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Analysis of Risk Diversification --Based on Bitcoin

Analysis of Risk Diversification --Based on Bitcoin
Junchao Xia1, *
1Chongqing BI Academy, Chongqing, 401120, China
*Corresponding author. Email:
Bitcoin is an essential component in the cryptocurrency system and plays a vital role in the economic system. This
paper uses analytical methods to conduct in-depth research on Bitcoin. I will explain their opinions about its ability to
invest and risk diversification, and then we try to verify some conclusions of the MPT model. First, my research
shows that based on the modern portfolio theory, the risks of bitcoin could be diversified with some trading assets on
the actual market. Second, two essential risks of Bitcoin are the legality and the cyber risk. On the one hand, the
research in this article provides a theoretical speech on Bitcoin. On the other hand, it provides theoretical suggestions
for the application and development of Bitcoin.
Keywords: Bitcoin, cryptocurrency, MPT, risk
Bitcoin has been viewed as an investable product
because of its sharp price growth. It took more than ten
years to go from less than a few cents to sixty thousand
dollars. Therefore, many investors reckon that they
could make much money by investing in bitcoins. In
April and May of this year, countless people began to
mine due to the sharp rise in the price of Bitcoin. Same
as the Gold Rush in the U.S. in 18TH century, the price
of high-end graphics cards has risen a lot.
Bitcoin is an essential component in the
cryptocurrency system and plays a vital role in the
economic system. Nakamoto first introduced Bitcoin in
2008 in the form of peer-to-peer digital currency.
Peer-to-peer transmission means a decentralized
payment system. The most salient characteristic is that
Bitcoin does not rely on specific currency institutions to
issue, unlike traditional currencies. The only way to
produce Bitcoin is through extensive calculations based
on specific algorithms, known as "mining." Therefore,
mining Bitcoin can be considered as a reward for getting
an excellent answer to a puzzle. The calculation of
network nodes generates Bitcoin. Anyone can
participate in manufacturing Bitcoin that can be
circulated all over the world. It can be bought and sold
on any computer connected to the Internet. Anyone can
mine, buy, sell or collect Bitcoin from any location, and
outsiders cannot identify the user's identity information
during the transaction.
Economists have polarized attitudes towards
Bitcoins. Economists of the Keynesian school believe
that Bitcoin's fixed aggregate currency sacrifices its
controllability, and it will inevitably lead to deflation
and harm the overall economy. Paul Krugman stated that
crypto-assets such as Bitcoin are a Ponzi scam. The
Austrian school of economists holds the opposite view.
They believe that the less government intervention in
currency, the better. Deflation caused by a fixed amount
of money is not a big deal, and it is even a sign of social
Besides some economists in the world, several
cohorts studied analyses have examined the function of
Bitcoin. Wang, Tang, Xie, and Chen (2019) shown that
Bitcoin acts as a hedge for stocks, bonds, and SHIBOR
(Shanghai Interbank Offer Rate) and is a safe haven
when extreme price changes occur in the monetary
market [1]. Kristoufek (2020) discussed the correlation
between Bitcoin, S&P500, and VIX. They compared
gold with Bitcoin as well, suggesting that Bitcoin was
unsubstantial and its proposed role as a safe haven was
far-fetched. On the other hand, gold came out as a clear
winner compared to Bitcoin. Nevertheless, Kristoufek
(2020) found strange phenomena in the COVID-19
period. Bitcoin started to become a possible safe haven
asset to prevent financial catastrophes [2].
A large and growing body of literature has
investigated the characteristics and functionality of
Bitcoin and other types of cryptocurrencies. Bitcoin has
a short history compared with fiat currency like the U.S.
Advances in Economics, Business and Management Research, volume 203
Proceedings of the 2021 3rd International Conference on Economic Management and
Cultural Industry (ICEMCI 2021)
Copyright © 2021 The Authors. Published by Atlantis Press International B.V.
