China’s secretive stance on digital currencies is starting to reveal traces of long-term aspirations. On one hand, the country does not allow any form of crypto-trading, even calling for the shut The upcoming negative interest rates in the US and Europe are a great opportunity for Bitcoin and other cryptocurrencies. China’s secretive stance on digital currencies is starting to reveal traces of long-term aspirations. PDF | This paper examines the volatility of cryptocurrencies, with particular attention to their potential long memory properties. Using daily data for… | Find, read and cite all the research you need on ResearchGate
Justin Sun, the 29-year-old entrepreneur behind Tron, has been a controversial figure in the crypto industry, often evoking mixed reactions to his publicity stunts and outspokenness on social media.
Nonetheless, Sun is an important driving force in the sector as both his past and future endeavors put him among the most prolific entrepreneurs in tech today.
We take a look at the life of the self-proclaimed “protégé of Jack Ma” and the face of the TRON empire.
Born in 1990 as Sun Yuchen, Justin Sun has always shown a strong proclivity for fame and attention. A good student, Sun was enamored with liberal ideas and never shied away from standing up to authority.
In an early GQ profile of Sun published in China, he recalled his school days, saying he was often the “campus opinion leader” who often went against the mainstream. A vocal critic of school policies, Sun was also a prolific writer churring out articles filled with heavy criticism of the Chinese government.
The first time Sun got a taste for fame came after the middle school he attended in the city of Huizhou announced plans to tailor academic guidance to students according to various categories.
That meant that students from low-income families and those believed to have “extreme views” would receive alternative guidance from teachers than those headed to college.
Sun heavily criticized the decision in a widely circulated online post that made the rounds across China.
He called the effort “a cruel thing” that aims to institutionalize the tight control over students and compared the school system with Nazi Germany.
It was through posts like this that helped Sun gain nation-wide fame both online and in print media. He was featured on the cover of Hong Kong-based magazine Yazhou Zhoukan, which described him as a young “opinion leader.”
“Some might argue that Sun became an opinion leader just to become famous, but I think it was more of a natural result of the overall social atmosphere back then in China,” journalist Zhang Jieping, who interviewed Sun for the Yazhou Zhoukan cover story, told Quartz.
The outspoken and energetic Sun went on to attend Peking University and earn a bachelor’s degree in history in 2011. Two years later, he obtained a master’s degree in political economy from the University of Pennsylvania.
According to Quartz, this is when he first came across the very niche world of cryptocurrencies. Through incredible foresight or just sheer luck, Sun became a millionaire by investing in Bitcoin in its early days.
While the extent of his investments in Bitcoin is still unknown, upon his return to Beijing in 2013, he was already one of the youngest crypto millionaires.
Sun’s return to China marked the beginning of a busy year for the ambitious entrepreneur.
He soon joined Ripple Labs, a then-young company working on the creation of a cross-border payment settlement system that would yield XRP, the third-largest cryptocurrency by market cap.
As Ripple’s first employee in the country, he served as the company’s chief representative for the greater China region and later became an advisor.
At the time, Sun’s time was divided between Ripple and Peiwo, a social media app he created that connects like-minded users via live audio chats based on ten-second pre-recorded voice samples.
The platform quickly became popular among China’s teens, with a 2018 report saying the app’s users were mainly between the ages of 16 and 25. With more than ten million registered users and more than one million monthly active users, Peiwo, loosely translated to “call me,” was what put Sun on the map.
The Chinese government praised the young entrepreneur, who, in turn, said that China had “the best environment for entrepreneurs in the world.” Even Jack Ma, the legendary founder and CEO of online giant Alibaba, took notice of Sun and personally invited him to become one of the thirty students in the inaugural class of his Hupan University in 2015.
Sun attended the university for three years and graduated in 2018 with a thesis titled “The Birth of a Decentralized Internet.”
However, it remains unclear what subjects Sun took while at the university, as the only classes mentioned to the public were taught by Ma himself and were titled “CEO 101.”
Jack Ma presenting Justin Sun with a diploma from Hupan University in 2018
(Source: Tron Foundation)
Nonetheless, he said the time he spent at Hupan taught him both moral and business values, which he was eager to implement in all of his business ventures.
“I was able to take the experiences and knowledge shared by my professors and classmates and immediately put it into practice,” Sun told the South China Morning Post last year.
It was also the connections he made at Hupan that propelled him to fame both in China and worldwide.
Soon after enrolling, Sun was invited by Yu Jianjun, a Hupan University alumni and co-founder of the Chinese audio streaming company, Ximalaya FM, to share his story as a successful young entrepreneur online.
The podcast he launched in 2016, called “The Revolutionary Road to Financial Freedom,” earned him a cult following online.
A quick rise to fame propelled by his online presence and powerful connections led Sun to establish the Tron Foundation in 2017. The Singapore-based company was tasked with creating TRON, a blockchain-based, decentralized protocol project with an internal digital currency, Tronix (TRX).
To fund the ambitious project, the Tron Foundation conducted an initial coin offering (ICO) on Binance from Aug. 31, 2017, to Sep. 2, 2017, raising $70 million in the sale.
Apart from raising a significant amount of money, Sun couldn’t have picked a better time for the ICO—the sale was completed just before China clamped down on token sale s with its notorious ICO ban. Most other token issuers were forced to migrate to more ICO-friendly places such as Hong Kong or Japan.
This positioned Tron as a leader in blockchain in China. With no apparent consequences from the state’s clampdown on the token issuance and $70 million to spend, the company quickly established partnerships with a series of major companies, including Chinese video hardware and software provider Baofeng (called the “Netflix of China”), and oBike, the largest bike-sharing company in Singapore.
Justin Sun is one of the wealthiest entrepreneurs in the cryptocurrency industry. His wealth comes primarily from his TRX token holdings. His wallet size is unknown, and he has refused to disclose his exact holdings.
It would be fair to estimate he owns roughly 10-20% of the total supply, which would value his TRX worth between $100 and $200 million.
He has also made significant investments in acquisitions of Poloniex—a cryptocurrency exchange that was once valued at $400 million, Steemit platform, and BitTorrent, which he acquired for $140 million. BitTorrent also has its tokens, which are called the BTT tokens with a market cap of $60 million.
Factoring all the data above, his net worth is expected to be between $200 to $400 million.
Despite his high net-worth, Justin Sun was recently found claiming small business relief funds for Tron from the U.S. government.
While Sun’s outspoken personality might have pushed Tron into the spotlight, it was also what kept the spotlight on Tron when it faced some of its many scandals and controversies.
Sun famously quarreled with Vitalik Buterin, the founder of Ethereum, on Twitter, saying that Tron’s capabilities vastly exceeded that of Ethereum. Sun’s incredibly flawed comparison earned him a lot of criticism, both from Tron users and other industry figures.
Buterin himself accused Sun of copying Ethereum’s whitepaper, an allegation that follows the project to this day.
The year was especially busy for Sun, who acquired BitTorrent, the largest file-sharing platform in the world, for $126 million. Famously said to be responsible for almost 5% of all internet traffic, BitTorrent was regarded as an incredibly bold move for Tron.
The goal of the acquisition was to turn BitTorrent’s 100 million monthly active customers into TRX users—a notion that pushed TRX’s price through the roof immediately after the acquisition was announced. Ryan Selkis, chief executive officer at researcher Messari, said the market response to the purchase was “wild to watch.”
This wasn’t the first, nor the last, controversy that surrounded Sun or Tron. Few have managed to attract as much press as Sun’s, now legendary, lunch with Warren Buffet did.
In 2019, Sun famously paid $4.5 million for the opportunity to have lunch with the legendary investor and CEO of Berkshire Hathaway, Warren Buffett. Buffett has hosted similar lunches every year for decades, with all of the proceeds from the payment going to the Glide Foundation, a San Francisco-based charity which helps the poor, homeless, and those battling substance abuse.
Justin Sun’s $4.5M Dinner With Warren Buffett
Sun famously invited the U.S. President Donald Trump and other industry leaders to join him for lunch, but postponed two days before it was supposed to take place due to “health reasons.”
The cancellation had been met with widespread criticism and ridicule in the TRON community, particularly in China. Rumors began to circulate that Sun was unable to leave China due to a government-enforced “exit ban.”
However, the Tron Foundation denied these claims, saying that Sun was recovering from kidney stones in his San Francisco home.
Eventually, the adamant Bitcoin-critic and Sun met at a private country club in Buffett’s home city, Omaha, Nebraska, on Jan. 23, 2020. It was joined by eToro CEO Yoni Assia, Head of Binance Charity Foundation Helen Hai, Litecoin founder Charlie Lee, and Huobi CFO Chris Lee.
But, before the dust from his long-awaited lunch with Buffett even settled, Sun was embroiled in yet another controversy, this time surrounding the decentralized content sharing platform Steemit.
After Tron acquired Steemit in February, Sun was accused of using the company to consolidate power over the once wholly decentralized blockchain. However, Steemit users managed to take back control of the Steem blockchain within days, pushing Sun out and leaving him at the mercy of the crypto community.
