The Individual Assignment relates to the following Learning Outcomes:
• Apply econometric methods to modelling, analysing and forecasting financial data
• Demonstrate and explain different estimation methodologies.
• Critically evaluate empirical econometric work.
These learning outcomes support development of the following Graduate Capabilities:
• Discipline Specific Knowledge and Skills
• Critical, Analytical and Integrative Thinking
• Effective Communication
• The assignment must be submitted via Turnitin by 4pm on Thursday 15 October 2020. The submission link is available on iLearn under the “Assignment” tab from 5pm on Monday 12 October 2020.
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• Marks will be assigned based on the quality of the responses to each question and in line with the rubric at the end of this document.
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The EViews workfile “Assignment_S2_2020_Workfile.wf1” located under “Assignment” heading on iLearn contains six monthly return series for the period January 1980 – February 2020 (482 observations). We do not include the returns for the most recent months as they may have an undue influence on the analysis due to the severe economic effects of the pandemic. (Note: 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.)
The following monthly return series appear in the file:
A. The excess return on a portfolio of two industry stocks from Fama and French, namely, consumer goods and services, and health.
• cnsmr rf _ (Average monthly excess return on a stock portfolio comprising firms which operate in the provision of consumer goods and services, both in retail and wholesale. The consumer goods industry stocks are listed on U.S. exchanges and the return is in excess of the U.S. risk free rate).
• hlth rf _ (Average monthly excess return on a portfolio of health industry stocks. The stocks in the health industry are listed on U.S. exchanges and the return is in excess of the U.S. risk free rate).
B. Returns on four pricing factors from Fama and 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. It is the 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. It is the 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. It is the average monthly return on a portfolio of stocks for firms with robust operating profitability less the average monthly return on a portfolio of stocks for firms with weak operating profitability).
Note: All of the returns are expressed in percent, e.g. 2.65% is represented by 2.65, not by 0.0265.
Answer the following questions based on this dataset:
1. What sign would you expect the estimated coefficient on each factor to have in a regression of a portfolio return on the four factors? (Hint: To read about the factors, hml and smb, search under Fama-French three factor model and to read about rmw,search under Fama-French five factor model) (6 marks)
2. Estimate the following regression for the excess return on the portfolio of consumer goods stocks for the full sample 1980m01 to 2020m02 and include a table of results from EViews. 1 2 3 4 5 _ _ t tt t t cnsmr rf mkt rf hml smb rmw u =+ + + + + ββ β β β Are the estimated coefficients on the factors statistically significant at the 5% level? (2 marks)
3. Estimate the following regression for the excess return on the portfolio of health stocks for the full sample 1980M01 to 2020M02 and include a table of results from EViews. 1 2 3 4 5 _ _ t tt t t hlth rf mkt rf hml smb rmw u =+ + + + + ββ β β β Are the estimated coefficients on the factors statistically significant at the 5% level? (2 marks)
4. Compare the corresponding signs on the estimated coefficients on all the factors in both regressions (i.e. for consumer goods and health portfolio regressions). What does this comparison suggest about the average characteristics of stocks in the consumer good and health industries? (Hint: For example, are stocks in the consumer goods industry value stocks on average, etc?) (8 marks)
5. Is the estimate of β1 statistically significant at the 5% level in each of the regressions? How do you interpret this result? (4 marks)
6. 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). (4 marks)
7. 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).
The EViews workfile “Assignment_S2_2020_Workfile.wf1” contains data on the Australian term spread. This series is shown as spread au _ in the workfile. The spread is defined as the yield on 10-year Australian Government Bonds less the yield on 3-month Australian Bank Accepted Bills, expressed in percent per year, e.g. 1.60% is represented by 1.60, not by 0.0160. The data is obtained from the Reserve Bank of Australia website. The data are monthly for the period January 1980 – February 2020 (482 observations).
8. Using EViews, plot the term spread with a line chart (and with a horizontal line for the x-axis on the graph). Identify the episodes in the graph when the term spread is negative. What was about to happen to the Australian economy soon after these episodes? (Hint: With EViews10, click on the series spread au _ and the data appears. Choose View, then Graph and for graph type: select Basic and for specific: select Line and Symbol. Click O.K. and the graph appears without the horizontal xaxis line. ‘Freeze’ the graph by clicking on Freeze and then O.K. The ‘frozen’ graph comes up. Right click anywhere in the frozen graph and you will see a list of options. Select ‘Add lines and Shading’. Then for Type, select line and for Orientation, select Horizontal-left axis, and for Data Value under Position, type in 0. Click O.K. You will now have the horizontal axis shown in your graph. In EViews11, the horizontal axis will automatically appear). (4 marks)
9. Conduct an ADF unit-root test on the series spread au _ . Be careful to properly 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? (6 marks)
10. Compute the ACF and PACF for the series spread au _ for the first twelve lags using EViews. Comment on the pattern of the ACF and PACF and what they may say about the time series process for spread au _ . (4 marks)
11. Consider the three models where t y denotes the spread i.e. spread au _ .
Model 1: t t tt 1 11 11 yc y u u =+ + + φ θ − −
Model 2: t t tt 2 11 2 2 yc y y u =+ + + φ φ − −
Model 3: t t t tt 3 11 2 2 33 yc y y y u
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 1980m04 to 2020m02 (i.e. beginning in December 1980). In the equation estimation box, change 1980m01 to 1980m04). (6 marks)
12. Using EViews, compute the ACF and PACF (the first 12 lags) of the residuals of the preferred model, estimated from the sample running from 1980m04 to 2020m02. Comment on the results. (2 marks)
13. Estimate Model 2 for the sample 1980m04 to 2017m12 and generate a dynamic forecast for the period 2018m01 to 2020m02. (Hint: First estimate Model 2 being sure to specify 1980m04 2017m12 in the estimation settings box. Having estimated the model, select the forecast tab, select dynamic forecast, set the forecast sample to 2018m01 to 2020m02, and in the forecast name box, type spread auf _ which saves the dynamic forecasts on the workfile under this series name).
(i) Explain what is meant by a dynamic forecast. (2 marks)
(ii) 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.
(3 marks) (iii) Graph the actual spread au _ series and the dynamic forecast of the spread series i.e. spread auf _ on the same graph for the period 2018m01 to 2020m02. Comment on the graph. (Hint: Click on Quick/Sample and change the sample to 2018m01 2020m02. Then click on Object/New Object/Group and OK. In the list of series box, type spread au _ and spread auf _ and click O.K. Then click on View/Graph to graph both series together). (3 marks)
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