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Finance Discipline Group
UTS Business School
FINANCIAL METRICS FOR DECISION MAKING – SUMMER 2020
ASSIGNMENT
General Instructions and Information
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This assignment accounts for 40% of students’ final grade for 25624 Financial Metrics
for Decision Making.
The assignment is to be undertaken individually.
The assignment is due on Friday the 5th of February 2021 (Week 11) by 5pm.
The assignment must be submitted via UTSOnline. You’ll need to provide a written
report and an Excel spreadsheet:
• The written report must be self-contained and formatted as a PDF file.
• Excel files will also be examined and will constitute 20% of the value of the
assignment. The Excel file should include all calculations.
The scope of this assignment is limited to [5] pages not including appendices and cover
sheet. Use standard fonts (think Calibri, Times New Roman, Arial) and standard font
sizes. There is no specific word count.
You are encouraged to use figures and tables when reporting your results.
The file names, for both the report and the Excel spreadsheet, will take the form:
“Name – Student number”. For example, if your name is Jane Doe and your student
number is 12345, then your file name will be “Jane Doe - 12345”. Please don’t write
the words “name”, “student number” or anything else in the file name.
All assignment-related questions should be posted to the Discussion Board on
UTSOnline.
Marking
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This assessment will be graded on the quality of both, the written report and the
quantitative analysis in Excel.
Marks will be awarded 70% for content and analysis, and 30% for effectiveness of
communication and presentation.
Late submissions will be allocated a mark of zero with no exceptions unless via special
consideration filing.
Files
In the Assignment folder on UTSOnline, you’ll find the following files:
§ Cover Sheet: is the cover sheet you’ll need to fill in, sign, and submit along with your
written report.
§ Data: this Excel spreadsheet contains the following worksheets:
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Cover: you’ll need provide your student details here.
Part 1 to Part 4: these worksheets contain the data (when applicable) for each
part and should be used to perform all relevant data analysis required.
Instructions
Part 1 – Hypothesis Testing [10 marks]
The national average annual salary for a campus manager is $89,000 a year. A state official
took a sample of 25 campus managers in the state of New South Wales (NSW) to learn about
salaries in the state and see if they differed from the national average.
The data for this question is provided in the worksheet named ‘Part 1’.
a. [5 marks] Formulate the null and alternative hypotheses that can be used to
determine whether the annual salary mean of a campus manager in NSW differs from
the national mean of $89,000.
b. [5 marks] What is the p-value for your hypothesis test in part (a)? At a 5% significance
level, can your null hypothesis be rejected? What is your conclusion?
Part 2 – Modelling [40 marks]
Background Information
Your boss, a real estate business manager, has approached you for financial advice. She is
interested in either purchasing or leasing a new car for her personal use. Aware of your
financial expertise, she has asked you to develop a Spreadsheet Model that allows her to
decide whether to buy or lease the vehicle.
The retail price of the car she is interested in is $50,000.
Buy Scenario
In the Buy Scenario, your boss would like to purchase the car by making an initial down
payment of $15,000 dollars and finance the difference with a conventional car loan to be
repaid monthly for 3-years at a 5% interest rate. The following table summarises the relevant
information for the Buy Scenario.
Buy Scenario
Car Price
$ 50,000.00
Down Payment
$ 15,000.00
Interest Rate
5%
Term
3 years
Lease Scenario
In the Lease Scenario, there is no initial down payment. Instead, your boss would like to use
a Finance Lease to rent the car for 3 years. At the end of this 3-year period, she plans to
purchase the car from the lease financier (lessor) by paying a residual value of $25,000. In
this scenario, to rent the car, your boss would have to pay a monthly rent of $850 for 3 years.
The following table summarises the relevant information for the Lease Scenario.
Lease Scenario
Car Price
$ 50,000.00
Residual Value
$ 25,000.00
Monthly Rent
$850
Term
3 years
Note: A Finance Lease is a common way people can use a car without actually buying it. Under
a Finance Lease, the car belongs to the financier (lessor) who rents it out to the borrower
(lessee) in exchange for monthly instalments. At the end of the lease term, the lessee has the
option to claim ownership of the car by paying a residual value.
a. [5 marks] Lay out the decision-making problem, the alternatives, and the overall
criteria you would use to evaluate the different alternatives.
b. [5 marks] Carefully establish all the inputs and assumptions you would include in the
Spreadsheet Model for each scenario. If you include inputs/variables other than the
ones provided (e.g. interest rate on savings), justify your choices based on data from
the Australian market.
c. [10 marks] Based on your answers to a) and b), build a Spreadsheet Model which helps
your boss decide whether to buy or lease the vehicle. Make your spreadsheet selfexplanatory.
d. [5 marks] Perform What-If analysis for at least one of your inputs (e.g. down payment).
