Price shocks of and correlation to other

Master Thesis

Student name: Marko Jelčić ANR:929706 SNR:2016639 November 2018 Supervisor: dr. Ole Wilms Second reader: dr. Fatemeh Hosseini Tash Abstract

The purpose of this study is to examine how the correlation between Bitcoin and other changes after Bitcoin price shocks that happened in 2017 and early 2018, when the market experienced a great increase and introduced cryptocurrency to the broader public. Using time series data of returns and using 14-day rolling correlations between Bitcoin and nine other cryptocurrencies, the empirical research will focus on correlation shifts. Quantitative analysis was performed on correlations between cryptocurrencies during the aforementioned period, generalized autoregressive conditional heteroskedasticity analysis was performed as well as a thorough analysis on structural breaks in correlation levels between Bitcoin and other cryptocurrencies. Main hypothesis of the thesis is that correlation levels rise after Bitcoin experiences a price shock. The results indicate that the correlation coefficient shifts after every Bitcoin price shock, but not necessarily in an upwards direction. These results have implications on using Bitcoin and other cryptocurrencies in a portfolio and creating a cryptocurrency portfolio itself, especially concerning diversification possibilities in a portfolio consisting of cryptocurrencies alone. After a structural break happens, the portfolio should be readjusted accordingly, whether it was made of different types of assets or cryptocurrencies alone.

Keywords: Bitcoin, cryptocurrency, correlation, diversification, price shocks

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Contents

Abstract ...... 1 1. Introduction ...... 3 2. Literature Review ...... 7 2.1. Bitcoin ...... 10 2.2. Currency ...... 11 2.3. Legality ...... 13 2.4. Transactions ...... 13 2.5. Dominance ...... 14 2.6. Usage as a payment ...... 14 3. Alternative cryptocurrencies ...... 15 4.1. Ether ...... 19 4.2. ...... 20 4.3. Ripple ...... 21 4.4. ...... 22 4.5. ...... 23 4.6. Stellar ...... 24 4.7. NEO ...... 25 4.8. NEM ...... 26 4.9. Bytecoin ...... 27 5. Empirical research ...... 28 5.1. ARCH and GARCH models ...... 28 5.2. Correlation studies and methodology ...... 30 5.3. Structural Break test Methodology ...... 33 5.3.1. Bitcoin Price Shocks ...... 35 5.3.2. Break dates for the hypothesis ...... 36 5.4. Empirical testing ...... 37 6. Conclusion ...... 44 7. References ...... 46 8. Appendix ...... 47

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1. Introduction

The aim of this thesis is to provide a background on the cryptocurrency market as a whole and investigate how the correlations between cryptocurrencies act before and after price shocks. Correlation analysis is important because it shows how the currencies act together in such a new and volatile market. This analysis is also important for understanding the volatility of alternative cryptocurrency and how does it tie into Bitcoin, which in a broader scope of things also provides an analysis on a possibility of a cryptocurrency portfolio. Diversification possibilities are weakened if strong correlation between cryptocurrencies persist so this analysis would provide an answer whether extreme cases of Bitcoin price volatility affect them.

Cryptocurrencies, or as the European Central Bank (2015) called them, schemes created a whole new payment system by itself, along with many new subjects that create and act in the cryptocurrency market. As in most markets, the inventors are the most important actors, since they develop the technology behind the cryptocurrency. These individuals are usually programmers and computer scientist, as it takes considerable technical prowess to create such powerful systems. Once these units are created, they need to be generated. The volume of these currencies is either predetermined or simply depends on the demand. In centralized cryptocurrency systems, issuers can issue more cryptocurrency, dictate rules of usage and control the supply.

In decentralized cryptocurrency systems, miners create new units of currency, by generating new units as a reward for validating a set of transactions and adding them to the payment to avoid double spending, in other words, marking each unit that has been used in a transaction in order to avoid malicious behavior. For a market to work, it needs users, which accumulate and spend their cryptocurrency units on goods and services, or simply accumulate them as a storage of wealth.

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Number of users who accumulated cryptocurrency, during the mentioned period far surpasses the volume of purchases with vendors that are expected for that volume. According to the Cambridge business school study (2017), number of active cryptocurrency users is between 2.9 million and 5.8 million. On the other hand, number of wallets open in Coinbase1, according to their website is currently over 20 million. This information is highly indicative of the cause of the extreme market growth cryptocurrencies experienced. Most of the people see cryptocurrencies as an investment rather than a payment vehicle.

To keep units of cryptocurrency, users have wallets, which are commonly divided into two commonly used categories. Cold wallets, which are usually hardware based and located offline on a physical piece of hardware, usually an USB drive. These types of wallets are deemed safer because of lowered risk of theft. Hot wallets are based online, stored on different types of software, which keeps users’ currency in one place.

Exchanges exist in order to provide users with options of trading for their currencies either with a fiat currency, such as US dollars, Euros, Renmimbi or Yen, or with another cryptocurrency. Most popular exchanges include Binance, Bitfinex, etc. Volume of trading on Binance, which accounts for more than 20% of the exchange market share, can reach over 500 million US dollars a day. A wide range of payment options is usually accepted, such as bank transfers, cash etc. Important role these exchanges have is also reporting the public with statistics about the volumes of trading. A big indicator of volume is security. The more secure the exchange is, more users will use it for supporting their trading habits.

Trading platforms are similar to exchanges, since they bring users together to bid and offer on cryptocurrency. The only difference between them is that trading platforms do not buy and sell cryptocurrencies themselves.

1 Most popular /exchange, founded in 2012. Reporting 1 billion US dollars in revenue and employing over 500 employees as per their website.

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The lines between trading platforms and exchanges are blurry, and wallets are becoming increasingly interchangeable with both of them since some wallets offer direct exchanges and some exchanges and trading platforms can act as wallets.

The cryptocurrency market itself is very new, but has certain geographical trends. As Cambridge Business School study points (2017), the main cryptocurrency actors are located in North America, Europe and the Asia-Pacific zone. North America contains 27% of global users and 39% of wallets; Europe had 29% of global users and 42% of wallets, while the Asia-Pacific zone has 36% of global users and 50% of global mining operations. This information can be tied with the fact that cryptocurrency is technology-based since emerging markets hold a miniscule percentage in a global frame of things.

The size of the market is a popular topic of discussion, as it is positively correlated with the number of users of cryptocurrency. In January 2018, according to coinmarketcap.com2, the market cap of all cryptocurrencies reached 795 billion US dollars. For comparison, the same market was worth 18 billion US dollars, or 2.3% exactly a year before, in January 2017. The sudden rise in the popularity and wealth that generated in the market garnered mass media interest and inspired many articles. A paper by Garcia, Tessone (2014) suggests that social interactions have an impact on price shocks of Bitcoin, investigating the impact of word of mouth and number of new adopters as well as the number of web searches as independent variables. This study, among many others tries to explain the phenomena that is the cryptocurrency market.

The social factors surely influence the volatility of such instruments, along with a big number of other factors, which is why this thesis focuses on the correlation levels instead of analyzing price changes. Price volatility of Bitcoin and cryptocurrencies in general is something simply incomparable with standard financial instruments. Investing in Bitcoin is a considerable risk, and the price variance itself is enough of a reason for investors to stay away. Correlation analysis should provide a deeper and more complex picture of the cryptocurrency market as a whole, as it helps understanding economical behavior between two variables.

2 Market quoting website, a trusted source for cryptocurrency data with accurate historical data

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This thesis provides results that support the hypothesis that there is a shift in correlation levels after a price shock. Both positive and negative Bitcoin price shocks were monitored and investigated in order to look at the variation as a whole, not just positive price surges. Important to mention is that correlation levels between Bitcoin and all cryptocurrencies are positive, either weak or moderately positive in general.

