Hlavní práce75924_kubg01.pdf, 3.3 MB Stáhnout

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Prague University of Economics and Business

Faculty of Economics

Programme: Economics and Economic Administration

COULD BITCOIN BE A NEW DIGITAL GOLD?

Bachelor thesis

Author: Gabriela Kubíková

Thesis supervisor: doc. Ing. Helena Chytilová, Ph.D., M.A.

Year: 2021

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I hereby declare that this thesis is entirely the result of my own work and I acknowledge all the sources of information which have been used in the thesis.

Gabriela Kubíková

Prague

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Acknowledgment

I would like to express my thanks to my supervisor doc. Ing. Helena Chytilová, MA, PhD., for the thoughtful comments and recommendations provided to me throughout the writing of this thesis. She was always willing to assist in any way she could. Her support, guidance and overall insight in this field have made this an inspiring experience for me.

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Abstrakt

Táto bakalárska práca si kladie za cieľ preskúmať vlastnosti Bitcoinu a porovnať ich s tradičnými aktívami, S&P 500 indexom a zlatom v časovom rozhraní 2014 -2020. Prvým cieľom tejto práce je analyzovať vzťah medzi rizikom a výnosom., čo je dosiahnuté s pomocou Capital Asset Pricing modelu. Ako proxy bezrizikového výnosu sú vybrané štvortýždňové americké dlhopisy a S&P 500 index ako trhový proxy. Výsledky odhadov naznačujú silnú nezávislosť výnosov Bitcoinu od pohybov na trhu. Druhým cieľom bolo určiť charakteristické vlastnosti volatility Bitcoinu. Výsledky APARCH modelu naznačujú, že volatilita Bitcoinou má dlhodobo pretrvávajúcu pamäť a je citlivejšia na svoje minulé hodnoty ako na zmeny na trhu. Ďalej, výsledky naznačujú absenciu leverage efektu. Tretím

cieľom bolo preskúmať vzťah medzi volatilitou Bitcoinu a tradičnými aktívami.

DCC-GARCH model ukazuje historicky nízku koreláciu medzi Bitcoinom a tradičnými aktívami. Avšak od začiatku roka 2020 sa korelácia medzi nimi začala zvyšovať.

Poslednými cieľom bolo preskúmať úlohu Bitcoinu v investičnom portfóliu. Výsledky naznačujú, že zakomponovanie Bitcoinu do investičného portfólia ponúka výhody v oblasti diverzifikácie a zvyšuje očakávaný výnos portfólia vzhľadom na riziko.

Kľúčové slová: kryptomeny, Bitcoin, zlato, „digitálne zlato“, korelácia, volatilita, riziko, diverzifikácia, portfólio

JEL klasifikácia: C58, G01, G11, G23, G28

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Abstract

This bachelor thesis aims to examine properties of Bitcoin in comparison with traditional assets, the S&P 500 index and gold over the period of 2014 – 2020. First goal of this thesis is to investigate relationship between the risk and return, which is accomplished with the use of Capital Asset Pricing Model. Four weeks and one-year US Treasury Bills are used as a risk-free proxy, and S&P 500 index as a market proxy. Estimates show strong detachment from the market risk, thus, suggesting independency of Bitcoin returns on market movements. Second goal was to estimate characteristic properties of Bitcoin market volatility. The results of APARCH model indicate that Bitcoin market volatility has a long memory to persist in the future, and the volatility is more sensitive to its past values than to the new shocks of the market values. The estimates of APARCH model indicate the absence of leverage effect in Bitcoin market. Third goal was to examine the relationship between volatility of Bitcoin and traditional assets. The results of DCC-GARCH model show historically low correlation between Bitcoin and traditional asset classes. However, since the beginning of 2020, the conditional correlation has slightly increased. Last goal was to investigate the role of Bitcoin in a portfolio. The results indicate that Bitcoin investment offers significant diversification benefits, and even a small proportion of Bitcoin may dramatically improve the risk-return trade-off of investment portfolio.

Key words: cryptocurrencies, Bitcoin, gold, “Digital gold”, correlation, volatility, risk, diversification, portfolio

JEL classification: C58, G01, G11, G23, G28

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Introduction

The rapid pace at which the pandemic is spreading and global actions taken to curtail it have an unprecedent impact on the way we live and do business. While the full impact and long-term effects of these events is yet to be determined, it is expected that the adverse impacts are likely to continue from the virus’ knock-on effects. The outbreak is causing widespread concern and economic hardship for consumers and businesses across the globe.

While central banks are printing money at unprecedented rate to save the economy hit by the COVID-19 pandemic, people are searching for an asset which would help to protect their investments against the rising inflation. Crises are the ultimate consequence of a breakdown in the relationship between customer and the financial institutions. While people slowly loose trust in the financial system, a new promising technology excluding banks and other financial intermediaries has been developed.

On October 31, 2008, the white paper that first described Bitcoin was published by Satoshi Nakamoto, Bitcoin’s pseudonymous creator. The popularity of cryptocurrencies has risen significantly since then. Cryptocurrencies, mainly Bitcoin, has recently gained a lot of attention from finance researchers and practitioners. It was originally developed as an online peer-to-peer transaction system, which users can use directly without needing an intermediary, (Nakamoto, 2008). Bitcoin is a financial product that has the potential to disrupt existing economic payment system. I have chosen to research Bitcoin with focus to few specific areas for reasons stated below.

As it has been already indicated, Bitcoin offers its users significantly more control over their personal information and financial data, relative to traditional financial infrastructure.

Recently, the debate on whether the world’s largest digital currency could be the digital successor of gold is heating up. There is an argument that Bitcoin is very much a competitor to the gold. It is an excellent narrative of decentralization that appeals to millennials with robust security and cheap transactions. Despite its potential abilities and high market value, Bitcoin still lacks stability as its value is highly volatile.

To elaborate on Bitcoin’s role as a “digital gold” and its potential acceptance into global financial system, the analysis will start with evaluating the risk of investment in Bitcoin. The first section will focus on the relationship between the risk and return, and the decomposition of total risk. The first hypothesis considers the systematic part of the total risk. I hypothesize that systematic risk will only explain small portion of Bitcoin returns.

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The analysis will be done with the use of Capital Asset Pricing Model (CAPM), (Sharpe, 1964). Models are estimated using adjusted and unadjusted daily returns with two different market proxies. Final interpretation of results is based on the best-fitting model.

Second hypothesis, which considers properties of Bitcoin returns is stated as follows.

Bitcoin market is not affected by either good or bad news. In other words, Bitcoin market does not exhibit leverage effect, (Black, 1976). Characteristic properties of Bitcoin returns will be examined by applying the asymmetric power ARCH model. The same GARCH-type modelling will be applied also to S&P 500 index and gold in order to compare characteristic properties of Bitcoin price volatility with the volatility of traditional assets.