Despite the controversies, the crypto industry might not be that young anymore, but Sun certainly is, which leaves him ample time to do both good and bad for the space.
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Source: https://cryptobriefing.com/who-is-justin-sun-entrepreneur-behind-tron/
Source: zephyrnet.com
Author: Published 15 hours ago on May 29, 2020
By Republished by Plato
Negative interest rates are opportunities for cryptocurrencies
Interest rates have been falling for years and whoever thought the interest rate would come to a standstill at zero percent at the latest was wrong. Since more and more banks introduce negative interest rates, investors are looking for other ways to invest. A study now shows that Bitcoin could benefit extremely from the negative interest rate.
New York (U.S.A.). In the past, there was still good interest on his savings in the savings book or call money account. Today, however, things look very different: Most savers can still be happy that their house bank does not charge negative interest on their financial reserves – not yet! After the first banks introduced the negative interest rate, larger and smaller financial institutions are following suit. If the key interest rate does not rise again, it is only a matter of time before all banks charge money for their customers' credit balances.
To protect their money, more and more people are looking for other investment opportunities. In addition to the classic exchange, the focus has recently been increasingly on the crypto market. Cryptocurrencies have been around for several years, but only everyone has known them since the Bitcoin boom in late 2017. A recent US study has analyzed the current situation and comes to the conclusion that the negative interest rate could be a great opportunity for Bitcoin.
Since cryptocurrencies can now be traded easily on the computer screen or even via an app, such as BitQT, there are no longer any technical hurdles. In addition, digital currencies are no longer new and enjoy greater public confidence from year to year – even in times of crisis (we reported).
A report by Stack Funds, released on May 14, 2020, wrote that negative interest rates are increasingly becoming a reality in the United States. This forces investors to look for alternative investment opportunities. Again, according to the study, this could be a huge opportunity for Bitcoin.
However, it must be noted that an economy depends not only on a single key interest rate, but on many different interest rates. The so-called Federal Funds Rate of the USA was considered in the course of the current study. This indicates the interest rates at which US banks can borrow money from one another.
In this context, the study explains that negative interest rates are usually a sign of a weak economy. “In theory, negative interest rates only occur if a central bank wants to use them to stimulate a weak economy. In deflation, people and businesses prefer to save their money rather than spend it, and negative interest rates should encourage them not to park it in the bank, ”the final report said.
When interest rates are low or no or negative in a country for the most part, it is all the more difficult for investment companies since all traditional investment products hardly generate any returns. Therefore, at such a time, they have to look for alternatives that are still profitable despite the circumstances.
“It is difficult to argue why a fund manager shouldn't add cryptocurrencies to his portfolio. As I like to say: 'Bitcoin was born in an economic crisis and will be ready for the market in a new economic crisis,' it continues.
As other Bitcoin studies have already shown, cryptocurrencies – but especially Bitcoin – are on the rise. For example, the renowned hedge fund manager Paul Tudor Jones had recently campaigned for the digital currency, which has generally attracted great attention in the financial world.
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Source: www.forschung-und-wissen.de
China: Parliament passes law allowing inheritance of Bitcoin and cryptocurrencies; a changing crypto narrative?
China’s secretive stance on digital currencies is starting to reveal traces of long-term aspirations. On one hand, the country does not allow any form of crypto-trading, even calling for the shut down of the Bitcoin mining business in a province earlier this month.
But a recent development indicates cryptocurrencies may be on China’s radar all the time, especially the regulatory and legal aspects of a world run on stateless currencies.
Earlier this week, locals reports suggested new civil legislation had been submitted for the government’s approval, including “virtual assets” in the list of items that could be passed down. The law was adopted in a now-concluded parliament meeting, as Beijing’s Xinhua Net confirmed on May 28.
In the third sessions of the Thirteenth National People’s Congress presided by President Xi Jinping, China updated the country’s existing civil code; new legislation that now includes “virtual currencies” as part of a citizen’s civil rights. The drafts were first submitted on May 22 to the committee, after “years of deliberation.”
This means if a Chinese citizen holding Bitcoin, Ethereum, or any other digital asset dies, his “will” would legally allot all holdings to a nominated person. Other “internet”-based properties, such as in-game currencies, can also be passed down.
Dovey Wan of Primitive Ventures tweeted in the regard, voicing some concerns:
China’s Inheritance Law has expanded the scope of inheritance to include internet property and cryptocurrency (so Bitcoin is included)
🤔 but I would rather my Bitcoin be protected by the key itself not the law tho , the problem with law is always enforcement not legislation
— Dovey 以德服人 Wan 🪐🦖 (@DoveyWan) May 25, 2020
The new inheritance law comes into effect on January 1, 2021. Previously, prominent academics in China voiced their opinions about the country’s outdated civil laws, which did not change over time to include digitalized aspects of the 21st century.
Lixin Zhang, professor at the Renmin University, told in an interview with China’s top television broadcaster that the country was developing rapidly, and multiple laws and regulations needed to improve for meeting the “current needs of 2020 Chinese society.”
Chinese regional courts have been treating cryptocurrencies as lawful property, even before the signed dictum.
Last month, Baijiahao Baidu reported that Shanghai’s No.1 Intermediate People’s Court had considered Bitcoin as “foreign property” for a theft case tracing back to 2018, which had defendants seeking compensation.
Determining Bitcoin as “virtual property,” the court stated any stolen and forcibly-obtained cryptocurrency must be returned to its lawful owners either immediately or be available for purchase at a massively discounted price.
In another similar case in 2019, the local courts of Hangzhou considered Bitcoin a “virtual property.” The proceedings involved a now-defunct crypto exchange and its estranged users seeking millions in damages.
Despite China’s lack of crypto framework, the country has stepped up time and again with legal judgments about cryptocurrencies. Such proceedings indicate the country’s stance on digital assets, including how lawmakers view the idea of crypto as a legal, “virtual,” property.
With China’s Digital Yuan coming up and said to feature at the 2022 Bejing Winter Olympics, the country may well be creating legal infrastructure around digital currencies, unbeknownst to other governments, or even its own citizens.
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Source: cryptoslate.com
Author: Shaurya Malwa ·
(PDF) Long Memory in the Volatility of Selected Cryptocurrencies: Bitcoin, Ethereum & Ripple
This paper examines the volatility of cryptocurrencies, with particular attention to their potential long memory properties. Using daily data for the three major cryptocurrencies, namely Ripple, Ethereum, and Bitcoin, we test for the long memory property using, Rescaled Range Statistics (R/S), Gaussian Semi Parametric (GSP) and the Geweke and Porter–Hudak (GPH) Model Method. Our findings show that squared returns of three cryptocurrencies have a significant long memory, supporting the use of fractional Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) extensions as suitable modelling technique. Our findings indicate that the Hyperbolic GARCH (HYGARCH) model appears to be the best fitted model for Bitcoin. On the other hand, the Fractional Integrated GARCH (FIGARCH) model with skewed student distribution produces better estimations for Ethereum. Finally, FIGARCH model with student distribution appears to give a good fit for Ripple return. Based on Kupieck’s tests for Value at Risk (VaR) back-testing and expected shortfalls we can conclude that our models perform correctly in most of the cases for both the negative and positive returns.
J. Risk Financial Manag. 2020, 13, 107; doi:10.3390/jrfm13060107 www.mdpi.com/journal/jrfm
Article
Long Memory in the Volatility of Selected
Cryptocurrencies: Bitcoin, Ethereum and Ripple
Pınar Kaya Soylu
1
, Mustafa Okur
2
, Özgür Çatıkkaş
3
and Z. Ayca Altintig
4,
*
1
Department of Business Informatics, Faculty of Business Administration, Marmara University,
34722 Istanbul, Turkey; pinar.kaya@marmara.edu.tr
2
Department of Capital markets, School of Banking & Insurance, Marmara University,
34722 Istanbul, Turkey; mustafaokur@marmara.edu.tr
3
Department of Insurance, School of Banking & Insurance, Marmara University, 34722 Istanbul, Turkey;
ozgurcatikkas@marmara.edu.tr
4
Peter F. Drucker and Masatoshi Ito Graduate School of Management, Claremont Graduate University,
Claremont, CA 91711, USA
* Correspondence: ayca.altintig@cgu.edu
Received: 6 March 2020; Accepted: 27 May 2020; Published: 29 May 2020
Abstract: This paper examines the volatility of cryptocurrencies, with particular attention to their
potential long memory properties. Using daily data for the three major cryptocurrencies, namely
Ripple, Ethereum, and Bitcoin, we test for the long memory property using, Rescaled Range
Statistics (R/S), Gaussian Semi Parametric (GSP) and the Geweke and Porter-Hudak (GPH) Model
Method. Our findings show that squared returns of three cryptocurrencies have a significant long
memory, supporting the use of fractional Generalized Auto Regressive Conditional
Heteroscedasticity (GARCH) extensions as suitable modelling technique. Our findings indicate that
the Hyperbolic GARCH (HYGARCH) model appears to be the best fitted model for Bitcoin. On the
other hand, the Fractional Integrated GARCH (FIGARCH) model with skewed student distribution
produces better estimations for Ethereum. Finally, FIGARCH model with student distribution
appears to give a good fit for Ripple return. Based on Kupieck’s tests for Value at Risk (VaR) back-
testing and expected shortfalls we can conclude that our models perform correctly in most of the
cases for both the negative and positive returns.
