Corporate Finance Group Assignment – ESCP 2022
All copyright reserved by Paul Karehnke. Not to be distributed without written consent.
Corporate Finance Group Assignment
This assignment provides an opportunity for students to engage and work together. Each
group will
1. Analyze the returns on a set of stocks, compute optimal portfolios, betas, and conduct
performance analysis in excel, AND
2. Reflect on the results, final output, and teamwork experience.
Instructions
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Groups of five students must complete the assignment.
Blackboard assigns the groups randomly, and the group distributions will be available
after the first lecture. Please contact your group members as soon as possible, and let
me know if you encounter any difficulties.
Submissions are due on November 7 at 23:59 Paris time. No late submissions are
accepted.
Each group must submit its own work via the Blackboard submission link. The
submission takes the form of three documents:
o All the data used in the assignment (i.e., the total returns of the selected stocks,
the index, the risk-free rate, and the ESG ratings of the stocks) inserted in the
excel template (“TemplateData.xlsx”).
o An excel file with all the calculations to back up the results in the response
document.
o A self-contained pdf document that responds to each numbered question
below plus a short team report (one page max).
Important:
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Any element/response that is not in the pdf document will be marked as
missing (even if it is somewhere in the excel file).
 Marks will be deducted for any incorrect input of the data into the excel
template or changes to the template.
Read the additional information at the end of this pdf.
Formatting:
o Use 12-point font and 1.5 line spacing in the pdf document.
o Round all numbers in the pdf document to four digits (two digits for
percentages).
o Include your group number in the name of each file.
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Corporate Finance Group Assignment – ESCP 2022
All copyright reserved by Paul Karehnke. Not to be distributed without written consent.
Tasks
Part A: Risk and Return
Select ten stocks from the EURO STOXX 50 Index (the current composition is available at
https://www.stoxx.com/index-details?symbol=SX5E). Download their end of month prices
over the past fifteen years (for example from https://finance.yahoo.com/). The first adjusted
closing price should be from August 31, 2007 and the last adjusted closing price should be
from August 31, 2022. Compute the monthly total returns (using the adjusted closing prices).
You should have 180 monthly returns for each stock.
1. Report the names of the selected stocks, their average monthly returns and standard
deviations. Report also the annualized average returns and standard deviations.
Construct the monthly returns on an equally weighted portfolio of your ten stocks (Remark:
in each month, the return on this portfolio equals the average of the individual returns.)
2. Report the average monthly return and standard deviation of the equally weighted
portfolio, and annualize these numbers. Verify that the average return on the equally
weighted portfolio is equal to the average of the average return on the individual stocks.
3. Represent the ten stocks and the equally weighted portfolio in a scatter plot with the
annualized average returns on the vertical axis and the annualized standard deviations on
the horizontal axis.
4. Comment on the difference between the volatility on the individual stocks and the
equally weighted portfolio.
Part B: Optimal Portfolio Choice
Use the Solver function in Excel to perform this analysis. Begin with the equally weighted
portfolio analyzed in Part A. Establish the return of this portfolio using a formula that
depends on the portfolio weights. Initially, these weights will all equal 1/10. You would like
to allow the portfolio weights to vary, so you will need to list the weights for each stock in
separate cells and establish another cell that sums the weights of the stocks. The portfolio
returns for each month must reference these weights for the Excel Solver to work. Compute
the values for the monthly mean return and standard deviation of the portfolio. Convert these
values to annual numbers (as you did in Part A) for easier interpretation.
Compute the efficient frontier when short sales are not allowed. Use the Solver tool in Excel
(on the Data tab in the analysis section). In the solver parameters, first set the target cell as
the cell of interest, making it the cell that computes the (annual) portfolio standard deviation.
Minimize this value. Second, establish the “By Changing Variable Cells” by selecting each of
the ten cells containing the weights of each stock. Third, add constraints by clicking the Add
button next to the “Subject to the Constraints” box. One set of constraints will be the weight
of each stock that is greater than or equal to zero. Calculate the constraints individually. A
second constraint is that the weights will sum to one. Finally, compute the portfolio with the
lowest standard deviation. If the parameters are set correctly, you should get a solution when
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Corporate Finance Group Assignment – ESCP 2022
All copyright reserved by Paul Karehnke. Not to be distributed without written consent.
you click “Solve.” If there is an error, you will need to double-check the parameters,
especially the constraints.
1. Report the lowest standard deviation, and the corresponding portfolio weights and average
return of the portfolio you just calculated. This portfolio corresponds to the minimum
variance portfolio when short sales are not allowed.
Next, compute portfolios that have the lowest standard deviation for a target level of the
expected return. Start by finding the portfolio with an expected return 2% higher than that of
the minimum variance portfolio. To do this, add a constraint that the (annual) portfolio return
equals this target level. Click “Solve” and record the standard deviation and mean return of
the solution (and be sure the mean return equals the target—if not, check your constraint).
Repeat the previous step raising the target return in 2% increments and recording the result
for each step. Continue to increase the target return and record the result until Solver can no
longer find a solution.