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dollar or Chinese Yuan. Nakamoto (2008) created
Bitcoin. He firmly believes that Bitcoin is the
peer-to-peer version of electronic cash and a
cost-efficient way to transact because Bitcoin can work
without a financial intermediary [3].
During the Covid-19 era, much more information
has become available on whether Bitcoin or any other
cryptocurrencies can be used as hedging instruments
and a safe haven for the capital market. Surveys such as
those conducted by Yuhanitha and Robiyanto (2021)
have shown that Bitcoin can act as a hedge for the
Indonesian capital market in the Covid-19 pandemic era.
Still, Bitcoin cannot be the safe haven for the Indonesian
capital market in the Covid-19 pandemic era[4]. Also,
Yuhanitha and Robiyanto (2021) find that the CSPI
(Composite Stock Price Index) price began to rise
slightly, and the movements were relatively stable. On
the same date, it also showed that cryptocurrencies have
the opposite cycle movements or negative correlations
from the CSPI price. Therefore, when the CSPI's
movements strengthen, the price movements of
cryptocurrencies weaken [4]. In addition, Nguyen,
Bodisco, and Thaver (2018) draw our attention to other
factors that affect the price of Bitcoin. They found that
Bitcoin's price is driven by transactional demand, such
as the supply of Bitcoin or the size of the Bitcoin
economy, and speculative demand, namely media
attention or prices of other cryptocurrencies [5].
Many scholars also find that Bitcoin could be a
haven during extreme periods. For example, in the
COVID-19 period, some scholars found that Bitcoin
will be affected by the market sentiment, which gave
them the idea of whether bitcoin could be used as a
financial tool in hedging. Meanwhile, some
professionals put forward that the market risks of bitcoin
are a little bit different from our regular hedge tools.
Because of its unique characteristics, its price
fluctuations may be easily affected by investors'
One paper mentioned that bitcoin plays different
roles in different areas. For example, in a developing
country, Bitcoins could be used as a strong hedge for
investors. On the contrary, it effectively diversifies
developed countries' markets, regional indices, and
commodities for investors. In addition, Bitcoin is also a
safe place for some national equity indices, regional
indices, and commodities.
To sum up, based on the above studies, we can find
that research on Bitcoin mainly exist in function, while
there are few types of research on risk. Therefore, we
will discuss the external risks, cyber risks, and market
risks of Bitcoin. In addition, we will show that the risk
of Bitcoin can be divided by using some portfolios.
2.1 Data
We use the Bitcoin market price in USD (Code:
BTC), the S&P 500 index (Code: SPX), the 3-month
U.S. Treasury Bond Rate (Code: FBTB3M), the
Thomson Reuters/Core Commodity index (Code: CRB),
and S&P 500 Investment Grade Corporate Bond Index
(Code: SP5IGBIT) as our portfolio components. We
captured the data from Bloomberg and selected the
weekly data for the period of 08/18/2017 to 07/30/2021.
The statistic indicators will be listed in Table.1.
Table 1. Statistic indicators of 5 indexes
2.2 Method
I will use the MPT model to try to verify the result
MPT (Modern portfolio theory) is the basic
framework in our project. Modern portfolio theory
(MPT) is a theory on how risk-averse investors can
construct portfolios to maximize expected returns based
on a given level of market risk. In his paper "Portfolio
Selection," Harry Markowitz pioneered this theory,
published in the Journal of Finance in 1952. He was
later awarded a Nobel Prize for his work on modern
portfolio theory[6]. After Harry Markowitz won the
Nobel Prize, other economists have attribution towards
the MPT. Myles E. Mangram tries to simplify the MPT
by suggesting efficient computer-based 'short-cuts' to
these performing these intricate calculations[7]. The
paper of Omisore, I., Yusuf, M., & Christopher, N.
(2011) shows the relevance of the modern portfolio
theory as an investment portfolio tool in portfolio
decision making[8].
