Bitcoin and NAB Rate of Return Analysis

This study evaluates the recent prices of Bitcoin and NAB and analyzes their rate of return. Find out the average rate of return, standard deviation, and probability of loss.

ECON 1030 1
ECON 1030 – BUSINESS STATISTICS 1
by (Name)
Course
Professor’s Name
University
The City and State
Date

ECON 1030 2
Executive Summary
This study was geared towards evaluating the recent prices of Bitcoin and using this
information to advise investors on whether there is sufficient confidence and security in
investing in it. The study investigated the trend and rate of return of four securities in the
Australian market. From the confidence intervals computed for each of the securities, Bitcoin
had a positive rate of return of between 0.05% and 3.12%. This was the highest compared to the
rest. This, therefore, is a worthy investing project than an investor can risk investigating in.
Introduction
Cryptocurrencies are some of the blockchain technology that is gaining popularity at a
high rate in most parts of the world. One of these technologies is the Bitcoin. Considering the
myths and stories underlying these technologies, there is a need to carry out an informed
investigation using past data to predict their future and security. This study, therefore, evaluates
the recent prices of Bitcoin allows the use of this data to advise an investor on whether there is
sufficient confidence in investing in it.
Part A
Question1

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1/1/2014
3/26/2014
6/18/2014
9/10/2014
12/3/2014
2/25/2015
5/20/2015
8/12/2015
11/4/2015
1/27/2016
4/20/2016
7/13/2016
10/5/2016
12/28/2016
3/22/2017
6/14/2017
9/6/2017
11/29/2017
2/21/2018
5/16/2018
8/8/2018
10/31/2018
1/23/20190
5000
10000
15000
20000
25000
30000
Bitcoin Weekly closing prices Trend
Dates
Weekly closing price
Figure 1: Bitcoin Weekly Closing Price Distribution
From the data collected from March 2014, it shows that the closing prices of Bitcoin have been
increasing steadily over time. From 2014 to the end of 2016, the average closing prices were
about 572 AU$. The closing prices increased steadily from 2017 to mid-2018 when they started
going down. From mid-2018, the price has been fluctuating and closely catching up. The highest
recorded price was 10th December 2017 with a closing price of 25,986.55 AU$.
-39.755--29.755
-29.755--19.755
-19.755--9.755
-9.755-0.244999999999997
0.245-10.245
10.245-20.245
20.245-30.245
30.245-40.245
40.245-50.2450
20
40
60
80
100
Bitcoin Weekly Rate of Return
Rate Groupings
Frequency
Figure 2: Bitcoin Rate of Return Histogram

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The histogram shows that the weekly rate of return for Bitcoin is normally distributed with no
outliers. The data bars are forming a bell shape that proofs normality of a distribution.
Question 3
Table 1: Bitcoin Descriptive statistics
Descriptive Statistics Weekly Return
Mean 1.59
Standard Error 0.78
Median 1.22
Standard Deviation 12.61
Sample Variance 159.01
Kurtosis 3.01
Skewness 0.61
Range 105.44
Minimum -39.76
Maximum 65.68
Sum 412.35
Count 260.00
Mean =Sum of the Return /Number of Observations=412.35/260=1.59
Standard Error (= σ
√ n = 12.61
√ 260 =0.78
Standard deviation=√ ∑ ( ( x−xbar )2
n−1 ¿)¿=√ ¿41,183.21 / (260-1)) =√ (159.01)=12.61
Median is the value at the middle when all the entries are arranged in ascending order. In this
case it is 1.22.
The maximum value =65.68
Minimum value=-39.76
Range =Maximum-Minimum=65.68—39.76=105.44
According to the above calculations, the average rate of return for bitcoin is 1.59% with a
standard deviation of 12.61 from the mean. The highest recorded rate of return was 65.68% with
the lowest return of -39.76%.This results in a range of 105.44. Also, the distribution has a