Another two hypotheses consider relationship among Bitcoin and traditional assets, and are outlined as follows. Bitcoin has a low correlation to traditional assets. Bitcoin’s correlation to gold has increased since the COVID-19 pandemic outbreak. This area will be examined by implementing DCC-GARCH model to estimate the time-varying conditional correlation between Bitcoin, S&P 500, and gold. The correlation among asset returns is one of the key components when considering risk management. This section focuses mainly on the impact of COVID-19 pandemic on the correlation among these assets, as the asset correlation can differ significantly in different periods of economic cycle.

Finally, the last hypothesis is dedicated to investigate the role of Bitcoin as portfolio component. To verify whether including Bitcoin in a portfolio improves the expected risk-return trade-off, eight portfolios with different weights of Bitcoin will be composed and their performance will be evaluated based on the corresponding Sharpe ratio.

The structure is as follows. Chapter 1 introduces Bitcoin and market overview. In chapter 2, trends in 2020/2021 and impact of COVID-19 pandemic on financial sector and Bitcoin are discussed. Chapter 3 discusses literature overview. Chapter 4 includes description of properties of safe-haven asset, the intrinsic value of Bitcoin, and the idea of Bitcoin as a “digital gold”. Chapter 5 presents drivers of Bitcoin volatility. In chapter 6, five specific hypotheses are outlined. Chapter 7 includes descriptive statistics of data sets and is dedicated to explore the relationship of risk and return with the use of CAPM. In the Chapter 8, the characteristic properties of Bitcoin price volatility are investigated and compared to traditional asset volatilities. Chapter 9 inspects the changes in return correlation among Bitcoin, gold, and S&P 500, and chapter 10, the last part of the analysis evaluates effects of including Bitcoin in a portfolio.

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This study suggests possible remedies with regards to limitations of my analysis and proposes possible directions for further research. My study adds to the existing literature by investigating the relationships between Bitcoin and traditional financial assets in contrast to gold, especially during the COVID-19 pandemic, which is the first significant crisis considering the lifetime of Bitcoin.

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1. Bitcoin

Bitcoin was introduced to the world on October 31, 2008, as the first decentralized currency to run on Blockchain technology. In August 2008, two programmers using the names Satoshi Nakamoto and Martti Malmi registered a new domain, bitcoin.org. The first mention of Bitcoin occurred in the white paper that was published by a pseudonymous person called Satoshi Nakamoto on bitcoin.org. Nakamoto posted a message on a cryptography mailing list titled: “Bitcoin P2P e-cash paper,” (Bitcoin 101, 2020).

On January 3, 2009, the Blockchain was launched when the first block, called genesis block, was mined. On May 22, 2010, Laszlo Hanyecz used Bitcoin for the first commercial transaction. He bought two Papa John’s pizzas, valued $25 for 10 000 Bitcoins. This day is known as a Bitcoin Pizza Day, (Hicks, 2020).

Bitcoin creation is done by mining similar to gold mining. Bitcoin mining is performed by high-powered computers, called nodes. They run a Bitcoin software, solve complex computational math problems, and fully validate transactions and blocks. They are special software or hardware that solve complex math problems, include the answer in the block and receive certain number of Bitcoins in exchange, (Bitcoin 101, 2020). Anyone could possibly mine Bitcoin. However, mining has changed from activity possible from own home to a specialized occupation that requires a lot of time and capital. The total supply of Bitcoin is limited and pre-defined in Bitcoin protocol at 21 million. There are currently (02.02.2021) 18 616 950 Bitcoins in existence, (Blockchain, 2021). Hence, 88,652% of all Bitcoin coins have been already issued.

Because Bitcoin does not have a physical form, it is necessary to store it somewhere.

Quality storage is essential to keep the digital currency safe. To manage Bitcoins and keep them secure, a cryptocurrency wallet is needed. The cryptocurrency wallet is a software program designed to store public and private keys, send and receive digital currencies, monitor their balance, and interact with various blockchains, (Cryptonews, 2021). Each wallet has specific address, which is a shorter version of the public key, and consists of 26 to 35 random alphanumeric characters. The private key, which is kept secret is used for authentication and encryption.¹ It grants a cryptocurrency user ownership of the funds on a given address. There are many cryptocurrency wallets, but the essential distinction between

1 Encryption is the method by which information is converted into secret code that hides the information’s true meaning. The science of encrypting and decrypting information is called cryptography, (Loshin and Cobb, 2021).

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them is whether they are cold or hot wallets. Hot wallets are connected to the internet, while cold wallets are not, (Lielacher, 2021).

Figure 1- Bitcoin transaction mechanism

Source: Bitpanda (2021)

Figure 1 describes the transaction process. Bitcoin transactions are messages, like email, which are digitally signed using cryptography and sent to the entire Bitcoin network for verification, (Saint Bitts LLC, 2021). Sending Bitcoin requires access to the public and private keys associated with that particular number of Bitcoins. When somebody wants to make a transaction with Bitcoin, they have to use the private key to verify their ownership of those Bitcoins and sign a message. This message is then sent to the block in the Blockchain with other transactions waiting for the confirmation. The block is broadcasted to all miners in the network. The confirmation of transaction is done by mining. Miners are solving for “nonce”, to validate the block.² The first miner to get a resulting hash announces its victory to the rest of the network, gets the reward, and all other miners immediately start

2 “Nonce” is a portmanteau of “number used once”. It is a numerical value, found by Bitcoin miner, which is necessary to generate a block, (Bitcoin 101, 2021).

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trying to figure out the next nonce. The transaction is completed and new block is added to the Blockchain waiting to be validated.

Using Bitcoin has many benefits but also some disadvantages. The benefits include faster and easier international payments, low transaction costs, user’s autonomy and discretion, and potential hedge against inflation. On the other side, there is a risk of mining monopoly (51% attack), cyber-attack with quantum computers, and most importantly, the limited acceptance due to government regulations and legality status.³

1.1. Blockchain

The blockchain, for all its merits, is not a new technology. It is built from 3 technologies: Private Key Cryptography, P2P Network and Program (blockchain protocol).

The result is a system for digital interactions that does not need a trusted third party, (Blockchain 101, 2020). Blockchain, sometimes referred to as Distributed Ledger Technology (DTL) is similar to the balance sheet of a bank. Like a bank’s ledger, the blockchain tracks all the money flowing into, out to, and through the network. It is a list of transactions that anyone can view and verify, (Blockchain 101, 2020). But unlike a bank, crypto blockchain is not centralized. Instead, it is secured by a large peer-to-peer network of computers running open-source software.