MPT theory will research the relationship between
standard deviation and the expected return . With the
combination of different components in the portfolios,
the return and standard deviation will be described as
 
      
Then we define the parameters in the above, is a
   vector which means the weights of each equity in
Standard deviation
Advances in Economics, Business and Management Research, volume 203
the portfolio, means the th component in the
portfolio, and we will have the . 
stands for a    vector which is composed by the
return of each included component. means the
covariance matrix of the equities in the portfolio.
After we have the Efficient frontier, we may
consider adding the risk-free assets into our portfolio,
the CML (Capital Market Line) and CAL (Capital
Allocation Line). The return of a risk-free asset will be
located on the point (0, ), which means the risk of
these assets is 0, and we can connect these points with
any other points on the efficient frontier. The straight
line is CAL (Capital Allocation Line). And we define the
slope as sharp ratio
   
We could find the line tangent to the efficient
frontier, where we may have the maximized Sharp Ratio,
and we call this line CML(Capital Market Line).
Sharp Ratio provides us a target to measure the price
of the unite of risk. A higher Sharp Ratio means a higher
return when we are going to take the risk; also, we could
say we may suffer from lower risk at the same return
lever when we have the higher sharp Ratio. Some
scholars also studied the Sharp Ratio in the portfolio.
Bailey, D. H., & Lopez de Prado, M. analysis the Sharp
Ratio with Python [9]. And Sharpe, W. F. is the first one to
define Sharpe Ration and apply it to different fields [10].
In this part, we will explain their opinions about its
ability to invest and risk diversification, and then we
will try to verify some conclusions with the MPT model.
3.1 Steps and analysis
In this project, we follow the following steps to
generate the efficient frontier:
Step 1: Download weekly market data from
Step 2: Data cleaning (including check the N.A. and
abnormal values, match the time).
Step 3: Calculate the returns of the indexes.
Step 4: calculate the mean, standard deviation,
covariance, and correlation coefficient.
Step 5: use the random function to generate weights
of portfolios and standardization.
Step 6: plot the portfolios and fine the efficient
portfolio that satisfies our requirements.
Based on the MPT model, we created a portfolio of 5
And the covariance matrix:
Table 2. The covariance matrix of 5 indexes
From Table 1, we can conclude that Bitcoin is a
high-risk and high-return investment product. That is
because its price rises too fast. It only took more than
ten years to go from less than a few cents to sixty
thousand dollars. Therefore, many people earn money
through "mining" and transaction of Bitcoin. Through
the analysis of statistics from 2017-08-18 to 2021-07-30,
we know that the mean return of bitcoin is 0.9287, and
its standard deviation is 0.8308. Hence, it is clear to say
the bitcoin is a high-risk and high-return investment
product. Also, we made a plot of Bitcoin return in
Figure 1 to easily show Bitcoin's entire return.
Advances in Economics, Business and Management Research, volume 203
Figure 1. Return Plot of Bitcoin in USD from 08/18/2017 to 07/30/2021
Based on the idea of MPT, our next step is to prove
that bitcoin could diversify the risks of the market
portfolio. Our real financial market was mainly
composed of commodity trading, equity trading, and
Fixed income trading. That is why we choose such five
indexes above as our portfolio. Thus, our portfolio could
be a relatively comprehensive one to reflect the situation
in a real market.
We first draw the efficient frontier of the 5 indexes
and have the following plot in Figure 2.
Figure 2. Plot of Efficient Frontier with bitcoin
We totally simulated 500,000 possible weights of
portfolios and have the above plot. Because of the High
risk and High return of Bitcoin, the plot is stretched very
long. Meanwhile, we also created another portfolio
without Bitcoin and plotted the Efficient Frontier, which
seems to be much fatter. We can see the plot in Figure3.