Limitations of this model come in the way of measuring the correlation itself. If a time series of a correlation factor is created, a rolling correlation has to be used.

A 90-day rolling correlation is much more robust than a 14-day correlation, but at the same time creates more overlaps due to a small sample. This is why the quantitative research was done with 14-day rolling correlations, to accommodate for both the smaller sample, as well as the highly volatile behavior of cryptocurrencies.

Accounting for limitations, this thesis should still provide results that are applicable in assessing the trends between the volatility of Bitcoin and its correlation to other cryptocurrencies. Structural break test should provide results that are significant enough to make a conclusion about correlation patterns before and after major price shocks.

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2. Literature Review

Literature concerning correlation between Bitcoin and other cryptocurrencies is limited, but there are quite a few articles analyzing the cryptocurrency market and the implications it has on the general world of finance, in relation to equity markets etc. Correlation analysis is still lacking in terms of scientifical papers, but some sources with basic research show the sentiment towards correlation between Bitcoin and other cryptocurrencies gaining traction after price shocks. A factor that needs to be taken into consideration is that not all cryptocurrencies can be purchased with fiat money. Thus, their value is calculated through Bitcoin, which can be expressed in US Dollars and other fiat currency afterwards. Usually, financial instruments are purchased with fiat currency, but in the case of cryptocurrencies, that may not always be the case. This way, in order to buy certain currency, an investor has to buy Bitcoin first, which directly implies a certain level of correlation.

Because of certain disconnect with the standards of investment strategies, Bitcoin and other cryptocurrencies separate themselves into a completely new category of investments. An interesting paper by Liu (2018) investigating the risk-return relationship of Bitcoin, Ripple and shows that the relationship differs from typical investments such as stocks. Bitcoin and other cryptocurrencies have higher volatility, but also a significantly higher alpha. No exposure to typical investment assets is shown, which again confirms the intricacies cryptocurrencies provide.

In order to investigate how exactly does the whole cryptocurrency market perform, a correlation analysis seems like a proper tool to analyze behavior of Bitcoin and other cryptocurrencies. In Gandal (2016), a paper that addressed competition in the cryptocurrency market, it was concluded that correlation changes usually happen because of two reasons. First of them, which seemed to stop according to this thesis was reinforcement, which happens when one currency goes up in value, thus devaluing other ones, in a certain market race where it is a winner-takes- all situation. The second one is more common today, and it is simply a case where other cryptocurrencies are substituting Bitcoin. A case in which investors look at cryptocurrencies as investments, and start looking at cheaper options than Bitcoin, but still an option that has great

7 potential for high returns. This effect makes the correlation go up, because cryptocurrencies are seen in a more similar light.

The thesis will start with a general introduction to Bitcoin, and then a short description of other investigated cryptocurrencies. Sources for most of these cryptocurrencies are found online in shapes of “white-papers”. When a cryptocurrency is first issued, it is done during an (ICO for short). Not every currency is issued this way, but majorities of them are. A “white-paper” is a document prepared by the developers to explain the technology behind their cryptocurrency and the problems that technology could solve, in a sense it is a document which strives to explain why people should invest in a certain technology.

To investigate the variance of Bitcoin prices, a GARCH (Generalized ARCH) model is used. As per Engle (1982), the autoregressive conditional heteroskedasticity model is a statistical model for time series data that describes the variance of the current error term. This model is useful to analyze and predict volatility.

The ARCH model exhibits autocorrelation in variance, which cover two stylized facts, leptokurtosis, which explains fat tails, and volatility clustering which could be present while looking at cryptocurrency returns. The model also covers mean reversion.

To examine the hypothesis of this thesis that correlation values between Bitcoin and other cryptocurrencies go up after Bitcoin price shocks, this thesis is employing structural break test with known break dates. First, a time series of correlation factors needs to be established. For this variable, a 14-day rolling correlation between Bitcoin and a certain currency is used. The reasoning behind such a small correlation sample is the variance of the underlying instruments. Taking a 90-day rolling correlation does not make sense, since it could incorporate many breaks inside the sample itself.

To notice abnormal changes in correlation, a structural break test is performed. As per Andrews (1993), structural break tests are used for parameter instability and structural change with a known or unknown change point. This means that it is logical to use it to see whether there are structural breaks in a time series of correlation pairing between Bitcoin and other currencies in order to see whether a sudden shift in the correlation even exists. This test determines whether

8 the shift in the correlation through time is significant enough to be a structural break, a great change in parameters.

Once the structural break test is done, more detail is provided then with a structural break test is applied to a certain date. This date is chosen based on daily return of Bitcoin. Comparing daily returns of Bitcoin and finding the biggest percentage changes will dictate the dates chosen for the study.

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2.1. Bitcoin

The main currency researched in this thesis is Bitcoin, and as stated in Nakamoto (2008), Bitcoin is a purely peer-to-peer version of electronic cash that would make online payments easier. Bitcoin was introduced as a solution to a number of problems that were connected to the existing online payment systems.

Usually, online payments were made through intermediaries between the two users that incurred additional costs and fees, making each transaction more expensive than it should be. This is because it was a system based on trust in the intermediary. The transactions generally asked the user to provide a lot of information, incurred fees, and were susceptible to fraud every now and then, a part of the online economy that is considered unavoidable as long as there is a human factor in the transaction chain.

Bitcoin is defined as a chain of digital signatures, and coins are transferred from one to another by digitally signing off the transaction. Another factor separating Bitcoin from traditional banking is the new privacy model, which separated the identities of customers from the start, providing privacy and separation from ties to the transaction.

Technical information aside, Bitcoin was designed in a way to act as a new currency used in online payments. A big problem Bitcoin and the technology behind it solved as per Halaburda (2016) was the problem of double spending the money. To simplify, we can think of cryptocurrencies as a string of ones and zero’s (which they are, along with some intricacies). These ones and zero’s can be copied and used multiple times, if not monitored properly. The Bitcoin technology was the first one to provide the solution to the aforementioned problem, and its technology is a basis for a number of other cryptocurrencies.

Standing as the biggest technological innovation behind Bitcoin is the technology. Users do not need an intermediary because all of the Bitcoin transactions are registered on a public ledger, where each transaction is named with an address of the sender as well as the receiver, written with 25 to 36 alphanumeric characters. This blockchain is public, and along with transactions it registers new currency being made. Along with getting rid of the intermediary, this technology also prevents fraudulent activities in a sense that once made blocks

10 in a blockchain are almost impossible to manipulate in order to change the information of the transaction.

2.2. Currency

Bitcoin (BTC) is a cryptocurrency without a central issuing authority, limited to 21 000 000 BTC once all the currency is mined. Bitcoin mining is the process in which a computer adds transaction records to public ledger of past transactions. Often used “mining rigs” which solve complex problems in order to generate new blocks in the blockchain do this process. Once a new block is discovered, a reward is given to the solver, currently at 12.50 BTC, as mentioned in Kroll (2013).

Picture1: Blockchain supply and reward graph

Shown in the above graphic is the block reward structure and the limited supply of Bitcoin, the more blocks are solved, the lower the reward in Bitcoin is.3

3 Information gathered from www.Bitcoin.com, Satoshi Nakamoto’s paper on Bitcoin

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Looking at the critical roles of money, we can see that Bitcoin is a unit of account and a medium of exchange, but the problem arises when looking at the store of value. The volatility of Bitcoin prevents it from holding value stable enough, and that may present some problems. Trading with Bitcoin started in 2010 with prices hovering around 10 cents for a Bitcoin, humble beginnings to say the least.

Today we can see that Bitcoin has a market cap of 128 billion dollars, more than two times as small as it was during the big boom of cryptocurrencies at the end of 2017 and beginning of 2018 where the market cap of Bitcoin reached 294 billion dollars.