2. Report all the statistics of all the calculated portfolios (portfolio weights, average return,
and standard deviation). At what level does Solver fail to find a solution? Why?
3. Plot the efficient frontier with the constraint of no short sales. To do this, create an XY
Scatter Plot (similar to the one you did in Part A); with portfolio standard deviation on
the horizontal axis and the return on the vertical axis, using the data for the minimum
variance portfolio and the portfolios you computed in Question B.1 and B.2. How do
these portfolios compare to the mean and standard deviation for the equally weighted
portfolio analyzed in Part A?
Redo your analysis with short sales allowed by removing the constraint that each portfolio
weight is greater than or equal to zero. Use the Solver to calculate the (annual) portfolio
standard deviation for the minimum variance portfolio, and when the annual portfolio returns
are set to 0.05, 0.1, 0.2, 0.3, and 0.4.
4. Report the statistics of all the calculated portfolios (portfolio weights, average return, and
standard deviation). Plot the unconstrained mean-variance efficient frontier on an XY
scatter plot. How does allowing short sales affect the frontier?
Redo your analysis adding a new risk-free security that has a return of 0.04% (0.0004) each
month. Include a weight for this security when calculating the monthly portfolio returns. That
is, there will now be eleven weights, one for each of the ten stocks and one for the risk-free
security. Again, these weights must sum to one. Allow for short sales, and use Solver to
calculate the (annual) portfolio standard deviation for the minimum variance portfolio, and
when the annual portfolio returns are set to 0.05, 0.1, 0.2, 0.3, and 0.4.
5. Report all the statistics of all the calculated portfolios (portfolio weights, average return,
and standard deviation). Plot the results on a XY Scatter Plot that includes the
unconstrained mean-variance frontier calculated in Question B.4. Compute and report the
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Corporate Finance Group Assignment – ESCP 2022
All copyright reserved by Paul Karehnke. Not to be distributed without written consent.
weight of each stock divided by the sum of the portfolio weights of all stocks excluding
the risk-free security. What do you notice about this relative weight as you change the
target return? Can you then identify the tangency portfolio?
Continue to assume the existence of a risk-free asset with return of 0.04% each month (i.e.,
0.48% annually).
6. Compute the Sharpe ratio of the equally weighted portfolio (from part A), and the
tangency portfolio identified in Question B.5. Report the results and interpret them.
7. Report the weights of the portfolio that invests only in the risk-free security and the
tangency portfolio and that has the average return as the equally weighted portfolio.
What is the volatility of that portfolio?
Part C: Alphas and betas
Download the end of month index levels of the Euro Stoxx 50 Index over the past fifteen
years (for example from https://finance.yahoo.com/ using the symbol ^STOXX50E). The first
adjusted closing price is as in Part A from August 31, 2007 and the last adjusted closing price
is from August 31, 2022. Compute the monthly returns. You should have 180 monthly
returns for the index.
Remark: The Euro Stoxx 50 is a price index; that is, index levels are calculated using prices
and ignoring dividend payments. While a total return index is preferable for the calculations
conducted below, such an index is hard to find on yahoo finance for the European market.
Download the German three-month interbank rate from the Federal Reserve Web site
https://fred.stlouisfed.org/series/IR3TIB01DEM156N.1 Select Dates—From September 2007
to August 2022. Click on the Download button and select the Excel data button. Then open
and save these rates to an Excel file.
To obtain a monthly rate, take the yield and divide it by 100 to convert it to a decimal. Then
divide the decimal by 12 (because it is a monthly-compounded rate). The resulting rate will
be the monthly risk-free return in the CAPM (you may need to re-sort the dates to match the
Yahoo! data).
Create separate return columns that compute the excess returns on your ten stocks and the
Euro Stoxx 50. Recall that the excess return is the actual monthly return minus the risk-free
rate.
1. Compute and report the beta of each stock, using the SLOPE function in Excel. (Remark:
these betas should be similar to those provided by Yahoo! Finance on the Summary page
of the respective stock on the Yahoo Finance website.)
2. Compute and report the alpha of each stock, using the INTERCEPT function in Excel.
How can you interpret these alphas? How is the magnitude of alpha impacted by the
1
This rate approximately corresponds to the three-month EURIBOR rate (see https://www.emmibenchmarks.eu/euribor-org/euribor-rates.html). It has the advantage of being easy to download.
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Corporate Finance Group Assignment – ESCP 2022
All copyright reserved by Paul Karehnke. Not to be distributed without written consent.
usage of a price index (rather than a total/gross return index) as a proxy for the market
return?
3. Collect the ESG (environmental, social, and governance) score for each of your stocks
from the sustainability tab on Yahoo finance (entries can be missing). Represent the
stocks for which ESG scores are available in a XY scatter plot with the ESG scores on
the horizontal axis and the alpha (calculated for the previous question) on the vertical
axis. Report the correlation between the two variables and discuss the results in light of
the CAPM theory and possible deviations from the CAPM due to investors’ tastes.