That is, show what would happen to your model’s output at, at least, three different
values of the chosen input. In your spreadsheet, highlight the section you would
present to your boss to help her with her decision-making problem.
e. [5 marks] Of all the inputs included in your model, which one do you think is the most
important in determining whether buying or leasing is the best option for your boss?
Provide an explanation.
f. [5 marks] Describe the model’s limitations and/or aspects that could be improved.
What other factors haven’t been considered?
g. [5 marks] Are there any cognitive biases you would suggest your boss to be aware of
when finally making her decision?
Part 3 – Simple Linear Regression [20 marks]
The Toyota Hilux is the top selling car in Australia. The price of a previously owned Hilux
depends on many factors, including the number kilometres (kms) travelled. To investigate the
relationship between a car’s kms and its sales price, data was collected on a sample of 20
used Hilux in Sydney.
The data for this question is provided in the worksheet named ‘Part 3’.
a. [2 marks] Create a scatter plot for this data with kms as the independent variable.
What does the scatter plot indicate about the relationship between price and kms?
b. [5 marks] Estimate a simple linear regression model with price as the dependent
variable and kms as the independent variable. What is the estimated regression model
(equation)?
c. [5 marks] Test whether each of the regression parameters (intercept and coefficient)
is equal to zero at a 5% significance level. Interpret the coefficients of the estimated
regression parameters and discuss whether these interpretations are reasonable.
d. [4 marks] Using the model estimated in part (b), calculate the predicted price for each
of the cars in the sample. Based on the difference between the true and predicted
prices, identify the two cars that were the biggest bargains.
e. [4 marks] Suppose that you are considering purchasing a previously owned Hilux that
has been driven 100,000 kms. Use the model estimated in part (b) to predict the price
for this car. Is this the price you would offer the seller?
Part 4 – Multiple Linear Regression [30 marks]
A financial institution has a large dataset of information provided by its customers when
they apply for a credit card. This customer information includes the following variables:
• Annual household income (in thousands of dollars)
• Household size (number of people)
• Number of years of post-high school education
• Number of hours per week watching television
• Age
• Gender
In addition, the financial institution has records of the credit card charges accrued by each
customer over the past year.
The data for this question is provided in the worksheet named ‘Part 4’.
a. [5 marks] Plot histograms to contrast the distribution of annual credit card charges for
1) People with zero years of post-high school education vs. People with at least 1 year
of post-high school education, and 2) Female vs. Male. Describe the overall shape of
each histogram and comment on any observable differences.
b. [10 marks] Estimate a multiple linear regression model in which the dependent
variable is the credit card charges accrued by each customer in the data over the past
year, and the independent variables are all the variables the financial institution
collected when the customer first applied for a credit card (e.g. annual household
income). What is the estimated regression model (equation)?
a. Hint: For Gender, create a dummy variable that takes 1 if the customer is
female and 0 if male.
c. [15 marks] Interpret each of the regression coefficients and comment on both their
economic and statistical significance. For each significant regressor (at a 5%
significance level) provide a potential explanation for its statistical relationship with
the dependent variable.
Finance Discipline Group
UTS Business School
FINANCIAL METRICS FOR DECISION MAKING – SPRING 2020
ASSIGNMENT COVER SHEET
1. Name: ________Wei Xiang_______________________
2. Student No.: ________13338900__________________
Declaration
I have carefully read, understood, and have taken into account all the requirements and
guidelines for this assignment. I affirm that this assignment is my own work; that it has
not been previously submitted for assessment; that all material which is quoted is
accurately indicated as such; and that I have acknowledged all sources used fully and
accurately according to requirements. I am fully aware that failure to comply with these
requirements is a form of cheating and could result in disciplinary action in accordance
with UTS Student Rules Section 16 – Student misconduct and appeals.
Signature(s): Wei Xiang
Date: 16/10/20
Table of Contents
Part 1-Optimisation……………………………………………………………………………...3
Part 2 – Descriptive Analysis………………………………………………………………..3-4
Part 3 – Hypothesis Testing…………………………………………………………………4-5
Part 4 – Simple Linear Regression…………………………………………………………5-6
Part 5 – Multivariate Linear Regression……………………………………………………6-7
References……………………………………………………………………………………….8
Appendix……………………………………………………………………………………..9-14
Part 1 – Optimisation
Following are the 10 stocks that are randomly selected from the S&P500 list, using the
‘stock selector’ cells in the spreadsheet.