Over the old financial system, blockchain is global, allowing transactions to be sent across the planet quickly and cheaply. It also increases privacy, as cryptocurrency payments do not require any personal information. And lastly, because every single transaction is published in the form of the blockchain, anyone can scrutinize them. Leaving no space for manipulation of transactions, changing the money supply, or adjusting the rules in the mid of game, (Blockchain 101, 2020).

3 All benefits and risks are discussed in the Appendix B, and detailed description of Bitcoin’s history, mining process, types of Bitcoin storage (wallets), Bitcoin transactions and transaction fees is included in Appendix A.

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1.2. Market Overview

In this moment, (07.02.2021) 8 407 different cryptocurrencies exist, out of which 51 have market capitalization over $1 billion. The total market capitalization of all existing currencies at the moment is $1,186,563,981,812 with the traded volume in last 24 hours

$156,640,190,905, (Coinmarketcap, 2021).

Table 1 - Market capitalization of 5 leading cryptocurrencies

Name Symbol Price Market Cap Volume(24h) Circulating Supply Bitcoin BTC $39,100.92 $728,136,551,365 $67,170,671,186 18,621,981 Ethereum ETH $1,626.00 $186,293,361,266 $35,953,254,707 114,571,296 Tether USDT $1.00 $28,253,573,093 $116,102,737,312 28,227,332,458 Cardano ADA $0,6860 $21,342,761,999 $10,403,147,333 31,112,484,646 XRP XRP $0.4355 $19,772,618,194 $7,536,072,931 45,404,028,640

Source: Coinmarketcap, (2021)

As we can see in Table 1, Bitcoin is leading cryptocurrency with the highest price and market capitalization, followed by hundreds of new developing cryptocurrencies. When we compare the five top cryptocurrencies, even though the price of Bitcoin significantly exceeds prices of other cryptocurrencies, the market capitalization of Ethereum with only ~4,16% of Bitcoin price reaches almost ~25,58% of its total value.

As shown on the Figure 2, the total market value of all cryptocurrencies rose above

$1 trillion for the first time on January 7, 2021, as Bitcoin surged to a record high, according to data by crypto coin tracker Coinmarketcap, (Coinmarketcap, 2021).

In the cryptocurrency world, Bitcoin has consistently held the top spot when it comes to overall market capitalization. As we can see on the Figure 3, Bitcoin has been dominating the market capitalization of all cryptocurrencies since the beginning. As of February 07, 2021, Bitcoin captures around 62% of the cryptocurrency market. Ethereum comes in second, making up almost 16% of total market cap, (Coinmarketcap, 2021).

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8 Figure 2 - Total market capitalization

In January 2021, Bitcoin market cap reached an all-time high and had grown by over 400 billion U.S. dollars, when compared to the summer months. Bitcoin market capitalization increased from approximately one billion U.S. dollars in 2013 to several times this amount since its surge in popularity in 2017, (Best, 2021).

Figure 3 - Percentage of total market capitalization

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2. Bitcoin and COVID-19 pandemic

Fears over the prospect of COVID-19 pandemic are impacting the financial services sector and hampering global economic growth all over the world including that of crypto currencies. As the COVID-19 pandemic continues to disrupt global markets, investors search for an asset that could offer a hedge against macro events. Bitcoin could potentially present inflation-resistant hedge against economic slowdown, government bailouts, and fiscal stimulus, aka money printing.

Even people like Holger Zschaepitz, German market expert, and Anthony Scaramucci, an American financier who served as the White House Director of Communications, admit that Bitcoin could be superior to gold, and the competition between them has already begun.

Holger Zschaepitz (2021) tweeted “Bitcoin’s competition with gold has already started as evidenced by more than $3bn of inflows into Grayscale Bitcoin Trust & more than $7bn outflows from Gold ETFs since Oct, JPM says: Competition with gold as alternative currency will continue given millennials will become over time more important.”⁴ Anthony Scaramucci said that Bitcoin is superior to gold if investors take the time to study it. Arguing that gold may have been the choice for a store of value for 4 000 years, but nothing is forever, (Suberg, 2021).

Year 2020 saw the biggest drop-off in economic output since the Great Depression.

At the beginning of the year Bitcoin price was around 7 000 dollars. When the economy shut down due to the pandemic, Bitcoin price burst into activity once again. By the end of the year, Bitcoin has nearly quadrupled in value, thrusting itself into the center of conversation among big investors. What caused the change in Bitcoin price trajectory? One reason could be the potential currency debasement that might come from trillions of dollars of COVID-19 related stimulus payments from central banks and governments around the world, (Keoun, 2020).

In March 2020, the U.S. braced for the impact of the COVID-19 pandemic, putting restrictive measures in place in an attempt to slow down the viral spread. At the beginning of the year 2020, economists were already speculating whether the U.S. dollar could survive another decade as the world’s dominant currency. China’s proposal of their own digital currency was seen as a potential threat to dollar, (Keoun, 2020). After a U.S. drone strike

4https://twitter.com/schuldensuehner/status/1346200375871856649

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killed a top Iranian military commander during the first week of January, speculations about economic turmoil might spur demand for cryptocurrency. Bitcoin price jumped 5% to

$7 300. Based on these events, analysts started to say that Bitcoin might serve as a safe-haven asset, whose value is expected to hold in times of geopolitical or economic

instability, (Keoun, 2020).

Throughout February, Bitcoin market’s event of the year had doubled the Google searches on the term “Bitcoin halving” to their highest levels since 2016, (Keoun, 2020).

Halving refers to the number of coins that miners receive for adding new transactions to the blockchain being cut in half. This event took place on May 11, 2020, when the block reward dropped from 12,5 to 6,25. It has caused passionate debate about Bitcoin price predictions and how the market will respond as the supply entering the system will shrink, which could possibly drive the price up, (Hertig, 2020).

By late February, prices suddenly dropped alongside U.S. stocks as authorities globally struggled to stem the spread of the coronavirus beyond China, (Keoun, 2020). U.S.

stock market experienced the biggest fall in more than 20 years. Between March 4 and 23, the S&P 500 fell approximately 30%. Bitcoin also decreased in similar fashion, dropping around 58% between March 7 and 13, (Pirus, 2020). On March 12, Bitcoin touched an hourly low of $3 850, crashing from $7 900+ levels in a single day. That day goes into history as a Black Thursday, (Keoun, 2020). By the end of the April, Bitcoin again increased to about

$8 600. Bitcoin slowly showing potential properties of hedge against central-bank money-printing, big investors started to be curious about it.

The blockchain network finally reached block number 630000 on May 11. Over the course of the month, prices never climbed much over $9 000. However, the reduction in the pace of Bitcoin issuance provided a sharp contrast with the monetary policies pursued by the Federal Reserve and other major central banks. Dealing with a massive money-printing by the U.S. central bank, the Blockchain quadrennial halving might provide confidence to investors searching for an asset that is not subject to human discretion, (Keoun, 2020).