Keywords: volatility modelling; cryptocurrency; value at risk; expected shortfall; long memory
1. Introduction
Since the early 2000s, the perception of investors about traditional financial markets, their
systems and policies has changed dramatically. There is a global loss of confidence in the central bank
based, fiat currency centered, interconnected financial system. There are many reasons for this shift
in confidence. First of all, loose monetary policies of central banks and the simultaneous global
imbalances created an asset price bubble in early 2000s, which led to the global financial crisis in 2008
and the resulting Great Recession (Allen and Carletti 2010; Carmassi et al. 2009). Financial crises are
like storms for economies: they increase unemployment rates and financing costs, deepen recessions,
and negatively affect global trade. Economies, especially emerging economies, need increasingly
more financing in order to refinance their debts in an environment of increasing risk premiums
(Dominguez et al. 2012).
The 2008 financial crisis, at the same time, increased the volatility and thus changed the risk
perception of investors in global financial markets. Therefore, many investors trading in financial
markets, especially those invested in markets which did not fair the storm well, lost their confidence
J. Risk Financial Manag. 2020, 13, 107 2 of 21
in the ability of central banks to manage financial crises (Bordo and Siklos 2017; Cukierman 2013;
Wagner 2010).
Simultaneously, during this period since 2000, many countries have tried to use currency
depreciations via lower interest rates as a competitive tool in global trade. These currency wars
between the major central banks have contributed to the excessive asset price increases during the
early part of the century. On the other hand, these currency manipulations have negatively impacted
investors’ confidence in financial markets, their regulators and central banks and the overall global
financial system (Blanchard 2016; Caballero et al. 2015; Cline and Williamson 2010).
The policy uncertainty, market volatility and change in investor confidence in the financial
system, coupled with recent developments in blockchain technology has led to the invent of, and
(very quickly) increasing demand for, cryptocurrencies (Çağlar 2007; Liu and Tsyvinski 2018;
Panagiotidis et al. 2018, 2019, 2020).
Since its initial introduction, Bitcoin—the first and most common cryptocurrency—has received
unexpected attention and even notoriety in financial markets and has become part of commonplace
financial metrics to be followed by investors. According to Hileman and Rauchs (2017), the rise of
cryptocurrencies in financial markets can be attributed to the fact that unlike traditional fiat
currencies, cryptocurrencies are fully digital assets; have fast, reliable, low cost and anonymous
exchange systems; and are not controlled by a central authority such as central banks.
Barber et al. (2012) explored the Bitcoin as a potential solution to the structural problems in
financial systems. While examining the advantages of Bitcoin over other cryptographic currencies,
they conclude that Bitcoin has the potential to be a long-term stable currency. They state that, if the
system design is properly supported, decentralized digital currencies can have a strong influence on
financial markets (Barber et al. 2012).
In the last decade, the increasing popularity of cryptocurrencies has resulted in many to be
created. By the year 2018, there were approximately 1700 different cryptocurrencies in existence with
a total global daily transaction volume of 11 billion US dollars (Hileman and Rauchs 2017). Yet, three
major cryptocurrencies make up 60% of the transaction volume and 86% of the total cryptocurrency
market capitalization: namely Bitcoin, Ethereum and Ripple (BitInfoCharts 2018).
This fast development and increasing spread of cryptocurrencies evidenced by their increasing
transaction volume and market capitalization, has identified cryptocurrencies as a major disruptive
instrument in international financial markets. Thus, the academic and practitioner debate of how to
classify a cryptocurrency in the world of investments, namely whether as a “security,” a
“commodity,” or a “currency”, has become more significant and heated over the years. This
classification is important in many aspects of the study of these instruments, especially in
determining the role cryptocurrencies will play in diversified portfolios of rational investors (Jackson
2018). The debate on this issue is still ongoing both in academic and practitioner worlds.
Cryptocurrency valuations, especially that of Bitcoin, have increased excessively against the
dollar in the last decade. As a result, they have become an attractive investment option to many
investors. An increasing number of investors now include, or consider including, cryptocurrencies in
their portfolio selection processes. Even though the traditional risk-return trade-off establishes the
positive correlation between risk and return, investors, when making portfolio decisions, tend to
overestimate the potential returns of an asset, while often ignoring or underestimating the risk.
There are two major risks that cryptocurrency investors are exposed to. First of all, the
cryptocurrencies do not have intrinsic asset values due to their blockchain based structures. Second,
cryptocurrency returns have significantly higher volatility than the returns of more traditional
financial assets such as stocks or precious metals etc. (Bouri et al. 2019; Liu and Tsyvinski 2018).
Similarly, cryptocurrency returns have been shown to have significantly higher volatility than major
world fiat currencies (Caginalp and Caginalp 2018; Catania et al. 2018; Sahoo 2017).
Since volatility of investment returns is a fundamental issue for the smart investor and portfolio
manager in contemporary financial markets, adequate modeling for volatility of cryptocurrencies
becomes vital for risk management. In this study, we model the volatility of cryptocurrencies by
appropriate Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) type models.
J. Risk Financial Manag. 2020, 13, 107 3 of 21
Unlike similar studies in the literature, the scope of the research is not limited to Bitcoin only, but
includes all three largest market capitalization cryptocurrencies: Bitcoin, Ethereum and Ripple.
Bitcoin and Ethereum are decentralized digital currencies without a single administrator and
operate on public blockchain ledgers. Unlike the other two, Ripple, is a centralized cryptocurrency,
which operates on a distributed ledger controlled by the Ripple Labs. In other words, all the ledger
books on which Ripple cryptocurrency (XRP) is traded, are managed by the Ripple Labs itself.
Whereas Bitcoin and Ethereum are released and added to the network as they are mined by
independent sources, Ripple Labs releases a certain amount of Ripple cryptocurrency tokens each
month. In addition, unlike its other cryptocurrency counterparts, Ripple cryptocurrency is
intentionally designed to be an effective tool in international fiat money transfers. Even with their
slight differences in structure, these three cryptocurrencies make up most of the market capitalization
and more than half the world trading volume. Therefore, correctly modelling their volatilities is a
very important contribution to the literature.
On the other hand, literature using persistency analysis on cryptocurrencies is continuously
growing. Specifically, the increasing evidence of long-term dependence in cryptocurrency markets
provides evidence that cryptocurrency price changes are not random and future prices of
cryptocurrencies are predictable. This predictability in prices contradicts with the efficient markets
hypothesis and random walk expectations of Malkiel and Fama (1970). If cryptocurrency prices
exhibit long memory, investors can predict future prices and beat the market (Mensi et al. 2019).
Therefore, the presence of long-term memory in cryptocurrency returns and volatility has gained a
lot of importance for both academics and practitioners. Gil-Alana et al.
(2014) show that market
analysts and investors can use long-term memory models of cryptocurrency returns in order to
improve the risk-adjusted performance of their portfolios. Our study also contributes to this growing
literature on persistence and long-term memory in cryptocurrency returns by expanding the research
into the three major cryptocurrencies.
The study is designed as three basic sections. In the first part, the literature on cryptocurrencies
and specifically their volatility is summarized. In the next section, GARCH family models are used
in the estimation of the volatility the three major cryptocurrencies. In the final part, the results of the
selected GARCH model are presented and their contribution of findings to the efficient
diversification of international investors’ portfolios is discussed.
2. Literature Review
Forecasting volatility is very important for both investment decisions and risk management.
However, it is possible to say that simple methods of measuring volatility, such as standard deviation,
are no longer sufficient to adequately measure volatility of complex financial instruments in today’s
globally integrated financial markets. At its simplest, the standard deviation gives equal weight to all
past observations, which is not adequate for contemporary forecasting exercises. GARCH models, on
the other hand, provide a means for measuring time-varying volatility (Engle 1982). Therefore
GARCH family of volatility models have become the standard in the estimation of the volatility in
financial markets and for most traditional financial instruments (Baillie 1996; Bollerslev et al. 1992;
Ding and Granger 1996; Lo 1989; Pati et al. 2018; Poon and Granger 2003; Wang et al. 2018). However,
since cryptocurrencies are relatively a new phenomenon, there is still not a lot of literature on the
modeling of their volatility. The existing academic literature on the volatility of cryptocurrencies is
limited and also focuses exclusively on the most popular cryptocurrency, Bitcoin.