Table 1. Selected Stocks
Stock 1
CE
Stock 2
NOW
Stock 3
CTAS
Stock 4
SJM
Stock 5
SNA
Stock 6
NDAQ
Stock 7
LLY
Stock 8
HLT
Stock 9
CNC
Stock 10
AVGO
Based on the sample selected, the study forms an equally weighted portfolio of the daily
returns (Appendix). Using Excel Solver, the study formulates portfolio B, maximising
Sharpe Ratio for the given period. Following the portfolio weights and the Sharpe ratio.
Table 2. Portfolio weights
Stock selector
93
413
107
265
418
331
290
231
94
78
Stock Symbols
CE
NOW
CTAS
SJM
SNA
NDAQ
LLY
HLT
CNC
AVGO
Portfolio A weights
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
Portfolio B weights
7%
123%
124%
85%
-115%
-15%
-45%
-48%
-30%
14%
Table 3. Sharpe Ratio
Mean
0.17%
0.62%
Portfolio A
Portfolio B
Standard Deviation
2.94%
4.84%
Sharpe Ratio
0.057
0.127
It can be observed that the Sharpe ratio for portfolio B is greater than portfolio A. It means
that investing in portfolio B is financially more feasible and profitable. However, a Sharpe
ratio higher than 1 is generally considered acceptable (CFI, 2020).
Part 2 – Descriptive Analysis
Table 4. Portfolios’ descriptive analysis
Daily
Annualised
Risk-adjusted measures
Portfolio
Obs.
Average
Returns
Standard
Deviation
Downside
Risk
Average
Returns
Standard
Deviation
Downside
Risk
Sharpe
Ratio
Sortino
Ratio
Portfolio A
126
0.17%
2.94%
2.08%
43.19%
46.75%
33.04%
0.91
1.29
Portfolio B
126
0.62%
4.84%
3.08%
155.97%
76.95%
48.94%
2.02
3.17
Portfolio B have more the daily average returns and the risk associated. Moreover, the
annualised returns follow the same pattern as for the daily returns. The annualised returns
for portfolio B are more than three times the annualised returns for portfolio A.
Figure 1. Portfolio A Daily Returns
The returns for portfolio A follow a normal distribution with the majority of the returns lie
between 0 % and 2 %.
Figure 2. Portfolio B Daily Returns
On the other hand, the returns for portfolio B are mostly greater than -3% (from -3% to
4%). It may suggest that Portfolio B is more profitable but exhibits a greater variation
(standard deviation). It also has a greater downside risk, as shown in table 3, suggesting
greater financial risk associated with the portfolio (Sortino & Van Der Meer, 1991).
Part 3 – Hypothesis Testing
Figure 3. Portfolio A and S&P500
Using figure 3, the distribution of portfolio A and S&P 500 returns can be compared. Both
the returns have a similar distribution with a mean value around 0. Similarly, the histogram
of portfolio B is also compared with the S&P 500 (Figure 4). It can be observed that the
mean value of portfolio B is greater than zero.
Figure 4: Portfolio B and S&P500
To test the difference in the mean daily returns of the portfolios with S&P500 index
returns, a t-test was conducted between portfolio A and S&P 500, and portfolio B and
S&P 500.
The hypothesis for the tests is as follows:
Table 4. Portfolio A vs S&P500
Null hypothesis
Alternative hypothesis
Table 5. Portfolio B vs S&P500
uA = uS&P500
Null hypothesis
uB = uS&P500
uA > uS&P500
Alternative hypothesis
uB > uS&P500
The null hypothesis for the first test states that the mean returns portfolio A and S&P 500
are equal. Based on the results given below, the mean for portfolio A is 0.17 %, and the
returns of the S&P 500 are 0.14 %. Moreover, since the p-value of the t-test is 0.467,
which greater than the level of significance. Therefore, the null hypothesis is failed to be
rejected at 5 % level of significance (t-test is applied using the excel T. Test function).
The null hypothesis for the second test states that the mean returns portfolio B and S&P
500 are equal. In the second t-test, the mean return for portfolio B is 0.62 % in contrast
to 0.14 % for the S&P 500, based on the data of daily returns. However, despite
difference, the null hypothesis is again not rejected at 5% level since the p-value = 0.1703.
It means that the mean daily returns of portfolio B is also not higher than mean returns of
S&P500 statistically.
