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BE314: Financial Modelling – Spring 2022 Coursework Reassessment

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 three other variables.

1) The question set for coursework reassessment is the same as the main coursework, but using different dataset. The dataset for reassessment is provided on Moodle.

2) On Moodle -> ‘Assessment Information’ section, the Excel file that contains the dataset can be found under ‘REASSESSMENT OF COURSEWORK – DATASETS’. This is the dataset you are required to use in your coursework reassessment. If for some reason your name is not on that list, email Dr Ming-Tsung Lin at [email protected] to find out your dataset number. Note: you will lose marks if you do not use the dataset that is assigned to you.

3) You are asked to answer the questions below. Fill in this Word document and submit it as your coursework. 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.

COURSEWORK QUESTIONS

1) [15 marks] In the Excel dataset file column B contains gross monthly percentage 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, F and G contain values for three further variables denoted by SMB, HML and MOM, which are used in later questions.

a) Import these data into EViews with the same variable names as in the Excel file (e.g. rp, rm, etc.).

b) 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 portfolio returns minus the risk-free asset returns).

c) In EViews Calculate the following descriptive statistics for rp_ex and rm_ex: mean, standard deviation, skewness and kurtosis. Insert a table containing these values in the box below.

d) In the same box, briefly interpret the sample values of the descriptive statistics in your table (mean, SD, skewness and kurtosis) and explain what they imply about excess returns on the two portfolios.

2) [10 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:

3) [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.

4) [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 2.1%. Show your calculations/working in your answer.

5) [15 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 may use the default EViews coefficient standard errors that are valid for the case of homoscedastic errors.

6) [10 marks] We will now examine if including the three additional variables SMB, HML and MOM 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:

7) [15 marks] Use the F-statistic to test the null hypothesis that the coefficients on the three new explanatory variables (SMB, HML and MOM) added in the second model are all simultaneously equal to zero (i.e. whether they are jointly statistically insignificant). 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 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.

8) [15 marks] Based on your answer to the previous questions and all other relevant information from the regression output of the two models, which of the two models is more suitable for explaining the excess returns on the portfolio? Clearly explain and justify your answer.