ECOM 2001 Term Project Description
Due Monday, May 29, 2023 at 9:00 AWST
Introduction
The aim of this project is to prepare, evaluate and analyse stock market data and to recommend an optimal portfolio
consisting of two stocks. You have been assigned three stocks, all three must be included in the analysis which
works towards your recommendation of a final optimal portfolio. The project requires a deep understanding of both
the statistics and the mathematics components of this unit. It is recommended that you work on this on a weekly
basis.
YOU MUST USE THE STOCKS ASSIGNED TO YOU. Any deviation from the assigned stocks will results in a grade of
zero.
Refer to the rubric at the end of this document to understand how this assessment will be graded. In particular, note
that all figures need to be numbered and labelled, and you need to include all the steps to involved with arriving at
each of your answers.
Your final report should be a pdf document. An RMarkdown document to get you started is available on the unit
Blackboard site. Show all of your coding by keeping echo = TRUE. Make sure to update your name and student ID
in the YAML of the document.
You are NOT ALLOWED to engage any AI-assistive platforms to complete this assessments, unless you are told
otherwise (in 1 question below).
1 Import Data (2 points)
Import the adjusted stock prices for the three stocks which you have been assigned. See the Markdown file for hints.
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).
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.
1
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?
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?
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)
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)
2.7 Correlations (2 points)
Calculate and present the correlation matrix of the returns.
Discuss the direction and strength of the correlations.
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.
2.9 Advising an investor (12 points)
Note: You need to show all steps in this questions in RStudio to be able to get full marks.
2
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, andw1 andw2 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, andVar(r) is the variance of the portfolio.1
Given your values for E(r1), E(r2),Var(r1),Var(r2) andCov(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.)
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?
Submission
1. Submit the pdf output of your completed project to the Turnitin.com link on the BlackBoard site for our unit.
i. Keep the sections as they are in this document
ii. Ensure that all Figures and Tables are numbered, and have appropriate captions.
iii. All your calculations and steps used to produce the results should be included. So include any math-
ematical calculations and set echo=TRUE in all of your code chunk headers, including those used to
generate figures.
2. Additional details
• All results (numbers) should be accurate to 3 decimal places.
• Proof-read your report - do not include spelling or grammatical errors.
1Note thatE(r) = w1E(r1) + w2E(r2), andVar(r) = w21Var(r1) + w22Var(r2) + 2w1w2Cov(r1, r2)
3
Rubric
The submission is worth 50 Points in total and will be worth 50% of your final grade.
Table 1: Rubric
Question (Maximum Score) Fail (<25) Pass (25) Meets Expectations (25-40) Above Expectations (40-50]
1 2 (0/2) The data are not
imported into R, or the
incorrect stock symbols were
imported.
(1/2) The data were imported
but the code or assigned
symbols are not clear.
(2/2) The assigned stocks are
correctly imported and
identified in the report title.
2.1 3 (0/3) A time series plot of the
prices of each stock is
missing.
(1.5/3) Plots are present but
with omitted details or
formatted poorly.
Explanations are unclear
and/or have spelling and
grammatical errors. Coding
is omitted.
(2/3) Plots are clear, but
missing components such as
captions or numbers.
Explanations are present but
may have spelling,
grammatical or other minor
errors. Coding is present but
inadequately commented.
(3/3) Plot axes are labelled
and the plot has an
appropriate caption and
Figure number. Explanations
are clear, concise and free of
spelling and grammatical
errors. Plot coding is clear
and commented.
2.2 4 (0/4) The calculation of
returns is not present, no
time series plot of the
returns of each stock is
included.
(2/4) Calculation of the
returns is present, but may
include errors. A time series
plot is included by is missing
details or poorly formatted.
Coding is not commented.
(3/4) Calculation of returns is
present and correct. A time
series plot of the returns is
present but details such as a
caption and Figure number
are missing. Code may be
partially commented.
(4/4) Returns are correctly
calculated and coding is
clearly commented. A
well-formatted time series
plot of the returns to each
stock is present, axes are
labelled, the figure has a
caption and a Figure
number.
2.3 4 (0/4) A histograms of the
returns are missing.
(2/4) A histogram of the
returns is present for each
stock, but is missing key
details such as axis labels,
caption or figure number.
The selection of the number
of bins to include is not
discussed. Code may be
uncommented.
(3/4) A histogram of returns
is present for each stock, but
some details may be
missing. The selection of the
number of bins to include is
discussed, but may be poorly
motivated or contain spelling
or grammatical errors. Code
is partially commented.
(4/4) Histograms of the
returns to each stock are
present, clearly formatted
and include figure captions
and numbers. A discussion
of the method used to select
the number of bins in the
histogram is included. Code
is commented. No spelling
or grammatical errors are
present.
2.4 4 (0/4) A summary table of the
returns to each stock is
missing.
(2/4) A summary table of the
returns to each stock is
included but omits key
summary statistics (or
included summary statistics
which were not requested),
poorly formatted and/or
missing a table caption and
number. Code is absent or
uncommented. No
conclusiosn or erroneous
conclusions are drawn.