Team Report
Briefly discuss the following points (one page max):
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List of team members and the division of labor, tasks and contributions.
o Who is the leader (main coordinator)?
o Has everyone proofread the final report?
o Who is going to confirm submission?
o Has everyone learned to use Excel?
o Have all calculations been performed independently by at least two group
members (or subgroups) to ensure accuracy?
Diary entries of key milestones
o First and last face-to-face/online meeting
o Completion of draft and final version
o Completion team report, etc.
Overall team experience
o What arrangement works?
o What do you enjoy?
o What would you improve the next time?
Self-evaluation (out of 20) against the marking criteria.
Marking Criteria
1. Correct calculations and responses to all numbered questions in Part A to C.
2. Accurate economic reasoning.
3. Concise and professional communication:
a. Not vague and not wordy
b. Free from spelling or grammatical errors
c. Clear figures and labels.
d. Reader-friendly formatting.
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Corporate Finance Group Assignment – ESCP 2022
All copyright reserved by Paul Karehnke. Not to be distributed without written consent.
Corporate Finance Group Assignment
Additional Practical Information
General comment
The assignment assumes knowledge of Excel’s main functionalities. A useful resource to
learn more about excel and fill some gaps in knowledge is https://support.microsoft.com/enUS/excel. It is recommended to use this resource in the language of your excel
version/computer.
Collecting stock return data
You can collect stock price information from Yahoo! Finance (http://finance.yahoo.com) as
follows:
1. Enter the stock symbol. Then, on the page for that stock, click “Historical Prices” on
the left side of the page.
2. Enter the “start date” as August 31, 2007 and the “end date” as August 31, 2022 to
cover the fifteen-year period. Make sure you click “monthly” next to the date; the
closing prices reported by Yahoo! will then be for the last day of each month (even
though the date indicates the first day of the month).
3. After hitting “Get Prices,” scroll to the bottom of the first page and click “Download
to Spreadsheet.” If you are asked if you want to open or save the file, click open.
4. Copy the entire spreadsheet, open Excel, and paste the Web data into a spreadsheet.
Delete all the columns except the date and the adjusted close.
5. Keep the Excel file open and go back to the Yahoo! Finance Web page and hit the
back button. If you are asked whether you want to save the data, click no.
6. When you return to the prices page, enter the next stock symbol and hit “Get Prices”
again. Do not change the dates or frequency, but make sure you have the same dates
for all the stocks you will download. Again, click “Download to Spreadsheet” and
then open the file. Copy the last column, “Adj. Close,” paste it into the Excel file and
change “Adj. Close” to the stock symbol. Make sure that the first and last prices are in
the same rows as the first stock.
7. Repeat these steps for the remaining stocks, pasting each adjusted closing price right
next to the other stocks, again making sure that the correct prices on the correct dates
all appear on the same rows.
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Corporate Finance Group Assignment – ESCP 2022
All copyright reserved by Paul Karehnke. Not to be distributed without written consent.
Computing monthly total returns
The “adjusted close” series from Yahoo! Finance is adjusted for dividends and splits, so you
can compute total returns based on the percentage change in monthly-adjusted prices. Notice
that it is usually more convenient to create a separate worksheet within the Excel file, and be
sure to have all price data sorted from the oldest to newest date.
Annualizing the monthly average return and monthly standard
deviation
Multiply the mean monthly return by 12, and multiply the monthly standard deviation by the
square root of 12. This annualization procedure is not exact for arithmetic returns, but a good
approximation that is widely used in practice.
Computing the returns on an equally weighted portfolio
Add a column in your Excel worksheet with the average return across stocks for each month.
This is the monthly return to an equally weighted portfolio of your stocks. Compute the mean
and standard deviation of monthly returns for the equally weighted portfolio. Double check
that the average return on this equally weighted portfolio is equal to the average return of all
of the individual stocks.
Constructing a scatter plot with standard deviation on the horizontal
axis and average return on the vertical axis
Create three columns on your spreadsheet with the ticker in the first column, the annual
standard deviation in the second column, and the annual mean return in the third column.
Then, highlight the data in the last two columns (standard deviation and mean),
choose>Insert>Chart>XY Scatter Plot. Complete the chart wizard to finish the plot. After
creating the scatterplot, be sure to add the axis labels and the title.
Adding the “Analysis ToolPak” and “Solver Tool” (if not already
available)
If the Solver tool is not available, you must load it into Excel as follows:
1. On the File Tab, click Excel Options.
2. Click Add-Ins, and then, in the Manage box, select Excel Add-ins.
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Corporate Finance Group Assignment – ESCP 2022
All copyright reserved by Paul Karehnke. Not to be distributed without written consent.
3. Click Go.
4. In the Add-Ins available box, select the Analysis ToolPak and Solver Add-in check
box, and then click OK. [If Analysis ToolPak or Solver Add-in is not listed in the
Add-Ins available box, click Browse to locate the add-in. If you are prompted that the
Analysis ToolPak/Solver Add-in is not currently installed on your computer, click
Yes to install it.]
5. After you load the Analysis ToolPak and Solver Add-in, the Data Analysis and
Solver commands are available in the Analysis group on the Data tab.
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