ECOM 2001 Term Project: (Your Assigned Stocks Here)
Your Name Here (Your Student ID here)
Due May 29,2023 at 9:00 AWST
# Include comments in your coding to explain what you are doing.
# You can delete unnecessary comments/hints that I have provided.
# Replace your name, student ID and your three assigned stocks in the YAML.
# Knit frequently to ensure your coding is working and explanations are formatted
# in the text as you intend.
# YOU MUST ONLY USE THE STOCKS ASSIGNED TO YOU
# Any deviation from the assigned stocks will results in a grade of zero.
# packages
library(tidyquant) # for importing stock data
library(tidyverse) # for working with data
# library(broom) # for tidying output from various statistical procedures
library(knitr) # for tables
# library(kableExtra) # for improving the appearance of tables
# Add any additional packages that you use to this code chunk
1 Import the Data (2 points)
## 1) Import your assigned stocks
## Use the package tidyquant. You may need to install this package first.
## Replace Stock1, Stock2, Stock3 with your assigned stock names (in quotation marks),
## uncomment the code, and Run
## The beginnig date is January 01,2000
## The ending date is the date you knit and submit your project
# yourDataName<-c("Stock1", "Stock2","Stock3") %>%
# tq_get(get = "stock.prices", from = "2000-01-01")%>%
# select(symbol, date, adjusted)
## This is your data set for this project (rename yourDataName to something more descriptive)
1
## output the first 6 rows of your data frame:
# head(yourDataName, n = 6 )%>%
# kable(caption = "Your caption.")
2 The Analysis
2.1 Plot prices over time (3 points)
Plot the prices of each asset over time separately.
Succinctly describe in words the evolution of each asset over time. (limit: 100 words for each time
series).
## Don't forget to add fig.cap= "Your caption" to the code chunk header.
## facet_wrap() may be useful
2.2 Calculate returns and plot returns over time (4 points)
Calculate the daily percentage returns of each asset using the following formula:
rt = 100 ∗ ln
( Pt
Pt−1
)
Where Pt is the asset price at time t. Then plot the returns for each asset over time.
## Hint: you need to add a column to your data frame (yourDataName).
## You can use the mutate() function
## Don't forget to group_by()
## The lag() function can be used to find the price in the previous date
## Double check your results!!
2.3 Histogram of returns (4 points)
Create a histogram for each of the returns series.
You have to explain your choice of bins. (Hint: Discuss the formula you use to calculate the bins)
2.4 Summary table of returns (4 points)
Report the descriptive statistics in a single table which includes the mean, median, variance, standard
deviation, skewness and kurtosis for each series.
What conclusions can you draw from these descriptive statistics?
## Your summary table here. Be sure to format the table appropriately.
2.5 Are average returns significantly different from zero? (5 points)
Under the assumption that the returns of each asset are drawn from an independently and identically
distributed normal distribution, are the expected returns of each asset statistically different from zero at
the 1% level of significance?
2
Part 1: Provide details for all 5 steps to conduct a hypothesis test, including the equation for the
test statistic.
Part 2: Calculate and report all the relevant values for your conclusion and be sure to provide an interpretation
of the results. (Hint: you will need to repeat the test for expected returns of each asset)
## Hint: you can extract specific values from t.test objects using the $
## Eg. using t.test(x,y)$statistic will extract the value of the test statistic.
## Consult the help file for the other values generated by the t.test() function.
## The relevant values are: the t-test method, the estimated mean , the test statistic,
## whether the test is one or two tailed, the degrees of freedom, and the p-value. (You might wish to present this in a table)
2.6 Are average returns different from each other? (6 points)
Assume the returns of each asset are independent from each other. With this assumption, are the
mean returns statistically different from each other at the 1% level of significance?
Provide details for all 5 steps to conduct each of the hypothesis tests using what your have learned
in the unit.
Calculate and report all the relevant values for your conclusion and be sure to provide and interpretation of
the results. (Hint: You need to discuss the equality of variances to determine which type of test to use.)
