Assignment Task (Assignment Number: UA522)

ECOM 2001 Term Project

S Thomas

Due Thursday, 10th June 2021 23:59 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
   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).

1. Calculate returns and plot returns over time

Calculate the daily percentage returns of each asset using the following formula:

_∗

tr = 100 ln ^Pt

^Pt−1

Where P_tis the asset price at time t. Then plot the returnsfor each asset over time.

1. Histogram of returns

Create a histogram for each of the returns series (explain how you determined the number of bins to use).

1. 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?

1. 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 all5stepstoconductahypothesistest, including theequationfortheteststatistic. Calculate and report all the relevant values for your conclusion and be sure to provide an interpretation of the results.

1. 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 detailsforall5stepstoconducteach 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 equalityofvariancestodeterminewhichtypeoftesttouse.)

1. Correlations

Calculate and present the correlation matrix of the returns. Discuss the direction and strength of the correlations.

1. Testing the significance of correlations

Is the assumption of independence of stock returns realistic? Provide evidence (the hypothesis test including all5stepsofthehypothesistestand theequationfortheteststatistic) and a rationale to support your conclusion.

1. Advising an investor

Suppose that an investor has asked you to assist them in choosing twoof 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.)

1. 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

1. Any of the stocks in your data exhibit positive returns over time.
2. 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.
   2. Keep the sections as they are in this document
   3. Ensure that all Figures and Tables are numbered, and have appropriate captions.
   4. Allyour 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 that E(r) = w₁E(r₁) + w₂E(r₂), and Var(r) = w²Var(r₁) + w²Var(r₂) + 2w₁w₂Cov(r₁,r₂)

1 2

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.

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	–	–	–	–

Assignment Solution/Sample Answer

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ECOM 2001 TERM PROJECT

INTRODUCTION

Unilever

Unilever plc, based in London, Uk, It is an Uk based consumer products corporation. Food, ice cream, wellness pills, mineral, and vitamins, tea, coffee, frosted flakes, cleaning agents, air and water filters, pet food, toothbrushes, beauty goods, and personal care are just a few of the Unilever items. Unilever is the nation’s biggest soap manufacturer.

Unilever holds around 400 brands, with a revenue of 51 billion euros in 2020 and sales of over one billion with sales over one billion euros, On Sept 2, 1929, the Dutch margarine company Margarine Unie and the British soapmaker Lever Brothers merged to form Unilever. And during second part of the twentieth century, the company diversified from becoming a manufacturer of oils and fats goods and started its reach globally. It has acquired a number of businesses, notably Lipton (1971), Brook Bond (1984), Waste stabilization (1987), Good Social (2000), Ben & Jerry’s (2000), Jorge (2010), Legacy Rewards Club (2016), & Pakora Herbs (2017) are some of the companies that have been featured on the show (2017). In 1997, Unilever sold its medical devices division to ICI. Under Peter Polman’s leadership in the 2010s, the company progressively moved its focus away from slow-growing food businesses and toward hair and wellness businesses.

Unilever share price

€50.724 billion (2020) decrease in income

Operating earnings €8.303 billion decrease (2020) Net revenue Growth 6,073 billion euros (2020) Overall Assets €67,659 billion Increase (2020)

Market capitalization €17,655 billion (2020) increased Staff number 155 000 decrease (2021)

Regeneron Pharmaceuticals

A US biotechnology corporation based in Northern Virginia, New York approximately 25 kilometres north of Midtown of Manhattan, Regeneron Pharmaceuticals, Inc. The corporation was launched in 1988. Originally concentrated on neuropeptides and their system service, the business became known as cytokine as well as kinase synapses.

Regeneron Pharmaceuticals share price

Type of Nasdaq Public Traded: REG Compound S&P 500

Pharma sector;

It was founded in 1988;

Eastview/Tarrytown Head office, New York, United States (global headquarters) Global Service Area

Significant people Schleifer Leonard (CEO) Mr Yancopoulos (CSO)

$7.86 billion (2019) increase in revenue

Net revenue $1.4 billion Net revenue (2019)

$5.6 billion in asset value (2019) Staff number 8,100 (2019)

Royal Bank of Canada

The Royal Bank of Canada (RBC) is a multinational company financial services provider and, through market cap, the biggest bank in Canada. The Bank serves more than 16 million customers and employs more than 86,000 people worldwide. Established in 1864, it has its corporate offices in Toronto and its corporate headquarters in Montreal in Halifax, Nova Scotia. The number of RBC institution (or bank) is 003. RBC was added to the list of worldwide banks and financial institutions of the Financial Action Task force in Nov 2017.

