MATH GR5280, Capital Markets & Investments
Final Project
The aim of this Final Project is to practically implement the ideas from the course, specifically from Chapters 7 and 8 of [BKM13]. Using Bloomberg, you will be given a recent 20 years of recent historical daily total return data for ten stocks, which belong in groups to three-four different sectors (according to Yahoo!finance), one (S&P 500) equity index 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):
wi ≥ 0, for ∀i ;
2. Now, having the efficient risky portfolio {w(ˆ)i }i(1)1 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 {w(ˆ)i }i(1)1 for the solution for the above problem 3, you
will need to solve the problem 3 above with the following constraint on ESG:
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 filename adjusted with your “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:
P2:AC3, P5:AC6, P8:AC9, P11:AC12. The curves (frontiers) for MM: C33:F113, I33:L113, O33:R153.
The points for IM: AI2:AV3, AI5:AV6, AI8:AV9, AI11:AV12. The curves (frontiers) for IM:
AM33:AP113, AS33:AV113, AY33:BB153. 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 ten 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. Therefore, each group will have its own results and conclusions.
Below, please, find the table of stock ticker symbols (aka, tickers) for each group to work with:
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Group #1
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Group #2
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Group #3
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Group #4
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Stock #1
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ADBE
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AMZN
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NVDA
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QCOM
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Stock #2
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IBM
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AAPL
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CSCO
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AKAM
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Stock #3
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SAP
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CTXS
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INTC
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ORCL
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Stock #4
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BAC
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JPM
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GS
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MSFT
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Stock #5
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C
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BRK/A
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USB
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CVX
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Stock #6
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WFC
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PGR
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TD CN
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XOM
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Stock #7
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TRV
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UPS
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ALL
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IMO
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Stock #8
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LUK
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FDX
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PG
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KO
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Stock #9
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ALK
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JBHT
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JNJ
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PEP
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Stock #10
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HA
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LSTR
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CL
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MCD
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Below, please, find the table which shows the details for each of the stocks and which stocks belong to the same sector in each group.
# Group #1 Full Name Sector (Yahoo!finance)
1 ADBE Adobe Inc. Technology
2 IBM International Business Machines Corporation Technology
3 SAP SAP SE Technology
4 BAC Bank of America Corporation Financial Services
5 C Citigroup Inc. Financial Services
6 WFC Wells Fargo & Company Financial Services
7 TRV The Travelers Companies, Inc. Financial Services
8 LUV Southwest Airlines Co. Industrials
9 ALK Alaska Air Group, Inc. Industrials
10 HA Hawaiian Holdings, Inc. Industrials
# Group #2 Full Name Sector (Yahoo!finance)
1 AMZN Amazon.com, Inc. Consumer Cyclical
2 AAPL Apple Inc. Technology
3 FFIV F5 Networks, Inc. Technology
4 JPM JPMorgan Chase & Co. Financial Services
5 BRK/A Berkshire Hathaway Inc. Financial Services
6 PGR The Progressive Corporation Financial Services
7 UPS United Parcel Service, Inc. Industrials
8 FDX FedEx Corporation Industrials
9 JBHT J.B. Hunt Transport Services, Inc. Industrials
10 LSTR Landstar System, Inc. Industrials
# Group #3 Full Name Sector (Yahoo!finance)
1 NVDA NVIDIA Corporation Technology
2 CSCO Cisco Systems, Inc. Technology
3 INTC Intel Corporation Technology
4 GS The Goldman Sachs Group, Inc. Financial Services
5 USB U.S. Bancorp Financial Services
6 TD CN The Toronto-Dominion Bank Financial Services
7 ALL The Allstate Corporation Financial Services
8 PG The Procter & Gamble Company Consumer Defensive
9 JNJ Johnson & Johnson Healthcare
10 CL Colgate-Palmolive Company Consumer Defensive
# Group #4 Full Name Sector (Yahoo!finance)
1 QCOM QUALCOMM Incorporated Technology
2 AKAM Akamai Technologies, Inc. Technology
3 ORCL Oracle Corporation Technology
4 MSFT Microsoft Corporation Technology
5 CVX Chevron Corporation Energy
6 XOM Exxon Mobil Corporation Energy
7 IMO Imperial Oil Limited Energy
8 KO The Coca-Cola Company Consumer Defensive
9 PEP PepsiCo, Inc. Consumer Defensive
10 MCD McDonald's Corporation Consumer Cyclical
Using this data and the template Excel spreadsheet you will need to make all the necessary calculations to produce 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:
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Minimal Risk or Variance Frontier:
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Minimal Return Frontier:
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Efficient Frontier:
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Two unique points that you need to find on the Efficient Frontier are of special interest:
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Minimal Risk Portfolio:
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and
Efficient Risky Portfolio:
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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 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 2/28/2003;
• end date 3/6/2023.
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).
As we have described this in detail above, each of these optimization problems MM and IM you will need to implements and solve with the following additional four optimization constraints:
where {w(ˆ)i }i(1)1 in each case corresponds to the efficient risky portfolio solution of the corresponding non
ESG-constrained problem.
As we have already mentioned, your task is to 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 -10% to 50% 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 10% to 50% 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 10% to 50% with step of 0.5%.
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 (see the file “Final Project Group0.xlsx” provided).