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DAT 537: Final Project

Siddhartha Chib

November 18, 2019

Project Instructions

Each of the two projects described below aims to help you gain some hands-on experience

in processing and analyzing real marketing or financial data. Each team should consist of

no more than 6 members. Each team completes both projects. Project parameters are as

follows.

1. Only one student in each team should submit the team report. The report is due by

23:59 pm on December 9, 2019.

2. The first page of the report should list the name of each team member followed by the

program track (MBA, MSCA, MSF in quantitative finance or MSF in corporate finance

etc).

3. BOTH the knitted output file and the Rmd file used to generate the report have to be

submitted.

4. The Rmd file should be such that all results are fully reproducible.

Finance Project: Diversification Effects

This project helps you observe the principle of diversification in action. Diversification means

that the portfolio risk can be reduced by investing in a variety of assets.

1. Select 30 stocks that you are interested in. Find their yahoo symbols. This

website can help you find the symbols that yahoo is using http://investexcel.net/

all-yahoo-finance-stock-tickers/. Remember to double check the symbols at yahoo

finance.

2. Download 4 years of weekly price data for each stock from June 1, 2015 to June 1, 2019.

Remember this requires that all 30 stocks you select in step 1 should be available for

these 4 years.

3. Assume that the desired portfolio mean return levels are .03, .06, .09 and .12, each in

annual terms.

4. Now form 6 portfolios for each desired return level (each portfolio includes the risk-free

asset). Each portfolio has 5, 10, 15, 20, 25 and 30 stocks. The smaller set of assets

should be a subset of the larger set. For example, if you have IBM in the set of 5 stocks,

you must include IBM in the portfolios of 10, 15, 20, 25 and 30 stocks.

5. Assume that the stock premium is explained by the Gaussian SURE CAPM model

without an intercept.

6. Now form each portfolio, use the default training sample prior. Comment on the prior

in the case of the SURE model with 15 assets.

7. Now compute the optimal portfolios for each group of assets at each target portfolio

return level. Give the weights of each asset in each portfolio as well as the standard

deviation of the optimal portfolios.

8. Use ggplot to plot the standard deviation vs. the number of stocks in the assets.

Comment on your findings.

9. Redo questions 5-8 with student-t errors. For each set of assets, use log-marginal

likelihoods to find the appropriate-degrees of freedom of the student-t distribution on a

grid of 10 equally-spaced values between 3 and 5.

Marketing Project: Tuna Market Share

This project helps you understand how to set a price level consistent with marketing objectives.

1. Load the tuna data set from package bayesm. There are seven brands in the data

set. For each brand, estimate separate independent student-t models where logsales

for each product is regressed on an intercept, the product’s log price and display

activity. Use the default training sample prior and use log-marginal likelihoods to

find the appropriate-degrees of freedom of the student-t distribution on a grid of 20

equally-spaced values between 3 and 6.

2. Now estimate a SURE student-t model for the seven brands. Again use marginal

likelihoods to find the appropriate degrees of freedom on a grid of 20 equally-spaced

values between 3 and 6. From your estimation results, which pair of products is the

most correlated?

3. Now suppose you are managing the sales of Star Kist 6 oz, and you want to know what

price to charge for your product, given the other six other products in the market.

Suppose your main competitor is Chicken of the Sea 6 oz and you would like to generate

(on average) twice the total sales compared to Chicken of the Sea 6 oz. How would you

determine your own price? Assume that the other products in the market have the

following attributes:

Product Price($) Display Activity

Star Kist 6 oz ? 0.31

Chicken of the Sea 6 oz 0.70 0.35

Bumble Bee Solid 6.12 oz 1.80 0.29

Bumble Bee Chunk 6.12 oz 0.85 0.23

Geisha 6 oz 1.40 0.35

Bumble Bee Large Cans 3.49 0.25

HH Chunk Lite 6.5 oz 0.75 0.24

In providing your solution, assume that Star Kist prices are one of these prices

0.44, 0.54, 0.64, 0.74 and 0.84 (all in dollars).

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