# Discuss the obtained parameters and the intuition behind them. What is the relationship between the returns of your portfolio and each explanatory variable?Explain

Empirical Project

OVERVIEW
You are required to work individually on a research project. Although you should feel free to discuss aspects of your project with your fellow students if you wish, each student must be responsible for his/her own individual work. The project’s aim is to perform an econometric analysis of the time-series of equity returns in the US market.

All the data that will be required for the empirical analysis is available on Moodle in the spreadsheet Empirical Project_Data.xlsx.This file contains the time-series of monthly returns for 100 US equity portfolios in the sheet dependent. As a first step, each student must choose ONE out of the 100 portfolios, and this portfolio will constitute that student’s dependent variable of interest. Choosing a portfolio is not particularly important, so you might as well choose at random. The main idea here is that each student should be working with a different portfolio.

After selecting the equity portfolio of interest, you will conduct a preliminary analysis by providing some descriptive statistics for the time-series.
Then, you will estimate the following bivariate regression
, , = + +
Where , , is the excess return of the portfolio I that you have selected (provided in the spreadsheet) at time t, and is the excess return of the market. The above equation refers to the most widely known asset pricing model, namely the Capital Asset Pricing Model (CAPM).

After estimating the CAPM regression, you will perform the following multivariate regression
, , = + 1 + 2 + 3 +

The above regression model is commonly referred to as the Fama and French 3-factor model, and it is a very well-established model in asset pricing. The SMB factor refers to the returns of a portfolio of Small stocks minus the returns of a portfolio of Large stocks(in terms of market capitalization).The HML factor refers to the returns of a portfolio of High-value stocks minus the returns of a portfolio of Low-value stocks(in terms of book-to-market value).

The time series of the 3 explanatory variables are provided in the sheet explanatory of EmpiricalProject_Data.xlsx. The sheet explanatory also contains 2 additional explanatory variables termed RMW and CMA. The RMW factor refers to the returns of a portfolio of Robust stocks minus the returns of a portfolio of Weak stocks (in terms of operating profitability). The CMA factor refers to the returns of a portfolio of Conservative stocks minus the returns of a portfolio of Aggressive stocks (in terms of investment). Together, all 5variables describe a more recent extension of the Fama and French model.

It is not mandatory to use these2extra variables in your empirical analysis in order to pass the coursework. However, estimating an extended version which includes the 3 initial factors plus the 2 additional factors might result in extra marks.

After estimating the regression models, you should
Discuss the obtained parameters and the intuition behind them. What is the relationship between the returns of your portfolio and each explanatory variable?
Perform hypothesis tests on the estimated parameters. Is there a statistically significant linear relationship between y and x?
Conduct diagnostic tests for each of your regressions.
Compare your results for each estimated model. Which model best fits your data?

Once you have completed your empirical analysis, you need to submit a report setting youre your findings. The report should include tables and graphs where relevant, and should clearly indicate what you have done and what your results mean. The report should not exceed 1,500 words (plus tables and graphs), and should focus on the interpretation of the empirical work rather than reproducing huge chunks of theory or merely presenting statistics without discussion.

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