Statistical Evaluation of Bitcoin Prices

ECON 1030 – BUSINESS STATISTICS 1
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Statistical Evaluation of Bitcoin Prices
Executive Summary
Globally, the popularity of blockchain and cryptocurrencies has exponentially risen
in the recent past. Hence, the growing interest for Bitcoin as an alternative investment class
and medium of exchange. There is a lot of uncertainty that is associated with Bitcoin, which
make many individuals wary of investing in it. Amid or the controversies and uncertainty, the
recent prices of Bitcoin provide factual evidence for evaluating whether investing in Bitcoin
is advisable or not. We obtained recent weekly closing price for Bitcoin and three other
Singaporean shares; Singtel, Wilmer International, and Olam International. The evaluations
involved a trend analysis of the weekly closing prices of Bitcoin and the three shares, and
descriptive tactical analysis of weekly returns to Bitcoin and the three shares.
The results indicated that recent prices of Bitcoin had an upward trend, while those of
Singtel shares had a downward trend. The prices of Wilmar International followed a
nonsignificant upward trend, while those of Olam international largely remains constant with
no apparent general upward or downward trend. The analysis of returns to Bitcoin resulted to
a high mean weekly return of 2.05% which outperforms the other three shares whose returns
were close to 0.00%. Additionally, as an investment, the probability of a loss in Bitcoin is
much lower than the probability of a loss in the other three shares. Despite the price volatility
of Bitcoin, we would recommend that individual consider it as an investment option because
it has higher returns than investing in company shares.
Introduction
In the current world, it is becoming more and more common to come across the terms
blockchain, cryptocurrency, and Bitcoin. Interestingly, blockchain technology has been
existence for decades. However, combining blockchain technology and peer-to-peer (P2P)
networks has propelled the technology to new heights. The internet makes it more accessible
to many people globally. Hence, the great innovations using such as cryptography and
distributed computing in various industries. In finance, the exponential growth of
cryptocurrencies has garnered global attention. Cryptocurrencies are considered a medium of
exchange and store of value like any other currencies and assets. Cryptocurrency and
blockchain technology are terms used interchangeably because one would not exist without
the other. The first successful implementation of blockchain and cryptocurrency was Bitcoin
hence its popularity worldwide. Bitcoin uses the technology that allows participants to send
accounting units from one user account to another user account without intermediaries. The
popularity of Bitcoin as a medium of exchange and store of value is growing exponentially
because individuals can transact any amount at anytime of day in any place in the world. It is
important to note that Bitcoin are not physical or digital coins. Instead, Bitcoin is a chain of
electronic signatures that represent units on a digital ledger. From an investment perspective,
Bitcoin is compared to gold because both are limited in supply, have functional use and are
considered by many to be good stores of value. In comparison, Bitcoin greatly outperformed
gold in terms on annualize returns for the past few years, thus attracting the attention of
investors as an alternative asset class. However, there are many risks associated with Bitcoin
compared to gold. There is great uncertainty associated with Bitcoin which is reflected in its
price volatility. Additionally, Bitcoin is unregulated as an alternative currency and investment
asset class.
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In this report we statistically evaluate whether individuals should invest in Bitcoin
based on its recent prices. The report is divided into various section. First, the executive
summary which gives a clear overview of the information in the report. Next is the
introduction which gives an extensive background of the problem. Part A of the report
comprises of the detailed statistical analysis of the prices of and returns to Bitcoin and three
Singaporean shares; Singtel, Wilmer International, and Olam International. Lastly, we
provide a ministerial brief. The objectives of this report are to:
 Outline the new investment frontier that is cryptocurrencies, and in particular Bitcoin.
 Statistically evaluate the recent prices of Bitcoin
 Compare the returns to Bitcoin and other shares
To achieve the objectives, we obtained weekly closing prices of Bitcoin, Singtel, Wilmer
International, and Olam International. We then calculated the weekly returns to Bitcoin and
the other three shares using the formula: (Current Price – Previous price)/Previous price
*100. Then, we analyzed the trend of the prices using line graphs, and a descriptive analysis
of the histogram for the weekly returns was also carried out. Using the probability theory, we
found out the empirical probability of a loss in investing in Bitcoin and the other three shares.
Lastly, we find use hypothesis testing to evaluate the claim of an investment advisor that the
return to Bitcoin is 4% while the returns to the other three shares are no different from zero.
Part A
Bitcoin Analysis
We used a line graph to present the weekly closing price of the Bitcoin. The line
graph indicated a general upward trend in the closing price of the Bitcoin over the period
under consideration. The change in weekly closing price was minimal between 2014 and
2016. However, there is a sharp rise in the weekly closing price in the year 2017, with sharp
increase in the last weeks of the year. The sharp increase is followed by similar sharp
decrease in the first week of 2018. The graph indicates that the weekly closing price have
been fluctuating a lot in 2018.
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Date
Weekly Closing Price
Figure 1: A Line Graph of Weekly Closing Price of Bitcoin
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We calculated the weekly return of Bitcoin. The resulting histogram indicate that the
data could be normally distributed. On the right-hand side, there is evidence of outliers.
Figure 2: Histogram of Weekly Returns of Bitcoin
The shape of the histogram indicates that the distribution of weekly return of Bitcoin
is approximately symmetrical with few outliers. The descriptive statistics results to skewness
value of 0.614, which indicates that the data is relatively right-skewed. Moreover, the mean,
2.05% is greater than the median, 1.43% which indicates positive skewness. The center of
distribution, as measured by the median, lies at 1.43%. The spread of distribution, as
measured by the range is 105.44% (65.68% - -39.76%). Most Bitcoin weekly returns are
located around the mean (2.05%).
The empirical probability of a loss is calculated as:
P(L) = Number of times loss in weekly return/ Total number of weekly returns
= 89/ 208 = 0.4279 = 42.79%
Singtel Analysis
The line graph of Singtel weekly closing prices indicates an overall downward trend.
Nonetheless, the price has been fluctuating tremendously over the period under consideration
with the price ranging from 3.18 and 4.45. the company’s weekly closing prices were
increasing from October 2014 to April 2015, and again from November 2015 to July 2016.
From there, the price has been declining steadily.
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