Advances in Economics, Business and Management Research, volume 203
Figure 3. Plot of Efficient Frontier without bitcoin
Then, we will compare these two portfolios' Sharp
Ratio at the same specific standard deviation. Sharp
Ratio stands for the return of unit risk; a higher sharp
Ratio means the lower risk cost. Here are the sheets
which show us the sharp ratios under specific standard
Table 3. Portfolio with Bitcoin at specific standard deviation
Standard Deviation
Sharp ratio(%)
Table 4. Portfolio without Bitcoin at specific standard deviation
Standard Deviation
Sharp ratio(%)
It is clear that the sharp Ratio of the portfolio that
contains Bitcoin is always higher than the one without
Bitcoin. It means that bitcoin could improve the 'price'
of our risk. In other words, if we want to have the same
return, the risk of the portfolio with bitcoin will be
lower than the portfolio without bitcoin. This has proven
the ability of bitcoin to diversify the risks of the market.
3.2 Risk analysis
3.2.1 Legality
Bitcoin is a cryptocurrency and is difficult for the
government to trace. Different countries have regulated
Bitcoin transactions and mining. There are polarizing
opinions about the regulation of Bitcoin. One of the
bellwethers in the United States advocates an open
attitude towards Bitcoin. The other is China, which
advocates prohibiting all virtual currency transactions,
including Bitcoin. Therefore, different policies caused
by disparate views are the risks of Bitcoin, and it is also
a topic worth discussing.
Countries have polarized attitudes towards the
legitimacy of Bitcoin. Some countries like China and
the United Kingdom prohibit the transaction of Bitcoin.
In Chinese legislations, the trading platform shall not
engage in the exchange business between legal currency
and tokens or "virtual currency," shall not buy or sell
tokens or "virtual currency" as a central counterparty
and shall not provide pricing or information for tokens
or "virtual currency" Intermediary and other services.
The Bank of England recently released a report: When
the market fully accepts digital currency, it will threaten
Advances in Economics, Business and Management Research, volume 203
the stability of the British financial system. However,
there are other voices from some countries like the
United States. From 2009 to 2017, the U.S.
government's attitude towards Bitcoin has always been
an open one. The U.S. Treasury Department and
regulatory authorities have not made too many
statements or policies to regulate Bitcoin.
As of June 2021, bitcoin was legal in the U.S., Japan,
the U.K., and other developed countries. From 2009 to
2017, the U.S. government's attitude towards Bitcoin
has always been an open attitude. The regulations for
cryptocurrency mining in the United States are simple:
if you can have cryptocurrency in a state, you can mine
cryptocurrency in that state without any limitation.
Differences between U.S. state regulations lead to
differences in the details of mining permits of the
different states. For example, New York is currently
considering suspending all cryptocurrency mining
operations for three years. On the other hand, Kentucky
has recently passed two bills to encourage
cryptocurrency mining, providing substantial property,
electricity, and wage tax exemptions or tax rebates for
the commercialization of cryptocurrency mining.
New York and Texas have entirely different
regulations, but the states' environmental policies drive
all regulations. New York State owns Greenidge
Generation, one of the biggest bitcoin miners. Because
more and more people are worried that mining will
conflict with the state's aggressive environmental goals,
the state recently introduced a bill that seeks to suspend
all cryptocurrency mining for three years. Instead,
Greenidge Generation proposes a plan to purchase
carbon offsets to achieve carbon neutrality.
First, because China has foreign exchange control,
Bitcoin's online anonymous transactions can
theoretically bypass the central bank's foreign exchange
defences, making foreign exchange control policy
virtually useless. Bitcoin also provides the potential for
money laundering transactions in an otherwise tightly
controlled domestic regulatory zone. Thus, convenience
has dramatically threatened the Chinese central bank's
foreign exchange policy and regulatory policy. In
addition, Because the RMB internationalization strategy
has begun to advance fully, the essence of RMB
internationalization is a regional centralized currency
strategy. Nevertheless, the decentralization of Bitcoin is
precisely the opposite of the Chinese RMB
internationalization strategy. The collision made
China's central bank have to take a "capital punishment"
on Bitcoin after weighing and weighing repeatedly.