CA$47.2 billion in income increase (2020) CA$11.4 billion in net earnings (2020) CA$843.6 billion more AUM AUM (2020) CA$1.62 billion (2020) [4] Increase. Total assets Employee number 83,842 (2020) increased Subsidiary companies

National Bank of City Bank of RBC

Trinidad & Tobago Royal Bank

Royal Bank of Canada share price

RETURNS OVER TIME

Stock name	2016-2017	2017-2018	2018-2019	2019-2020	2020-2021
Unilever	-7.14	37.17	-6.85	13.63	-2.39
Regeneron Pharmaceuticals	-14.47	2.05	17.08	-21.28	49.09
Royal Bank of Canada	40.26	19.20	-11.08	3.65	2.24

SUMMARYTABLEOFRETURNS

MEDIAN, VARIANCE, STANDARD DEVIATION, SKEWNESS AND KURTOSIS OF ROYAL BANK OF CANADA

MEDIAN, VARIANCE, STANDARD DEVIATION, SKEWNESS AND KURTOSIS OF UNILEVER

MEDIAN, VARIANCE, STANDARD DEVIATION, SKEWNESS AND KURTOSIS OF REGENERON PHARMACEUTICALS

CORRELATIONS

CORRELATIONS BETWEEN RY, REGN AND UL

ADVISING AN INVESTOR

Royal Bank of Canada:

Another one of his favourites. Even though it is on a worldwide scale, tax-favoured dividends are available. Markets understand the importance of quality. I’m not sure if dividend increases are on the horizon. His concern is that they will overextend themselves in capital markets and deviate from the crown jewels of Canadian banking brands. Own it, store it, and don’t believe about it again.

The United States accounts for 25% of all business, owing to the country’s active capital markets. The stock world has grown, but there will be more as the Canadian and US markets open up. The stock is still trading at a reasonable multiple. Dividends and stock buybacks will be reinstated at some point. Unused loan reserves help strengthen the company’s capital base. 3.68 percent is the rate of return.

Regeneron Pharmaceuticals:

They created a Covid diagnosis drug, but U.S government was unkind to them and managed to make it unavailable to a public. It’s a great brand, but it can’t work for peanuts.

It perplexes him. They make great drugs and have a great CEO, but their Covid cocktail isn’t making them a lot of money. He refused to sell despite the fact that the stock had been performing poorly.

The FDA has granted the US President Emergency Use Authorization during his treatment. Despite the fact that vaccine options are on the way, this will provide treatments available for those who have been infected and will help reduce hospital admissions. We would buy it with a $425 stop-loss and aim for a $630 – 21% gain.

A higher-risk/reward bet. This life sciences have a number of core product lines that generate a lot of net income. They are collaborating with Sanofi on Dupixent, which will be used to treat acute acne and potential serious asthma. They have another drug that can be used to successfully treat eye diseases. REGN has a number of late-stage drug trials. Regeneron is a new Top Pick for us, owing to a significant decrease in valuation due to concerns about U.S. Medicare Part B financial regulation proposed policies. We believe that these are more than adequately reflected in the current price. Their dermatitis medication is gaining traction. This inventory has taken a beating for all the right reasons.

THE IMPACT OF FINANCIAL EVENTS ON RETURNS

This question is addressed in a new International Finance Corporation (IFC) report, “Creating Effect: The Promise of Investment Opportunities.” The growing desire of private companies to demonstrate that profit isn’t the only goal: they can do good whilst also doing well is fuelling the desire to eat for impact investing. This strategic planning shift represents a historic opportunity for the developer community to mobilise additional funds to accomplish the SDGs (SDGs). The IFC, the world’s largest bank limited focused on the private industry in developing economies, has recently compiled a major evaluation of the international economy for investment opportunities.

Even though it is currently small, the effect investing industry is expected to grow to grow to trillions of dollars. However, numerous challenges lie ahead, from achieving investment returns to accurately measuring impact and removing regulatory impediments.

On April 8, the Strong mobile Global Advancement and Economic system programme and the IFC offered to host a discussion about these topics, as well as the findings of the IFC report. Going to follow the demonstration of the study’s findings, IFC CEO Philippe Le Houérou discussed his organization’s leveraging role as well as the fast-changing investment fund landscape. Following that was a panel discussion with representatives from investment firms and corporate social responsibility academics. Homi Kharas, Provisional Vice President of Global, mediated the discussion.

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