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positive kurtosis and Skewness figures of 3.01 and 0.61 respectively. This show that the
distribution is spread towards the positive side of the distribution
Question 4
Empirical probability =Number of times an event occurred/Total number of times the experiment
was carried out
Empirical probability of loss= Number of times a loss occurred / Total Occurrences
P=114/260=0.44 .This is a 44% chance of getting a loss
Question 5
1/1/2014
3/26/2014
6/18/2014
9/10/2014
12/3/2014
2/25/2015
5/20/2015
8/12/2015
11/4/2015
1/27/2016
4/20/2016
7/13/2016
10/5/2016
12/28/2016
3/22/2017
6/14/2017
9/6/2017
11/29/2017
2/21/2018
5/16/2018
8/8/2018
10/31/2018
1/23/2019
-
10.00
20.00
30.00
40.00
NAB Weekly closing prices Trend
Dates
Weekly closing price
Figure 3: NAB Rate of Return Trend
The NAB weekly closing prices show a fluctuating trend from 2014 to date

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-8.767--6.767
-6.767--4.767
-4.767--2.767
-2.767--0.766999999999999
-0.766999999999999-1.233
1.233-3.233
3.233-5.233
5.233-7.233
7.233-9.233
0
20
40
60
80
NABWeekly Rate of Return
Rate Groupings
Frequency
Figure 4: NAB Rate of Return Histogram
This shows that the distribution is normally distributed.
Table 2: NAB Descriptive statistics
Descriptive Statistics Weekly Return
Mean -0.058
Standard Error 0.172
Median 0.074
Standard Deviation 2.776
Sample Variance 7.706
Kurtosis 0.742
Skewness -0.186
Range 17.863
Minimum -8.768
Maximum 9.095
Sum -15.167

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Count 260
Confidence Level(95.0%) 0.339
According to table 2, the average rate of return for NAB is -0.058%% with a standard deviation
of 2.776% from the mean. The highest recorded rate of return was 9.095% with the lowest return
of -8.768%. This results in a range of 17.86. Also, the distribution has a positive kurtosis and
negative Skewness figures of 0.742 and -0.186 respectively. This show that the distribution is
spread towards the negative side of the distribution
Empirical Loss=126/260=0.48 probability of incurring a loss
1/1/2014
3/26/2014
6/18/2014
9/10/2014
12/3/2014
2/25/2015
5/20/2015
8/12/2015
11/4/2015
1/27/2016
4/20/2016
7/13/2016
10/5/2016
12/28/2016
3/22/2017
6/14/2017
9/6/2017
11/29/2017
2/21/2018
5/16/2018
8/8/2018
10/31/2018
1/23/2019
-
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
West Farmers Weekly closing prices Trend
Dates
Weekly closing price
Figure 5: West Farmers Rate of Return trend
The West farmer’s weekly closing prices show a fluctuating trend from 2014 to date with the
highest being in mid-2018.

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-8.612--
6.612
-6.612--
4.612
-4.612--
2.612
-2.612--
0.612
-0.612-
1.388
1.388-
3.388
3.388-
5.388
5.388-
7.388
0
20
40
60
80
100
120
West Framers Weekly Rate of Return
Rate Groupings
Frequency
Figure 6: West Farmer Rate of Return Histogram
This shows that the distribution is normally distributed.
Table 3: West Framers Descriptive statistics
Descriptive Statistics Weekly Return
Mean 0.079
Standard Error 0.150
Median 0.162
Standard Deviation 2.426
Sample Variance 5.886
Kurtosis 0.907
Skewness -0.441
Range 15.651
Minimum -8.613
Maximum 7.038
Sum 20.607
Count 260.000
Confidence Level(95.0%) 0.296
According to table 3, the average rate of return for West farmers is 0.079% with a standard
deviation of 2.426% from the mean. The highest recorded rate of return was 7.038% with the

