ECON3034 FINANCIAL ECONOMETRICS S2 -Statistics Assignment Help

Part 1

Part 1 - Total number of marks: 32

The ‘Assignment_Question 1 EViews Workfile’ located under the ‘Assignment’ heading on iLearn contains seven monthly return series for the period January 1980 – February 2020 (482 observations).

The following monthly return series appear in the file:

1. The excess return on a portfolio of stocks of U.S. companies in two different industries. The first industry is food. Here the companies produce food products e.g., agricultural crops and livestock, wholesale grocery and drink products, sugar and flour products, fish, dairy and meat products etc. The second industry is transportation. Here the companies supply transportation services e.g., airlines (passenger and freight), buses (Greyhound), trucking and freight companies etc. The data on the portfolio industry excess returns are from the website of Kenneth French under 17 Industry Portfolios.

• food _ rf (Average monthly excess return on a portfolio of food industry stocks. The food companies are listed on U.S. exchanges and the return is in excess of the U.S. risk free rate).

• transp _ rf (Average monthly excess return on a portfolio of transportation

industry stocks. The transportation companies are listed on U.S. exchanges and the return is in excess of the U.S. risk free rate).

1. Returns on five pricing factors from Fama and French, also on the website of Kenneth French.

• mkt _ rf (Excess return on a weighted portfolio of all stocks in the U.S. market. It

is the U.S. Market Risk Premium).

• hml (High minus Low. Average monthly return on a portfolio of High Book-to-Market (Value) stocks less the average monthly return on a portfolio of Low Book-to-Market (Growth) stocks).

• smb (Small minus Big. Average monthly return on a portfolio of small capitalization stocks less the average monthly return on a portfolio of large (big) capitalization stocks).

• rmw (Robust minus Weak. Average monthly return on a portfolio of stocks for companies with robust operating profitability less the average monthly return on a portfolio of stocks for companies with weak operating profitability).

• cma (Conservative minus Aggressive. Average monthly return on a portfolio of stocks of companies which invest conservatively less the average monthly return on a portfolio of stocks of companies which invest aggressively).

To read about the factors, mkt _ rf , hml and smb, search under Fama-French three factor model and to read about the factors rmw and cma search under Fama-French five factor model.

Note: All of the returns are expressed in percent, e.g., 2.65% is represented by 2.65, not by 0.0265. Also, please see the document ‘How to save images from AppStream’ on our iLearn site under ‘Assignment’ in order to obtain an image of a table or graph in EViews.

Answer the following questions based on this dataset:

1. Estimate the following regression for the excess return on the portfolio of food industry stocks for the full sample 1980m01 to 2020m02 and include a table of

results from EViews.

food _ rf _t = ₁ + ₂ mkt _ rf _t + ₃ hml_t + ₄ smb_t + ₅ rmw_t + ₆cma_t +u_t

Are the estimated coefficients on the five factors jointly statistically significant at the 5% level?

(2 marks)

2. For the food industry stocks regression, perform a test of the hypothesis that

₃ = ₄ against the alternative that _{3 4} using EViews. What do you conclude? (2 marks)

3. Estimate the following regression for the excess return on the portfolio of transportation industry stocks for the full sample 1980M01 to 2020M02 and include a table of results from EViews.

transp _ rf _t = ₁ + ₂ mkt _ rf _t + ₃ hml_t + ₄ smb_t + ₅ rmw_t + ₆cma_t +u_t

Are the estimated coefficients on the five factors jointly statistically significant at the 5% level?

(2 marks)

4. For the transportation industry stocks regression, perform a test of the hypothesis that ₃ = ₄ against the alternative that _{3 4} using EViews. What do you conclude?

(2 marks)

5. Compare the estimated value of the coefficient ₂ in the two regressions. Is the estimated coefficient statistically different from one in each case? (Perform the test in EViews). What do you conclude about the sensitivity of each portfolio to the market risk premium?

(4 marks)

6. Compare the corresponding estimated coefficients on the other factors in terms of their sign and significance in both regressions (i.e., compare the estimated coefficient on hml in the food industry regression with that in the transportation industry regression. Do similarly for the estimated coefficients on smb, rmw and cma. What does this comparison suggest about the average characteristics of stocks in the food and transportation industries? (Hint: For example, are food industry stocks value stocks on average, etc?).