Suddenly, at the beginning of summer, Bitcoin market went cold when the new exciting sector of Decentralized finance (DeFi) has exploded in popularity. Decentralized finance is a blockchain-based financial infrastructure that has recently gained a lot of traction. It is an open and global financial system built for internet age, (DeFi, 2021) DeFi might have a significant impact on how banks operate in the future, and even has the potential to shift the structure of the whole financial system, (Sandner, 2021). It replicates

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existing financial services in a more open and transparent way. It does not rely on intermediaries and centralized institutions. Thus, it can create an immutable and highly interoperable financial system with unprecedented transparency, equal access rights, and little need for custodians, central clearing houses, or escrow services, as most of these roles can be assumed by “smart contracts,” (Schär, 2021). Services that were previously slow and at risk of human error, are now automatic and safer, when they are handled by code that anyone can inspect and scrutinize, (DeFi, 2021). DeFi sharpened many investors’ focus on what might be Bitcoin’s most-compelling use case, as a tool for hedging against central bank money printing, (Keoun, 2020).

Then, a major shift happened. Big corporations and money managers started to pile into Bitcoin. Michael Saylor, the CEO of MicroStrategy announced that MicroStrategy bought $250 million in Bitcoin on August 11. Purchasing additional $175 million in Bitcoin one month after that, (Nelson, 2020). On December 21, MicroStrategy announced that it had purchased an additional Bitcoins for approximately $650 million. As of December 21, 2020, the company holds an aggregate of approximately 70 470 Bitcoins, which were acquired at an aggregate purchase price of approximately $1.125 billion, (Corner, 2020). Following by the digital asset industry’s biggest wins to date, the PayPal acceptance of Bitcoin. On October 21, 2020, PayPal, a global e-commerce payments platform, made public its entrance into the crypto market with its new digital assets service, announcing, that its customers will be able to buy and sell Bitcoin using their PayPal accounts, (Leech, 2021).

Bitcoin delivered a very happy ending to 2020 for all long-term holders or anyone who jumped into Bitcoin market. The price drastically accelerated from mid-December, breaking through the $20 000 level. In general, Bitcoin performance in 2020 was quite spectacular. It ended 2020 at around $29 000 and started 2021 pushing up to a new record high, (Coinmarketcap, 2021). In hindsight, Bitcoin was the biggest winner from the COVID- 19 crisis of 2020.

Starting a new year, Bitcoin reached its peak almost $42 000 on January 8, 2021. In a matter of days, it plunged to around $31 000, loosing 26% of its value. On February 18, the price of Bitcoin jumped above $50 000 the first time, bringing its year-to-date gain to 74%. On March 30, 2021, Bitcoin reached a price around $59 000, (Coinmarketcap, 2021).

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3. Literature Overview

There are several studies investigating characteristics of financial asset volatility or returns using different models, such as GARCH family models. However, only few studies have focused so far on the volatility of the new digital currency and cryptocurrency market.

The overall results show that all GARCH models fitted to different cryptocurrencies exhibit extreme volatility and low correlation to traditional asset classes.

First line of research focuses on the volatility of seven most popular cryptocurrencies, including Bitcoin. The study used 12 different GARCH models in order to examine the market volatility. The overall results show that all seven cryptocurrencies exhibit extreme volatility especially when it comes to their inter-daily prices. Suggesting that cryptocurrency investment is more suited for risk-seeking investors looking to invest into technology markets, (Chu et al, 2017). Study of Bouuiyour and Selmi, (2015) analyzed daily Bitcoin prices using an optimal-GARCH model and showed that the asymmetry in the Bitcoin market was significant, suggesting that Bitcoin prices were driven more by negative than positive shocks. Conversely, Urquhart (2017) also examined the volatility of Bitcoin by using different GARCH and ARCH models. His results indicate no evidence of the leverage effect in Bitcoin market. This suggests that Bitcoin price is neither affected by good or bad news.

Second line of research examines whether Bitcoin can be used as a hedging or safe haven instrument in the US market, and explores Bitcoin’s attributes of gold. Dyhrberg (2016) applies asymmetric GARCH models to test whether Bitcoin has hedging capabilities of gold. The findings indicate that Bitcoin can be used as a hedging instrument against the American dollar and stocks in the Financial Times Stock Exchange Index in a short term.

This suggests that Bitcoin can serve as a financial instrument to hedge market specific risk.

Dyhrberg (2015) classified Bitcoin as something between gold and American dollar, on a scale from pure medium of exchange to pure store of value. Contrary, the study of Stavroyiannis and Babalos (2017) indicates that Bitcoin does not hold any of the hedges, diversifiers or safe-haven instruments.

Third line of research focused on the volatility dynamics and correlations of Bitcoin in relation to other assets. Most of the researchers have used multivariate GARCH models like BEKK-GARCH, DCC-GARCH, or ADCC-GARCH models to investigate the relationship between Bitcoin and traditional assets. Bouri, Azzi and Dyhrberg (2020)

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compared the safe-haven roles of Bitcoin, commodities, and gold against global and country stock market indices. The results indicate that Bitcoin is isolated from financial assets and can be seen as a new virtual gold. Their results are similar to that of Dyhrberg (2016).

Similarly, study of Conrad, Custovic and Ghysels (2018) dealing with the drivers of long-term volatility of Bitcoin and comparing them to other asset class, e.g. gold, concludes that Bitcoin volatility is distinct compared to other assets, suggests that cryptocurrencies are not connected to conventional markets and may offer short-term diversification benefits.

Lastly, some of the studies considered Bitcoin as an individual alternative asset in the construction of portfolio. Research of Trimborn, Li and Härdle (2017) used a Liquidity Bounded Risk-return Optimization (LIBRO) approach for risk-return portfolio optimization.

They introduced a number of cryptocurrencies into portfolios formed with S&P 100, US-Bonds and commodities. The results show that including cryptocurrencies can indeed improve the portfolio’s risk return trade-off. Correspondingly, the research results of two studies, Briere, Oosterlinck and Szafarz (2013) and Eisl, Gasser and Weinmayer (2015) show that Bitcoin should be included in optimal portfolio, and the inclusion of even a small proportion of Bitcoin may dramatically improve the risk-return trade-off of well-diversified portfolio.

Even though a lot of research studies have been conducted in modelling the structure of asset volatility in different financial sectors, cryptocurrency market still witnesses lack of scientific literature, which would enable to understand complexity of Bitcoin. This study enriches current research literature with the analysis of the effect of asymmetric information on the Bitcoin market volatility, followed by closer investigation of the risk-return trade-off.

