BU.232.620 Empirical Project 2 (Linear Econometrics for Finance)
Extending the the analysis in the Empirical Project 1 that focuses on the single-factor CAPM model, you will analyze the performance of multi-factor models for returns of U.S. common stocks in the Empirical Project 2.
There are two tasks you are expected to take on:
1. For the 25 stock portfolios formed on Size and Book-to-Market that you analyzed before, we now want to use the following multivariate linear regression
R (t) − RF(t) = a + b [RM(t) − RF(t)] + sSMB (t) + hH ML(t) + e(t). (1)
To analyze this model and report the results, consider the following issues:
• For the two new factors (or explanatory variables in econometric language) SMB (t) and HM L (t), report their summary statistics similar to the summary statistics of RM(t) − RF(t) you reported before. Importantly, examine the correlations of the three factors—refer to Table 2 of Fama and French (1993, page 14)—to understand whether multicollinearity is a problem.
• Tabulate the results of the multivariate linear regression model Eq. (1); refer to Table
6 in Fama and French (1993) (page 24)
• Questions to answer: Are the loadings of the 25 portfolios on the two new factors significant? Is the three-factor model better in accounting for time series variation in the return of each portfolio better than the CAPM model used in the Empirical Project 1?
• Conduct a test for the hypothesis that neither SMB (t) nor H ML (t) has significant explanatory power beyond the market excess return.
2. Read the following seminal article (you can download it from our Canvas course site).
Fama, Eugene F. French, Kenneth R., 2015. “A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
Based on your reading and understanding, do the following analyeses:
• Download the monthly return series of the 25 stock portfolios formed on Size and Operating Profitability and the 25 stock portfolios formed on Size and Investment, again, from Ken French’s Data Library
https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
Once more, you are expected to be able to find the right data; this is one of the most important skills in practice!
• Like for the portfolios formed on Size and Book-to-Market that you analyzed before, summarize the returns of these two new sets of portfolios.
• For each of the new portfolios (50 in total), examine whether the three-factor model in Eq. (1)can account for their variations.
Write a project report of the aforementioned analyses. The report should still contain the following three sections in general, but with more meat given the multiple tasks involved
1. The first section is Introduction, which should contain a high-level summary of the re- search question, model, and findings.
2. The second section should describe the data, including the data source and summary.
• There are multiple sets of portfolios considered, so you want to highlight the differ- ences between them.
3. The third section should explain the model used and the findings.
• There are more than one tasks involved. For example, in the first part, you are asked to compare the performance of the one-factor and three-factor models, while in the second part, you use the three-factor model to explain two new sets of portfolios. Hence, it is naturally interesting and important to compare whether the three-factor model fares better in explaining the portfolios sorted on Size and Book-to-Market than in explaining than the two new sets of portfolios.
4. The last section is Conclusion.
What You Need to Submit
• The project report
• The code you use in generating all the empirical results in the report
– The TA Regression Demonstration Session will teach you the key Python proce- dures necessary in conducting regression analyses.
– The TA Regression Demonstration Session will only cover the key procedures rather than showing a complete code that you can simply copy and run to generate all the results needed for the report!! You will need to learn the key procedures and then write your own complete code to generate all the results.
– Some notes that discuss the main Python procedures are provided; see Canvas an- nouncements.
– I will check the code to make sure no one simply copies the code from other people (the code will look somewhat different if one really writes his/her own code)!