Market Cap of Bitcoin 350,000,000,000$ 300,000,000,000$ 250,000,000,000$ 200,000,000,000$ 150,000,000,000$ 100,000,000,000$ 50,000,000,000$

0$

Jul 12, 2014 Jul12, 2017 Jul16,

Jan 28, 2014 Jan 13, 2016 Jan

Jun 26, 2016 26, Jun Jun 22, 2013 Jun22, 2015 Jun07,

Oct 10, 10, 2013 Oct 30, 2014 Oct 14, 2016 Oct

Apr2013 28, Apr2015 13, Apr2018 17,

Sep 05, 2014 Sep 17, 2015 Feb 25, 2015 Sep 01, 2017 Feb 09, 2017 Sep 21, 2018 Feb

Dec 04, 2013 Dec 24, 2014 Dec 08, 2016 Dec 28, 2017 Dec

Aug 16, 2013 Aug 01, 2015 Aug 20, 2016 Aug

Nov 19, 2015 19, Nov 2017 03, Nov

Mar 24, 2014 Mar 08, 2016 Mar 28, 2017 Mar

May 18, 2014 18, May May 02, May 2016 22, May 2017

Chart1.1: Market Capitalization of Bitcoin (April 2018)

As shown in the table above, Bitcoin reached its peak of over 300 billion US dollars in late December. This was not only a peak in price but also in volume, where 14 billion US dollar worth of Bitcoin traded in one day.4

4 Source www..com

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2.3. Legality

Since its inception, Bitcoin became a topic of discussion in governments worldwide. Although most of the countries are permissive towards Bitcoin, some are not so much. According to Hendricks, Hogan and Luther (2016), soon after Baidu, a web services company began accepting Bitcoin, The People’s Bank of China issued a statement prohibiting financial institutions and payment companies from buying, selling, quoting prices in, or insuring products linked to Bitcoin. This is partially due to Bitcoin prevalence in grey economy and illegal online markets in the beginning of its existence.

Fortunately for Bitcoin and other cryptocurrency, the majority of other developed countries such as the USA or the European Union accept Bitcoin although some countries such as Canada issued a banking ban on it in order to research the cryptocurrency market.

2.4. Transactions

As per Christin (2013), the majority of Bitcoin transactions in the beginning were made for illegal purposes in order to protect the privacy of sellers and buyers of illegal goods online such as drugs including cannabis, cocaine, LSD and other goods such as fake money, stolen digital goods, and interestingly, books.

Since then, Bitcoin made way into the public in a big way, with big online retailers starting to accept Bitcoin, one of them being Microsoft5. Today, Bitcoin can buy almost everything, from travel packages to electronic gadgets, and from gift cards to something as simple as a pizza. Personally, a big shock to the author on a personal level was seeing Bitcoin accepted as a method of payment in a small restaurant in Belgrade, capital of a frontier market economy Serbia, a country that has long ways to go in financial development. Vendors obviously don’t mind the uncertainty that payments in Bitcoin brings.

5 https://money.cnn.com/2014/12/11/technology/microsoft-bitcoin/index.html

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2.5. Dominance

Following its inception, Bitcoin was considered a flag bearer for other cryptocurrencies and a sort of representative of the technology as a whole. Along with that, came the dominance of the market cap of the whole cryptocurrency market and thus invoking the interest of investigating the correlations between the cryptocurrency and its alternatives. Before 2017, the dominance rarely dipped below 80%, but starting in March 2017, a steady fall has been recorded, with the dominance in May 2018 being lower than 40% on average. This can be accredited to the rise of other cryptocurrencies and diversification on the market as a whole as a part of the development of the market. This Data is important as it helps to show how Bitcoin has the power of “anchoring” other cryptocurrencies to itself.

Concerning the Bitcoin “dominance” in the market, it would be interesting to see how the dominance correlates with correlation levels with different cryptocurrencies. Do the return differences between cryptocurrencies fade when Bitcoin gains market share or not, as it would make investors uncertain whether even to bother investing into other cryptocurrencies other than Bitcoin, in reference to their volatile and illiquid nature. 2.6. Usage as a payment

As explained in Virtual currency schemes – a further analysis (ECB 2015), the term “virtual currency” is used, although the ECB does not recognize Bitcoin as full forms of money, the ECB continues to use the term “virtual currency schemes” in order to explain cryptocurrencies and similar instruments.

First usage of Bitcoin was for a website called Silk Road, an illegal online marketplace which accepted payments strictly in Bitcoin, referring to its anonymity for the users. Since then of course, the number of vendors accepting Bitcoin as a valid payment has risen, delimiting themselves from e-commerce sites, expanding to cafes and restaurants.

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3.Alternative cryptocurrencies

To understand the researched alternative cryptocurrencies, down below there is basic information provided about each cryptocurrency in order to distinguish them one from another. Technical differences are hard to interpret, so some general information about the currency is provided as well as some distinguishing features.

From a purely economic point of view, looking at the alternative currencies, many cryptocurrencies are based on a similar technology with an aim to provide similar services. To say they are the same would be over-simplifying them in a major way, but it is common for an average investor to think of certain cryptocurrencies as perfect substitutes.

Researching these cryptocurrencies, one cannot help but notice that at some level, the highly technical terms that explain the process that happens behind the technology start lacking sense to any person not educated in area, including financially educated people as well. The researched cryptocurrencies and the general information about them provided framework for the research, as among the biggest cryptocurrencies, there are striking similarities that pose an important question about the possible correlation between these types of assets.

The rise of cryptocurrencies, especially alternatives can be attributed to several factors according to the European Central bank (ECB 2015). The following alternatives all share some of these factors as a reason of their launch:

-One of the main reasons alternative cryptocurrencies launch is because they claim to correct some of Bitcoins’ weaknesses. A good example is Litecoin, which features better processing times of transactions. -Another reason for an alternative is supplying willing miners to mining alternatives, as Bitcoin mining requires hardware that is both expensive and energy draining.

-Since the high dependence on functioning technology, there is a possible risk included in holding Bitcoin as the only cryptocurrency as there are risks such as people hacking into

15 accounts to steal money, making unwanted transactions etc. To diversify such risks, other cryptocurrencies present an alternative investment to Bitcoin in order to lower the risk.

-Lastly, some alternative cryptocurrencies were established in a way that a lot of the currency was pre-mined before the ICO (Initial Coin offering) in order to gain profit from all the attention the cryptocurrencies are currently getting. Bitconnect presents itself as a good example, where as Chohan (2018) describes it “The lack of transparency around the flow of funds and around the functioning of their “volatility bots” should have rung alarm bells, less-than-savvy investors continued to dive in, and an aggressive marketing strategy helped to draw in further capital.” Moreover, even goes on to say the Bitconnect system behind the Bitconnect coin function as a sort of a pyramid scheme.

The 9 researched alternative cryptocurrencies during this research were picked in such a way that the data can be accessible throughout the whole time window, and that during the chosen time window the currency played an important factor in the market at least one point in time between January 1st 2017 and March 1st 2018.

Unfortunately, some major cryptocurrencies had to be left out due to lack of data. At the end of the investigated time window on March 4th 2018, the following cryptocurrencies had a total market cap of 349 billion dollars.

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In the chart below market caps of researched coins on 4th of March 2018 are shown. Bitcoin is the undisputed market leader, but the amount of capital invested in other cryptocurrencies is significant as well.

