for both search engines with Bitcoin price being the lead from 2011 to 2012. In 2013 however the interest becomes the lead and drives the Bitcoin price. Matta, Lunesu and Marchesi (2015) showed interest in the effect of social media on Bitcoin price as well. They compared price trends of Bitcoin with Google trend and volume of tweets using an automated sentiment analysis and cross-correlation techniques from January 2015 to March 2015. To analyse subjective information in tweets and understand whether a positive or negative sentiment towards Bitcoin is shared through the tweet, some machine learning techniques were used. The authors results showed that positive tweets could be used to try to predict the price change of Bitcoin with a lag of 3 to 4 days and that Google trends can be considered as a predictor since it has a high cross correlation with a zero lag. Kristoufek (2015) mentioned that the price of Bitcoin might be dependent on technical drivers such as the computational mining power measured by hashes. A positive correlation between the price of Bitcoin and both the hash rate and mining difficulty was observed although the relation with difficulty was clearer. Research studies came up with different conclusions when focusing on the same factors depending on the method and time horizon used. Hypothesis and data One of the main limits of the articles mentioned in the literature review is the short period of time used for the studies. To understand if Bitcoin really depends on the different factors mentioned in the articles above, one or two variables will be used to represent an economic, hedge, social media or technological factor. In this article the research is extended on a longer period of time. The variables will be sourced from 1st November 2011 to 1st November 2017 as Bitcoin started to be more liquid around this period. The chosen explanatory variables are DXY (US dollar index), Google, fed funds rate, hash rate, MSCI, S&amp;P500, gold and West Texas Intermediate (WTI), the price of future contracts on crude oil. All the variables are sourced as daily observations. As Bitcoin has different prices depending on the exchange platform where it is traded, the USD Bitcoin Price Index (BPI) from Coindesk Price Index will be used. It is an average of Bitcoin prices across the main and most liquid exchanges. Bitcoin trades 24 hours a day and 7 days a week. The Bitcoin price index used is called the &ldquo;closing price&rdquo;. It represents the price of the last trade before 23:59:59 UTC. Hash rate (Hash) is extracted from blockchain.info. The hash rate is a measure of the computer power of the Bitcoin network when mining. It is measured as the number of hashes in trillions per second. The federal funds rates (Fed) are collected from the federal reserve bank of St. Louis. The federal funds rate is the rate at which financial institutions lend money to each other overnight. Gold represents its spot price per once in US dollar. DXY is a U.S Dollar Index that measures the value of the U.S Dollar relatively to a basket of 6 currencies: the Euro, the Japanese Yen, the Pound Sterling, the Canadian Dollar, the Swedish Krona and the Swiss Franc. As a currency is considered appreciating or depreciating relatively to another, it is more accurate to use the DXY to see if U.S dollar moved up or down as it takes into account several currencies. The Morgan Stanley Capital International World (MSCI) is an index of stocks from 23 developed countries. It is a proxy for global stock market. Standard &amp; Poor&rsquo;s 500 (S&amp;P500) is a U.S stock market index based on the market capitalisations of the 500 largest U.S companies. West Texas Intermediate (WTI) is the price of future contracts on crude oil. The number of research for the word &ldquo;Bitcoin&rdquo; is gathered using Google trend queries (Google). The data on the period chosen is given weekly. To collect daily observations, the data are downloaded on three-month blocks for the whole period and then rescaled using the overlapping month. This variable is given as an index going from 0 to 100, 100 being the peak of the number of research during the period. After selecting the variables, a stationnarity test is run on each one of them to see whether the series can be studied together in a model. Three tests are used : the Augmented Dickey-Fuller (ADF) test, the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test, and the Phillips-Perron one. The results from these tests give the same conclusion and therefore the series are considered to be non-stationary and are integrated of order one (I (1)) [1] . Since the variables share the same level of non-stationnarity I (1), a cointegration test can be run to see if there is a long-term relationship between the series. The Engle-Granger test is used. Long Term Model First, the test is run by pairs using the Bitcoin Price Index (BPI) and each one of the variables separately. Results show that the only significant long-term relationship is between Bitcoin price and the number of Google research with a p-value of 0.0000 and there is a positive relationship between them. Since the only variable cointegrated with BPI is Google, the cointegration of the series with BPI will be tested when adding Google to the models. Therefore 7 models are run and reported in table 1. BPI becomes cointegrated with DXY, Hash, Gold, Wti and S&amp;P500 when Google is added to the model. Consequently, a regression can be run on those 5 models. According to the regressions that have been run, most of the variables have a positive relationship with the price of Bitcoin but oil price (Table 1). Finally, a