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lowest return of -8.613%. This results in a range of 15.65. Also, the distribution has a positive
kurtosis and negative Skewness figures of 0.907 and -0.441respectively. This show that the
distribution is spread towards the negative side of the distribution
Empirical Loss=119/260=0.46 probability of incurring a loss
1/1/2014
3/26/2014
6/18/2014
9/10/2014
12/3/2014
2/25/2015
5/20/2015
8/12/2015
11/4/2015
1/27/2016
4/20/2016
7/13/2016
10/5/2016
12/28/2016
3/22/2017
6/14/2017
9/6/2017
11/29/2017
2/21/2018
5/16/2018
8/8/2018
10/31/2018
1/23/2019
-
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
Woodside Weekly closing prices Trend
Dates
Weekly closing price
Figure 7: Woodside Rate of Return Trend
The Woodside weekly closing prices show a fluctuating trend from 2014. In 2014 a high
rate of return was experienced but decreased from 2015 to 2017. From 2017, the prices have
been going up and down gradually.

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-8.294--
6.294
-6.294--
4.294
-4.294--
2.294
-2.294--
0.294
-0.294-
1.706
1.706-
3.706
3.706-
5.706
5.706-
7.706
7.706-
9.706
0
10
20
30
40
50
60
70
80
90
Woodside Weekly Rate of Return
Rate Groupings
Frequency
Figure 8: Wood Side Rate of Return Histogram
This shows that the distribution is normally distributed.
Table 4: Woodside Descriptive statistics
Descriptive Statistics Weekly Return
Mean 0.023
Standard Error 0.195
Median 0.209
Standard Deviation 3.138
Sample Variance 9.850
Kurtosis 0.629
Skewness -0.058
Range 18.687
Minimum -8.294
Maximum 10.393
Sum 5.981
Count 260.000
Confidence Level(95.0%) 0.383
According to table 4, the average rate of return for Woodside is 0.023% with a standard
deviation of 3.138% from the mean. The highest recorded rate of return was 10.39% with the
lowest return of -8.294%. This results in a range of 18.69. Also, the distribution has a positive

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kurtosis and negative Skewness figures of 0.629 and -0.058 respectively. This show that the
distribution is spread towards the negative side of the distribution (King'oriah,2004)
Empirical Loss=124/260=0.48 probability of incurring a loss
Question 6
Confidence interval (C.I)   ∓ z -population mean, z-z score and () = σ
√ n ) is the
standard error.
If the confidence level is 95%
At 95% confidence interval, Z =1.96
Bitcoin average rate of return is 1.59
Therefore z= (1.96*12.61/√ 260¿=1.533
Upper Level  1.59 (1.533) = 3.12 and Lower Level  1.59  (1.533) =0.05
Confidence Limit is [0.05, 3.12]
The rate of return ranges between 0.05%and 3.12% at 95% confidence level.
If the confidence level is 90%
At 90% confidence interval, Z =1.645
Bitcoin average rate of return is 1.59
Therefore z= (1.645*12.61/√ 260¿=1.286
Upper Level  1.59 (1.286) = 2.87 and Lower Level  1.59  (1.286) =0.30

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Confidence Limit is [0.30, 2.87]
The rate of return ranges between 0.30% and 2.87% at 90% confidence level.
If the confidence level is 99%
At 99% confidence interval, Z =2.576
Bitcoin average rate of return is 1.59
Therefore z= (2.576*12.61/√ 260¿=2.015
Upper Level  1.59 (2.015) = 3.60 and Lower Level  1.59  (2.015) =-0.43
Confidence Limit is [-0.43, 3.60]
The rate of return ranges between -0.430% and 3.60% at 99% confidence level.
Comparing the confidence intervals
The 99% confidence level is more accurate compared to 90% and 95% confidence level. As the
confidence level increases from 90% to 99%, the interval of the return widens. That explain why
the interval increases from [0.30, 2.87] to [0.05, 3.12] and [-0.43, 3.60]
Question 7
 The 95% confidence level for NAB
Upper Level  -0.0583 (0.337) = 0.28 and
Lower Level  -0.0583 (0.337) =-0.40
Confidence Limit is [-0.40, 0.28]

