MATH GR5280, Capital Markets & Investments

Final Project

Note: All files and information related to the final project are e-mail’ed to you and need to be uploaded into the separate folder “Final Project”.

The aim of this Final Project is to practically implement the ideas from the course, specifically from Chapters 7 and 8. You will be given a recent 20 years of historical daily total return data for 21 stocks, which belong in groups to 4-5 different industry sectors, one (S&P 500) equity index (a total of 22 risky assets) and a proxy for risk-free rate (1-month Fed Funds rate). Additionally, you will be given contemporaneous ESG [ESG3] scores data also from Bloomberg for all of your companies with detailed explanations to them. In order to reduce the non-Gaussian effects, you will need to aggregate the daily data to the monthly observations, and based on those monthly observations, you will need to calculate all proper optimization inputs for the full Markowitz Model (“MM”), alongside the Index Model (“IM”). Using these optimization inputs for MM and IM you will need to find the regions of permissible portfolios (efficient frontier, minimal risk portfolio, optimal portfolio, and minimal return portfolios frontier) for the following four cases of problems:

1. This optimization is designed to simulate the typical limitations existing in the U.S. mutual fund industry: a U.S. open-ended mutual fund is not allowed to have any short positions, for details see the Investment Company Act of 1940, Section 12(a)(3) (https://www.law.cornell.edu/uscode/text/15/80a-12):

2. Now, having the efficient risky portfolio  for the solution for the above problem 1, you will need to solve the problem 1 above with the following constraint on ESG:

3. This optimization constraint is designed to simulate the Regulation T by FINRA (https://www.finra.org/rules-guidance/key-topics/margin-accounts), which allows broker-dealers to allow their customers to have positions, 50% or more of which are funded by the customer’s account equity:

4. Lastly, having the efficient risky portfolio  for the solution for the above problem 3, you will need to solve the problem 3 above with the following constraint on ESG:

All your work must be done individually!

You will need to numerically solve the above problems using the template “FinalProject AlexeiChekhlov Group0.xlsx” and submit your numerical solutions as such file, with your filename adjusted with your FirstName and LastName and your Group# as follows: “FinalProject FirstnameLastname Group(your group#).xlsx”. Please, do not insert or delete any cells, keep the existing format – it is very nicely done and the graphs will allow you to “see” your solutions. The areas of cells that you will need to fill-in with your numerical solutions are as follows.

The points for MM: AA2:AY3, AA5:AY6, AA8:AY9, AA11:AY12.

The curves (frontiers) for MM: C44:F186, I44:L186, O44:R564.

The points for IM: BE2:CC3, BE5:CC6, BE8:CC9, BE11:CC12.

The curves (frontiers) for IM: AM44:AP186, AS44:AV186, AY44:BB564.

The grading will be done by comparing your tabulated results to exact solutions. The calculations should be done on a Windows computer with licensed Microsoft Office installed.

Again, you will be given 20 years of daily data of total returns for the S&P 500 index (ticker symbol “SPX”), and for 22 stocks (ticker symbols see the table below) such that there are three-four sectors of stocks with stocks in each group belonging to one (Yahoo!finance) sector and an instrument representing risk-free rate, 1-month annual Fed Funds rate (ticker symbol “FEDL01”). Note that stocks in each group are completely different.

Below, please, find the table of instruments’ ticker symbols (a.k.a. tickers) for each group to work with:

Below, please, find the table which shows the details for each of the stocks and which stocks belong to the same industry sector in each group.

Using this data you will need to fill-in your Excel spreadsheet, using the template (“Final Project AlexeiChekhlov Group0.xlsx”) provided, that makes all the necessary calculations to plot the Permissible Portfolios Region, which combines: the Efficient Frontier, the Minimal Risk or Variance Frontier, and the Minimal Return Frontier for a given set of constraints (1-4 above). The Minimal Return Frontier and the Efficient Frontier together are forming the Minimal Risk or Variance Frontier – it is just a matter of reformulating the optimization problem, as follows:

Minimal Risk or Variance Frontier:

Minimal Return Frontier:

Efficient Frontier:

Two unique points that you need to find on the Efficient Frontier are of special interest:

Minimal Risk Portfolio:

and

Efficient Risky Portfolio:

As we have already mentioned, your task is to numerically produce the following objects on the Permissible Portfolios Region in the numerical (and the template spreadsheet does it in the graphical for you) form.

 Minimal Risk or Variance Frontier (a curve), range for portfolio returns: from -130% to 130% with step of 0.5%;

 Global Minimal Risk or Variance Portfolio (a point);

 Maximal Sharpe Ratio or Efficient Risky Portfolio (a point);

 Maximal Return or Efficient Frontier (a curve), range for portfolio standard deviation: from 8% to 79% with step of 0.5%;

 Capital Allocation Line or CAL (a straight line);

 Minimal Return or Inefficient Frontier (a curve), range for portfolio standard deviation: from 8% to 79% with step of 0.5%.

This Final Project in an open-book which means that you can and should use the Instructor’s handouts and the corresponding Chapter copy reading material provided by the Instructor, as well as any additional materials provided to you. Instructor and TAs have performed all these calculations for each of the group’s portfolios and will be able to compare your numbers, specific points and graphs to theirs. If your spreadsheet calculations are done correctly, you and we should be able to match the results with sufficient accuracy.

The main tool that we would like you to use to solve the optimization problems for each point on the Minimal Risk or Variance Frontier is the Excel Solver. Please, try to learn how to use it on your own, if you have not done so already. The TAs will be helping you to address any issues related to Solver during the TAs sessions. To calculate large numbers of multiple points on any of the required frontiers, you will need to use the Excel Solver Table, which the TAs will teach you how to install and use. Both Excel Solver and Excel Solver Table will also be covered in lectures with illustrations which are very similar to your Final Project.

For your calculations, you need to use the full available historical data range:

 start date 9/17/2004;

 end date 9/20/2024.

As it was mentioned above, you will need to calculate the solutions to two optimizations covered in lectures:

 The full Markowitz Model (MM);

 The Index Model (IM).

The curves above must be produced in tabular form. (Excel), using the template provided, preserving the formats in the template, with which comparison to exact solution will be made for grading, using specifically the above ranges. If a numerical solution cannot be found, just leave the corresponding cell empty. The points above should also be tabulated. All the tabulation should be done similar to example provided by the Instructor in the template “Final Project AlexeiChekhlov Group0.xlsx” provided.

You are given two weeks to complete the Final Project and to prepare the Excel file for submission into the portal on CourseWorks. We encourage you not to delay starting the work as workload is meant for several days of work and not as a one-night effort.

Final Project is due on December 13th, 2025 at 11:59 PM EST.

References:

[BKM13] Z. Bodie, A. Kane, A. J. Marcus, “Investments”, Thirteenth Edition, McGraw Hill, 2024.

[ESG3] “Certificate in ESG Investing Curriculum”. CFA Institute. Edition 3. CFA Society of the UK, 2021.