ES50108 Econometrics for Finance Assignment, Department of Economics - University of Bath, UK

Answer all 3 questions.

Q1. The 'market model' of asset returns states that;

R_jt = β₀ + β₁R_mt + u_t

where: R_jt = return (including capital gains and dividends) to shareholders of the j'th asset at time t, R_mt = equivalent return on the 'market portfolio' of assets at time t, β₁ is the slope coefficient, β₀ = a constant and u_t is an iid random disturbance term.

Use the data file ftdata, containing 252 daily observations and the company return allocated to you, mrpi the market return and the monthly dummy variables.

a) Estimate the market model with OLS, using the company (dependent variable) allotted to you. (The company return variable is labelled rxxx and mrpi is the variable for the return on the market portfolio). Report and interpret your results with respect to the coefficients, while also commenting on the sign, magnitude and testing the significance of these coefficients.

b) Use the Durbin-Watson d-statistic to test for first-order autocorrelation. Interpret your result. Explain and illustrate.

c) Does the above model suffer from 10^th order (LM test) autocorrelation at 1% level of significant? If so, explain and illustrate.

d) Explain how you would conduct the Breusch Pagan's test for heteroskedasticity. Is there any evidence of heteroskedasticity being present at 1% level of significant?

e) Re-estimate the model adding monthly dummy variables (jan, feb mar etc) to account for any seasonal effects that might be present (add 11 dummy variables, omit dec). Test the joint significance (Using the F-test) of the monthly dummies, briefly explaining the procedure used. Comment on your findings. This test requires you to run 2 separate regressions, a restricted model without the dummies and an unrestricted model including the dummies. Collect the RSSes from both and calculate the test statistic.

Q2. Run a regression of the initial market model, but in this test include two more explanatory variables, 3 months Treasury bill (TB_1t) and lagged dependent R_jt-1:

R_jt = β₀ + β₁R_mt + β₂TB_1t + β₃R_jt-1 + u_t

a) Interpret the above model in terms of the coefficients and t-statistics, particularly the Treasury bill (TB_1t) and lagged dependent variable R_jt-1. Explain carefully.

b) To see that there is evidence of the first order autocorrelation by using Durbin's h-test.

c) Does the above model suffer from 10^th order autocorrelation at 1% level of significance?

d) Is there any evidence of heteroskedasticity being present by using Breusch Pagan's test at 1% level of significance?

e) Using an F-statistic is the explanatory power of the regression model significant at the 1% and 5% level of statistical significance. What do you conclude and why?

f) Carry out the Chow test on the 140^th observation, by estimating both sub-samples and the total time span, then using the RSS from these regressions to calculate the Chow test statistic. Is there a structural break?

Q3. Make some conclusions regarding your results - which of the above two models (question 1 and 2) should be preferred? Justify you arguments with reference to your findings. What do you conclude and why? (Hint: carry out the t-test, R², F-test etc.).

Attachment:- Econometrics for Finance Assignment Files.rar