For instance, Urquhart (2018) argues that the increase in transaction volume and volatility of
Bitcoin are significant factors in its popularity. Caginalp and Caginalp’s (2018) findings also support
Urquhart’s (2018) results about the valuation of cryptocurrencies. Iwamura et al. (2014) explores the
reasons for price instability in cryptocurrencies and argues that a new monetary policy strategy
without central banks could stabilize the value of Bitcoin and other cryptocurrencies. In the study,
mentioning Satoshi Nakamoto’s 2008 paper, authors suggest that Bitcoin’s price inflation can be
avoided by limiting the fluctuations in market value due to the previously announced limited amount
of supply (Iwamura et al. 2014).
J. Risk Financial Manag. 2020, 13, 107 4 of 21
Although Bitcoin has extremely high volatility, many researchers still consider it to be a valuable
diversification instrument for a portfolio (Bouri et al. 2018). Briere et al. (2015), document a low
correlation between Bitcoin and both traditional assets (stocks, bonds, and hard currencies) and
alternative investments (commodities, hedge funds, and real estate). Dyhrberg (2016), similarly, finds
that Bitcoin can be used as a hedging instrument for UK currency and equities, since positive and
negative shocks do not affect Bitcoin returns asymmetrically. Bouri et al. (2017) state that Bitcoin can
serve as an effective diversifier for most of the assets and a strong hedge for the commodity market.
Recent empirical studies on cryptocurrencies focus on the long memory behavior. In their recent
study, Bouri et al. (2019) investigate persistency in the price and volatility of Bitcoin. By using both
parametric and semiparametric methods, they find evidence that there exists a long memory in the
volatility of Bitcoin.
Chu et al. (2017) investigate the volatility of the most traded seven cryptocurrencies by using
various GARCH class models. Their results show that the IGARCH and GJRGARCH models provide
the best fits, in modelling the volatility in the most popular cryptocurrencies. They conclude these
extreme volatility characteristics of cryptocurrencies make them interesting for the risk-seeking
investors who want to enter into technology markets.
Sahoo (2017) also uses GARCH to model the volatility of Bitcoin prices, and comes to the
conclusion that Bitcoin is a high volatile currency. Peng et al. (2018) try to find the best GARCH model
fit that estimates volatility for three different cryptocurrencies by using daily and hourly closing price
data for Bitcoin, Ethereum and Dash for the 2016–2017 period. (Peng et al. 2018). Similarly, Katsiampa
(2017), also models the volatility of Bitcoin using closing prices with different GARCH models, and
presents evidence of long memory in the volatility in Bitcoin prices. Lahmiri et al. (2018) show the
long-term volatility of seven different cryptocurrency markets using the FIGARCH method and
conclude that the volatility shocks in these markets have long memory.
Mensi et al. (2019) investigate the impacts of structural breaks on the dual long memory levels
of Bitcoin and Ethereum price returns. By using four GARCH-class models (e.g., Fractional Integrated
GARCH (FIGARCH), Fractional Integrated APARCH (FIAPARCH), and Hyperbolic GARCH
(HYGARCH), they determine dual long memory and structural changes on cryptocurrency markets.
They suggest that the FIGARCH model with structural breaks variables provides a comparatively
superior forecasting accuracy performance.
In a VaR context, Likitratcharoen et al. (2018) predict the Value at Risk (VaR) of Bitcoin,
Ethereum and Ripple using historical and Gaussian parametric, VaR. They use Kupiec’s proportion
of failures (POF) test, independence test, and the Christoffersen (1998) and joint test in order to
backtest their VaR model. Their findings show that historical VaR model is suitable for measuring
cryptocurrency risk over delta normal VaR only for a high confidence level of critical values.
Similarly, Osterrieder and Lorenz (2017) and Gkillas and Katsiampa (2018) apply extreme value
theory to estimate VaR. Gkillas and Katsiampa (2018) analyze the tail behavior of the returns of five
major cryptocurrencies in order to find while Bitcoin Cash is the riskiest cryptocurrency analyzed,
Bitcoin and Litecoin are the least risky. Other studies also utilize Value-at-Risk methodologies on
returns of different cyrptocurrencies to analyze their time varying-volatilities. They use
methodologies based on vine copulas and robust volatility models. (Ardia et al. 2019; Stavroyiannis
2018; Troster et al. 2019; Pele and Mazurencu-Marinescu-Pele 2019; Trucíos et al. 2019).
As the literature summarized above shows, the evidence on time-varying properties of the
volatility of cryptocurrency returns are fragmented. This study carries out a more comprehensive
analysis by using all three of the largest market cap and most liquid cryptocurrencies (namely,
Bitcoin, Ethereum, Ripple) and applying four different long-memory tests in the returns and
volatilities of cryptocurrencies to investigate their stochastic properties. Moreover, after worldwide
adoption of the Basel II Accord, Value at Risk (VaR) became the most widely used risk measure in
quantitative finance. Value-at-Risk measures the approximate market risk of all regulated financial
institutions following the Basel Accords (Alexander 2009). Therefore, investors in cryptocurrencies
need to accurately predict VaR of their portfolio in order to acquire a sufficiently covered risk. Our
J. Risk Financial Manag. 2020, 13, 107 5 of 21
analysis extends the findings from the literature (Chu et al. 2017) by focusing not only on the risk
measurement with VaR model, but also expected shortfalls which is a coherent measure of risk.
3. Data
Most studies summarized above concentrate their GARCH models on Bitcoin only. In this paper,
however, we investigate the optimal GARCH model for not only Bitcoin but also the two other major
cryptocurrencies in the market: Ethereum and Ripple. The daily price data of three major crypto
currencies was extracted from Bitfinex, which provides advanced services such as cryptocurrency
exchange for digital currency traders and liquidity providers. Bitfinex is the world’s largest exchange
by volume for trading Bitcoin against the US Dollar. In order to obtain the longest uninterrupted
period possible for each cryptocurrency, we use different starting points for each. Bitcoin has the
longest data stream starting from January 1, 2014, followed by Ethereum we use data starting from
October 3, 2016. Finally, the data stream for Ripple starts on May, 20, 2017. Data for all three
cryptocurrencies end on February 28, 2018.
Daily return series are calculated as log differences of price levels as follows:
(1)
where r
t
represents return at time t, lnP
t
is the natural logarithm of the opening price at date t and
lnP
t−1
is the natural logarithm of the opening price at date t − 1.
The price and return series for Bitcoin, Ethereum, and Ripple are plotted in Figures 1–3,
respectively. From Figure 1A, we can see that Bitcoin prices started a gradual increase at the
beginning of 2017, but suddenly started rising rapidly at the end of 2017. This large and sudden
increase corresponds to the introduction of the bitcoin futures trading. The return series in Figure 1B,
supports the same observation. Returns of Bitcoin show high volatility all throughout the time period,
however volatility spikes are bigger and more frequent after 2017. Figure 2A,B show that Ethereum
prices and returns follow a very similar pattern, with increase in prices after 2017 and constantly high
volatility since the beginning of trading. In the case of Ripple; however, there is no gradual price
increase. According to Figure 3, the climb in Ripple prices begins with a rapid increase in December
of 2017. Volatility pattern is slightly different than Bitcoin and Ethereum as well. According to Figure
3B, Ripple return volatility is relatively stable, but starts to spike after December 2017 as well.
(A)
Time series plots of Bitcoin price.
J. Risk Financial Manag. 2020, 13, 107 6 of 21
(B)
Time series plots of Bitcoin return.
Figure 1. Time Series Plots of Bitcoin price and return. (A) Presents the plot historical plot of daily
closing prices for Bitcoin between January 1, 2014 and February 28, 2018. (B) Presents the daily returns
for Bitcoin for the same time period. The data is obtained from Bitfinex.
(A)
Time series plots of Ethereum price
(B)
Time series plots of Ethereum return
Figure 2. Time Series Plots of Ethereum Price and Return. (A) Presents the plot historical plot of daily
closing prices for Ethereum between October 3, 2016 and February 28, 2018; (B) presents the daily
returns for Ethereum for the same time period. The data is obtained from Bitfinex.
J. Risk Financial Manag. 2020, 13, 107 7 of 21
(A)
Time series plots of Ripple price
(B)
Time series plots of Ripple return
Figure 3. Time Series Plots of Ripple Price and Return. (A) Presents the plot historical plot of daily
closing prices for Ripple between May 20, 2017 and February 28, 2018; (B) presents the daily returns
for Ripple for the same time period. The data is obtained from Bitfinex.
Descriptive statistics for cryptocurrencies’ return series are shown in Table 1. Results show that
all series have high excess kurtosis. Bitcoin and Ethereum have negative skewness. These statistics
indicate that the distributions of the series seem to be leptokurtic. Moreover, Ljung-Box Q (20)
statistics for all returns are insignificant, while it is significant for squared returns of all
cryptocurrencies. Besides, regardless of the lag chosen, all ARCH (Autoregressive conditional
heteroskedasticity) test statistics are highly significant. Therefore, conditional heteroscedasticity and
serial correlations should be taken into account while modeling these series.
Table 1. Descriptive Statistics.
