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ECON11035 – BUSINESS STATISTICS 1 ECON 1035 BUSINESS STATISTICS PROJECT

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ECON 1035 BUSINESS STATISTICS 1 ECON

1035 Business Report

Executive Summary In this report, we will provide provides an analysis and evaluation on the stocks of Bitcoin, DBS, OCBC and Singapore Airlines. This report will subsequently aim to use the data analysis to infer the practicality of Bitcoin investment while comparing with the 3 other companies. Line graphs and histograms were used to represent the data to identify trends of rise and fall of closing prices and weekly returns for the four companies to give a more comprehensive analysis. Outcomes will also be gathered through the uses of the hypothesis testing and various other methods. The conclusion of the strengths and weaknesses to determine the promise of Bitcoin investment will be provided based on our calculations at the end of this report.

Introduction Bitcoin is a cryptocurrency, a form of digital currency. One can purchase using real money to keep or send to others without the need for intermediaries. The main purpose of Bitcoin is to have a decentralized currency which is accepted through-out the world. Transactions are made through a secure and unaltered network called the blockchain. Bitcoin’s venture has always been a debatable topic for financial specialist and investors. Some would trust that Bitcoin speculation will deliver its promises in years to come, while others believe that the venture is a major risk not worth taking. Nevertheless, Bitcoin investment is slowly rising and through this report we will deliver our take on whether it is worth the venture.

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Part1035 A: BUSINESS StatisticalSTATISTICS Analysis1and Professional Report ECON 1. Bitcoin 1.1 Weekly Closing Prices

Figure 1: Weekly Closing Price for Bitcoin

Figure 1 shows the column chart of Bitcoin’s Weekly closing price from 02/02/2014 to 20/01/2019. The weekly closing price for Bitcoin was fairly stable from 2014 to 2016. It increased gradually at the start of year 2017 with the peak closing at $19065.71 on 17/12/2017. However, that did not maintain for long as the price starts to plunge downwards rapidly causing it to fluctuate till date

1.2 Weekly Returns Figure 2 shows the weekly return of Bitcoin. It appears that Bitcoin’s weekly return graph is symmetrical and therefore it appears to be normally distributed. It was found to be 112 weeks where weekly returns are in the negative margins. There are 3 outliers that we have found through the weekly returns for Bitcoin. Figure 2: Weekly Returns of Bitcoin 1.3 Evidence of Outliers With the range of Z =¿ 3∨←3, When Z =−3, Z =3, ¯ ¯) ( X− X ) ( X− X Z= Z= σ σ X −1.2848 X −1.2848 3= −3= 12.4785 12.4785 37.4355= X−1.2848 −37.4355= X−1.2848 X =38.7203 X =−36.1507 ∴ X ≈ 38.72(2 d . p .) ∴ X ≈−36.15(2 d . p .) With the upper and lower limit found, we can conclude that there are 3 outliers in Bitcoin’s weekly returns which are -54.55, 44.02 and 75.57 respectively. When

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ECON1.4 1035Descriptive BUSINESSAnalysis STATISTICS 1 Mean

Median

Mode

Standard Deviation

Standard Error of mean

1.2848

0.82403

0

12.4785

0.7753

Sample Variance 155.714

Range

Skewness

130.114

0.61594

Table 1: Bitcoin’s statistics 1.5 Empirical Probability of Loss Number of weeks where weekly return price is negative divided total by weeks of observations. 112 ¿ 0.4324 EPL= 259 ≈ 0.43(2 d . p .) 1.6 Confidence Interval Tests To conduct 95% CI test, Z = 1.96 σ 95 % CI = ¯X ± 1.96 × √N

(

) ¿ 1.2848 ± 1.96 × ( 12.4785 √ 259 ) ¿ 1.2848 ±1.5197 ∴−0.2349 ≤ μ ≤ 2.8045

To conduct 90% CI test, Z = 1.64 ¯ ± 1.64 × σ 90 % CI = X √N

(

) ¿ 1.2848 ± 1.64 × ( 12.4785 √259 ) ¿ 1.2848 ±1.2716 ∴0.0132 ≤ μ ≤ 2.5564

With the information that we have found from the above, we can with 95% confidence say that the average return of bitcoin is between -0.2349 to 2.8045. On the other hand, with a 90% confidence the average return would be 0.0132 to 2.5564. 1.7 Hypothesis Test Based on the information given, we can come up with the hypothesis of: H 0 : μ=4 H 1: μ ≠ 4 α =0.025 2 Z ≤−1.960∨Z ≥1.960