Furthermore, the study investigates the relationship between Bitcoin and financial assets in contrast to gold, especially during the COVID-19 outbreak. And lastly, it examines the impact of replacing gold with Bitcoin on investment portfolio characteristics and returns.

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4. Bitcoin as “Digital gold”

4.1. “Safe-haven” asset

A safe-haven is a term that refers to an investment that is anticipated to maintain or increase in value during times of economic downturn. Such investments are believed to be a safe option for investors, as they are not related to economy – meaning that a financial crisis would not reduce the value of the investment, (CFI, 2021). An asset is considered

“safe” when it meets these characteristics. It serves as a store of value – i.e. generally maintains or even increases in value through market cycles. Asset has a high liquidity, it can be readily converted to cash easily and without significant loss of value, (Maharaj, Scholte and Aguirre, 2019). Its supply is limited and it is lower than the demand in order to maintain its value due to the scarcity of the asset. It should be able to maintain demand in the long- term, should exhibit low volatility, and does not decline in quality, (CFI, 2021). Most importantly, safe-haven asset has low or negative correlation to the general market, (Maharaj, Scholte and Aguirre, 2019).

There are number of investment securities that are considered to be safe. Gold is without a doubt the most commonly known safe-haven asset. Investors often flock to gold in times of turmoil because of its long history as a store of value. As a physical commodity, the price of gold is not often influenced by the decisions of central banks on interest rates, and unlike paper currencies, its supply cannot be manipulated by actions such as printing.

Other examples of traditionally considered safe-haven assets are U.S. Treasury Bonds and even some currencies, such as U.S. dollar, the Japanese yen or the Swiss franc, (Botte, 2020).

However, safe-haven assets do not have to be only traditional assets, lately, also Bitcoin has been performing as a safe-haven asset.

4.2. Intrinsic value of Bitcoin

Financial dictionary describes intrinsic value as: “The actual value of an asset. That is, the intrinsic value is what an asset is actually worth, rather than its current market value, which is overly influenced by market conditions such as recession or a speculative bubble.

One may think of the intrinsic value of an asset as its value “in a perfect world,” because one may not always be able to receive the intrinsic value,” (Farlex, 2012).

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Bitcoin’s intrinsic value has been heavily discussed in the crypto community. Andrew Baily, the Governor of Bank of England talked about Bitcoin intrinsic value saying: “It may have extrinsic value in the sense that people want it,” (Helms, 2020, p.1). Michael Saylor, the CEO of Nasdaq-listed company MicroStrategy reacted to Bailey’s comment by tweeting:

“Bitcoin is the first digital monetary system capable of storing all the money in the world for every individual, corporation, and government in a fair & equitable manner, without losing any of it. If that’s not intrinsically valuable, what is?”⁵ (Saylor, 2020, p.1). Saylor’s tweet started a discussion on Twitter where many people pointed out that Bitcoin may have no intrinsic value, but neither do fiat currencies. Back in 2018, the Federal Reserve Bank of St. Louis published a report stating: “Bitcoin is not the only currency that has no intrinsic value. State monopoly currencies, such as the U.S. dollar, the euro, and the Swiss franc, have no intrinsic value either,” (Helms, 2020, p.1).

Using the definition mentioned at the beginning of this section, and the key point being

“rather than its current market value”, we could logically state that in the absence of any market value that thing would still have vital value to people. We can highly doubt that fiat currencies are going to be still valued if they had no market value. The same holds for stock shares, bonds, and also gold. Would gold still be valued without market value? Yes, as a shiny thing and for use in electronics, (Kronenberg, 2020). In contrast, fiat money is a government-issued currency that is not backed by a physical commodity, but rather by the government that issued it. The value of fiat money is derived from the relationship between supply and demand and the stability of government decree. The supply and demand are decided by the participants of the network who are bringing a fiat currency into use, (Gupta, 2020). Similar to fiat currency, Bitcoin is also not backed by any commodity. The value of any currency comes from the backing of the state and the trust that people have over the government. Hence, for any money to be established as an exchange of the value within a network, it is important for the network to trust it, regardless of who (or what) is backing it, (Gupta, 2020).

Economic theory defines two essential characteristics for a commodity to have value:

scarcity and utility. Scarcity mean a finite supply. Bitcoin has set a cap of 21 million coins.

Thus, Bitcoin meets the first condition. In the case of gold, although the supply is limited, we do not know the total amount available. As Tom Lee said: “There are potentially millions

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of times more gold underground that actually has been extracted,”⁶ (Lee, 2020, p.1). Many analysts note that setting the cap makes Bitcoin more desirable than other assets, even gold.

Because unlike with gold, there is no worry about a digital Gold Rush, (Bearman, 2018).

But scarcity alone is simply not enough to prove intrinsic value. In an interview with Cointelegraph, BlockTower Capital chief investment officer Ari Paul explained that the

value of Bitcoin comes from the control it gives to users that own the asset. The non-confiscatable characteristic of Bitcoin provides users with an unprecedented level of

financial freedom when compared to traditional assets, (Young, 2020). According to Tom Lee: “Anyone who thinks digital gold isn’t a store of value is overlooking the fact that most businesses today are built around digital trust, including the financial system,”⁷ (Lee, 2020, p.1).

On the other side, Bitcoin skeptics argue that Bitcoin cannot be a medium of exchange.

Because of its high volatility, they consider it to be rather short-term investment, as it does not have any real-world use. This argument is partially correct, at least for now. At this moment, it is not realistic to use Bitcoin as means of exchange, due to its high price volatility.

But money is an evolutionary process. It does not suddenly come into existence as a functioning store of value, medium of exchange, and unit of amount simultaneously. Instead, those functions are developed in stages, (Invao, 2021). Hence, it will take some time before the real function of Bitcoin will be established.

4.3. Bitcoin as a store of value or medium of exchange?

The comparison between gold and Bitcoin has been long-standing tradition. Aside from their similarities, what is the reason why these two assets were always compared with one another? One reason might be that gold is an excellent store of value while Bitcoin’s debate as a store of value continues. By definition, a store of value is an asset, currency, or commodity that maintains its value over a long period. An asset would be considered as store of value if it is able to avoid depreciation over a long period of time. Anything with value that may be stored and retrieved at a later date with the expectation that it will still have value, (Farlex, 2012).

6 https://www.cnbc.com/video/2021/02/04/tom-lee-on-bitcoin-vs-gold-as-a-safe-haven-asset.html

7 https://www.cnbc.com/video/2021/02/04/tom-lee-on-bitcoin-vs-gold-as-a-safe-haven-asset.html

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Bitcoin, just like gold, is scarce. Because it is hard-coded into its protocol, the supply of Bitcoin will never exceed 21 million coins. Also, it is not easy to create it. Bitcoin creation requires mining, the process of Bitcoin mining is described in Appendix A.