If you have a chance to engage Chat-GPT, how would you approach this question? That is, you need to
clearly lay out ALL STEPS that you would ask the question to Chat-GPT. (0.5 points)
Now, compare your answer to Chat-GPT, why do you think your answer is different or similar?
Please attach a picture of the screenshot of the answer you have got from Chat-GPT. What do you learn
from this exercise? (0.5 points)
## Decide on which test is appropriate for testing differences in mean returns
## Hint: Include the results of your supporting test for the differences in variances
## (include all 5 hypothesis step tests and the equation for the test statistics, and a clear interpretation of the result).
## Hint: http://www.sthda.com/english/wiki/one-way-anova-test-in-r
## So this section has (at least) 2 significance tests.
2.7 Correlations (2 points)
Calculate and present the correlation matrix of the returns.
Discuss the direction and strength of the correlations.
## Include a formatted correlation matrix here
## Hint: http://www.sthda.com/english/wiki/correlation-matrix-a-quick-start-guide-to-analyze-format-and-visualize-a-correlation-matrix-using-r-software
2.8 Testing the significance of correlations (2 points)
Is the assumption of independence of stock returns realistic?
Provide evidence (the hypothesis test including all 5 steps of the hypothesis test and the equation for
the test statistic) and a rationale to support your conclusion.
3
## Report the results of tests for statistical significance of the correlations here.
## Hint: http://www.sthda.com/english/wiki/correlation-matrix-a-quick-start-guide-to-analyze-format-and-visualize-a-correlation-matrix-using-r-software
2.9 Advising an investor (12 points)
Suppose that an investor has asked you to assist them in choosing two of these three stocks to include in
their portfolio. The portfolio is defined by
r = w1r1 + w2r2
Where r1 and r2 represent the returns from the first and second stock, respectively, and w1 and w2 represent
the proportion of the investment placed in each stock. The entire investment is allocated between the two
stocks, so w + 1 + w2 = 1.
The investor favours the combination of stocks that provides the highest return, but dislikes risk. Thus the
investor’s happiness is a function of the portfolio, r:
h(r) = E(r)− Var(r)
Where E(r) is the expected return of the portfolio, and Var(r) is the variance of the portfolio.1
Given your values for E(r1), E(r2), Var(r1), Var(r2) and Cov(r1, r2) which portfolio would you recommend
to the investor? What is the expected return to this portfolio?
Provide evidence to support your answer, including all the steps undertaken to arrive at the result. (*Hint:
review your notes from tutorial 6 on portfolio optimisation. A complete answer will include the optimal
weights for each possible portfolio (pair of stocks) and the expected return for each of these portfolios.)
# You can use this section to create a table of your results.
2.10 The impact of financial events on returns (Bonus Questions - 2 points)
Note: This is a bonus question. If you do not choose to complete this question, that would be fine! However,
you are encouraged to complete this question as we may have provided some hints in the tutorials.
Two significant financial events have occurred in recent history. On September 15, 2008 Lehman Brothers
declared bankruptcy and a Global Financial Crisis started. On March 11, 2020 the WHO declared COVID-19
a pandemic. Use linear regression to determine if
a. Any of the stocks in your data exhibit positive returns over time.
b. Either of the two events had a significant impact on returns.
Report the regression output for each stock and interpret the results to address these two questions. How
would you interpret this information in the context of your chosen portfolio?
## Add a column to your returns data set.
## This is a factor variable with three levels:
## 'Lehman Bankruptcy' for the date 2008-09-15,
## 'Pandemic' for the date 2020-03-11, and
## 'BAU' (Business as usual) for all other dates.
1Note that E(r) = w1E(r1) + w2E(r2), and Var(r) = w21Var(r1) + w22Var(r2) + 2w1w2Cov(r1, r2)
4
## Then run a regression analysis to determine whether returns to each stock are
## increasing over time and if the events had and statistically significant impact on the returns of each stock.