(TIỂU LUẬN) RMIT international university vietnam assignment cover page question 5 a) central tendency

Question 3: Figure 1: Weekly closing prices of Dogecoin in 2020 Figure 2: Weekly closing prices of Darling in 2020... Figure 4: Histogram of Darling’s weekly returnsFor both Dogecoin and

RMIT International University Vietnam

Assignment cover page

Table of Contents

PART A 3

Question 1: 3

Question 2: 3

Question 3: 4

Question 4: 5

Question 5: 6

a) Central Tendency 6

b) Variation 7

c) Box-and-Whisker Plot 7

Question 6: 8

Question 7: 9

Question 8 & 9: 10

a) Question 8: 10

b) Question 9: 10

Question 10: 10

a) Dogecoin: 10

b) Darling: 12

PART B 13

REFERENCES 14

PART A

Question 1:

The measures of investment have become more diverse over time, thanks to technological advancement, particularly a new asset has had a significant attraction in the financial market -cryptocurrency Cryptocurrency can be defined as a special type of currency existing in non-material and digital form (Mikhaylov 2020) All transactions related to cryptocurrency are recorded and monitored by a blockchain, which is a digital and open-distributed ledger (Chuen et al 2018) This decentralization provides higher capacity, lower transaction costs, faster settlement, better transparency and security The cryptocurrency examined in this case

is Dogecoin, which was created by the end of the year 2013 as a joke by Billy Markus, based

on a famous meme on the social media (Chohan 2021) Its original capitalization (in 2014) was $60 million, but it has surged to $10 billion in 2021 (Chohan 2021), which means that the popularity and investment volume of Dogecoin has strikingly increased after more than seven years

On the other hand, another method is to invest in a company shares, which is the most traditional measure of passive wealth building for investors (Mladjenovic 2006) A company share or stock is a unit of security and/or equity, illustrating the portion of ownership in a financial asset or company If the value of a company rises, investors of this company can receive returns, in the form of capital gains (Mladjenovic 2006), which means that share investment would have a high potential of liquidity and profit The company examined in this case is Darling Ingredient Inc., founded in 1889, is an American company about renewables and environment, headquartered in Irving, Texas (Darling Ingredients n.d.) This company focuses on developing and producing feed ingredients, food ingredients and fuel ingredients from bio-nutrients (Reuters n.d.) With more than 200 factories and offices over the world, and reaching top 57 mid-cap companies of the world, Darling has affirmed the position of prestige in their industry - renewables and environment (Darling Ingredients n.d.)

Question 2:

Events happened in recent days have had an effect on Dogecoin cryptocurrency and Darling company share For Dogecoin, according to Browne (2021), the price of Dogecoin has soared after Elon Musk and Mark Cuban tweeted In specific, according to Coin Metrics, the price of Dogecoin has risen by 20%, to 32 cents This is thanks to Elon Musk and Mark Cuban, the two billionaires who posted tweets which support Dogecoin However, the extraordinary rise

of Dogecoin price could be a sign of warning for investors, as Dogecoin can be seen as a speculative bubble, and the bubble can burst Therefore, Dogecoin has a great performance in the cryptocurrency market, but it could be risky for investors to invest

About Darling, there is a positive view in terms of Darling’s production in Q4 - 2020

(Darling Ingredients Inc 2021) Specifically, Darling’s Q4 report indicates that the processing

of raw materials is strong, as well as biodiesel manufacturing achieves a record Moreover, Darling also gains benefits from high commodity prices, involving demand for the renewable diesel Furthermore, a facility-expanding project has been set to be done by the end of 2021, which contributes to a long-term development, as well as help the company to affirm their position of prestige in their industry Therefore, the performance of Darling is positive and stable, which means that its share/stock could be an ideal option for investors

Question 3:

Figure 1: Weekly closing prices of Dogecoin in 2020

Figure 2: Weekly closing prices of Darling in 2020

According to Figure 1 and 2, it is clear that both the prices of DOGE and DAR experienced

an approximately twofold increase throughout the time frame However, the price of DOGE seems to be erratic, while it is more stable for that of DAR

About DOGE, the price of it started at nearly $0.0025 Then it rose to $0.0030 in February, before a significant decrease to slightly more than $0.0015 in March After that, the price rose

to slightly higher than $0.0025, then experienced a minor decrease before strikingly

recovering to approximately $0.0035 by the end of July However, it significantly dropped to about $0.0027 just before September, but then the decreasing speed became slower

Ultimately, in the last two months, the price of DOGE rose dramatically to about $0.0047, despite a significant fluctuation

About DAR, the price of it started at nearly $30 It was approximately stable until the mid of February, then significantly dropped to nearly 20% However, after that, if overlooking minor fluctuations, the price of DAR increased significantly and regularly to nearly $60 by the end

of the year 2020

Question 4:

Figure 3: Histogram of Dogecoin’s weekly returns

Figure 4: Histogram of Darling’s weekly returns

For both Dogecoin and Darling, the histograms of both Dogecoin and Darling appear as bell shapes, and also symmetric and concentrate around the mean This means that both of them are normally distributed Moreover, the data range of Dogecoin is wider, while it is more concentrated to the mean for Darling However, as seen from the table below, both datasets include outliers, which could make some future data calculations become less reliable

Table 1: Outlier test of Dogecoin and Darling

Question 5:

a) Central Tendency

Table 2: Measurement of Central Tendency for Dogecoin and Darling (%)

In this case, Median is the most suitable measurement, as it represents the central value and cannot be affected by extreme values or outliers In addition, as seen in Figure, both

investment types include outliers, which means that Mean is an inappropriate choice

The Median of Darling (0.97) is higher than Dogecoin (0.35), which indicates that overall return of Darling is higher than that of Dogecoin, if overlooking extreme values However, for a larger picture, Measure of Variation should be considered

b) Variation

Table 3: Measurement of Variation for Dogecoin and Darling (%)

In this case, Standard Deviation (SD) is a considered choice, as it could represent variation around the average weekly return and evaluate the fluctuation of weekly return Specifically,

SD of Dogecoin (12.57) is nearly twofold that of Darling (7.15), which means that Dogecoin has significantly high or low weekly returns more frequently than Darling, or Dogecoin’s volatility level is higher than Darling in 2020

c) Box-and-Whisker Plot

Figure 5: Box-and-Whisker plot of Dogecoin and Darling (%)

As seen in Figure, the position of Darling is higher than Dogecoin (-1.34% - 4.93% compared

to -3.4% - 3.74%), which indicates that 75% of Darling and Dogecoin’ returns are higher than -1.34% and -3.4% respectively Furthermore, Darling’s box is smaller than Dogecoin,

illustrating that Darling is more frequent to get higher returns from 25%-50% than Dogecoin Moreover, the distinction between minimum return of Dogecoin and Darling is minor (-28.09% and -27.35% respectively), while maximum return of Dogecoin (43.19%) is

significantly higher than that of Darling (17.54%) Overall, while Dogecoin seems to be more profitable at some points, Darling is less risky for investors

Question 6:

To test which quarter the investment is made, and probability of a loss are statistically dependent, the conditional probability of two related variables should be investigated In specific, a probability of a loss (P(L)) is compared to the conditional probability of a loss in the first quarter (P(LQ1/L))

Table 4: Contingency table for Dogecoin weekly returns (weeks)

For DOGE:

P(L)=24

52=0.46

P(LQ 1)= 6

52=0.12

P( L

LQ 1)=P (LQ 1)

P (L) =

6/52

24/52=

6

24=0.25

P( L

LQ 1)≠ P (L)( 6

24≠24

52)

Table 5: Contingency table for Darling weekly returns (weeks)

For DAR:

P(L)=21

52=0.40

P(LQ 1)= 7

52=0.13

P( L

LQ 1)=P(LQ 1)

P(L) =

7 52 21 52

= 7

21=0.33

P( L

LQ 1 )≠ P(L)( 7

21≠21

52)

In general, the probability of a loss and first-quarter investment are statistically dependent events, and there can be a similar result for the following quarters Hence, the possibility of a loss in both Dogecoin and Darling depends on which quarter the investment is made

Question 7:

The confidence level chosen to calculate the confidence interval for the weekly return of

Dogecoin and Darling Thus, the significant level ( α ) is 0.05 (=1-0.95).

Table 6: Statistic summary table for Dogecoin and Darling

For both investment types, n=52>30 means that the Central Limit Theorem (CLT) is

applicable Hence, the sampling distribution is normally distributed Moreover, the

Population standard deviation ( σ ) is unknown, then the Sample standard deviation (S)

become the substitute The t distribution is used, as replacing normal distribution

For Dogecoin:

μ = ´X ± t a

2,d f

× S

√n =1.98 ± 2.0076×12.57

√52 =1.98 3.5±

→1.52 <μ<5.48

Therefore, we are 95% confident that the true mean of Darling’s weekly return is -1.52% and 5.48%

For Darling:

μ = ´X ± t a

2,d f × S

√n =1.65 ±2.0076 ×7.15

√52=1.65 ± 1.99

→ −0.34 <μ<3.64

Therefore, we are 95% confident that the true mean of Darling’s weekly return is -0.34% and 3.64%

Despite the non-appearance of Population standard deviation in this case, as explained earlier, the distribution of the sample mean for both investment types is normal (CLT is applicable) This means that there are no assumptions required to calculate the confidence interval

Question 8 & 9:

The confidence interval is based on two factors, which are the sample mean ´X and the Margin of Error (ME) (t a

2,d f

× S

√n) , as ME could affect the size of the confidence interval

a) Question 8:

If there is longer time for investment, the sample size could be wider As seen at the formula for the Margin of Error, the relationship between Sample size and ME is negative, which means that a wider sample size can lead to the reduction of ME and the narrowing of

confidence interval As the sample size for both Dogecoin and Darling are the same, the investment type with larger confidence interval could have more volatility in longer time In this case, it is Dogecoin, as its confidence interval (-1.52% to 5.48%) is wider than that of Darling (-0.34% to 3.64%)

b) Question 9:

If there is a global economic crisis in 2021, the volatility of both investment types will be higher Therefore, the standard deviation of both investment types will experience rise, more noticeable than the rise of sample size Furthermore, as seen in the aforementioned formula, the relationship between the sample standard deviation and ME is positive Thus, the Margin

of Error will rise, widening the confidence interval for both Dogecoin and Darling This means that they have higher risk for investors

Question 10:

a) Dogecoin:

This is claimed that the Dogecoin’s average weekly return in 2019 was 3%, among the aforementioned confidence interval of Dogecoin (between -1.52% and 5.48%) Hence, it is assumed that Dogecoin’s average weekly return could remain stable from 3%

Significance level (α) 0.05

● Step 1

- As the sample size n=52>30, CLT is applied This means that the sampling distribution is normally distributed

● Step 2

- The null hypothesis H0:μ=3

- The alternative hypothesis H0:μ ≠ 3

● Step 3

- Significance level α =0.05 , Sample size n=52

- As H0:μ ≠ 3 , a two-tailed test is used.

● Step 4

- As the population standard deviation ( σ ) is unknown and sampling

distribution is normally distributed, the t-table will be used in this case

● Step 5

- Significance level α=0.05

- Degree of freedom d f =n−1=52− =511

- Two-tailed test

→ =± 2.0076

● Step 6

- Test statistic: t=´X−μ

S

√n

=1.9812.57−3

√52

=−0.59

● Step 7

- As -2.0076 < t = -0.59 < 2.0076, the test statistic is among the non-rejection

● Step 8

- Since H0 is not rejected, we can conclude with 95% confidence level that there is not enough evidence to prove the true mean of Dogecoin’s 2020 weekly returns is different than 3% like in 2019

● Step 9

- As H0 is not rejected, we may have committed Type II error, we could conclude that there is not enough evidence to prove the true mean of Dogecoin’s 2020 weekly returns is different than 3% like in 2019 However, actually Dogecoin’s true mean returns can be different

b) Darling:

This is claimed that Darling's average weekly return in 2019 was 1%, among the

aforementioned confidence interval of Darling (between -0.34% and 3.64%) Hence, it is assumed that Darling’s average weekly return could remain stable from 1%

● Step 1

- As the sample size n=52>30, CLT is applied This means that the sampling distribution is normally distributed

● Step 2

- The null hypothesis H0:μ=3

- The alternative hypothesis H0:μ ≠ 3

● Step 3

- Significance level α =0.05 , Sample size n=52

- As H0:μ ≠ 3 , a two-tailed test is used.

● Step 4

- As the population standard deviation ( σ ) is unknown and sampling

distribution is normally distributed, the t-table will be used in this case

● Step 5

- Significance level α=0.05

- Degree of freedom d f =n−1=52− =511

- Two-tailed test

→ =± 2.0076

● Step 6

- Test statistic: t=´X−μ

S

√n

=1.657.15−1

√52

=0.66

● Step 7

- As -2.0076 < t = 0.66 < 2.0076, the test statistic is among the non-rejection

region Hence, H0 is not rejected

● Step 8

- Since H0 is not rejected, we can conclude with 95% confidence level that there is not enough evidence to prove the true mean of Darling’s 2020 weekly returns is different than 1% like in 2019

● Step 9

- As H0 is not rejected, we may have committed Type II error, we could conclude that there is not enough evidence to prove the true mean of Darling’s

2020 weekly returns is different than 1% like in 2019 However, actually Darling’s true mean returns can be different

In general, we could conclude with 95% confidence that Dogecoin and Darling’ 2020 average weekly returns are approximately similar to 3% and 1% in 2019, respectively Nevertheless,

in reality, the returns of both investment types could be different from the claim

PART B

This report represents an analysis and evaluation of the 2020 for two investment types - Dogecoin (cryptocurrency) and Darling Ingredients Inc (company share), to determine whether an investment type is more beneficial to invest than the other one There are a number of measures to analyse, including Histogram analysis, the calculation of Descriptive Statistics (Central Tendency, Variation, Box-and-Whisker Plot), Probability analysis,

calculation of Confidence Interval and Hypothesis testing The two main criteria to evaluate both investment types are profitability and volatility, for both the main time frame (2020) and longer-term perspective (longer time for investment and supposed 2021 global economic crisis) Throughout this report, there are some important findings Throughout the year 2020, both investment types have experienced an approximately twofold rise regarding the value,