Market Caps

€ 0 € 50,000,000,000 € 100,000,000,000 € 150,000,000,000 € 200,000,000,000

Bytecoin (31) NEM (13) Dash (12) Monero (10) Stellar (8) Neo (6) Litecoin (5) Ripple (3) Ethereum (2) Bitcoin (1)

Chart1: Bitcoin and other cryptocurrency market capitalization (March 2018.) 6

As the chart above shows, Bitcoin is still the dominant force in the cryptocurrency market, which makes sense since it was the first cryptocurrency to exist. Furthermore, one of the first followers Litecoin also has a significant market cap, fifth highest. Seven out of ten biggest cryptocurrencies have been around before the market exploded, which means they have been trading since at least before 2017.

The extreme volatility of cryptocurrencies showed in some historical snapshots, with some of the biggest cryptocurrencies by market cap simply disappearing. (e.g. Bitconnect had 2,1 billion market cap on December 17th 2017, today it has 5,2 million, which is not even close to the 500 biggest cryptocurrencies., Veritaseum went from 11th biggest cryptocurrency on July 23rd to 88th today, losing 65% of its value in the meantime.7)

6 The numbers in the parentheses represent the ranking by market cap among all cryptocurrencies. 7 Source: www.coinmarketcap.com, www.coindesk.com

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Following cryptocurrencies showed “constant” appreciation of value, with data available at latest from January 1st 2017.

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4.1. Ether

Ether is a cryptocurrency supported by the Ethereum platform initially released on July 30th 2015. According to the cryptocurrency’s website, Ethereum is an open blockchain platform that lets anyone build and use decentralized applications that run on blockchain technology. The technology is built on the same basis as Bitcoin, making it a kind of a successor in the blockchain technology in a way of creation of new possibilities. The cryptocurrency recognizes Bitcoin as the father of all cryptocurrencies and to directly quote from the website “Ethereum would never be possible without bitcoin—both the technology and the currency—and we see ourselves not as a competing currency but as complementary within the digital ecosystem.” Below you can see the development of the Ethereum market capitalization. Reaching almost 140 billion during the January cryptocurrency craze shows that Ethereum is more than a formidable cryptocurrency which should be properly investigated.

Ethereum Market Cap

$140,000,000,000.00 $120,000,000,000.00 $100,000,000,000.00 $80,000,000,000.00 $60,000,000,000.00 $40,000,000,000.00 $20,000,000,000.00

$0.00

01-06-17 01-02-17 01-03-17 01-04-17 01-05-17 01-07-17 01-08-17 01-09-17 01-10-17 01-11-17 01-12-17 01-01-18 01-02-18 01-03-18 01-01-17 Table2: Ethereum market capitalization (March 2018.)

Ethereum started gaining major traction in March of 2017 as can be shown above, reaching the 20 billion US dollar mark in June. Considered by many the biggest cryptocurrency after Bitcoin. Ethereum ie easily purchasable, and does not need Bitcoin as an intermediary.

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4.2. Litecoin

Launched on October 13th 2011, commonly known as “Silver to Bitcoin’s gold”. It was one of the first existing alternative coins, actually the oldest one still traded. This coin is also heavily modelled after Bitcoin. Difference between Litecoin and Bitcoin is mostly technical, with Litecoin having faster processing times in order to try and complete transactions faster. The Litecoin blockchain is capable of handling higher transaction volume than its counterpart Bitcoin. It is also a cryptocurrency which aims to provide instant, near-zero payment costs anywhere in the world, making it one of the many. Below you can see the market cap development of Litecoin. Difference between other cryptocurrencies can be seen in December of 2017 where Litecoin already started showing explosive growth in its market cap.

Litecoin Market Cap $25,000,000,000.00

$20,000,000,000.00

$15,000,000,000.00

$10,000,000,000.00

$5,000,000,000.00

$0.00

01-04-17 01-02-17 01-03-17 01-05-17 01-06-17 01-07-17 01-08-17 01-09-17 01-10-17 01-11-17 01-12-17 01-01-18 01-02-18 01-03-18 01-01-17 Table3: Litecoin market capitalization (March 2018.)

Litecoin, Bitcoins’ closest substitute exemples a similar growth, albeit on a smaller scale. Both Bitcoin and Ethereum market caps experienced an unprecedented similar growth in December 2017. Further analysis will show that the correlation levels between the two cryptocurrencies is the 2nd highest of the whole sample.

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4.3. Ripple

Ripple is a real-time gross settlement system, whose purpose is to enable secure, instant and nearly free global transactions of money. Ripple differentiates itself from its competitions advertising faster payment settlement, better scalability and stability among other qualities. Ripple is known for also being a bridge currency, meaning allowing exchange between two rarely traded currencies in order to settle a transaction. Also worth noting is that Ripple has been focusing on the banking market a lot since the aforementioned technology behind it has some distinguishable features that commercial banks wanted to employ. Multiple publicly known partnership with banks like UBS, Santander, Royal bank of Canada, National Australia bank etc. have been made during the years. The graph below shows the development of the market cap of Ripple with the already known peak in January as other currencies

Ripple Market Cap $140,000,000,000.00

$120,000,000,000.00

$100,000,000,000.00

$80,000,000,000.00

$60,000,000,000.00

$40,000,000,000.00

$20,000,000,000.00

$0.00

01-06-17 01-02-17 01-03-17 01-04-17 01-05-17 01-07-17 01-08-17 01-09-17 01-10-17 01-11-17 01-12-17 01-01-18 01-02-18 01-03-18 01-01-17 Table4: Ripple market capitalization (March 2018.)

Differencing itself from the others, Ripple had a much longer “quiet period” than other cryptocurrencies, before the explosive growth in December. Ripple is one of the cheapest cryptocurrencies to buy currently available to buy on the market.

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4.4. Dash

Dash was originally released as Xcoin on January 18th 2014, designed as a Bitcoin alternative which proposed technical improvements that would make Bitcoin more effective. On January 28th it was renamed to Darkcoin to reflect its focus on user anonymity. In March 2015 it was renamed to Dash, short for digital cash. This name change was crucial as it represented a pivot towards focusing on their vision to create a private and instant payment platform. Dash works as a decentralized autonomous organization (DAO). Differently from other blockchain networks Dash coin miners do not get the 100% of the reward of solving a block in a blockchain. A part of the reward also goes to the “treasury” from where innovation is funded, as chosen by the general consensus between people in the community. The graph below shows the historical market cap of Dash. Dashcoin reached 12 Billion market cap on the 21st of December 2017, losing value steadily (as one cryptocurrency can) ever since.

Dash Market Cap $14,000,000,000.00

$12,000,000,000.00

$10,000,000,000.00

$8,000,000,000.00

$6,000,000,000.00

$4,000,000,000.00

$2,000,000,000.00

$0.00

01-04-17 01-02-17 01-03-17 01-05-17 01-06-17 01-07-17 01-08-17 01-09-17 01-10-17 01-11-17 01-12-17 01-01-18 01-02-18 01-03-18 01-01-17 Table5: Dash market capitalization (March 2018.)

As can be seen above, percentage-wise, it can be said Dash experienced one of the lowest growths during the December .

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4.5. Monero

Monero was launched in April of 2014, based on a technology called , which secures the anonymity of the users but also lacks the traceability of the money senders. As per their brief history, Monero has always focused on privacy and security, as well as ease of use and efficiency. Cryptographical encryption secures the privacy of transactions. Monero is designed to provide full block awards to miners, as they are thought of as the most critical members of the network.

Monero Market Cap $8,000,000,000.00 $7,000,000,000.00 $6,000,000,000.00 $5,000,000,000.00 $4,000,000,000.00 $3,000,000,000.00 $2,000,000,000.00 $1,000,000,000.00

$0.00

01-02-17 01-03-17 01-04-17 01-05-17 01-06-17 01-07-17 01-08-17 01-09-17 01-10-17 01-11-17 01-12-17 01-01-18 01-02-18 01-03-18 01-01-17 Table6: Monero market capitalization (March 2018.)

