Financial Modelling – 2021 Resit Coursework

BE314: Financial Modelling – 2021 Resit Coursework

In this coursework, our goal is to explore whether the returns on a portfolio of stocks can be explained by the returns on the market portfolio and a selection of other variables.

• If your student registration number ends with a 0, a 1, a 2 or a 3 you will use the data contained in the Excel file ‘BE314 resit dataset 1’, if it ends with a 4, a 5 or a 6 then you will use the data contained in the Excel file ‘BE314 resit dataset 2’, and if it ends in any other number you will use the data contained in the Excel file ‘BE314 resit dataset 3’. If you are unsure about which dataset you are required to use, then email Dr Mark Hallam at hallam@essex.ac.uk. Note: you will lose marks if you do not use the dataset that is assigned to you.

• Using the data in your allocated dataset you are asked to answer the questions below using EViews. Fill in this Word document and submit it as your coursework (you do not need to submit any EViews files). Keep the margins of this document and the templates given underneath each question as they are and use a 11 pt. font or larger when writing up your answers. Note: you will lose marks for changing the size of the answer boxes or for badly formatted answers.

• As discussed earlier in the year, instructions for using EViews off-campus can be found in the PDF file named ‘Guide to using EViews software off-campus’ in the ‘Module Information’ section of the module’s Moodle page.

COURSEWORK QUESTIONS

• [14 marks] In your Excel file, column B contains gross monthly returns on a portfolio of US stocks (denoted by rp), column C contains gross monthly returns on the market portfolio (denoted by rm) and column D contains monthly returns on the risk-free asset (denoted by rf). Columns E and F contain values for two further variables denoted by SMB and HML, which are used in later questions.

1. Import these data into EViews with the same variable names as in the Excel file (e.g. rp, rm, etc.).
2. Generate two new series named rp_ex and rm_ex containing the excess returns above the risk-free rate for the industry portfolio and the market portfolio respectively (i.e. the gross portfolio returns minus the corresponding risk-free asset returns).
3. In EViews calculate the following descriptive statistics for rp_ex and rm_ex: mean, standard deviation, skewness and kurtosis. Insert the values in the box below and use them to answer the following questions, again in the same box:

Which return series is more variable, rp_ex or rm_ex? What is your interpretation of the skewness and kurtosis statistics for the two return series?

• [8 marks] Estimate the following regression model using your dataset in EViews:

where  is an error term. Copy and paste the EViews regression output into the box provided below:

 Insert your EViews regression estimation output here. Make sure that it fits and is easily readable.

• [15 marks] Interpret the estimated values of the intercept and slope coefficients and the value of R-squared, clearly explaining in each case what the value implies about the estimated relationship between the excess returns on the two portfolios. Note that all returns are in percentage terms e.g. a value of 2 corresponds to a 2% return.

• [5 marks] Based on your estimated regression model, what is the predicted value of the excess return on the portfolio of stocks when the excess return on the market portfolio is 2.5%. Show your calculations/working in your answer.

• [14 marks] Test the null hypothesis that against a two-sided alternative hypothesis at a significance level of 5%. Clearly show your calculation of the test statistic and explain how you reach your conclusion. Make sure that you state the null and alternative hypotheses, the degrees of freedom used and the critical value you use. Note: you must compute the test statistic yourself using the relevant values in your regression output from Question 2 and not use the hypothesis testing feature in EViews. You may use the default EViews coefficient standard errors that are valid for the case of homoscedastic errors.

• [8 marks] We will now examine if including the two additional variables SMB and HML as additional explanatory variables will improve the ability of the model to explain portfolio returns. Estimate the following multiple regression model in EViews:

Copy and paste the EViews regression output into the box provided below:

 Insert your EViews regression estimation output here. Make sure that it fits and is easily readable.

• [12 marks] Use the F-statistic to test the null hypothesis that the coefficients on the two new explanatory variables (SMB and HML) added in the second model are both equal to zero (i.e. whether they are jointly statistically significant). You must calculate the F-statistic yourself using the formula from the lecture notes and not use the F-test function in EViews. Carefully state your null and alternative hypotheses, the numerator and denominator degrees of freedom for the test and the relevant 5% critical value from the F-distribution. Clearly show how you calculate the value of the test statistic and clearly explain what the outcome of the test is.

• [14 marks] Based on your answer to the previous questions and any other information from the regression output of the two models that you think is relevant, which of the two models is more suitable for explaining the excess returns on the portfolio? Clearly explain and justify your answer.