Statistic BTC ETH XRP
Mean 0.158 0.605 0.351
Maximum 24.348 25.859 63.137
Std. Dev. 4.09 6.613 9.859
Skewness –0.442 –0.076 1.54
Kurtosis 9.873 6.363 11.715
Jarque-Bera 2951.355 339.707 1014.636
J. Risk Financial Manag. 2020, 13, 107 8 of 21
ARCH 1-2 52.23 *** 49.4 *** 6.16 ***
ARCH 1-5 25.45 *** 22.42 *** 2.88 ***
ARCH 1-10 14.02 *** 11.83 *** 4.33 ***
Q(20) 27.75 22.62 26.94
Qsq(20) 212.32 *** 159.79 *** 69.52 ***
Observations 1475 719 285
Table 1 provides the descriptive statistics for the returns of Bitcoin, Ethereum and Ripple daily
returns. BTC represents Bitcoin, ETH represents Ethereum and XRP represents Ripple. BTC data
series starts on January 1, 2014, ETH data series starts on October 3, 2016 and the Ripple data series
starts on May 20, 2017. All series end on February 28, 2018. In addition to traditional descriptive
statistics, the table also provides the ARCH 1-2, ARCH 1-5 and ARCH 1-10 estimations and Ljung-
Box Q20 statistics for the returns and squared returns for each of the cryptocurrencies. *, **, ***
represent statistical significance at 10%, 5% and 1% levels, respectively.
4. Methodology
In order to better detect various characteristics of cryptocurrency returns, we employ long
memory tests before modeling the volatility of these series. According to the results of these long
memory tests, we later estimate the appropriate GARCH class model, which accurately takes into
account the asymmetry in the relevant series. Long memory process could be described as a slowly
decaying autocovariance function. At this point it is necessary to remind that volatility is highly
persistent in high-frequency financial time series.
4.1. Long Memory Tests
In order to test for long memory properties in these series, we employ four different statistics:
The Hurst–Mandelbrot Rescaled Range (R/S) statistics; Lo (1991) Rescaled Range R/S; Geweke and
Porter-Hudak (1983) (GPH); and the Robinson and Henry (1999) Gaussian Semiparametric (GSP) test
statistics. Each one of these long-term memory statistics are detailed below. When testing for long-
term memory for all three cryptocurrencies, we use the absolute returns and squared returns as
proxies of daily volatility following Arouri et al. (2012).
4.1.1. Rescaled Range (R/S) Statistics
Rescaled range statistic R/S was introduced by Hurst (1951) and later revised by Mandelbrot and
Wallis (1969) in order to detect the presence of long-term memory in time series. According to
Mandelbrot (1971), R/S statistics could be used in economic and financial analysis. Essentially,
rescaled range statistic R/S is the range of partial sums of deviations of a time series from its mean
rescaled by its standard deviation (Zivot and Wang 2003). Consequently, Hurst exponent H
symbolizes the scaling behavior of the range of cumulative departures of a time series from its mean.
Formally, the range R of a time series
,
is determined as:
= max
(−̅)
− min
(−̅)
(2)
Here,
is given as an estimate of the sample mean. The classical rescaled range is the best
known R/S statistic:
(3)
J. Risk Financial Manag. 2020, 13, 107 9 of 21
This statistic is robust to data non-normality, but in the presence of autocorrelation the
coefficients may be biased. Therefore, Lo (1991) developed a modified rescaled range
, which
adjusts for possible short term dependence by applying the Newey West heteroscedasticity and
autocorrelation consistent estimator instead of the sample standard deviation S:
Q=
max
(−̅)
− min
(−̅)
(4)
2 2
1 1
2
T
T j i i j
j i j
T
j
1j
Here Mandelbrot’s null hypothesis is “there is no long-term dependence” under the assumption
of no autocorrelation, while Lo’s null hypothesis is only “there is no long-term dependence”.
4.1.2. Geweke and Porter-Hudak (GPH) Model
Geweke and Porter-Hudak (1983) suggested a semi-nonparametric approach to test for long-
term memory in the sense of fractionally integrated processes. Furthermore, Geweke and Porter-
Hudak (1983) used Fourier transformation and spectral density into the following formula.
Let
be the return series. The GPH estimator of the long memory parameter d for
can be
then determined using the following periodogram:
j
j
j
w
wI
2
sin4log)(log
2
10
(5)
Where
j
;
is the residual term and
represents the
Fourier
frequencies.
stands for the sample periodogram defined as:
I(w
j
)1
2
Tr
t
e
w
j
t
t1
T
2
where
is assumed to be a covariance stationary time series. The estimate of fractional difference
parameter d, namely
d
is
. GPH test for the null hypothesis is “there is no long memory (d
= 0)”.
4.1.3. Gaussian Semiparametric (GSP) Method
The Gaussian Semiparametric estimation model developed by Robinson and Henry (1999) is
based on the specification of the shape of the spectral density of the time series. The Robinson and
Henry (1999) GSP estimator of the long memory parameter for a covariance stationary series, which
is consistent and asymptotically normal under certain assumptions, is given by:
0)(
21
wasGwwf
H
(6)
where 1
H
,
0G
and
is the spectral density of
. The periodogram with respect
to the observations of
,
is defined as:
1
1
( ) 2
j
Titw
j t
t
I w re
T
(7)
Accordingly, the Hurst exponent parameter H is obtained by minimizing the function
.
J. Risk Financial Manag. 2020, 13, 107 10 of 21
)(minarg
21
HRH
H
where:
1 2
1 2
1 1
0 1
( )
1 1
0, / 2
2 /
m m
j
H
j j
j
j
I w
m w m
m n
w j T
4.2. Results of Long Memory Tests
Tables 2–4 provide the results of the long-range dependence tests for daily returns and daily
squared returns for Bitcoin, Ethereum and Ripple, respectively. According to the four tests utilized
(Hurst–Mandelbrot R/S, Lo R/S, GPH and GSP), and presented in Panels A in Tables 2–4, test statistics
do not reject the null hypothesis of no long-range dependence in return series. The results indicate
that daily returns for Bitcoin, Ethereum and Ripple do not exhibit the long memory effect.
Panels B in Tables 2–4, present results for the squared daily returns of these three
cryptocurrencies. Long-term memory test results demonstrate the presence of the long memory effect
at the 1% level. The d parameter is statistically significant and lies within the interval (0, 0.5),
indicating that the squared return series exhibit long memory process.
Table 2. Long Memory Tests for Bitcoin (BTC) Return and Squared Return.
Panel 2A: Bitcoin (BTC) Daily Returns
Statistic Hurst–Mandelbrot R/S Lo R/S GPH GSP
d parameter – – –0.027 (0.025) –0.01 (0.018)
Test Statistics 2.094 2.117
Critical values
Probability Probability
90% [0.861, 1.747]
[0.2722] [0.5635]
95% [0.809, 1.862]
99% [0.721, 2.098]
Panel 2B: Bitcoin (BTC) Squared Daily Returns
Statistic Hurst–Mandelbrot R/S Lo R/S GPH GSP
d parameter – – 0.175 (0.025) 0.175 (0.018)
Test Statistics 3.252 2.900
Critical values
Probability Probability
90% [0.861, 1.747]
[0.0000] [0.0000]
95% [0.809, 1.862]
99% [0.721, 2.098]
This table provides the results of the four different long-term memory tests run on daily returns of
Bitcoin and squared daily returns of Bitcoin between January 1, 2014 and February 28, 2018. The 4
different long memory test results presented are: Hurst–Mandelbrot Rescaled Range (R/S) statistics,
Lo (1991) Rescaled Range R/S statistics, Geweke and Porter-Hudak (1983) (GPH) statistics, and the
Robinson and Henry (1999) Gaussian Semiparametric (GSP) test statistics. Panel 2 A presents the
results for Bitcoin daily returns and Panel 2B represents the results for squared daily Bitcoin returns.
J. Risk Financial Manag. 2020, 13, 107 11 of 21
Table 3. Long Memory Tests for Ethereum Return and Squared Return.
Panel 3A: Ethereum (ETH) Daily Returns
Statistic Hurst–Mandelbrot R/S Lo R/S GPH GSP
d parameter – – 0.034 (0.038) 0.022 (0.026)
Test Statistics 1.676 1.665
Critical values
Probability Probability
90% [0.861, 1.747]
[0.3796] [0.3963]
99% [0.721, 2.098]
Panel 3B: Ethereum (ETH) Squared Daily Returns
Statistic Hurst–Mandelbrot R/S Lo R/S GPH GSP
d parameter – – 0.264 (0.038) 0.255 (0.026)
Test Statistics 2.482 2.139
Critical values
Probability Probability
90% [0.861, 1.747]
[0.0000] [0.0000]
95% [0.809, 1.862]
99% [0.721, 2.098]
This table provides the results of the four different long-term memory tests run on daily returns of
Ethereum and squared daily returns of Ethereum between October 3, 2016 and February 28, 2018. The
4 different long memory test results presented are: Hurst–Mandelbrot Rescaled Range (R/S) statistics,
Lo (1991) rescaled Range R/S statistics, Geweke and Porter-Hudak (1983) (GPH) statistics, and the
Robinson and Henry (1999) Gaussian Semiparametric (GSP) test statistics. Panel 3A presents the
results for Ethereum daily returns and Panel 3B represents the results for squared daily Ethereum
returns.