Although the market cap is much more modest than the biggest cryptocurrencies as can be seen above, the same price trend can be noticed as with the other cryptocurrencies. Worth noting is a significant rise in the value in late August of 2018, when Monero doubled its market cap in a span of a few days. Quite interesting how compared to other cryptocurrencies returns, this seems insignificant, but relating these price changes to a stock market shows how unique the cryptocurrency market really is.

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4.6. Stellar

The Stellar network is a community owned open source network that aims to facilitate cross- asset transfers of value. Lumens are the accompanying cryptocurrency that support the system. It is a centralized organization like similar to Ripple. Unlike Ripple, the Stellar network is a non- profit. It is a competitive crypto for both initial coin offerings and for commercial uses with commercial banks. Together with IBM, the Stellar network aims to provide blockchain banking around the world.

Stellar Market Cap

$18,000,000,000.00 $16,000,000,000.00 $14,000,000,000.00 $12,000,000,000.00 $10,000,000,000.00 $8,000,000,000.00 $6,000,000,000.00 $4,000,000,000.00 $2,000,000,000.00

$0.00

01-04-17 01-02-17 01-03-17 01-05-17 01-06-17 01-07-17 01-08-17 01-09-17 01-10-17 01-11-17 01-12-17 01-01-18 01-02-18 01-03-18 01-01-17 Table7: Stellar market capitalization (March 2018.)

On November 12th, Stellar cryptocurrency market cap was 460 million US dollars. Fifty days later, on January 3rd 2018, the currency was valued at over 12 billion US dollars. The influx of capital in the market was astonishing, and Stellar gained the investors trust as well. Along the lines of other cryptocurrencies, Stellar also experienced a significant drop in price starting in January.

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4.7. NEO

NEO is a non-profit community-based blockchain utilizing the technology and digital identities to digitize asset. The idea is to create a smart economy using digital assets, digital identities and smart contracts. Originally started as AntShares in February 2014, It was rebranded to NEO in June 2017. The biggest feature they advertise as a part of their technology is the creation of smart contracts which are possible due to seamless integration of the existing developer ecosystems, as per their website.

NEO Market Cap

$14,000,000,000.00 $12,000,000,000.00 $10,000,000,000.00 $8,000,000,000.00 $6,000,000,000.00 $4,000,000,000.00 $2,000,000,000.00

$0.00

01-04-17 01-02-17 01-03-17 01-05-17 01-06-17 01-07-17 01-08-17 01-09-17 01-10-17 01-11-17 01-12-17 01-01-18 01-02-18 01-03-18 01-01-17 Table8: NEO market capitalization (March 2018.)

NEO, as seen in the table above fits the cryptocurrency growth mold of most of the other cryptocurrencies. Explosive growth followed by a steady downfall clearly confirms a trend a shows the bubble in the market. Less known in the public eye, NEO still gathered a significant amount of capital as an investment in the technology behind it.

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4.8. NEM

NEM is a peer-to-peer cryptocurrency and blockchain platform launched in March 2015. The platform introduced new blockchain features, such as the proof-of-importance (POI) algorithm, multi-signature accounts etc. as a new technology. It has also introduced new types of assets that can use the blockchain technology in order to reach businesses other than the ones strictly connected to banking or finance.

NEM Market Cap $18,000,000,000.00 $16,000,000,000.00 $14,000,000,000.00 $12,000,000,000.00 $10,000,000,000.00 $8,000,000,000.00 $6,000,000,000.00 $4,000,000,000.00 $2,000,000,000.00

$0.00

01-04-17 01-02-17 01-03-17 01-05-17 01-06-17 01-07-17 01-08-17 01-09-17 01-10-17 01-11-17 01-12-17 01-01-18 01-02-18 01-03-18 01-01-17 Table9: NEM market capitalization (March 2018.)

As the graph shows, NEM experienced one of the sharpest drops after the cryptocurrency market crashed. Valued at more than 16 billion US dollars on January 3rd 2018, it dropped to 3.5 billion US dollars on March 1st 2018. Losing 75% of value in less than two months shows how certain cryptocurrencies lost even more than the market as a whole did percentage-wise.

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4.9. Bytecoin

Bytecoin is a private decentralized cryptocurrency founded in 2015. Bytecoin specific technology enables the user to be a participant of the transaction processing and not just a user. This means that an average investor can mine Bytecoin on his PC because the algorithms are adjusted to such systems. Out of the sampled cryptocurrencies Bytecoin is the lowest valued cryptocurrency, but with a significant amount of capital invested in it nonetheless.

Bytecoin Market Cap 3,500,000,000.00

3,000,000,000.00

2,500,000,000.00

2,000,000,000.00

1,500,000,000.00

1,000,000,000.00

500,000,000.00

0.00

Table9: Bytecoin market capitalization (March 2018.)

As shown in the graph above, Bytecoin has the same explosive growth as all the other cryptocurrency, but the effects of the growth vanished quite quickly.

Concluding from all of the graphs concerning specific cryptocurrencies, all of them experienced similar return patterns. This coupled with the fact that all of them are supposed to be based on different technologies makes the correlation question more significant. Why are these cryptocurrencies, although each representing a unique technology which differs from the others, having same return patterns? The correlation between them is positive, and in some cases, moderate and heavily positive

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5. Empirical research 5.1. ARCH and GARCH models

Using an autoregressive conditional heteroskedasticity (ARCH) model as a statistical model for time series data is common. The generalised autoregressive conditional heteroskedasticity model is used in this study because the time series data shows time-varying volatility and volatility clustering.

Before testing the correlation between cryptocurrencies, a GARCH model is done to show the volatility that Bitcoin experienced in the sampled time period. Showing the volatility of the Bitcoin, which is extraordinary to say the least, prefaces the question about correlation. Are all of the sampled cryptocurrencies as volatile as Bitcoin is remains to be answered.

Trends of Bitcoin volatility provides a background to correlation testing which will show that none of the cryptocurrencies exhibit a low-volatility trend.

In this thesis, a GARCH model analysis is found to be an appropriate tool for understanding volatility. Logarithmic returns are used to better fit the normal distribution.

ARCH family regression Sample: 1/2/2017/- 3/1/2018 Distribution: Gaussian Number of Obs. 424

OPG Standard Returns BTC Coefficient error Z P>|Z| [95% Conf. Interval] 0.0076612 0.0022426 3.42 0.001 0.0032657 0.0120567 _cons ARCH 0.169298 0.0292583 5.79 0.000 0.1119528 0.2266433 Arch L1 0.7977338 0.0346625 23.01 0.000 0.7297966 0.8656711 Garch L1 0.0001291 0.000046 2.81 0.000 0.0000391 0.002192 cons Table 1.1: Garch model tests

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.015

.01

.005

Conditionalvariance, one-step

0

0 100 200 300 400 A

Graph 1.1: 1 day lag GARCH model8

In the above mentioned graph, volatility clustering is noticeable. The sample shows that high variance periods group together, and they occur in almost a constant rhythm. The latter part of the graph shows constant high variance levels. This trend of volatility clustering shows that once a period of big variance starts, it usually follows for a couple of days.

What is also noticeable is that the conditional one-step variance is larger as time passes by. In the end of the sample, the model exhibits a constant period of higher variance.

8 The A variable stands for days surpassed from the beginning of the sample (1st January 2017) until the end of the sample (1st March 2018)

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5.2. Correlation studies and methodology

A correlation study is conducted in order to gain knowledge about the general trends in correlations between Bitcoin and other cryptocurrencies. The empirical findings are important in a sense that they provide a certain frame for creating a portfolio out of Bitcoin and other cryptocurrencies. A portfolio has to be well diversified to be efficient, but there is limited impact in diversifying if the cryptocurrencies are all highly positively correlated.