According to Aristotle (384 – 322 BC) there are four defining characteristics of money: durability, portability, divisibility and intrinsic value, (Lee, 2009). One of the essential properties of money is portability. The portability of Bitcoin is said not to be an issue, at least in more developed countries. Bitcoin is easy to carry around as it does not have a physical footprint. It is possible to store any number of Bitcoins without having to carry a heavy wallet.

Second important property is divisibility. Money should be effortlessly divisible into smaller units without losing value in order to allow for the purchase of cheaper goods.

Despite Bitcoin having a supply of 21 million, one coin can be divided into 100 million units. Currently one Bitcoin is divisible down to 8 decimal places (0,00000001), calling the smallest unit Satoshi, (Grill, 2017).

Another important properties of money are storability and durability. A good money should be storable at low cost and it should not depreciate with time. The cost relating to storability of Bitcoin is extremely low and it is not dependent on third party services. The storage is relatively simple. Bitcoin can be stored on electronic devices or even oven on a piece of paper with the keypair.

Last and probably the most important characteristic is recognizability. To serve as a medium of exchange, Bitcoin must be accepted for a sufficiently large set of goods, services, or other assets. Because Bitcoin is not backed by any sovereign entity like for example regular fiat money, it has to rely on the self-fulfilling expectation of private agents that it will be accepted in order to serve as a medium of exchange. In recent times, the acceptance of Bitcoin has spread to more mainstream vendors. With each passing year, Bitcoin is gaining significant prominence and legitimacy in both, the mainstream consciousness and the business world. Probably, the biggest reason behind the recent Bitcoin rallye is that major companies and investors are finally starting to accept Bitcoin. There are hundreds of companies that accept Bitcoin as a valid payment method. Among the biggest companies that accept Bitcoin are: Twitch; Restaurant Brands International Inc.; Etsy Inc.;

Overstock.com Inc.; Coca-Cola Amatil Limited; PayPal Holding Inc.; Starbucks Corporation; USSA; Bayerischen Motoren Werke AG; Microsoft Corporation, and AT&T Inc., (Haqqi, 2021).

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Additionally, the day-to-day use and exchange of Bitcoins for fiat is becoming easier due to companies providing Bitcoin ATM (Automated Teller Machine). The difference here is that traditional ATMs allow users to withdraw and deposit cash, whereas Bitcoin ATMs allow members of the public to buy or sell Bitcoins or other cryptocurrencies by using cash or debit card. Second difference is that they are not connected to a bank account. Instead, they are connected directly to a cryptocurrency exchange via the Internet. This is what allows users to buy and sell Bitcoins instantly, (Coin Cloud, 2018).

5. What drives Bitcoin volatility?

Bitcoin’s value has been historically quite volatile. Question is, what/who determines the Bitcoin price. Is the price driven by external forces such as financial markets, or by internal forces, i.e. by the Bitcoin market participants themselves? Unlike traditional currencies/assets, Bitcoin is not issued by a central bank or backed by a government, therefore, the monetary policy or inflation rates do not influence Bitcoin price. Contrary, Bitcoin price is influenced by different factors.

Bitcoin price is not set by anyone in particular. The price is mainly influenced by the Bitcoin supply and the market demand for it. The ultimate supply of Bitcoin is fixed at 21 million. In a macro sense, as the supply is fixed, it can’t really ever keep up with demand, so long as demand keeps rising. When demand increases, prices increase, but only if supply does not increase to meet demand. Bitcoin price behaves accordingly to the basic free market precepts of supply, demand, and pricing. This suggests that Bitcoin price will likely go up over time, (Gilbertie, 2021).

Even though the total supply of Bitcoin is determined, the number of Bitcoins circulating on the network can be affected by few factors. One of them is the cost of

“production”, the mining process. When prices of production inputs (computers, hardware, electricity etc.) go down, the market supply of Bitcoin increases. Second factor influencing the supply side is the complexity of algorithmic calculations and the performance capacity of mining computers. Another very influential factor is production environment, i.e. state interventions, competition, tax environment etc. For example, if government decided to ban cryptocurrency usage and its mining, miners will have two options: move to the country where it is legal or to leave the market altogether. These were factors influencing the supply side, however, the price is determined more by the demand side.

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The demand side is also influenced by many factors. First factor influencing the demand side is competition. While Bitcoin may be the most well-known cryptocurrency, there are hundreds of different cryptocurrencies. This could be good for investors as the widespread competition keeps prices low. Luckily for Bitcoin, its visibility gives it an advantage over its competitors. Demand, similarly as supply is also influenced by government regulations. If governments would prohibit the usage of cryptocurrencies, the demand for them will decrease, causing also fall in price. Figure 4 summarizes some possible factors and the direction of their influence of Bitcoin supply and demand.

Figure 4 - Factors influencing Bitcoin demand and supply

Source: own elaboration

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6. Hypothesis

This thesis aims to take a closer look at properties of Bitcoin, its connection to other markets, and potential risks and benefits of including Bitcoin into world financial system.

I. What is the relationship between risk and return?

II. What are the characteristics of Bitcoin volatility?

III. How is Bitcoin related to other assets?

IV. Should investors include Bitcoin in their portfolios?

Firstly, I decided to estimate the systematic risk of Bitcoin in comparison to the market as a whole. And secondly, to determine what part of the total risk is idiosyncratic.

The first hypothesis regarding the risk and return, considers the role of systematic risk.

When analyzing the descriptive statistics of Bitcoin, (mean, standard deviation, median, skewness and kurtosis of daily returns of Bitcoin) presented in Table 8 (Appendix C), question about the risk-adjusted return arises. The price of Bitcoin climbed from below

$1 000 to nearly $20 000 in year 2017. Which is about 1 900% of its value from beginning of the year. This spike in 2017 was followed by a sharp pullback the following year. At the beginning of 2020, Bitcoin price was around $7 000. By the end of the year, Bitcoin has nearly quadrupled in value, reaching an all-time high above $28 000 and becoming the center of conversation among big investors, (Coinmarketcap, 2021). However, with such enormous returns one problem arises, investors have to accept an extreme risk. First hypothesis is such as follows: Hypothesis I: Bitcoin market is not going to be affected by crisis or failure of the traditional financial system.

Systematic risk represents major failure of a financial system, it is not odd expectation that Bitcoin will be to large extent detached from broader market risk, as Bitcoin is emerging as a distinct asset class.⁸

Second hypothesis which considers characteristic properties of Bitcoin returns, is stated as follows. Hypothesis II: News don’t have a significant effect on Bitcoin volatility.

Bitcoin market is not affected by either good or bad news. In other words, Bitcoin market does not exhibit leverage effect. The leverage effect, originally introduced by Black

8 To prove or disprove the Hypothesis I, I will proceed with Chapter 7 Analysis of systematic risk of Bitcoin by introducing logic of CAPM model, choosing the most suitable data, estimating its coefficients and extracting its unsystematic variance and mean.