By using the two-tailed hypothesis test with a significance value of 5% and

,

the

decision rule would be to not accept the null hypothesis if: ( 1.2848 −4 ) Z =−2.7152 Z= 12.4785 12.4785 √ 259 √ 259 Z =−3.501784 We do not agree thatZ Bitcoin’s ≈−3.5018return is at 4% because at a significance value of 5%, the critical value can be determined by 3.5018 the use of the two-tailed graph at ±1.96. With that in mind and the rule ∴ Z=± that we have set above, we do not accept the null hypothesis as there is sufficient evidence that the return of bitcoin ≠ 4. 2. OCBC 2.1 Weekly Closing Prices Figure 3 shows the column chart of OCBC’s Weekly closing price from 02/02/2014 to 20/01/2019. In general, the closing price is trend is going upwards. With peak $13.82 on 29/4/18 and 4 lowest at $7.52 on 14/2/16. However, from 30 August 2015 to 1/1/17 and 25/3/18 to

ECON 1035 BUSINESS STATISTICS 1

Figure 3: Weekly Closing Price of OCBC 2.2 Weekly Returns

Figure 4 shows the weekly returns of OCBC. It appears that the graph is symmetrical and therefore it appears to be normally distributed. It was also found to be 114 weeks where the returns were in the negative margins.

Figure 4: Weekly Returns of OCBC 2.3 Evidence of Outliers

With the range of

Z =¿ 3∨←3,

Z =3, ¯) ( X− X Z= σ X −(0.1351) 3= 2.3629 7.0887= X−(0.1351) X =7.2238 ∴ X ≈ 7.22(2 d . p .)

Z =−3, ¯) ( X− X Z= σ X −(0.1351) −3= 2.3629 −7.0887= X−( 0.1351) X =−6.9536 ∴ X ≈−6.95(2 d . p .)

When

When

With the upper and lower limit found, we can conclude there are 3 outliers in OCBC’s weekly returns which are -7.98, 8.65 and 9.57 respectively. 2.4 Descriptive Analysis

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Mean

Median

Mode

Standard Deviation

Standard Error of mean

Sample Variance

Range

Skewness

0.1351

0.2865

0

2.3629

0.1468

5.5837

17.553

0.0276

ECON 1035 BUSINESS STATISTICS 1

Table 2: OCBC’s statistics

2.5 Empirical Probability of Loss

Number of weeks where weekly return price is negative divided by total weeks of observations. 114 EPL= ¿ 0.4402 259 ≈ 0.44(2 d . p .) 2.6 Confidence Interval Tests

To conduct 95% CI test, Z = 1.96 2.3629 ¯ ± 1.96 × σ 95 % CI = X ¿ 0.1351± 1.96 × ¿ 0.1351 ± 0.2878 √N √259 ∴−0.1527 ≤ μ≤ 0.4229 With the information that we have found from the above, we can conclude with 95% confidence interval that the average return of OCBC is between -0.1527 to 0.4229.

(

)

(

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2.7 Hypothesis Test

Based on the information given, we can come up with the hypothesis of: H 0 : μ=0 H1: μ ≠ 0 α =0.025 , the 2 decision rule would be not to accept the null hypothesis if: Z ≤−1.960∨if Z ≥ 1.960 By using a two-tailed hypothesis test with a significance value of 5% and

( 0.1351 −0 ) 0.1351 Z= Z =0.9202 2.3629 0.1468 2 √ 259 d.p.) ∴ Z=± 0.92 ¿level of 5%, critical value can be We agree that OCBC’s return is at 0% because with a significance determined using the two-tailed graph at ±1.96. With that in mind, we do not reject the null hypothesis as there is sufficient evidence that the return of OCBC = 0. Z=

3. DBS Holdings 3.1 Weekly Closing Price The graph represents the weekly closing price of DBS Holdings. The dotted line illustrations the trend of the closing price is going upwards. With peak of $30.60 on 29/4/18 and lowest at $13.14 on 14/2/16.

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ECON 1035 BUSINESS STATISTICS 1

Figure 5: Weekly Closing Price of DBS Holdings 3.2 Weekly Returns

The weekly returns for DBS Holdings were found to be right skewed. Furthermore, there is a total of 120 weeks in the negative percentage.

Figure 6: Weekly Returns of DBS Holdings 3.3 Evidence of Outliers

With the range of Z =¿ 3∨←3, When Z =3, ¯) ( X− X Z= σ X −0.2023 3= 2.7125 8.1375= X−0.2023 X =8.3398 ∴ X ≈ 8.34 (2 d . p .)

When Z =−3,

¯) ( X− X σ X −0.2023 −3= 2.7125 −8.1375= X−0.2023 X =−7.9352 ∴ X ≈−7.94 (2 d . p .) Z=

With the upper and lower limit found, we can conclude that there are 3 outliers in DBS Holdings weekly returns as there are 3 values which fall outside of our X range. There are -8.316, -8.322 and 13.8. 3.4 Statistics

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Mean

Median

Mode

Standard Deviation

Standard Error of mean

Sample Variance

Range

Skewnes s

0.2023

0.193

0

2.7125

0.1685

7.3576

22.125

0.3829

ECON 1035 BUSINESS STATISTICS 1 Table 3: DBS Holdings’ statistics

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3.5 Empirical Probability of Loss

Number of weeks where weekly return price is negative divided total by weeks of observations. 120 EPL= ¿ 0.4633 259 ≈ 0.46(2 d . p .) 3.6 Confidence Interval Tests

To conduct 95% CI test, Z = 1.96 σ ¿ 0.2023 ± 1.96 × 2.7125 95 % CI =X¯ ± 1.96 × ¿ 0.2023 ±0.3304 √N √259 ∴−0.1281 ≤ μ ≤ 0.5327 With the information that we have found from the above, we can conclude with 95% confidence interval that the average return of DBS Holdings is between -0.1281 to 0.5327.