(3/4) A summary table of the
returns to each stock is
included and is formatted
appropriately. Not more
than 1 summary statistic is
absent and no additional
summary measures are
included. Coding is
commented but is missing
some details. An explanation
is provided but may have
minor errors and/or spelling
and grammatical errors.
(4/4) A well formatted
summary table is presented
which includes the
requested summary
statistics for each stock.The
table has an appropriate
caption and Table number.
Code is well commented.
Explanations are clear,
concise and without spelling
or grammatical errors.
2.5 5 (0/5) An appropriate
statistical test is missing.
(2.5/5) Appropriate statistical
tests are present for each
stock but the results are
poorly formatted. The steps
involved in the hypothesis
test procedure are present
with errors. The equation of
the test statistic contains
errors. The results are
partially interpreted. Coding
is not commented.
(4/5) Appropriate statistical
tests are present for all three
stocks and the results are
appropriately formatted. All
five steps of the hypothesis
testing procedure are
present. The equation for
the test statistic is present.
Inference is drawn. Code is at
least partially commented.
(5/5) An appropriate
statistical test is present for
each stock and the results
appropriately formatted. All
five steps of the hypothesis
testing procedure are
present and correct. The
equation for the test statistic
is present and correct.
Inference is correct and well
presented. Coding is clearly
commented.
4
Table 1: Rubric (continued)
Question (Maximum Score) Fail (<25) Pass (25) Meets Expectations (25-40) Above Expectations (40-50]
2.6 6 (0/6) No statistical tests for
differences between average
stock returns are present.
(3/6) Statistical tests for
differences between average
stock returns are presented
but missing key details. The
testing procedure is partially
explained and equations for
test statistics may be present
but contain errors. Results
are poorly formatted. Coding
is incompletely commented.
(5/6) Appropriate statistical
tests are presented and
explained but poorly
formatted. Hypothesis
testing procedures are
included and coding is at
least partially commented.
Inferences are drawn but
may contain minor errors.
(6/6) Appropriate statistical
tests are presented and well
formatted. All five steps of
the hypothesis testing
procedures are clearly
explained. Inference drawn
from the test(s) is correct and
informs any follow up tests.
Code is fully commented.
2.7 2 (0/2) Correlations between
stocks are missing.
(1/2) Correlations are
present but formatted
poorly. The direction and
strength of correlations are
discussed but may contain
errors in interpretation.
(1.5/2) A correlation matrix is
present and appropriately
formatted. Direction and
strength of correlation is
discussed but may contain
minor errors in
interpretation, spelling or
grammar. Code is present
and at least partially
commented.
(2/2) A well formatted
correlation matrix is
presented and discussed.
Interpretations are accurate
and free of spelling and
grammatical errors. Code is
well commented.
2.8 2 (0/2) No test for the
significance of correlations is
present.
(1/2) A test for the
significance of correlation is
present but poorly formatted
and or incompletely
explained (steps to the
hypothesis testing procedure
and an equation for the test
statistic are incomplete).
Inference may be incorrect.
(1.5/2) Tests for the
significance of correlations is
present and appropriately
formatted. All five steps of
the hypothesis testing
procedure are present as
well as the equation for the
test statistic. Inference
drawn may contain minor
error including spelling
and/or grammatical errors.
(2/2) A complete set of tests
for significance of
correlations between stock
returns is present, all 5 steps
to the hypothesis testing
procedure are documented
and include the test statistic.
The results are well
formatted, code is well
commented and inferences
drawn are correct and free of
spelling and grammatical
errors.
2.9 12 (0/12) No response is
present.
(6/12) Some attempt to
explain the mathematical
process for arriving at the
optimal portfolio is
presented but may be poorly
formatted or contain errors.
A reccomendation is made,
but may be accompanied by
a weak rationale. Results of
all portfolios are present but
may be poorly formatted.
Coding may be present but
incompletely commented.
(8/12) The mathmatical
process for arriving at the
optimal portfolio is provided
but may contain minor
errors or lack appropriate
supporting tests. Results for
all portfolios are presented.
A recommendation is
provided and supported by a
rationale. The answer may
contain spelling and
grammatical errors. Code is
partially commented.
(12/12) A complete
explanation of the process
for arriving at the optimal
portfolio is explained, and
the result is supported by
appropriate follow up tests.
Coding is well commented
and intelligently applied.
Results are presented in a
well formatted table that
includes the optimal
proportion to invest in each
stock, as well as the
expected return for each
possible portfolio. A
recommendation for the
optimal portfolio is given
and supported by a clear
rational. No spelling or
grammatical errors are
present.
2.10 - Bonus 2 (0/2) No response is present. (1.5/2) A regression analysis
is presented but poorly
formatted. An explanation is
given but may contain errors
in interpretation. Coding is a
least partially commented.
(2/2) An appropriate
regression analysis if
presented and adequately
formatted. The results are
interpreted to answer the
posed questions, but may
contain minor errors.
Implications for the
recommended portfolio are
given but may lack clarity.
Coding is present and at
least partially commented.
(2/2) An appropriate
regression analysis is
presented and well
formatted. Results are
accurately interpreted to
answer the posed questions.
Implications for the
recommended portfolio are
discussed. Coding is well
commented and the
response is free of spelling
and grammatical errors.
Total 46 - - - -