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The rate of return ranges between -0.40%and 0.28% at 95% confidence level.
 The 95% confidence level for West farmers
Upper Level  0.079  (0.295) = 0.37 and
Lower Level  0.079  (0.295) =-0.22
Confidence Limit is [-0.22, 0.37]
The rate of return ranges between -0.22%and 0.37% at 95% confidence level.
 The 95% confidence level for Woodside
Upper Level  0.023  (0.381) = 0.40 and
Lower Level 0.023  (0.381) = -0.36
Confidence Limit is [-0.36, 0.40]
The rate of return ranges between -0.36%and 0.40% at 95% confidence level.
Question 8
Table 5:T-test
Test Value = 0
t df Sig. (2-tailed) Mean Difference
95% Confidence
Interval of the
Difference
Lower Upper
Weekly Return BIT 2.028 259 .044 1.586 0.046 3.126
Weekly Return NAB -0.339 259 .735 -0.058 -0.397 0.281
Weekly Return WEST 0.527 259 .599 0.079 -0.217 0.376
Weekly Return WOOD 0.118 259 .906 0.023 -0.360 0.406

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According to the t-test above, the claim that the return to Bitcoin is 4% is not correct.
However, the returns to other three shares are not different from zero is . The results above agree
with this notion since p<.05 at alpha=.05 at t(259)=2.028.
Conclusion
The study investigated the trend and rate of return of four securities in the Australian
market. The confidence intervals of each of them were also computed to ensure investors are
well guided on the best security to invest in. At 95% confidence interval Woodside had it rate of
return ranging from-0.36% and 0.40%, West farmers between -0.22% and 0.37%, NAB between
-0.40%and 0.28% and Bitcoin between 0.05% and 3.12%.From all the securities apart from
Bitcoin, there is a possibility of getting a negative return (loss) from your investment.
PART B
This section is meant to evaluate the 4 the rate of return as computed from the share
prices in the Australia Securities Exchange: National Australia Bank (NAB) from the financial
sector, Wesfarmers Limited (Wesfarmers) from the consumer discretionary sector, and
Woodside Energy (Woodside) from the energy sector.
From the analysis above Bitcoin had the highest average rate of return of 1.59% followed by
West farmers with 0.08% rate of return then Woodside and NAB with 0.02% and -0.06%
respectively. This shows that Bitcoin is still the leader in the market and is a security an investor
can put his/her money to. The trend reveals that the rate of return of the four securities was
fluctuating gradually over the 5 year period under review. Bitcoin registered the highest rate
return of 65.7% in January 2015 with NAB registering a high of 9.09%, West Farmer; 7.04% and
Woodside with 10.39%. Interestingly, most of the share price in the four securities have started
to go up in 2019.

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1/1/2014
6/25/2014
12/17/2014
6/10/2015
12/2/2015
5/25/2016
11/16/2016
5/10/2017
11/1/2017
4/25/2018
10/17/2018
0
5000
10000
15000
20000
25000
30000
Bitcoin Weekly closing prices Trend
Dates
Weekly closing price
1/1/2014
8/27/2014
4/22/2015
12/16/2015
8/10/2016
4/5/2017
11/29/2017
7/25/2018
-
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
NAB Weekly closing prices
Trend
Dates
Weekly closing price
1/1/2014
6/25/2014
12/17/2014
6/10/2015
12/2/2015
5/25/2016
11/16/2016
5/10/2017
11/1/2017
4/25/2018
10/17/2018
-
10.00
20.00
30.00
40.00
West Farmers Weekly closing prices
Trend
Dates
Weekly closing price
1/1/2014
8/13/2014
3/25/2015
11/4/2015
6/15/2016
1/25/2017
9/6/2017
4/18/2018
11/28/2018
-
10.00
20.00
30.00
40.00
50.00
Woodside Weekly closing prices
Trend
Dates
Weekly closing price
References

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https://www.data61.csiro.au/en/our-work/safety-and-security/secure-systems-and-platforms/
blockchain
https://www.pwc.com/us/en/industries/financial-services/fintech/bitcoin-blockchain-
cryptocurrency.html
King'oriah, G. K., 2004 Fundamentals of applied statistics. Nairobi: The Jomo Kenyatta
Foundation.