Conducting a correlation study paves the way for the structural break tests. The empirical results will show levels of correlation between cryptocurrencies, so that the structural break test can be structured with these results in mind. A structural break with a high significance level happening to already positively correlated cryptocurrencies could point to many possible conclusions which will be assessed after the empirical testing is finished completely.

A paper by Eisl, Gasser, Weinmayer (2015) indicates that Bitcoin is a welcome investment in an already diversified portfolio. This paper also notes that a classic mean-variance approach will not be optimal, rather a Conditional Value-at-Risk framework as a risk measure since it performs better when returns are not normally distributed. Interesting to note that the study confirms the premise that including Bitcoin in a well-diversified portfolio (Equity, Fixed Income, Money market, Real estate) increases the risk, but the expected returns outweigh the risk factor. Bitcoin should be weighted from 1.65% to 7.69% according to the study, a cautious weighing, which seems logical concerning certain liquidity issues Bitcoin seemed to have at the time. This thesis expands the possibility of investing in Bitcoin as a part of a portfolio, adding other cryptocurrencies as well in order to increase portfolio efficiency. If Bitcoin by itself could be a part of an efficient portfolio, investing in a cryptocurrency portfolio could show as a good investment as well. In order to create an efficient portfolio, a correlation study needs to be performed.

In order to measure Pearson’s correlation in a valid way, four assumptions are made. Variables need to be measured at a continuous level, there should be no big outliers in the sample, the

30 variables should be approximately normally distributed and most importantly, there needs to be a linear relationship between the two variables.9

The chosen variables are logarithmic returns of a chosen basket of cryoptocurrencies and with them; a correlation matrix was created based on the returns from January 1st 2017 to March 1st 2018.

Variable Explanation Cryptocurrency BTC Logarithmic daily returns Bitcoin ETH Logarithmic daily returns Ethereum LTC Logarithmic daily returns Litecoin XRP Logarithmic daily returns Ripple DASH Logarithmic daily returns Dash XMR Logarithmic daily returns Stellar XLM Logarithmic daily returns Monero NEO Logarithmic daily returns NEO XEM Logarithmic daily returns NEM BCN Logarithmic daily returns Bytecoin Table 1: Description of variables10

9 Scatter graph extracts from stata can be found in the appendix. 10 This table applies to multiple regression outputs throughout the empirical testing for formatting purposes.

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Number of obs. 424 5% significance

BTC ETH LTC XRP DASH XMR XLM NEO XEM BCN BTC 1 ETH 0.4580* 1 LTC 0.4951* 0.4423* 1 XRP 0.2318* 0.2399* 0.2982* 1 DASH 0.4295* 0.4652* 0.3931* 0.1558* 1 XMR 0.5259* 0.5435* 0.4643* 0.2978* 0.5866* 1 XLM 0.3144* 0.3161* 0.3532* 0.5606* 0.2427* 0.4592* 1 NEO 0.3185* 0.3726* 0.3597* 0.1676* 0.3379* 0.2907* 0.2675* 1 XEM 0.3621* 0.4132* 0.3906* 0.2915* 0.3602* 0.4245* 0.4003* 0.3031* 1 BCN 0.3423* 0.2377* 0.2492* 0.1827* 0.2155* 0.2829* 0.3190* 0.1773* 0.2506* 1

Table 2: Table of correlations

As the results above show, A Pearson's product-moment correlation was run to assess the relationship between different pairs of cryptocurrencies. There was at least a moderate positive correlation between Bitcoin and every other cryptocurrency. Correlation with Ripple was the weakest one. A strong positive correlation was found between Monero and Bitcoin. These results show promise for the structural break test because the correlation is already there, its just needs to be researched whether or not it rises with Bitcoin price shocks.

In a wider perspective, the above shown table of correlations shows that alternative cryptocurrencies show the same trends as Bitcoin. Ethereum and Litecoin have quite high levels of correlation with Bitcoin, which is an important fact to note considering they are one of the biggest “competitors” to Bitcoin in the market.

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5.3.Structural Break test Methodology

A CUSUM, or Cumulative sum control chart is a sequential analysis technique which can be used to test for structural breaks, or in this case it can be used to test the constancy of the correlation coefficients in a time series model. In the first paper published by E.S. Page (1954), he explains that a noticeable shift in data in a time series can be properly recorded as a break. The formula adds the sums day by day and forms a certain threshold value. When the sum breaks a certain threshold value, a shift is noted. This test can go both ways so both positive and negative correlation shifts are noticed.

A structural break happens when11:

푆푛 − 푚𝑖푛푆푖 ≥ ℎ Or 푚푎푥푆푖 − 푆푛 ≥ 푘

Where:

푆푛 = 퐶푢푚푢푙푎푡𝑖푣푒 푠푢푚

푆푖 = 푠푢푚 푎푓푡푒푟 𝑖 푣푎푙푢푒푠 (표 < 𝑖 < 푛)

ℎ = 푚푎푥𝑖푚푢푚 푡ℎ푟푒푠ℎ표푙푑 푣푎푙푢푒 푏푎푠푒푑 표푛 푡ℎ푒 푙𝑖푘푒푙𝑖ℎ표표푑 푓푢푛푐푡𝑖표푛

푘 = 푚𝑖푛𝑖푚푢푚 푡ℎ푟푒푠ℎ표푙푑 푣푎푙푢푒 푏푎푠푒푑 표푛 푡ℎ푒 푙𝑖푘푒푙𝑖ℎ표표푑 푓푢푛푐푡𝑖표푛

In correlation terms, when a cumulative sum of correlation values goes beyond a threshold value based on the beginning of the sample, and over a certain value based on the likelihood function, the test detects a break in the constancy of correlation factors. In the case of this paper, it should detect abnormal changes in rolling correlations in a time series.

11 Simplification of a formula found in E. S. Page (1954) “Continuous Inspection Schemes”

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The test results for structural breaks can be seen below. In this general test, the whole sample is used and the test determines whether there is a structural break in the levels of 14-day rolling correlation between Bitcoin and other cryptocurrencies.

Number of Obs. 410 Ho: No structural break 1% 5% 10% Critical values 1.143 0.9479 0.85

Structural break Test Statistic ETH XRP LTC DASH XMR XLM NEO XEM BCN BTC 2.9865 2.6203 2.2656 2.7367 2.6582 2.3678 1.5070 1.5805 2.6443

Table 3: Structural break test for correlation pairings

As shown above, the cumulative sum test for structural breaks shows that each cryptocurrency shows a structural break somewhere along the time series even at 1% significance. A better visualization of these structural breaks is a CUSUM graph.12

Most of the CUSUM graphs show structural breaks at a similar time. This timing coincides with one of the first periods of high Bitcoin price volatility. At this time, the correlation shifts up suddenly.

Surprising revelation comes in the CUSUM graphs concerning the period around January 1st, when the Bitcoin bubble reached its top, and the cryptocurrency market was capped at 800 billion US dollars. The trend suddenly shifts downwards. This goes against the hypothesis that correlation rises after shocks, but is an interesting discovery.These structural break test point to a reasonable amount of correlation shifts in the investigated period. Doing a structural break test on chosen dates will show whether it happens during Bitcoin price shocks as well.

12 All the CUSUM graphs can be found in the appendix

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5.3.1.Bitcoin Price Shocks

Once there is proof of structural break, to prove the hypothesis of the thesis, a structural break test with a known break date needs to be done. The dates chosen in the testing sample were the dates the prices of Bitcoin changed the most. Bitcoin is a highly volatile instrument, as can be seen in table 4, so to choose the biggest price shocks, 2 of the biggest daily drops and 2 of the biggest daily gains were recorded as Bitcoin price “shocks”.