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(

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3.7

Hypothesis Test Based on the information given, we can come up with the hypothesis of: H 0 : μ=0 H 1: μ ≠ 0 0.2023 α Z= Z =1.2003 =0.025 , the By using a two-tailed hypothesis test with a significance value of 5% and 0.1685 2 decision rule would be not to accept the null hypothesis if: Z2≤−1.960∨if d.p.) Z ≥1.960 ∴ Z=± 1 20 ¿ ( 0.2023 −0 ) Z= 2.7125 √259 We agree that DBS Holdings return is at 0% because with a significance level of 5%, critical value can be determined using the two-tailed graph at ±1.96. With that in mind, and the decision rule that we have set above, we do not reject the null hypothesis as there is sufficient evidence that the return of DBS Holdings = 0.

4. Singapore Airlines 4.1 Weekly Closing Price

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According to the figure 7, Singapore Airline hit its highest weekly closing price on 1/2/15 at $12.54. This was then followed by Fluctuating returns and they hit their lowest at $9.29 on the 28/10/18. The closing prices have since maintained at around the $

ECON 1035 BUSINESS STATISTICS 1

Figure 7: Weekly Closing Price of Singapore Airlines 4.2 Weekly Returns

Figure 8 shows the weekly return of Singapore Airlines. It appears that the graph is left skewed and therefore it appears to be negatively skewed. Furthermore, it is found that there is a total of 117 weeks in which the returns are negative.

Figure 8: Weekly Returns of Singapore Airlines 4.3 Evidence of Outliers

With the range of Z =¿ 3∨← 3, When Z =3, When Z =−3, ¯) ¯) ( X− X ( X− X Z= Z= σ σ X −0.0275 X −0.0275 3= −3= 2.2227 2.2227 6.6681=X −0.0275 −6.6681= X−0.0275 X =6.6956 X =−6.6406 ∴ X ≈ 6.70 (2 d . p .) ∴ X ≈−6.64 (2 d . p .) With the upper and lower limit found, we can conclude that there is 1 outlier in Singapore Airlines which is -8.71. 4.4 Statistics Mean

Median

Mode

Standard Deviation

Standard Error of mean

Sample Variance

Range

Skewness

0.0275

0.1031

0

2.2227

0.1381

4.9402

15.026 6

-0.111

Table 4: Singapore Airline’s statistics 9

ECON 1035 BUSINESS STATISTICS 1 4.5 Empirical Probability of Loss Number of weeks where weekly return price is negative divided by total weeks of observations. 117 EPL= ¿ 0.4517 259 ≈ 0.45(2 d . p .) 4.6 Confidence Interval Tests

To conduct 95% CI test, Z = 1.96 σ 2.2227 95 % CI =X¯ ± 1.96 × ¿ 0.0275 ± 1.96 × ¿ 0.0275 ±0.2707 N √ √259 ∴−0.2432 ≤ μ ≤ 0.2982 With the information that we have found from the above, we can conclude with 95% confidence interval that the average return of Singapore Airlines is between -0.2432 to 0.2982.

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)

(

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4.7 Hypothesis Test

Based on the information given, we can come up with the hypothesis of: H 0 : μ=0 H 1: μ ≠ 0 α =0.025 , the 2 decision rule would be not to accept the null hypothesis if: Z ≤−1.960∨if Z ≥1.960 0.0275 Z= ( 0.0275 −0 ) Z= 0.1381 2.2227 Z =0.1991 √259 2 d.p.) We agree that Singapore Airline’s return is at 0% because ∴ at aZ=± significance 0.20 ¿ value of 5%, the critical value can be determined using the two-tailed graph at ±1.96. With that in mind, we do not reject the null hypothesis as there is sufficient evidence that the return of Singapore Airlines = 0. By using a two-tailed hypothesis test with a significance value of 5% and

Conclusion Bitcoin merits for investing for individuals are that it has the lowest empirical probability of loss compared to the other three organizations. This implies that it has a reduced probability of attaining negative weekly returns. Additionally, we have found out that Bitcoin has the highest mean and median weekly return of 1.28% and 0.82% respectively amongst the other companies. Thus, we advise financial specialist and investors that it is more profitable to invest in them. Its steep bell-shape histogram indicates that its market weekly return has been constant throughout the years making it easier to anticipate the rise and falls for investors.

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