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What is the adjusted r square for each model

Assignment: Innovations in Contemporary Finance

Project: Factor Models

In this project you will apply several factor models to the stock of Verizon. You will run regression models based on these models and report the results.

Here are the models you will use:

1. CAPM:

E(Ri) = Rf + β[ E(Rm) - Rf ].

As a regression model, you will run:

E(Ri) - Rf = α + β[ E(Rm) - Rf ]

2. Fama - French 3-Factor model:

E(Ri) = Rf + β_{1}[ E(Rm) - Rf ] + β_{2}[ SMB ] + β_{3}[ HML ].

Here, SMB is the size factor representing small company stocks perform better than large company stocks. Therefore, SMB is the small minus big factor. On the other hand, HML is high minus low book to market value. High book to market is equivalent to low price to earnings ratio (P/E). Therefore, this factor represents the stylized fact that low P/E ratio stocks perform better than low P/E ratio models.

As a regression model, you will run:

E(Ri) - Rf = α + β_{1}[ E(Rm) - Rf ] + β_{2}[ SMB ] + β_{3}[ HML ].

3. Carhart 4- Factor model: Fama-French 3-factor + Momentum factor.

E(Ri) = Rf + β_{1}[ E(Rm) - Rf ] + β_{2}[ SMB ] + β_{3}[ HML ] + β_{4}[ UMD ].

Here, the fourth factor is the momentum factor; up minus down. If the stock has performed well over the last 11 months, it is supposed to perform well for the next month. Hence, this is called the momentum factor (UMD: up minus down past stock price movement)

As a regression model, you will run:

E(Ri) - Rf = α + β_{1}[ E(Rm) - Rf ] + β_{2}[ SMB ] + β_{3}[ HML ] + β_{4}[ UMD ].

Here is how you should proceed for this project:

1. I would like you to use Excel to run these regressions. You will use your stock's daily returns from December 30, 2013 through December 31, 2018. Download your stock's adjusted closing prices during this date range (December 27, 2013 through December 31, 2018) from finance.yahoo.com and then calculate daily returns as follows:

- Go to yahoo finance.
- Enter the ticker symbol of your company.
- Click on Historical Data tab.
- Set the date range from December 27, 2013 through December 31, 2018.
- Download the prices to an excel file (at the bottom it says download to a spreadsheet. Click on it and save it).
- Using the adjusted closing prices (the last column), find the daily returns on Excel. For example, if today's price is 50 (in excel cell C4) and yesterday's price is 40 (in excel cell C3), today's return on cell D4 should be =(C4-C3)/C3. You can then select and drag down the formula to find the other daily returns, R
_{i}.

2. Use the Excel file I have uploaded to BlackBoard to obtain the explanatory factors. The name of the file is Project-FF-Mmomentum-Daily.xls.

3. For each model, use the regression procedure in Excel and obtain the printout. You can access the regression procedure from:

Data -> Data Analysis -> Regression -> OK :

Select the range for Y (Y is your stock's excess returns) and the range for X (X is the explanatory factors, which will be different for each model). Check the box for 'Labels'. Click on Output Range and select the cell where you want the regression output to begin.

4. After you obtain the output, copy-paste into your report. Do this for each model above.

5. Answer the following questions for each model, 1. CAPM, 2. Fama-French, 3. Carhart:

- What is the adjusted R square for each model? Does the adjusted R square increase as the model gets more sophisticated? Note: Adjusted R square is the percentage of the variation in your stock's returns explained by the factors in the model.

- The estimate in front of the excess market return factor is the usual beta that we are familiar with. What is this beta in each model? Is it significant? (If the t-stat value is larger than 1.96, it is significant). Does it vary a lot with each model?

- Is the size (SMB) estimate positive or negative? If it is positive, that would mean that your stock is smaller than the average stock. If negative, your stock is larger than the average stock in the stock market. Is the size estimate significant?

- Is the book to market (HML) estimate positive or negative? If positive, your stock has a lower P/E ratio; otherwise a higher P/E ratio during the estimation period. Is the book to market estimate significant?

- Is the momentum estimate positive or negative? If positive, then your stock tends to follow a past positive trend. If negative, your stock tends to follow a past negative trend. Is the momentum estimate significant?

Format your assignment according to the following formatting requirements:

1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.

2. The response also include a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.

3. Also Include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.

**Attachment:-** Project-FF-Mmomentum-Daily.rar

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