Table 4. Long Memory Tests for Ripple Return and Squared Return.
Panel 4A: Ripple (XRP) Daily Returns
Statistic Hurst–Mandelbrot R/S Lo R/S GPH GSP
d parameter – – 0.076 (0.063) 0.038 (0.041)
Test Statistics 1.496 1.492
Critical values
Probability Probability
90% [0.861, 1.747]
[0.2298] [0.3613]
95% [0.809, 1.862]
99% [0.721, 2.098]
Panel 4B: Ripple (XRP) Squared Daily Returns
Statistic Hurst–Mandelbrot R/S Lo R/S GPH GSP
d parameter – – 0.18 (0.063) 0.122 (0.041)
Test Statistics 2.011 1.887
Critical values
Probability Probability
90% [0.861, 1.747]
[0.0047] [0.0035]
95% [0.809, 1.862]
99% [0.721, 2.098]
This table provides the results of the four different long-term memory tests run on daily returns of
Ripple and squared daily returns of Ripple between October 3, 2016 and February 28, 2018. The four
different long memory test results presented are: Hurst–Mandelbrot Rescaled Range (R/S) statistics,
Lo (1991) Rescaled Range R/S statistics, Geweke and Porter-Hudak (1983) (GPH) statistics, and the
Robinson and Henry (1999) Gaussian Semiparametric (GSP) test statistics. Panel 4A presents the
results for Ripple daily returns and Panel 4B represents the results for squared daily Ripple returns.
These results are in accordance with results in previous similar studies on cryptocurrencies.
Mensi et al. (2019) state that the persistence level of both returns and volatility of Bitcoin and
Ethereum decrease after considering long memory and switching states. In addition, Bouri et al.
J. Risk Financial Manag. 2020, 13, 107 12 of 21
(2016) show evidence of a long memory in two measures of volatility of Bitcoin. In this study, we
analyze all three major cryptocurrencies that make up close to 86% of the entire cryptocurrency
market cap and find that long-term memory exists in the squared terms for all three.
In short, these long-term memory test results confirm that GARCH-class models, which take into
account long-term memory properties, are the most appropriate models for the volatility of Bitcoin,
Ethereum and Ripple.
4.3. GARCH Models
The main assumption underlying Bollerslev’s (1986) GARCH modeling is that the market
variance depends not only on historical conditional market variance but also on market shocks.
Generalized Auto Regressive Conditional Heteroscedasticity (GARCH, p, q) equation is written in
the following form:
01 1
k h
i j
R X R
(8)
where
1
1 1
p q
i j
h h
(9)
where
2
h
The satisfying conditions for the equations are
1 1
p q
i i
i i
.
stands for disturbance term for mean equation,
describes the return of the asset at time t, and
’s denote explanatory variables. Equations (8) and (9) are the mean and the conditional variance
equations, respectively.
In this model, in order to assure a positive conditional variance, estimated parameters should
satisfy non-negativity constraints. Hence, GARCH models consider only the magnitude of the
shock—not its sign.
4.3.1. The Fractional Integrated GARCH (FIGARCH) Model
Most of the time, high frequency financial data follows a pattern that yields a sum of α
1
and β
1
close to one, with α
1
small and β
1
large. Therefore, the effect of shocks on the conditional variance
diminishes very slowly. In these situations, Baillie et al. (1996) suggest the class of Fractionally
Integrated GARCH (FIGARCH) models. This model captures slowly decaying volatility as well as
recognizing both the long memory and short memory characteristics of conditional variance (Chkili
et al. 2014). Fractionally integrated processes are significantly different from both stationary and unit-
root processes with their persistence and mean reverting features.
Formally, the FIGARCH (1, d, 1) can be defined with lag operator “L” as follows
1
1 1 1 1
d
h h L L L
(10)
where
> 0,
and λ < 1. The fractional integration parameter d reflects the degree of long
memory or the persistence of shocks to conditional variance, and satisfies the condition 0 ≤ d ≤ 1. If 0
< d < 1, the model implies an intermediate range of persistence and indicates the volatility shocks
disperse only at a hyperbolic rate. If the integration parameter d = 0 then the model has a short
memory and reduces to a GARCH (1,1) model. On the other hand, if d = 1, the model transforms to
IGARCH (1,1) whose variance process is no longer mean-reverting (Chkili et al. 2014).
J. Risk Financial Manag. 2020, 13, 107 13 of 21
4.3.2. Hyperbolic GARCH (HYGARCH) Model
Davidson (2004) has developed a new GARCH-class model called hyperbolic GARCH
(HYGARCH) model. This new model extends the conditional variance of the FIGARCH model by
introducing weights into the difference operator. The HYGARCH model allows for modeling long
memory property in conditional volatility with hyperbolic convergence rates. The HYGARCH (1, d,1)
model can be written as follows:
1
1 1 1 1 1
d
h L L L
(11)
where ω > 0, α ≥ 0, β ≺ 1, λ < 1 and 0 ≤ d ≤ 1.
Davidson (2004) argues that the HYGARCH model allows for the existence of both second
moments, and even more extreme amplitudes than the simple IGARCH and FIGARCH models.
4.4. The VaR and Backtesting
Value at Risk (VaR) is a risk measure that determines the losses that may happen in extreme
events for a given confidence level. Main parameters of VaR are the significance level (confidence
level 1-α) and the risk horizon (h), which is the period of time in terms of trading days.
VaR is an especially popular and useful tool for risk management in the sense that it measures
both risk factor and the sensitivity to the same risk factor, simultaneously. VaR finds most of its
universal applicability in its ability to quantify various types of risk (Alexander 2009).
VaR can identify extreme events, however it is not sub-additive, i.e., the total risk of a portfolio
does not equal the sum of the risks of the individual assets. Due to this shortcoming “Expected
Shortfall” has been developed as an alternative but related measure of risk (Scaillet 2000).
Expected shortfall is a risk measure, used to predict the expected value of the losses conditional
on the loss being larger than the VaR (Scaillet 2004).
ESF
t
= E(|L
t
| > |VaR
t
|)
(12)
where L
t
is the expected value of loss if a VaR
t
violation occurs. Hendricks (1996) interpreted the ESF1
as the excess value of the losses over the VaR, the ESF2 as expected value of loss exceeding the VaR
level, divided by the associated VaR values.
In this study, we use both long and short trading positions and estimate the relevant VaRs for
the FIGARCH and HYGARCH models under the student-t and skewed student-t distributions. The
daily VaR for long and short trading positions at time t can be calculated as
(13)
and
(14)
where
represents the left quantile at % α for the student-t distribution and
the right quantile
at % α.
denotes the estimated daily conditional mean whereas
represents the estimated standard
deviation of the cryptocurrency returns obtained from a FIGARCH and HYGARCH models.
The daily VaR’s for the skewed-Student-t distribution for long and short positions is given by
(15)
and
In order to determine the accuracy of the VaR model, estimations should be backtested. This
testing method enables us to compare the actual losses (or gains) in the past observations to the VaR
and determine exceedances or failures. The most widely known test is Kupiec’s (1995) POF-test that
J. Risk Financial Manag. 2020, 13, 107 14 of 21
examines whether the proportion of failures (POF) calculated from the data corresponds to its
theoretical value.
If =∑
, is the number of exceptions in the sample size T, then:
=1 <|(∝)
0 ≥|(∝)
(16)
where it follows a binomial distribution, N|B(T, α). If α = E(N/T) is the expected exception frequency,
then the null hypothesis is whether the failure rate of the model is equal to the expected one: H
0
: α =
α
0
and where α
0
is the pre-specified VaR level.
Under the null hypothesis, the Kupiec’s (1995) likelihood ratio test is given by:
=−2
(1−α
)
}+2
(1−
)
(17)
The Likelihood ratio statistics is asymptotically χ
2 (1)
chi squared distributed with one degree of
freedom. If the null hypothesis, H
0
: α = α
0
, cannot be rejected, then the model will be favored for VaR
prediction, which exhibits unconditional coverage measured by α = E(N/T) equals the desired
coverage level α
0
.
5. Findings
In this part, results from the estimated GARCH-type models are presented. Student-t and
skewed student-t distributions have been used since the returns have heavier tails than the normal
distribution. We estimate FIGARCH, HYGARCH, FIAPARCH models with regard to long memory
test results in order to account for the long memory properties of our cryptocurrency returns.
However, in Table 5 we only report the best results from the various estimated GARCH models. As
can be seen from the table, we fit HYGARCH, and FIGARCH both student-t and skewed student-t
distributions to the return series of Bitcoin, Ethereum, and Ripple.
Especially, d-FIGARCH coefficients are statistically significant at 1% level, which implies the
existence of long memory in the selected cryptocurrencies’ volatility. The values of AIC, SW, SB, and
H-Quinn are given in Table 5 for the fitted models. We only include the most appropriate methods
based on these information criteria and Log-likelihood statistics. However, there are small differences
between these models.