The price of Bitcoin is closely related to some of the
Bitcoin policies formulated by the government. When
more and more countries start to ban the mining and
trading of Bitcoin, the price of Bitcoin will fall.
However, when more countries show open attitudes
towards Bitcoin, the price of Bitcoin will rise steadily.
So, I think that one of the most significant risks of
Bitcoin is the uncertainty of the future country's policies.
At the same time, Bitcoin, as a decentralized virtual
currency, is contrary to the currency concept of some
countries. When countries realize this problem, the
future of Bitcoin will become more uncertain.
3.2.2 Cyber risk
In this part, we will focus on the risks that may
happen in online bitcoin transactions. One prominent
problem people might consider there is the risk of
whether bitcoin can be stolen. That would be an
incredible loss to someone who invested in
cryptocurrencies. Unfortunately, in the history of bitcoin
development, some events happened because of the
cyber risks.
The most famous one was Mt.Gox event in June
2011. Mt. Gox was a well-known trading center of
bitcoin located in Japan. The hacker got the credential of
the auditor and transferred 2609 bitcoins to an address
to which Mt. Gox had no keys. Therefore, Mt. Gox
suspended its activities for several days. Luckily they
found ways to maintain the reputation and were able to
survive this time. However, a similar script acted again
in 2014. At that time, Mt. Gox held 70% of the bitcoin
transactions in the world. The hackers successfully
caused more than 750,000BTC losses of Mt.Gox
(almost 350 million dollars at that time), which directly
caused Mt. Gox to announce that they were bankrupt.
And none of the investors recovered their losses.
Operational risk is a significant factor for every
investor to notice. A simple mistake or inadequate
protection made by staff or personal can cause a
tremendous loss of wealth. Take the hack event in 2011
and 2014, which caused Mt. Gox's bankruptcy as an
instance; additionally, mining bitcoin is a highly
high-cost project. It needs too much electricity and
computing power to gain a few bitcoins, which is not
worth it. There are two reasons to explain my point of
view. First, bitcoin is an unreal currency that not any
country made an official announcement. Also, it is a
currency that could be used in the market or used to
trade as traditional currency. The only value it has is just
people who want to raise its price; otherwise, it is worth
noting, just a single data in computers. However, there
are many issues that some risk-loving investors will still
decide to support bitcoin. Thereby, I also come out with
some ideas to help these people to invest. Nowadays,
cloud storage has become more reliable to everyone
because of its convenience and more robust security
than we have in the past.
In this paper, we talked about the risks that Bitcoins
have faced in the current market. We start with ideas
Advances in Economics, Business and Management Research, volume 203
about whether Bitcoin will be a proper way to invest and
use the MPT to determine the portfolios on the Efficient
Frontier. We could find that the risks of bitcoin could be
diversified with some trading assets on the actual market.
Meanwhile, if we add bitcoin into our actual market
portfolio, we could have a more efficient portfolio with
a higher sharp Ratio. However, under extreme situations,
the portfolio could only replicate the trend but will lose
most of the return if we fixed relatively low volatility.
Finally, I think everyone's Bitcoin must be secured
and properly controlled on this Bitcoin trading platform.
Each trading platform should increase the protection of
the server and increase the understanding of users. On
the one hand, this is to avoid the theft of Bitcoin or the
risk of Bitcoin being stolen as much as possible, and on
the other hand, to minimize illegal transactions through
Bitcoin. In the future, maybe the innovator of bitcoin
might post an official trading centre or authoritative
cooperation for their customers to use. Either in the
cryptocurrency from or the currency used to buy their
products. It would not be risky like it had before in the
early time. At least, this idea will not hurt your wealth.