model using the whole variables is tested to see if there is a long-term relationship when including all of the series. It is reported in Table 2. The variables are cointegrated with BPI. Consequently a regression can be run. The results in table 2 show a positive relation between BPI and the number of Google research, hash rate, Msci, S&amp;P500. It also presents a negative link between BPI and the DXY level, Fed funds rate, gold and Wti. When comparing the relationship sign of the variables from previous models to the new one, DXY and gold change sign depending on the model. Indeed, in Table 1, DXY is positively linked to BPI while in Table 2 there is a clear negative relation. The same problem can be observed with gold. Therefore, a strong conclusion about the effects of DXY and gold on BPI cannot be delivered. This issue can be due to a colinearity problem. Short Term Model To manage to study the impact of the different variables on BPI, their correlation is studied on shorter periods: 3 months, 6 months and one year over the whole period. The rolling correlations are realised using returns for DXY, Fed, Hash, Msci, Gold, Wti and S&amp;P500 since those series are not cointegrated with BPI. No strong correlation is observed between the variables and BPI but Google. On shorter periods the correlations are stronger than on longer periods. Moreover, on every series but Google, the correlations switch from positive to negative making it clear that no strong and clear correlation exists between the BPI and the variables [2] . Regarding the Google trend queries correlations, there is a strong positive correlation on short term but also on longer periods and the sign of the correlation is constant (Figure 2). There is only three periods on the 3 months correlation where the correlation is negative but overall it is positive. From these observations, it can be concluded that the only real determinant of Bitcoin price is the number of Google research and that no economical, hedging or technological variable is linked to its price. Bitcoin price is strongly correlated to investor&rsquo;s interest. To complete the study, Google and BPI cross-correlation is studied to see if Google can be a predictor of Bitcoin price movement. As the series are cointegrated the cross-correlation can be run. The cross-correlation is a statistical measure taking into account the correlation between two time series depending on their time alignment. Each series can be delayed or moved forward by i times of days. As observed in Figure 3 the cross-correlation is higher with a zero lag, which means that Google is an immediate predictor of Bitcoin price. The cross-correlation is also strong with 1 to 6 days lags and it can be observed that it is mostly stronger for Google being a lag predictor than a lead one. Therefore analysing the number of Google research from 3 to 6 days backward can give an indication in the prediction of Bitcoin price. With a lag of 1 or 2 days however, the cross correlation is stronger with Google being a lead variable which means that by observing the price of Bitcoin 1 to 2 days ago, the number of Google research can be predicted. This symmetrical relationship was mentioned by Kristoufek (2015). Conclusion The aim of this study is to see if Bitcoin price reacts to real economy factors or if it is due to pure speculation, focusing on a longer period from 2011 to 2017. From the results observed, it is clear that on the long run Bitcoin price is not linked to any of the economical, technical or hedging factors chosen but social media. In opposition to what has been discussed in other studies, in this paper no correlation was found between Bitcoin price and other financial or economical factors. This can be explained by the fact that those articles focused on periods where the Bitcoin price was not soaring. The rapid growth started to be observed from the beginning of 2017. A study of the rolling correlation between Bitcoin price and the different variables on shorter and longer periods shows that no clear sign of a correlation can be deducted. The only variable that shows a strong correlation with Bitcoin price is the number of Google research, which is a proxy for investor&rsquo;s interest and demand for the cryptocurrency. To push further the study of the relationship between Bitcoin and Google trend queries for the word &ldquo;Bitcoin&rdquo; the cross-correlation between the two series is computed with a lag and lead of 6 days. The cross-correlation between Bitcoin and Google was observed to be quite strong making Google a good predictor of Bitcoin price. Bitcoin price seams to be driven by the high interest and therefore soaring demand for it when its supply is limited. This phenomenon makes it scarce and develops a mania around it. It is one of the many signs that define a financial bubble. The price is driven by the excessive demand that is fuelled by a trend. One of the possible extensions to this article would be to introduce other social media variables such as Twitter or Wikipedia with a sentiment analysis method or to use a bubble predictive model on Bitcoin. 1 Data are available from the authors upon request. 2 Charts are available from the authors upon request.

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Cryptocurrency

Evolution of Bitcoin Dynamics

L’étude des determinants du prix du bitcoin sur la longue période de 2011 à 2017, avec un focus particulier sur l’année dernière, permet d’analyser si son prix est correlé à des facteurs économiques fondamentaux ou s’il représente un actif purement spéculatif.

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