Graph 3.1 Historical returns of Bitcoin in the sampled period13

The table above shows the daily returns on a time series graph. The level of variance in Bitcoin returns is astounding and cannot be compared to returns of typical assets such as stocks. Returns to mean are short-lasting, as the price changes wildly day through day. It has to be noted that there are no “working days” in Bitcoin trading, as markets are active 24/7. This also presents a risk in trading as people who own cryptocurrencies can stand to lose a lot of money if they are not present in the markets during high volatility periods.

13 Source: www.coinmarketcap.com historic data

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5.3.2.Break dates for the hypothesis

In the general sample of returns, first big Bitcoin shock happened on July 20th. Closing price on July 19th was 2,273$ for one Bitcoin, and on July 20th it closed on 2,817$, a remarkable 24% daily return. On September 14th, an opposite shock happened, where the Bitcoin price fell from 3,882$ to 3,154$ in one day, a 19% loss in one day. The next shock happened on December 7th, when the price rose from 14,291$ to 17,899$, a 25% daily return, which was coincidentally of one of the best 4-day runs in Bitcoin history. On December 4th, Bitcoin closed trading with the price of 11,657$, which would net a 53% return in 4 days. The last Bitcoin price shock included in the study happened on January 6th, when price fell 17% in one day, from 13,819$ to 11,490$.

These date presented themselves as the best idea to test the hypothesis. It was also logical to include both gains in losses in the study to have a balanced view. Including only positive or negative shocks could skew the results.

Establishing Bitcoin “shocks” proved to be quite a task, as there were multiple daily price changes above 10%, which is one of the factors that make Bitcoin, and cryptocurrency in general, an interesting investment. In order to lower the risk of investing in cryptocurrencies, correlation measures help investors in creating an efficient portfolio.

High levels of volatility, paired with a positive correlation make volatility decreasing a harder task, with a high level of volatility even for balances portfolios. Constant monitoring of these returns for investors are necessary, since it presents both a risk and an opportunity to make faster losses and gains in the market. Imagining a cryptocurrency version of Chicago Board options exchange’s volatility index, known as VIX, sounds interesting to say the least, since monitoring and indexing cryptocurrency volatility in the same way the S&P 500 volatility as an index would certainly prove as a challenge.

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5.4.Empirical testing

Stata uses the Wald test for a structural break with a known break point to determine whether there was a structural break in a time series data structure. In words, a wald tests if a critical value, Θ, which is an increase in correlation level between cryptocurrencies is significantly different from 0. This is tested by using a Wald statistic:

(휃̂ − 휃 )2 0 푣푎푟(휃̂)

Where: 휃̂ = 푚푎푥𝑖푚푢푚 푙𝑖푘푒푙𝑖ℎ표표푑 푒푠푡𝑖푚푎푡푒

휃0 = 푝푟표푝표푠푒푑 푣푎푙푢푒

The proposed value is then compared with a Chi-square statistic.

Following are the empirical test of structural break with a known break date done in Stata. Since the number of observations is limited, a 14-day rolling correlation was created to create daily data in order to create a time series model. The 14-day rolling correlation was also used in order to avoid overlapping of data when using different dates that are less spaced out. As a consequence, the structural break should happen exactly 14 days after the price shock since all the return data will then be sampled from after the shock. This is important to note since the structural break tests need to include correlation levels which only take into account cryptocurrency returns after the shock.

For this testing it means a Bitcoin price shock that happened on July 20th 2017 should produce a structural break in correlation on August 4th 2017. Same logic is applied to other dates.

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Wald test for a structural break: Known break date

Sample 02-04-17 01-03-18 Number of obs. 410 Break Date 04-08-17

Ho: No structural break

BTC correlation pairing ETH XRP LTC DASH XMR XLM NEO XEM BCN chi ² (2) 5.2918 20.3581 4.1342 20.9831 42.902 8.4093 22.9416 24.7085 19.437 P-value 0.0709 0.0000 0.1265 0.0000 0.0000 0.0149 0.0000 0.0000 0.0001

Table 4: August 4th structural break testing.

On August 4th, a structural break in correlation factors happened between Bitcoin and six out of the nine investigated currencies at a 5% significance. The results show that a correlation shift does happen when a Bitcoin price shock happens. The type of shift depends on the cryptocurrency. Some cryptocurrencies’ correlations shifted upwards, while some went downwards.

Graph 2.1: CUSUM plot of Bitcoin-Ripple sum correlation during the full sample

In the graph above, you can see the date of the Bitcoin price shock marked with a red line, and the consequent rolling correlation shift in the circle. As explained, the shifts are not exclusively positive, and this is a good example of a downwards correlation shift. Worth noting is that in the

38 sense of the full 424-day sample, more breaks happen even before the biggest price shock, and it could be investigated what the correlation between structural shift occurrence and volatility levels of Bitcoin are.

One of the limitations that this study presents is that structural breaks happen outside of Bitcoin price shocks as well, but it is worth noting that after price shocks of Bitcoin, and levels of exceptional volatility in price, the rolling correlations have sudden shifts.

To gain a better view in the same structural break, a smaller sample can be taken and tested for a structural break. In the graph below, it can be seen how a cropped sample can provide a better insight.

Graph 2.2:CUSUM plot of Bitcoin-Ripple sum correlation during the cropped sample

39 two weeks after a price shock. The Wald-test also confirms the structural break14.Taking a smaller sample helps explain the exact moment when the rolling correlation levels start to shift. In this case, the correlation shift happens exactly two weeks after the price shock, as predicted. These results deny the hypothesis price shock always shift the correlation levels up, but supports the theory there are significant correlation shifts after Bitcoin price shocks.The table above shows that during a smaller sample, the 14-day rolling correlation levels shift exactly

Wald test for a structural break: Known break date

Sample 02-04-17 01-03-18 Number of obs. 410 Break Date 28-09-17

Ho: No structural break

BTC correlation pairing ETH XRP LTC DASH XMR XLM NEO XEM BCN chi ² (2) 35.4223 41.2001 3.1016 32.9386 116.8474 36.2317 89.1843 77.2297 33.7268 P-value 0.0000 0.0000 0.2121 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Table 5: September 28th Structural break test

On 28th of September, a structural break in the correlation happened with with every cryptocurrency except Litecoin. This shock is the last one which did not trigger a structural break with all the cryptocurrencies. Litecoin is the only cryptocurrency which still did not experience a correlation level shift after Bitcoin price shocks, which is a significant outlier, since all the other cryptocurrencies experience rolling correlation shift. This can be due to many factors, but a significant one could prove to be the general high level of correlation between Litecoin and Bitcoin, so further upward correlation shifts should be theoretically less significant.

14 Chi-square:43.6336, p-value:0.0000

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Graph 2.3: CUSUM plot of Bitcoin-Dash sum correlation during the full sample

As can be seen in the table above in the Bitcoin-Dash correlation example, a downward shift happens in the rolling correlation cumulative sum plot. This once again shows that structural breaks don’t have to be shifted upwards. The graph shows that two weeks after the Bitcoin price shock, which is market with a red line in the time series, a downward shift in the cumulative sum plot happens, and it can be noticed visually as well.

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Again in order to visually show the structural break in a more precise way, a cropped sample can be taken. Even in this cropped sample, a significant15 shift can be noticed.

Graph 2.4: CUSUM plot of Bitcoin-Dash sum correlation with a cropped sample

Again, a significant downward structural shift can be noticed exactly two weeks after the Bitcoin price shock. As soon as the rolling correlation stops sampling the dates before the shock, it shifts down. This result, an example among more, confirms that during levels of high volatility of Bitcoin prices, other cryptocurrency prices either start behaving more like Bitcoin prices or less like Bitcoin prices, but significantly different nonetheless.