The student-t distribution gives the smallest value of AIC, SW, SB, and H-Quinn with
HYGARCH (1, 0.65, 1) model for Bitcoin. The best fitting model for Ethereum is the FIGARCH (1,
0.68, 1) with skewed student-t distribution. Asymmetric parameters are also positive and statistically
significant for Ethereum at a 1% level, indicating that Ethereum returns are skewed to the right. In
addition, the tail parameters in HYGARCH and FIGARCH models are statistically significant and
positive for both Bitcoin and Ethereum. These results reveal that these two cryptocurrencies are fat-
tailed. The student-t distribution gives the smallest values of information criteria for Ripple returns.
Thus, we may suggest that FIGARCH (1, 0.625, 1) is the best fitting model for Ripple.
Table 5. Estimation Results of Bitcoin, Ethereum, and Ripple returns.
Estimation Method
BTC ETH XRP
HYGARCH
Student HYGARCH sk.-t FIGARCH sk.-t HYGARCH
sk.-t
FIGARCH
Student
FIGARCH
sk.-t
Cst(M) 0.145 *** 0.114 ** 0.368 ** 0.351 ** −0.192 0.092
Cst(V) 0.128 0.146 272.83 1.127 0.722 0.377
ARCH(Alpha1) 0.207 ** 0.201 ** 0.281 ** 0.326 0.594 *** 0.586 ***
Student(DF) 2.737 ***
3.584 ***
Tail
2.739 *** 4.115 *** 3.73 ***
3.648 ***
Log Alpha (HY) 0.241 ** 0.238 **
0.106
No. Observations 1475 1475 719 719 285 285
J. Risk Financial Manag. 2020, 13, 107 15 of 21
No. Parameters 7 8 7 8 6 7
Log Likelihood −3758.126 −3757.843 −2256.649 −2256.91 −994.076 −993.21
AIC 5.105 5.106 6.296 6.30 7.018 7.019
SW 5.130 5.134 6.341 6.351 7.094 7.108
SB 5.105 5.106 6.296 6.29 7.017 7.017
H-Quinn 5.114 5.116 6.313 6.319 7.048 7.054
JB 34298 35411 177.96 168.64 210.67 281.64
Pearson (50) 54.322 * 53.847 * 81.486 *** 67.30 *** 49.912 48.50
This table presents the results of various estimated GARCH type models. HYGARCH, and FIGARCH
models with both student t and skewed student t distributions are fitted to all three return series.
Models with the best outcomes are presented. BTC, ETH and XRP represent the daily return series
for Bitcoin, Ethereum and Ripple respectively. BTC data series starts on January 1, 2014, ETH data
series starts on October 3, 2016 and the Ripple data series starts on May 20, 2017. All series end on
February 28, 2018. Sk.-t is the skewed Student-t distribution. *, ** and *** indicate statistical
significance at the 10%, 5% and 1% levels respectively.
In Sample VaR Estimations
In this section, the GARCH models were tested for VaR levels ranging from 5% to 1%. Table 6
displays the in-sample VaR estimations which are calculated from FIGARCH and HYGARCH
models for daily returns of Bitcoin, Ethereum and ripple, respectively. The Kupiec tests are conducted
for each of these models in order to investigate whether the empirical failure rate is equal to the pre-
specified VaR level.
The Kupiec test statistics are not significant in most cases, indicating that the FIGARCH and
HYGARCH models perform well in estimating the volatility of these cryptocurrency returns. Kupiec
test statistics is only significant at 5% level for Ethereum and 1% level for Ripple in short positions.
Moreover, the Kupiec test statistics are not statistically significant for any of the three
cryptocurrencies for long trading positions. More precisely, the results show that the FIGARCH and
HYGARCH models with skewed student t distributions outperform the other methods.
Table 6. In-sample Value-at-Risk (VaR) Backtesting for Cryptocurrency Returns.
Panel A: VaR Backtesting Results for Bitcoin (BTC) Returns.
Short positions Short positions
Quantile Success rate Kupiec LRT P-value Success rate Kupiec LRT P-value
0.975 0.974 0.034 0.851 0.974 0.0348 0.851
0.99 0.989 0.104 0.746 0.989 0.1041 0.746
Quantile Failure rate Kupiec LRT P-value Failure rate Kupiec LRT P-value
0.05 0.054 0.728 0.393 0.057 1.725 0.188
0.01 0.010 0.004 0.947 0.010 0.004 0.947
Panel B: VaR Backtesting Results for Ethereum (ETH) Returns.
ETH FIGARCH sk.-t ETH HYGARCH sk.-t
Short positions Short positions
0.95 0.933 3.864 ** 0.049 0.936 2.727 * 0.098
0.975 0.973 0.058 0.808 0.979 0.534 0.464
0.99 0.988 0.088 0.765 0.991 0.210 0.646
Long positions Long positions
Quantile Failure rate Kupiec LRT P-value Failure rate Kupiec LRT P-value
0.058 1.019 0.312 0.051 0.031 0.858
0.025 0.030 0.863 0.352 0.026 0.058 0.808
0.01 0.011 0.088 0.765 0.009 0.005 0.942
Panel C: VaR Backtesting Results for Ripple (XRP) Returns.
XRP FIGARCH XRP FIGARCH sk.-t
Quantile Success rate Kupiec LRT P-value Success rate Kupiec LRT P-value
J. Risk Financial Manag. 2020, 13, 107 16 of 21
0.95 0.933 1.515 0.218 0.940 0.527 0.467
0.968 0.467 0.494 0.968 0.467 0.494
0.99 0.975 4.341 ** 0.037 0.982 1.337 0.247
Long positions Long positions
0.05 0.045 0.118 0.730 0.052 0.040 0.839
0.025 0.017 0.724 0.394 0.028 0.106 0.744
0.01 0.007 0.285 0.592 0.010 0.007 0.929
Panels A, B and C represent the VaR backtesting results for Bitcoin, Ethereum and Ripple, respectively
using the models presented in Table 5. BTC data series starts on January 1, 2014, ETH data series starts
on October 3, 2016 and the Ripple data series starts on May 20, 2017. All series end on February 28,
2018. The table reports the Kupiec test statistics. Both short and long position VaRs are tested. Sk.-t is
the skewed Student-t distribution. *, ** and *** indicate that statistics are significance at the 10%, 5%
and 1% level of significant respectively. The best model is the one with the least rejections.
The next risk measure considered for the three cryptocurrencies is Expected Shortfalls (ESF). The
expected shortfall results for long and short positions are identified as ESF1 and ESF2, respectively,
and are presented in Table 7.
Table 7. In-sample Value-at-Risk (VaR) Expected Shortfalls.
Panel A: Expected Shortfalls for Bitcoin (BTC).
BTC HYGARCH HYGARCH sk.-t
α quantile ESF1 ESF2 ESF1 ESF2
Short positions
0.95 7.7225 1.5586 7.5319 1.5416
0.97 9.0107 1.4334 9.0107 1.4624
0.99 9.6857 1.2315 9.6857 1.26
Long positions
0.05 –8.72 1.6721 –8.88 1.6717
0.01 –13.46 1.5745 –13.46 1.537
Panel B: Expected Shortfalls for Ethereum (ETH).
ETH FIGARCH HYGARCH sk.-t
Short positions
0.95 13.8 1.3663 13.93 1.33
0.97 15 1.3255 15.15 1.3606
0.99 15.92 1.2213 16.59 1.2115
Long positions
0.05 −12.62 1.4874 −13.25 1.4821
0.025 −14.19 1.3998 −15.03 1.3772
0.01 −19.48 1.3946 −20.11 1.3148
Panel C: Expected Shortfalls for Ripple (XRP).
XRP FIGARCH FIGARCH sk.-t
α quantile ESF1 ESF2 ESF1 ESF2
Short positions
0.95 22.44 1.635 23.52 1.6362
0.99 34.19 1.3312 42.07 1.4082
Long positions
0.05 −17.24 1.3569 −16.84 1.4136
0.025 −23.05 1.2638 −20.02 1.2529
0.01 −28.26 1.0676 −27.22 1.1236
J. Risk Financial Manag. 2020, 13, 107 17 of 21
Panels A, B and C represent the VaR backtesting Expected Shortfalls for Bitcoin, Ethereum and Ripple,
respectively using the models presented in Table 5. BTC data series starts on January 1, 2014, ETH
data series starts on October 3, 2016 and the Ripple data series starts on May 20, 2017. All series end
on February 28, 2018. Expected Shortfalls for both long and short positions are presented. ESF 1
represents the excess value of losses above the VaR level and ESF 2 represents the expected value of
losses exceeding the VaR level divided by the associated VaR values.
According to our findings, expected shortfalls are the highest for Ripple and lowest for Bitcoin
for all risk levels. In conclusion, investors should be aware that Ethereum and Ripple are subject to a
much higher risk than Bitcoin and may require higher capital to cover for potential losses.