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(1976), considers that losses have a greater influence on the future volatility than do the gains. Meaning, when prices drop, panic kicks into the market and volatility rises. In the absence of leverage effect, when the prices drop, more and more investors enter into the market. If we consider Bitcoin as an asset rather than a currency, volatility estimation and prediction are very important for the purpose of portfolio management. Therefore, financial- market participants would benefit from a better understanding of Bitcoin volatility over time.

In order to explain the Bitcoin returns volatility, the APARCH model will be implemented.⁹ Hypotheses III and IV consider the relationship between Bitcoin and other traditional assets. Because the correlation among assets returns is one of the key components when considering the risk management, we look at the link between the volatility in Bitcoin market and the volatility in other traditional markets, i.e. the gold and stock market. These two hypotheses are stated as follows: Hypothesis III: Bitcoin has a low correlation with traditional assets. Hypothesis IV: Bitcoin’s correlation to gold is increasing since the COVID-19 pandemic outbreak.

According to existing data and previous studies, throughout most of Bitcoin’s history, Bitcoin has maintained a low correlation to traditional asset classes. Due to this uniqueness, Bitcoin is an attractive tool for portfolio diversification. However, since the COVID-19 outbreak, the correlation has slightly increased. Especially, the correlation between Bitcoin and gold moved to positive values showing a relationship between these two assets.¹⁰

Last hypothesis is dedicated to investigate the position of Bitcoin in investor’s portfolio. As already mentioned, the low correlation to other assets makes Bitcoin a unique portfolio diversification tool. The last hypothesis is stated as follows: Hypothesis V:

Including Bitcoin in portfolio improves the expected risk-return trade-off.

Investing in Bitcoin has become popular in recent years, and particularly in recent months. We can see major corporations investing massive sums of money into Bitcoin. Even though investing in Bitcoin does carry a significant amount of risk, including Bitcoin in well- diversified portfolio can substantially improve the risk-return trade-offs.

9 To prove or disprove Hypothesis II, I will proceed with Chapter 8 Analysis of Bitcoin’s price volatility by introducing the APARCH model along with connected theoretical background.

10 Verification of these (III and IV) hypotheses will be placed to Chapter 9. To prove or disprove these hypotheses, DCC-GARCH model will be implemented to illustrate to correlation changes among assets.

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7. Analysis of systematic risk of Bitcoin

7.1. Capital Asset Pricing Model

The relationship of the risk and return will be modeled by estimation of Capital Asset Pricing Model (CAPM). The CAPM model can be used to calculate an asset’s expected return versus its systematic risk. This risk/return relationship is called the Security Market Line (SML). The CAPM was developed in the early 1960s by William Sharpe (1964). It is based on an idea that not all the risks should affect asset prices. It gives an insight about what kind of risk is related to return, (Perold, 2004).

The CAPM model is based on four fundamental assumptions Sharpe, (1964): market participants are homogeneous, risk averse, they can borrow at risk free interest rate, and all securities are valued correctly. These assumptions represent a perfect capital market which requires, no taxes or transaction costs, and perfect information freely available to all investors who, as a result, are homogeneous and have the same expectations. All investors are thus, rational, risk averse, they desire to maximize their own utility, and all have the same information and expectations/estimates of future returns. Tolerance of CAPM’s assumptions, however fanciful, allows the derivation of a concrete, though idealized, model of the manner in which financial market measure risk and transform it into expected return, (Mullins, 1982).

The standard algebraic form of CAPM is as follows:

E

(

Ri) = Rf + i (Rm – Rf) (1) E(Ri) – Rf = i (Rm – Rf) (2) (E(Ri) - Rf )t = i + i (Rm – Rf)t + t (3) where, E(Ri) is the return of an asset, Rf is the “risk-free” rate of return, i is the measure of volatility of a stock with respect to the market in general, and E(Rm) is the return of the market. The equation (2) is rewritten equation (1) where, E(Rm) – Rf) is the market risk premium or excess return on market, and E(Ri) - Rf is the excess return on equity. The third equation (3) is a specification of simple linear regression where, the difference between return of equity E(Ri) and risk-free rate Rf depends on level of constant i and the difference between market’s returns E(Rm) and risk free-rate Rf with intensity i with deviations  in each time frame t.

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The equation for calculating  for each security i is as follows:



i

=

𝐶𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 (𝑅_𝑖,𝑅_𝑚)

𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 (𝑅𝑚) (4

)

Covariance (Ri, Rm) =  ^(𝑅^𝑖,𝑛^{− 𝑅}^{𝑖,𝑎𝑣𝑔}^{) 𝑥 (𝑅}^𝑚,𝑛^{− 𝑅}^{𝑚,𝑎𝑣𝑔}⁾

(𝑛−1) (5)

Variance (Rm) =  ^(𝑅^𝑚,𝑛^{− 𝑅}^{𝑚,𝑎𝑣𝑔}^{)^2}

𝑛 (6)

Equation (4) shows the way to calculate value of i parameter in the linear regression

of one independent variable. Equations (5) and (6) show decomposed calculations of .

 (slope) is an essential measure in the Security Market Line equation. It measures volatility or systematic risk of a security or a portfolio compared to the market as a whole. If the model correctly describes market behavior, the relevant measure of a security’s risk is its market- related, or systematic risk, risk measured by . Most stocks have positive , meaning most stocks move in the same direction as the general market. If  exceeds 1, then the stock moves more than the market does in the same direction. Hence, a stock with  of greater than 1 is riskier than the general market, but potentially more profitable;  of less than 1 is generally less risky than the general market. Some stocks have negative  because they have a negative correlation to the general market, they move in the opposite direction to the general market.

7.2. Risk decomposition

When talking about the risk, it is widely agreed that there are two main types of risk, systematic risk and unsystematic risk, also called idiosyncratic risk. The term systematic risk is also called non-diversifiable risk, market risk or volatility risk. As defined by Kaufman and Scott (2003, p.371) “Systematic risk refers to the risk or probability of breakdowns in an entire system, as opposed to breakdowns in individual parts or components, and is evidence by comovements (correlation) among most or all the parts.”

Systematic risk is a part of the total risk that is caused by external factors beyond the control of any specific company or individual. Therefore, all investments or securities are subject to systematic risk since this type of risk is not in their control, (CFI, 2021). We are experiencing a systematic risk even now. The COVID-19 pandemic is great example of systematic risk, as it has impacted almost every industry, leaving only a few of big players untouched. The COVID-19 pandemic is undeniably the most discussed topic in the last year,

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and it is not affecting only day-to-day life of every person but also the entire global market.