15 Wald test, Chi-square=67.1007, p value=0.0000

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Last two Bitcoin price shocks generated significant structural breaks in the correlation levels of all cryptocurrencies. All Chi-square test values go up significantly, and structural breaks are more extreme.

Wald test for a structural break: Known break date

Sample 02-04-17 01-03-18 Number of obs. 334 Break Date 21-12-17

Ho: No structural break

BTC correlation pairing ETH XRP LTC DASH XMR XLM NEO XEM BCN chi ² (2) 64.457 57.1007 27.338 106.6962 76.9747 23.2515 70.2361 58.0777 60.8475 P-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Table 7: December 21st Structural break test

Wald test for a structural break: Known break date

Sample 02-04-17 01-03-18 Number of obs. 334 Break Date 30-01-18

Ho: No structural break

BTC correlation pairing ETH XRP LTC DASH XMR XLM NEO XEM BCN chi ² (2) 41.4784 38.93963 12.7334 56.8154 70.588 45.8563 58.6613 36.541 35.9541 P-value 0.0000 0.0000 0.0017 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Table 8: January 30th Structural break test

On December 21st, and January 30th, a structural break happened with all cryptocurrencies. The December 7th shock and January 16th shock, which represented a 25% daily return and 17% daily loss respectively. These shocks shifted the levels of every correlation quite significantly.

The limitation that the last two structural breaks present is that that they are already so deep into the sample, structural breaks cannot be shown easily on a time series graph. The cumulative sum of the correlation is so far off the baseline level that its hard to show easily in a visually clear way.

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6. Conclusion

This thesis’ aim was to test whether correlation levels between Bitcoin and other cryptocurrency rise after a price shock to Bitcoin. Firstly, the volatility of Bitcoin was assessed in order to create a vision of what kind of an asset is investigated. Along with one-of-a-kind levels of volatility, Bitcoin returns displayed a trend of volatility clustering. These periods of high volatility should have exhibited significant shifts to the correlation.

A correlation matrix was created using the time period from January 1st 2017 to March 1st 2018. This matrix was used to assess the general state of cryptocurrency correlation in the sampled period. The matrix displayed weak and moderate positive relationships between Bitcoin and alternative currencies. This matrix was a basis on which the rest of the thesis continued. Correlation as the main measure in the study proved to be a challenge. To create daily correlation data, 14-day rolling correlation was used with the sampled date being a rolling correlation of returns of last two weeks. This approach enabled the data to be created on a daily basis to create a time series.

Next analysis was using a cumulative sum test for structural breaks in order to see whether there even are structural breaks in levels of correlation between cryptocurrencies. It was concluded that in the sampled period there was a structural break in correlation levels for each of the cryptocurrency pairings at 1% significance. These results were expected to be positive to do an analysis with known date breaks.

In order to choose the dates that were going to be investigated, the author chose four dates with the highest daily prices changes of Bitcoin. Two positive and two negative changes were used in order to balance the data. The dates needed to be more than 14 days apart in order to have no common data used in the correlation levels. Once the dates of the shocks were known, structural break tests were made for correlation levels of the sampled cryptocurrencies on the date that was exactly two weeks after the shock in order to avoid using pre-shock returns in the correlation calculation.

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The main empirical study of the thesis was done using a Wald test for a structural break with a known break date. Out of the 36 possible structural breaks, 33 were recorded, meaning 92% of the tested correlation levels exhibited shifts 2 weeks after a Bitcoin price shock. Results confirm there is a correlation shift after price shocks and periods of high volatility, but they are not necessarily shifted upwards.

The possible limitations of these results is that these correlation shifts happen more often, and not only during periods after Bitcoin prices surge or crash. The models simply state whether or not there was a shift in a certain period, but it is a fact that the levels of correlation change significantly more times than recorded in this study. To think that correlation levels change significantly only after price shocks would be wrong, but it does not take away from the findings of this thesis.

These findings have implications on asset allocation choices with potential investors. Results show that investors need to actively manage their portfolio if cryptocurrency is a part of it due to significant switches in correlation factors in volatile times.

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7. References

European Central Bank (2012), Virtual currency schemes European Central Bank (2015), Virtual currency schemes – a further analysis Dr Garrick Hileman, Michel Rauchs (2017), Global cryptocurrency benchmark study, University of Camridge Judge Business School

David Garcia, Claudio J. Tessone, Pavlin Mavrodiev, Nicolas Perony,(2014) The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy, Journal of the Royal society, Volume 11, issue 99 Satoshi Nakamoto, (2008) Bitcoin: A Peer-to-Peer Electronic Cash System, www.Bitcoin.com

Hanna Halaburda, Miklos Sarvary, (2016) Beyond Bitcoin: The Economics of Digital Currencies

Kroll, J. A., Davey, I. C., & Felten, E. W. (2013). The economics of Bitcoin mining, or Bitcoin in the presence of adversaries. In Proceedings of WEIS (Vol. 2013, p. 11).

Hendrickson, J. R., Hogan, T. L., & Luther, W. J. (2016). The political economy of bitcoin. Economic Inquiry, 54(2), 925-939.

Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 987-1007.

Eisl, A., Gasser, S., & Weinmayer, K. (2015). Caveat Emptor: Does Bitcoin Improve Portfolio Diversification?

Polasik, M., Piotrowska, A. I., Wisniewski, T. P., Kotkowski, R., & Lightfoot, G. (2015). Price fluctuations and the use of Bitcoin: An empirical inquiry. International Journal of Electronic Commerce, 20(1), 9-49.

Chohan, U. (2018). Bitconnect and Cryptocurrency Accountability.

Kim, Y. B., Kim, J. G., Kim, W., Im, J. H., Kim, T. H., Kang, S. J., & Kim, C. H. (2016). Predicting fluctuations in cryptocurrency transactions based on user comments and replies. PloS one, 11(8), e0161197. Andrews, D. W. (1993). Tests for parameter instability and structural change with unknown change point. Econometrica: Journal of the Econometric Society, 821-856. E. S. Page (1954) Continuous Inspection Schemes, Biometrika, Volume 41, Issue 1-2, 1, Pages 100–115 Liu, Y., & Tsyvinski, A. (2018). Risks and Returns of Cryptocurrency (No. w24877). National Bureau of Economic Research.

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8. Appendix

Graph 1: Cumulative Sum plot of Bitcoin – Ethereum 14-day rolling correlation

Graph 2: Cumulative Sum plot of Bitcoin – Ripple 14-day rolling correlation

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Graph 3: Cumulative Sum plot of Bitcoin – Monero 14-day rolling correlation

Graph 4: Cumulative Sum plot of Bitcoin – Stellar 14-day rolling correlation

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Graph 5: Cumulative Sum plot of Bitcoin – Bytecoin 14-day rolling correlation

Graph 6: Cumulative Sum plot of Bitcoin – NEM 14-day rolling correlation

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Graph 7: Cumulative Sum plot of Bitcoin – Dash 14-day rolling correlation

Graph 8: Cumulative Sum plot of Bitcoin – NEO 14-day rolling correlation

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Graph 9: Scatter Graph of Bitcoin – Bytecoin returns

Graph 10: Scatter Graph of Bitcoin – DASH returns

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Graph 11: Scatter Graph of Bitcoin – Ethereum returns

Graph 12: Scatter Graph of Bitcoin – Litecoin returns

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Graph 12: Scatter Graph of Bitcoin – NEM returns

Graph 13: Scatter Graph of Bitcoin – NEO returns

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Graph 14: Scatter Graph of Bitcoin – Stellar returns

Graph 15: Scatter Graph of Monero – Ripple returns

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Graph 16: Scatter Graph of Bitcoin – Ripple returns

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