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the one about Bitcoin being a safe haven: Evidence
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[6] Fabozzi, F. J., Gupta, F., & Markowitz, H. M.
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Advances in Economics, Business and Management Research, volume 203
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This study examines the potential of cryptocurrencies such as bitcoin, ethereum, ripple, tether, and bitcoin cash as hedging instruments and a safe haven for the Indonesian capital market, especially during the Covid-19 pandemic era. Now, Indonesia's capital market condition is in turbulence. The benefit of this research is to help the investors make decisions on which cryptocurrencies can be an instrument hedge and safe haven in this Covid-19 pandemic era for Indonesia Stock Exchange (IDX). The data used in this study are data on the closing price of the Composite Stock Price Index (CSPI), bitcoin (BTC), ethereum (ETH), ripple (XRP), tether (USDT), and bitcoin cash (BCH) from January 3 to June 16, 2020. Data analysis used Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Quantile Regression (QREG). This study found that bitcoin, ethereum, tether, and bitcoin cash can act as a hedge, but only the ripple cannot act as a hedge. Bitcoin, ethereum, ripple, tether, and bitcoin cash cannot act as a safe haven when the Indonesian capital market was getting extreme, like during the Covid-19 pandemic era. The roles of bitcoin, ethereum, ripple, tether, and bitcoin cash as safe havens will fade when conditions in the Indonesian capital market become more extreme. This research can be used as a reference for investors for their investments by looking top four cryptocurrencies as a hedging instrument. However, in severe conditions such as during the Covid-19 Pandemic, the top five cryptocurrencies cannot be used as a safe haven, as revealed in this study.
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Bitcoin being a safe-haven asset is one of the traditional stories in the cryptocurrency community. However, during its existence and relevant presence, i.e., approximately since 2013, there has been no severe situation on the financial markets globally to prove or disprove this story until the COVID-19 pandemic. We study the quantile correlations of Bitcoin and two benchmarks—the S&P 500 and VIX—and make comparison with gold as the traditional safe-haven asset. The Bitcoin safe haven story is shown and discussed to be unsubstantiated and far-fetched, while gold comes out as a clear winner in this contest even when a broader cryptocurrency index (CRIX) is considered.
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Noted economist, Harry Markowitz (“Markowitz) received a Nobel Prize for his pioneering theoretical contributions to financial economics and corporate finance. His innovative work established the underpinnings for Modern Portfolio Theory — an investment framework for the selection and construction of investment portfolios based on the maximization of expected portfolio returns and simultaneous minimization of investment risk. This paper presents a simplified perspective of Markowitz’ contributions to Modern Portfolio Theory, foregoing in-depth presentation of the complex mathematical/statistical models typically associated with discussions of this theory, and suggesting efficient computer-based ‘short-cuts’ to these performing these intricate calculations.
A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power. As long as a majority of CPU power is controlled by nodes that are not cooperating to attack the network, they'll generate the longest chain and outpace attackers. The network itself requires minimal structure. Messages are broadcast on a best effort basis, and nodes can leave and rejoin the network at will, accepting the longest proof-of-work chain as proof of what happened while they were gone.
We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns. We show that this new uncertainty-adjusted investment skill metric (called Probabilistic Sharpe ratio, or PSR) has a number of important applications: First, it allows us to establish the track record length needed for rejecting the hypothesis that a measured Sharpe ratio is below a certain threshold with a given confidence level. Second, it models the trade-off between track record length and undesirable statistical features (e.g., negative skewness with positive excess kurtosis). Third, it explains why track records with those undesirable traits would benefit from reporting performance with the highest sampling frequency such that the IID assumption is not violated. Fourth, it permits the computation of what we call the Sharpe ratio Efficient Frontier (SEF), which lets us optimize a portfolio under non-Normal, leveraged returns while incorporating the uncertainty derived from track record length. Results can be validated using the Python code in the Appendix.