support@essaywritingexpert.orgDue 30 September at 9:00AM 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 2 questions 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 (4 points)
Plot the prices of each asset over time separately.
Succinctly describe in words the evolution of each asset over time. All axes and figures have to be properly labeled
and described. (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.
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2.3 Histogram of returns (6 points)
Create a histogram for each of the returns series.
You have to explain your choice of bins.
You will need to carefully label all axes and figures.
You are expected to: – Write a short paragraph to describe the trend of each time series; – Discuss the formula to
calculate the bins.
(Hint: Discuss the formula you use to calculate the bins)
2.4 Summary table of returns (5 points)
Report the descriptive statistics in a single table which includes the mean, median, variance, standard deviation, skewness and kurtosis for each series. All tables need to be correctly labeled.
What conclusions can you draw from these descriptive statistics?
2.5 Are average returns significantly different from zero? (6 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.
All steps have to be shown and this part has to be repeated for each hypothesis test. (1 points)
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) (3 points – one for each stock)
Part 3: If you would have done this question using Chat-GPT, what answer will you get? (hints: you will need to
describe how you promptthe question in Chat-GPT to guide the answer (1 point), would expect your answer to be
different or similar to your answer above and provide your rationale? (1 point))
2.6 Are average returns different from each other? (7 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.
All steps have to be shown and this part has to be repeated for each hypothesis test. (2 points)
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.) (3 points)
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. (1 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? (1
points)
2
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. All steps have to be shown and this part has to be repeated
for each hypothesis test.
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
w1 + 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 forE(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. You will need to
solve the optinmisation problem using pen and paper, and you need to typeset your answer. You can then scan as
picture to attach here as your answer. You can show the summary statistics using the coding learned in class, but
the optimisation problem has to be solved by hand.
You will need to get your instructors to validate your identity of your work by asking them to sign your work when
you complete it. Without their validation, you will automatically get a zero for this question.
Note: You will need to typeset your answer. Then, you need to put your name and student ID number on every
page (and side) of your work. You will have the instructor to validate your information by signing your answer
sheet. Then, you can scan the answer as picture(s) and embed it here as your answer.
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.
1Note that E(r) = w1E(r1) + w2E(r2), and Var(r) = w2
1Var(r1) + w2
2Var(r2) + 2w1w2Cov(r1, r2)
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iii. All your calculations and steps used to produce the results should be included. So include any mathematical 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.
4
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 4 (0/4) A time series plot of the
prices of each stock is
missing.
(2/4) Plots are present but
with omitted details or
formatted poorly.
Explanations are unclear
and/or have spelling and
grammatical errors. Coding
is omitted.
(3/4) 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.
(4/4) 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 6 (0/6) A histograms of the
returns are missing.
(3/6) 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.
(5/6) 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.
(6/6) 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 5 (0/5) A summary table of the
returns to each stock is
missing.
(2.5/5) 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.
(4/5) 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.
(5/5) 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 6 (0/6) An appropriate
statistical test is missing.
(3/6) 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.
(5/6) 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.
(6/6) 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.
5
Table 1: Rubric (continued)
Question (Maximum Score) Fail (<25) Pass (25) Meets Expectations (25-40) Above Expectations (40-50]
2.6 7 (0/7) No statistical tests for
differences between average
stock returns are present.
(3.5/7) 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.
(6/7) 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.
(7/7) 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.
Total 50 – – – –
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