Part 4 – Simple Linear Regression
Portfolio B vs S&P500
20%
0%
y = 1.0066x + 0.0003…
-20%
-20%
-10%
0%
10%
Excess Return S&P500
Figure 5: Scatterplot Portfolio A vs S&P500
20%
20%
Portfolio B
Portfolio A vs S&P500
Excess Return
Portfolio A
Excess Return
In the first step, excess returns of both portfolios and S&P500 are computed. With the
help of excess returns, the following charts are formulated.
0% y = 0.8533x + 0.005…
-20%
-20% -10% 0%
10%
20%
Excess Return S&P500
Figure 6: Scatterplot Portfolio B vs S&P500
Based on figure 5 that is a positive linear relationship between returns of portfolio A and
S&P 500. The data points are very close to the line of best fit. The R square shows that
92.6% of the data is explained by the equation/model above.
However, in the case of excess returns of portfolio B and S&P 500 (Figure 6), the data
points are more scattered. The trend line shows a positive linear relationship between the
two variables. The R square is 24.56 % which shows that only 25 % of the data is
explained by the equation above.
The Beta for portfolio A is came out to be 1 and for portfolio B the beta was 0.853 (Shown
in figure 5 and 6). For portfolio A, beta value indicates that its price activity is strongly
correlated with the market. A stock with a beta of 1.0 has systematic risk. A beta value
that is less than 1.0 in the case of portfolio B, this suggests that security is theoretically
less prone to changes than the market. Inclusion of this stock in the portfolio makes it less
risky than the same portfolio without the stock.
Therefore, a 1% increase in an average excess return of the market would lead to a 1%
increase in the average excess return of Portfolio A and 0.85% increase in the average
excess return of Portfolio B.
Part 5 – Multivariate Linear Regression
To examine the impact of new COVID cases on portfolio returns, simple linear regression
is done. For the first regression, the dependent variable is the return of Portfolio A. The
result shows that a one per cent increase in COVID cases decreases the return of portfolio
A be 0.03 %. The regression model only explains 9.6 % of the data. Moreover, the overall
regression model is statistically significant due to low p-value, F = 13.15, p < 0.05 (Table
6).
Table 6. Excess Return Portfolio A & 7-day Moving
average % change
Table 7. Excess Return Portfolio B & 7-day Moving
average % change
In portfolio B (Table 7), new COVID cases decrease the return of portfolio B by 0.049 %
(based on the coefficient value). This regression model has an R square of 7.8 %, which
is lower than the previous regression model. Moreover, the regression model is also
statistically significant since the p-value is less than the level of significance, F =10.56, p
< 0.05.
It shows that an economic relationship exists between new COVID-19 cases and portfolio
returns, which is found to be negative. That means the economy, with respect to stock
performance, has declined due to changes in the COVID-19 cases.
Table 8. Excess Return Portfolio A, Excess Return S&P500
& 7-day Moving average % change
Table 9. Excess Return Portfolio B, Excess ReturnS&P500
& 7-day Moving average % change
To determine the impact of new COVID cases and S&P 500 on portfolio return, multiple
linear regression is conducted. Both S&P 500 and COVID cases have a positive impact
on the returns of portfolio A. In this regression model, S&P 500 has a significant impact
on the returns of portfolio A, whereas the new COVID cases are not significant in
predicting portfolio A returns. The R square is also very high, which is around 92% (Table
8). It means that controlling for excess returns of the market index, the impact of COVID
cases becomes insignificant in predicting individual portfolio returns.
In the case of portfolio B, S&P 500 (Table 9) has a positive impact, whereas new COVID
cases have a negative impact on the returns of portfolio B. Similar to the previous
regression model, the S&P 500 is statistically significant, and new cases are not
significant. The R square of the model was 26 %.
Based on the regression results, new COVID-19 cases do not have significant impact on
the returns of the portfolio.
References
CFI. (2020). Sharpe Ratio. Retrieved from
https://corporatefinanceinstitute.com/resources/knowledge/finance/sharpe-ratiodefinition-formula/
Sortino, F. A., & Van Der Meer, R. (1991). Downside risk. Journal of portfolio
Management, 17(4), 27.
Appendix
CE
NOW
CTAS
SJM
SNA
NDAQ
LLY
HLT
CNC
AVGO
3/3/2020
-1.78%
-4.29%
-2.59%
-0.46%
-3.07%
-0.05%
-1.90%
-3.24%
-2.54%
-3.76%
3/4/2020
3.41%
4.68%
5.04%
5.13%
3.75%
5.72%
7.73 ...