6. Conclusions
Volatility of various assets in financial markets has been broadly analyzed in the finance
literature. However, there exists little empirical research on modelling volatility and investigating
long memory property of cryptocurrencies. Studies on cryptocurrencies has recently prompted the
interest of researchers as their use has increased adequately.
The main purpose of this study is to model the volatility of the mostly mined cryptocurrencies:
Bitcoin, Ethereum, and Ripple. By modelling volatility, we take into account long memory properties
of these cryptocurrencies. This gives us the opportunity to examine market efficiency. Similar to
previous researches, Cheah et al. (2018), Bouri et al. (2019) and Mensi et al. (2019), our findings also
indicate that cryptocurrency market has a long memory and that such a memory implies inefficiency
in the market where the estimated memory in volatility can help investors capture speculative profits.
From the price data, it can be observed that cryptocurrencies are highly volatile especially over
the period spanning between July 2017 and February 2018. In addition, our findings indicate that
HYGARCH model appears to be the best fitted model for Bitcoin as reported by the AIC, SW, SB and
H-Quinn criteria, and Log likelihood. Considering long memory also improves the performance of
modelling cryptocurrencies with GARCH models. On the other hand, the FIGARCH model with
skewed student distribution produces better estimations for Ethereum. Further, FIGARCH model
with student distribution appears to give a good fit for Ripple return. All of the series for the selected
cryptocurrencies exhibit fat-tail problem which may be a sign for the probability that an investment
return in the selected cryptocurrencies may move beyond three standard deviations.
Other studies dealing with cryptocurrencies also attain almost identical results: Bouri et al.
(2019) found long memory in the volatility of Bitcoin. Mensi et al. (2019) argued that FIGARCH model
with structural breaks variables outperforms the other models in the forecasting accuracy
performance. Lahmiri et al. (2018) suggested that the FIGARCH model is the best suited for
estimating the volatility and volatility shocks in these markets have long memory. Moreover, like
previous study of Stavroyiannis (2018), VaR and expected shortfall analysis show that the capital
requirements of the cryptocurrencies are high. In conclusion, models which take into account
volatility clustering, asymmetry and long memory in the cryptocurrency volatilities predict more
accurately the VaR and ESF for both the short and the long trading positions.
The findings of this research will help investors and especially the institutional investors in
developing investment strategies by providing cryptocurrencies as a potential investment instrument
in order to achieve a better portfolio diversification. Furthermore, as the three of the cryptocurrencies
selected for this research cover 86% of market cap and more than 60% of trading volume in the recent
years, the findings of this study could also be a good benchmark point for the institutional investors
dealing with the other cryptocurrencies.
Cryptocurrencies might become a mainstream financial instrument in the future of the global
financial markets besides common stocks, commodities and precious metals or Fx instruments. Thus,
this research will also provide investors with a better understanding of the cryptocurrencies markets
and will encourage further studies.
Author Contributions: Conceptualization, P.K.S., M.O., Ö.C. and Z.A.A.; methodology, P.K.S.; formal analysis,
P.K.S.; writing—original draft preparation, P.K.S. and M.O.; writing—review and editing, P.K.S., M.O. and
J. Risk Financial Manag. 2020, 13, 107 18 of 21
Z.A.A.; supervision Ö.C.; funding acquisition, Z.A.A. All authors have read and agreed to the published version
of the manuscript.
Funding: APC was funded by Claremont Graduate University.
Conflicts of Interest: The authors declare no conflict of interest.
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ResearchGate has not been able to resolve any citations for this publication.
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We examine the significance of fourty-one potential covariates of bitcoin returns for the period 2010–2018 (2872 daily observations). The recently introduced principal component-guided sparse regression is employed. We reveal that economic policy uncertainty and stock market volatility are among the most important variables for bitcoin. We also trace strong evidence of bubbly bitcoin behavior in the 2017–2018 period.
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Risk management is an important and helpful process for investors, hedge funds, traders and market makers. One of its key points is the appropriate estimation of risk measures which can improve the investment decisions and trading strategies. The high volatility of cryptocurrencies turns them a really risky investment and consequently, appropriate risk measures estimation is extremely necessary. In this paper, we deal with the estimation of two widely-used risk measures such as Value-at-Risk and Expected Shortfall in a cryptocurrency context. To face the presence of outliers and the correlation between cryptocurrencies, we propose a methodology based on vine copulas and robust volatility models. Our procedure is illustrated in a seven-dimensional equal-weight cryptocurrency portfolio and displays good performance.
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In this paper we investigate the ability of several econometrical models to forecast value at risk for a sample of daily time series of cryptocurrency returns. Using high frequency data for Bitcoin, we estimate the entropy of intraday distribution of logreturns through the symbolic time series analysis (STSA), producing low-resolution data from high-resolution data. Our results show that entropy has a strong explanatory power for the quantiles of the distribution of the daily returns. Based on Christoffersen’s tests for Value at Risk (VaR) backtesting, we can conclude that the VaR forecast build upon the entropy of intraday returns is the best, compared to the forecasts provided by the classical GARCH models.
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This paper examines the comprehensive idea about the growth and future sustainability of bitcoin as a cryptocurrency. The transaction volume of bitcoin is used as the growth of the bitcoin and the bitcoin log return is used as the volatility which is helpful for the future sustainability of bitcoin. The study period says that the growth of bitcoin’s transaction volume is an increasing trend as more day to day transaction is minting with the exchange of Bitcoin. The study also uses ARCH & GARCH methodology to know the volatility of this emerging digital currency, and the GARCH result shows that it is a highly volatile currency. As a result, most of the governments have not given their legal status for the use of bitcoin in their country. But if bitcoin will be stable in the future, then it is easily accepted through worldwide and in the long run, people will have more faith in the cryptocurrency technology and its usability.
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We review the literature and examine the effects of shocks on bitcoin returns. We assess the effects of factors such as stock market returns, exchange rates, gold and oil returns, FED’s and ECB’s rates and internet trends on bitcoin returns. Alternative VAR and FAVAR models are employed and generalized as well as local impulse response functions are produced. Our results reveal (i) a significant interaction between bitcoin and traditional stock markets, (ii) a weaker interaction with FX markets and the macroeconomy and (iii) an anemic importance of popularity measures. Lastly, we reveal the increased impact of Asian markets on bitcoin compared to other geographically-defined markets, which however appears to have waned in the last two years after the Chinese regulatory interventions and the sudden contraction of CNY’s share in bitcoin trading volume.
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Motivated by the emergence of Bitcoin as a speculative financial investment, the purpose of this paper is to examine the persistence in the level and volatility of Bitcoin price, accounting for the impact of structural breaks. Using parametric and semiparametric techniques, we find strong evidence in favour of a permanency of the shocks and lack of mean reversion in the level series. We also reveal evidence of structural changes in the dynamics of Bitcoin. After accounting for the structural breaks in the level series, evidence of mean reversion is uncovered in some cases. Further analyses show evidence of a long memory in the two measures of volatility (absolute and the squared returns), whereas some cases of short memory are revealed in the squared returns series in particular. Practical implications are discussed on the inefficiency in the Bitcoin market and its importance for Bitcoin users and investors.
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We test the presence of regime changes in the GARCH volatility dynamics of Bitcoin log–returns using Markov–switching GARCH (MSGARCH) models. We also compare MSGARCH to traditional single–regime GARCH specifications in predicting one–day ahead Value–at–Risk (VaR). The Bayesian approach is used to estimate the model parameters and to compute the VaR forecasts. We find strong evidence of regime changes in the GARCH process and show that MSGARCH models outperform single–regime specifications when predicting the VaR.
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This study explores the impacts of structural breaks (SB) on the dual long memory levels of Bitcoin and Ethereum price returns. We identify dual long memory and structural changes on cryptocurrency markets using four different generalized autoregressive conditional heteroskedasticity models (e.g., GARCH, FIGARCH, FIAPARCH, and HYGARCH). Furthermore, the persistence level of both returns and volatility equations decreases after accounting for long memory and switching states. Finally, the FIGARCH model with SB variables provides a comparatively superior forecasting accuracy performance. These findings have significant implications for both cryptocurrency allocations and portfolio management.
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Cryptocurrencies have recently gained a lot of interest from investors, central banks and governments worldwide. The lack of any form of political regulation and their market far from being “efficient”, require new forms of regulation in the near future. From an econometric viewpoint, the process underlying the evolution of the cryptocurrencies’ volatility has been found to exhibit at the same time differences and similarities with other financial time-series, e.g. foreign exchanges returns. This short note focuses on predicting the conditional volatility of the four most traded cryptocurrencies: Bitcoin, Ethereum, Litecoin and Ripple. We investigate the effect of accounting for long memory in the volatility process as well as its asymmetric reaction to past values of the series to predict: 1 day, 1 and 2 weeks volatility levels.
Source: www.researchgate.net
Author: Mustafa Okur2.49Marmara University Özgür Çatıkkaş Pınar Kaya4.13Marmara University
Ethereum – Wikipedia
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