ECOM 2001 Term Project S Thomas Due Tuesday, 5th October 2021 16:00 AWST
Introduction The aim of this project is to prepare, evaluate and
analyse stock market data and to recommend an optimal portfo- lio
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.
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. 1 Import Data 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 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 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 Create a
histogram for each of the returns series (explain how you determined
the number of bins to use). 2.4 Summary table of returns 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 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 signif- icance Provide details for all 5 steps to conduct a
hypothesis test, including the equation for the test statistic.
Calculate and report all the relevant values for your conclusion and be
sure to provide an interpretation of the results. 2.6 Are average
returns different from each other 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.) 2.7 Correlations
Calculate and present the correlation matrix of the returns. Discuss the
direction and strength of the correlations. 2.8 Testing the
significance of correlations 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
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) 2 WhereE(r) is the expected return of
the portfolio, andVar(r) is the variance of the portfolio.1 Given your
values forE(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 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. ii. Keep the sections as they are
in this document iii. Ensure that all Figures and Tables are numbered,
and have appropriate captions. iv. 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 commen
ted. (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. All five steps of the hypothesis testing
procedure are included as well as an equation for the test statistic.
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 presetn, all 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 6 (0/6) No response is present.
(3/6) A regression analysis is presented but poorly formatted. An
explanation is given but may contain errors in interpretation. Coding is
a least partially commented. (5/6) 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. (6/6) 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 50 - - - -
5