Name:
FIN 235-A Advanced Statistical Modeling in Finance Spring Semester, 2024
Class Project
Instruction:
• Each group should have 3 members. Please email me the names of your group members by April 29, 2024.
• Type your researching findings in a file as a form of formal research report. Supporting documents are needed (e.g. the Eviews output must be cropped and copied in your file). You don’t need to attach the original data. Please note that the file of presentation slides is not a report.
• The deadline of submitting your report is May 8, 2024.
• Prepare to present your findings using PowerPoints in class on May 6, 2024.
• Each group should elect a group leader based on the collective opinion of your team. The group leader should be the one who will submit the project to me.
• Each project report should include a separate page, indicating what the contribu- tion of each group member is. For example, you can document which member did which subquestions. You need to give me a detailed list of every group member’s contribution to your project. The grade that I give to each team member will be based on the entire report’s quality and each member’s contribution. (So student A and B might receive different grades although they are in the same group.) However, the group leader should make sure every group member are notified of his/her contribution on this page before you submit your project to me. If this assessment page is missing on your report, I will assume all team members shared the work equally.
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Question: The traditional asset pricing model, known formally as the capital asset pricing model (CAPM) uses only one variable to explain the returns of a portfolio/stock, and this explanatory variable is the returns of the market as a whole. And we define the coefficient, β, to describe the systematic risks that the firm is facing. In particular, β is the coefficient of the following regression equation:
Rit–Rft = α+ β[Rmt −Rft] + uit
where Rit is the return of the stocks of firm i at time t, Rmt is the return of the market portfolio, and Rft is the return of the risk-free rate. uit is the error term. In contrast, the Fama–French model uses three variables. Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a high book-to-market ratio (B/P, customarily called value stocks, contrasted with growth stocks). They then added two factors to CAPM to reflect a portfolio’s exposure to these two classes:
Rit–Rft = α+ β1[Rmt −Rft] + β2SMBt + β3HMLt + uit
where Rit is the return of the portfolio i at time t, Rmt is the return of the market portfolio, and Rft is the return of the risk-free rate. SMB stands for “Small [market capitalization] Minus Big” and HML for “High [book-to-market ratio] Minus Low”; they measure the historic excess returns of small caps over big caps and of value stocks over growth stocks. uit is the error term.
1. Pick two stocks that you are interested in and download their historical price data from Yahoo! Finance. Plot the historical prices against time. Compute their monthly returns. Make sure that your data ranges from January 2018 to December 2022.
2. Assume that you invest 50% each of the stocks that you picked. Compute the monthly returns of the portfolio over the sample period above.
3. Download the monthly data of the three factors from Ken French’s website (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). Read the instructions on the website carefully to guarantee that you are downloading the correct data.
4. Draw the scatter plot the portfolio’s excess return (y-axis) against excess market return (x-axis) using Eviews.
5. Estimate Fama-French three factor model of your portfolio, and explain the coefficients in words.
6. Plot the residuals of the regression against time. And conduct the heteroskedasticity tests using Eviews.
7. Perform the Chow test using Eviews. The breakpoint is March 2020.
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