CS代写 GR5280

Final Project MATH GR5280

MATH GR 5280, Capital Markets & Investments

Copyright By PowCoder代写 加微信 powcoder

Start date: 12/3/2022 Due date: 12/17/2022

Final Project

Note: All files and information related to the final project are located in the 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 ten stocks,

which belong in groups to three-four different sectors (according to Yahoo!finance), one (S&P 500) equity

index (a total of eleven risky assets) and a proxy for risk-free rate (1-month Fed Funds rate). 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 (“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 five cases of the

additional constraints:

1. This additional 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:

Note that this is a difficult-to-converge case which requires “regularization” discussed in the

class, that is replace

w in the above constraint with

w , where 001.0=δ .

2. This additional optimization constraint is designed to simulate some arbitrary “box” constraints
on weights, which may be provided by the client:

∀≤ for ,1 ;
3. A “free” problem, without any additional optimization constraints, to illustrate how the area of

permissible portfolios in general and the efficient frontier in particular look like if you have no

constraints;

4. This additional optimization constraint 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):

∀≥ for ,0 ;
5. Lastly, we would like to see if the inclusion of the broad index into our portfolio has positive or

negative effect, for that we would like to consider an additional optimization constraint:

You will need to present the results in both the tabular and graphical form with the objective to make

inferences and comparisons between the sets of constraints for each optimization problem and between

the MM and IM models in general. The grading will be done by comparing your tabulated results to exact

solutions.

MATH GR 5280, Capital Markets & Investments

Start date: 12/3/2022 Due date: 12/17/2022

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 groups 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 variant

are completely different. Therefore, each groups will have its own results and conclusions.

Below, please, find the table of stock ticker symbols (aka, tickers) for each group to work with:

Variant #1 Variant #2 Variant #3 Variant #4

Index SPX SPX SPX SPX

Stock #1 ADBE AMZN NVDA QCOM

Stock #2 IBM AAPL CSCO AKAM

Stock #3 SAP CTXS INTC ORCL

Stock #4 BAC JPM GS MSFT

Stock #5 C BRK/A USB CVX

Stock #6 WFC PGR TD CN XOM

Stock #7 TRV UPS ALL IMO

Stock #8 LUK FDX PG KO

Stock #9 ALK JBHT JNJ PEP

Stock #10 HA LSTR CL MCD

Risk-free rate FEDL01 FEDL01 FEDL01 FEDL01

Below, please, find the table which shows the details for each of the stocks and which stocks belong to

the same sector in each variant.

MATH GR 5280, Capital Markets & Investments

Start date: 12/3/2022 Due date: 12/17/2022

Using this data you will need to prepare an Excel spreadsheet that makes all the necessary calculations to

plot a 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 (1-5 above). The Minimal Return

MATH GR 5280, Capital Markets & Investments

Start date: 12/3/2022 Due date: 12/17/2022

Frontier and the Efficient Frontier together are forming the Minimal Risk or Variance Frontier – it is just

a matter of re-formulating the optimization problem, as follows:

Minimal Risk or Variance Frontier:

:subject to

Minimal Return Frontier:

σ :subject to

Efficient Frontier:

σ :subject to

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

Minimal Risk Portfolio:

Efficient Risky Portfolio:

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

variant’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

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

their office hours. 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:

MATH GR 5280, Capital Markets & Investments

Start date: 12/3/2022 Due date: 12/17/2022

• start date 5/11/2001;
• end date 5/12/2021.

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

• The full (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 optimization constraints:

∀≤ for ,1 ;
3. no constraints;

∀≥ for ,0 ;

As we have already mentioned, your task is to produce the following objects on the Permissible Portfolios

Region in the graphical form:

1. Minimal Risk or Variance Frontier (a curve), range for portfolio returns: from -10% to 50% with
step of 0.5%;

2. Global Minimal Risk or Variance Portfolio (a point);
3. Maximal Sharpe Ratio or Efficient Risky Portfolio (a point);
4. Maximal Return or Efficient Frontier (a curve), range for portfolio standard deviation: from 10%

to 50% with step of 0.5%;

5. Capital Allocation Line or CAL (a straight line);
6. 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 also produced in tabular form (Excel), with which comparison for grading will

be made, 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 Variant0.xlsx” provided).

As a single value for the risk-free rate to draw the CAL, please, use the very last value of the “FEDL01”

time series.

You should analyze all your results with the purpose of comparison of different constraints for each

optimization problem (MM and IM), and the two optimization problem solutions between each other with

same constraints.

Do not hesitate to ask Lecturer or TAs any questions related to this.

Good luck!

MATH GR 5280, Capital Markets & Investments

Start date: 12/3/2022 Due date: 12/17/2022

You are given two weeks to complete the Final Project and to prepare the presentations. We encourage

you not to delay starting the work as workload is meant for several days of team work and not as a one-

night, single person effort.

Final Project is due as an Excel file with the graphs and tables requested, on December 17th, 2022

at 7:00 PM EST.

程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com