Beside the pandemic, other examples include financial crises, exchange rate changes, changes to laws, increase in interest rates, tax reforms, natural disasters, changes in foreign policy, political instability etc.¹¹

Many of the traditional systematic risks mentioned above might not affect cryptocurrencies. Since the nature of Blockchain is decentralization, the political instability, interest rate, or the health of the banking system would not have direct impact on the industry, (Kordyban, 2020). Therefore, systematic risks are different for traditional assets then for crypto. The major systematic risk for Bitcoin and other cryptocurrencies that must be considered is that of hacking. As the industry is technology-based, continues to grow and more money is invested, hackers become more and more of a risk. Cyberattack is serious problem, since there is no way to retrieve stolen Bitcoins.

On the other side, idiosyncratic risk, also known as unsystematic risk, is not correlated to the overall market risk. It is risk of price change cause by the unique circumstances of a particular security. One example of idiosyncratic risk of Bitcoin is its volatility. The price of Bitcoin is constantly changing, making the rate of return unpredictable. Second possible idiosyncratic risk is the regulatory/compliance risk. Some countries may decide to restrict the use of the cryptocurrency by stating that transactions break anti money laundering regulations, notwithstanding the global implication, (Thackeray, 2018). Another example is business risk. Considering that cryptocurrencies are not backed by any central bank, a national or international organization, their value is determined by the value that market

11 Although Bitcoin network is decentralized, the web and the exchanges that offer cryptocurrency-related services are not.

Therefore, cryptocurrencies are still partially a subject to systematic risk as long as they are affected through these networks. An alternative viewpoint is that the widespread use of cryptocurrencies might be the systematic risk that traditional assets should be aware of, (Kordyban, 2020). However, survey from the London-based Center for Macroeconomics asked whether cryptocurrencies exhibit a systematic risk, and whether they should be more tightly regulated. They found that nearly 73% of a pool of 50 European macroeconomists publishing in top economic journals do not think cryptocurrencies such as Bitcoin are currently a threat to the stability of the financial system, or can be expected to become a threat in the next couple of years. By contrast, 61% of them agreed that the regulatory oversight needs to be increased, (BRINK Editorial Staff, 2018). Many believe cryptocurrencies were designed to “threaten the financial system.” This claim might be supported by the key fundamentals that cryptocurrencies, in this case Bitcoin, are operating on. Firstly, they offer peer-to-peer transactions with no intermediary while still offering security through the blockchain. The second reason is that Bitcoin was preset to finite supply similar to assets that are precious metals like gold. Making it impossible for governments to inflate or deflate the prices as they can do with fiat money, (Kordyban, 2020). In consequence, it has the potential to undermine traditional assets classes. As people will begin to lose trust in traditional markets they will look at new markets like crypto for investment.

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participants place on them, which means that loss of confidence may an abrupt drop in value, (Thackeray, 2018).

Idiosyncratic risk of a single security can be calculated as follows:

Total Variance = Systematic Variance + Unsystematic Variance (7)

Total Risk = Standard Deviation (8)

Total Variance = (Standard Deviation)² (9)

Systematic Risk =  * market (10)

Systematic Variance = ( * market)² (11) Unsystematic Variance = Total Variance – Systematic Variance (12) Unsystematic Risk = √(𝑇𝑜𝑡𝑎𝑙 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 − 𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒) (13)

The total risk of a security is estimated by calculating the standard deviation of its historical returns (8). The total variance of an asset is composed of Systematic variance and Unsystematic (Idiosyncratic) variance (7). Total variance is calculated by squaring the total volatility of an asset (9). The unsystematic variance is calculated by subtracting the square of security’s market volatility from the square of security’s total volatility (12). The last formula (13) shows the estimation of idiosyncratic risk which is calculated by the square root of unsystematic variance.

7.3. Data

As it has been already stated, the CAPM model describes the relationship between the systematic risk and expected return for assets. Typical proxy a for risk-free interest rate are yields of U.S. Treasury Bills. Treasury bills are considered to have minimal risk since government cannot default on its debt. Yields on markets are priced at a spread over the corresponding risk-free Treasury rate. Yields on money market (crypto market) are often priced relative to yields on Treasury of a similar length. Yields on short-term Treasuries can behave differently from yields on long-term Treasuries. One-year US Treasury Bill is typical proxy for risk-free interest rate. However, because of the nature of this analysis, which is focusing on daily data, bonds of shorter maturity might be more suitable as risk free proxy.

For this reason, I will include both, 1-year US Treasury Bills and 4 weeks US Treasury Bills to choose the type of bonds which will fit best the estimated models.

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Second step, before estimating the CAPM model of Bitcoin is to choose what should be used as a market proxy. When choosing an appropriate market proxy for investment hypothesis, investors attempt to find proxies that reflect the fragment of the market in which they are interested in getting involved. That leads us to the limitation of any market proxy, which is an artificial representation of the entire market. The S&P 500 is recognized worldwide as one of the premier benchmarks for the U.S. stock market’s performance. The S&P 500 does not simply contain the 500 largest stocks; rather, it covers leading companies from leading industries. It represents a broad-section of the U.S. equity market, including common stock traded on U.S. exchanges, (S&P 500, 2021). The question is whether the U.S.

market and S&P 500 is relevant internationally? The S&P 500 represents about 80%-85%

of the U.S. stock market. From the global perspective, the U.S. is over one-half of the global stock market, as measured by the S&P Global BMI. If we should pick one macro indicator that the rest of the world watches to gauge not just the U.S. but the global economic health, it would be probably CBOE¹² Volatility Index (VIX), which is based on S&P options, (Gunzberg and Edwards, 2018). Because Bitcoin is detached from any specific territory I wanted to use market index representing the global economy. For these reasons, I decided to use U.S. market index S&P 500 as a proxy for my analysis. The data for S&P 500 index were taken from Yahoo Finance (2021).

In the analysis, data sets of three times series are included. Daily closing prices of Bitcoin were obtained from Coindesk (2021). Even though, Bitcoin trading started in 2009, the price did not experience any significant change till 2017, when the price climbed from below $1 000 to nearly $20 000 on the CoinDesk Price Index (BPI). For this reason, I have selected period from 01.01. 2014 to 31.12. 2020. This leaves us with 2 257 observations.

From daily closing prices, returns are calculated as a percentage change from the beginning of the period until the end, using the following formula:

rt = 100 x (Pt – Pt-1)/Pt-1, (14) where rt is the daily return for time t, pt is the closing price at time t, and pt-1 is the corresponding price in the period at time t-1.

Unfortunately, one significant problem came up during data collection. The differences between trading days of Bitcoin and S&P 500 caused discrepancy in collected data. Since cryptocurrencies are traded continuously, Bitcoin is traded every day without

12 Chicago Board Options Exchange https://www.cboe.com/