(10 marks)

7. Is the estimate of ₁ statistically significant at the 5% level in each of the

regressions? How do you interpret this result? (4 marks)

8. Perform White’s test (with no cross-product terms) for heteroscedasticity in the estimated residuals from each regression. (Write out the null and alternative hypotheses of the test, explain and provide the EViews output showing the results, and clearly state the conclusion of the test. Use a 5% significance level).

(2 marks)

9. In view of the results of White’s test, should you be concerned about

heteroscedasticity and if so, what should you do, and would that change any of the

conclusions you reached in earlier questions. (4 marks)

Part 2

Part 2 - Total number of marks: 28

The ‘Assignment_Question 2 EViews Workfile’ located under the ‘Assignment’ heading on iLearn contains three monthly yield series for the period June 1993 – August 2022, i.e., for 1993M06 to 2022M08. The series tb _ 3yr is the yield to maturity on 3-year Australian Treasury Bonds and the series bab _ 3m is the yield to maturity on Australian 3-month Bank Accepted Bills. The series spread is the tb _ 3yr yield less the bab _ 3m yield. The data are obtained from the Reserve Bank of Australia. The yields are represented, for example, as 5.95 which means 5.95% per year.

10. Conduct an ADF unit-root test on the spread Be sure to state the null and

alternative hypothesis for the test. Also conduct a KPSS unit root test and be sure to state the null and alternative hypothesis for the test. Are the results from both tests consistent with each other?

(4 marks)

11. Compute the ACF and PACF for the spread for the first 16 lags using EViews.

Comment on the pattern of the ACF and PACF and what they may suggest about the ARMA time series model for the spread.

(4 marks)

12. Consider the following two models where y_t denotes the series for spread :

Model 1: y_t = c₁ + ₁ y_{t ?1} + ₁u_{t ?1} + u_t

Model 2: y_t = c₂ + ₁ y_{t ?1} + ₂ y_{t ? 2} + ₁u_{t ?1} + ₂ u_{t ?2} + u_t

Estimate each model in EViews, comment of the significance of the coefficients (apart from the constant) and select the best model using the Akaike Information Criteria (AIC) and the Schwarz Bayesian Information criteria (SBIC). (Hint: Sample sizes need to be the same when comparing models with AIC or SBIC. That is, estimate the models over the sample period 1993M08 to 2022M08 (i.e., beginning in August 1993) because model 2, which has the most AR lags, namely two, uses up two observations for the lags in the estimation. In the equation estimation settings box, change 1993M06 to 1993M08).

(4 marks)

13. Using EViews, compute the ACF and PACF of the residuals (out to 16 lags) from Model 1 and Model 2, respectively. Based on the ACF and PACF of the estimated residuals, do you prefer one model over the other?

(4 marks)

14. Estimate Model 1 for the sample 1993M08 to 2020M12 and generate a dynamic forecast for the period 2021M01 to 2022M08. (Hint: First estimate Model 1 being sure to specify 1993M08 2020M12 in the estimation settings box. Having estimated the model, select the forecast tab, select dynamic forecast, set the forecast sample to 2021M01 to 2022M08, and in the forecast name box, type spread _ df .

• EViews generates a graph for the dynamic forecasts you generated together with the two-standard error band. Present this graph and comment on the convergence or otherwise of the forecast values and on the behaviour of the two-standard error band.

(4 marks)

• Graph the actual spread series and the dynamic forecast of the spread series i.e., spread _ df on the same graph for the period 2021M01 to 2022M08. (Hint: Click on Quick/Sample and specify the sample as 2021M01

2022M08. Click OK. Then, on the main menu bar at the top of the screen, click on Object/New Object/Group and OK. In the list of series box, type spread and spread _ df and click OK. Then click on View/Graph to graph

both series together). Comment on the graph. (Hint: Refer to recent movements in Australian interest rates).

(4 marks)

15. Now estimate Model 1 for the sample 1993M08 to 2020M12 and generate static

forecasts for the period 2021M01 to 2022M08. (Hint: Here select static forecasts, and in the forecast name box, type spread _ sf ).

• EViews generates a graph for the static forecasts. Present this graph and comment on it.

(2 marks)

• Graph the actual spread series and the static forecast of the spread series i.e., spread _ sf on the same graph for the period 2021M01 to 2022M08. Comment on the graph.

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