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Financial Modelling Assignment -
In this assignment, explore whether the returns on a portfolio of stocks can be explained by the returns on the market portfolio and two other factors. You have to transfer data to e-views and then do things like regression and then answer the questions.
QUESTIONS -
Q1) 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 Question 6 below. All data span the sample period January 1980 to December 2017.
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) Calculate the following descriptive statistics for rp_ex and rm_ex: mean, median, standard deviation, skewness, kurtosis, min and max in EViews. 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, th rp_ex or rm_ex? What is your interpretation of the skewness and kurtosis statistics for the two return series?
Q2. Estimate the following regression model using your dataset in EViews:
rp_ex_{t} = β_{0} + β_{1}rm_ex_{t} + ε_{t}
where ε_{t} is an error term.
Q3) Based on the R-squared value from the estimated model, how successful is this model at explaining the excess returns on the portfolio? Explain and justify your answer.
Q4. What is the predicted value of the excess return on the portfolio when the excess return on the market portfolio is 3.5% (i.e. when rm_ex= 3.5)?
Q5. Test the null hypothesis that β_{1} = 1 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 from the Student's t-distribution. Note: you may use the default EViews coefficient standard errors that are valid for the case of homoscedastic errors.
Q6. 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:
rp_ex_{t} = β_{0} + β_{1}rm_ex_{t} + β_{2}SMB_{t}+β_{3}HML_{t} + ε_{t}
Q7) 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. You must calculate the F-statistic yourself using the formula from the lecture notes and not use the 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 explain what the outcome of the test is.
Q8) Based on your answer to the previous question 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.
Attachment:- Assignment Files.rar