Financial Modelling Coursework Project One Schoolwork
Assignment ID Number AFFGEHU83939HD Type of Document Essay Writing Format APA/MLA/Harvard Academic Level Masters/University References/Sources 4 References
The requirements are as follows:
The coursework consists of two parts.
The first section (weight 60%) involves data manipulation, analysis and
The second section (weight 40%) is designed to enable you to demonstrate deeper technical understanding of econometric techniques.
All parts of each section are to be answered.
EViews or other output should not be pasted directly into the coursework. You should
present your results as they would be in academic papers. (Look at some papers sometimes output is in Tables, sometimes as estimated equations with s.e./t stats/p-
values in brackets under the corresponding coefficient, together with appropriate diagnostic statistics and their p-values).
There is a page limit of 14 pages of A4, bearing in mind there will be tables and charts. However, shorter submissions are acceptable. We are looking for clear
presentation and discussion, and short answers are better if they address the right issues, although clear explanations of results are essential. It should be word
processed, double spaced, and written in an appropriately academic style. It should include a full list of references for all articles, books and other sources (e.g. Internet
sites) that have been cited in the body of the text.
Students should ensure that they have fully acknowledged the work of others in the body of the text. Coursework will be subjected to plagiarism detection software.
All coursework is anonymous, so students should ensure that only their registration number is included in the header.
Coursework #1 Financial Modelling
Section 1 (60%)
In this section everyone will be performing the same exercises but we expect you each to choose different samples. We shall be watching to check that everyone has
Everything in the coursework may be done using EViews.
There is no guarantee you will get good results in your particular cases but this is not a problem. We expect you to recognise and comment when results are poor, eg
when nothing forecasts well.
We also expect you to explain what you are doing. Simply presenting results is not enough.
The file PredictorData2016m.xlsx contains data from 1871 to 2016 for stock returns and various predictors, as detailed in Amit Goyal and Ivo Welch (GW) (2008) A
comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies 21(4) 1455-1508 (see
http://www.hec.unil.ch/agoyal/docs/Predictability_RFS.pdf). In Section 1 of their paper they give the data sources and explain the construction of relevant variables used in
order to assess the problem of predictability. GW used data to 2007 but have updated the series and made them available to everyone. They provide data at monthly,
quarterly and annual frequencies but we will only look at their monthly data. Note that not all variables have the same starting dates, but all variables, with the exception of
csp, end in 2016m12.
Take a sample of your own choice that is not the whole data sample available (for example, the post-war period from 1948 to 1980, or the period before WW2, or any other
sample) and construct excess stock returns (stock returns minus the risk-free rate), as this is typically the variable of interest, that is, the return that an investor can achieve
after we remove the return of the safest investment available (typically a short-term bond issued by the US Treasury, called a T-bill).
In order to do that, first take the variable Index (which are stock prices), and convert it to (log) stock returns, ie, log(indext)-log(indext-1) which you should name sr.
(Remember to use natural logs, denoted LN in Excel but LOG in EViews.) Then subtract from variable sr the variable tbl/12 (as the T-bill rates are annual: note that they are
NOT defined as percentages but proportions, eg 0.045 not 4.5%). Call this variable xsr, standing for excess stock return.
1) Present a table of descriptive statistics of xsr, and plot the empirical distribution. Discuss whether this variable fits the usual stylized facts of excess stock returns.
2. 2) Briefly explain what the ACF and PACF are. Plot the ACF and PACF for xsr. Describe what type of ARMA model, if any, you would expect to fit based on a visual
inspection of the autocorrelations.
3. 3) Plot the ACF and PACF of squared returns (xsrsq= xsr*xsr). Comment on and explain the qualitative difference to the results for xsr in (2).
4. 4) Fit AR(p) models for p= 0,1,2,3,4,5,6. Choose an appropriate model based on either the AIC (Akaike) or SBIC (Schwartz). Explain what these criteria do.
5. 5) Givenyouroptimallychosenlag-lengthfrom(4)(callthisoptimallaglengthp*), estimate an AR(p*)-GARCH(1,1) model for stock returns xsr. Explain what the GARCH model
does and discuss the results.
6. 6) Now estimate an AR(p*)-EGARCH(1,1) model. Explain how this differs from the GARCH. Which model do you prefer?
[15 marks] Part B
In this section you will run predictive regressions with cumulated returns xsr(h) and some key predictor variables. The cumulated return xsr(h) is simply the sum of the
returns over h periods. Eg,
xsr(4)t = xsr t+xsr t-1+xsr t-2+xsr t-3
or, which amounts to the same thing,
xsr(4)t+3 = xsr t+xsr t+1+xsr t+2+xsr t+3
Estimate regressions of the form
??????(h)??+h?1 = ?? + ??????,???1 + ????,
where ????,?? is a single (ith) predictor variable, dated t, where h is the forecast horizon (as well as the period over which returns are cumulated). This type of regression is
known as a returns predictability regression.
Among the available variables in the dataset, use the following predictors:
??1,??: Dividend price ratio (defined as log(D12) log(Index) )
??2,??: Earnings price ratio (defined as log(E12) log(Index) )
1) Briefly explain why predictability may be expected from these series.
2) Using your monthly data, run them for each variable for h = 1, 4, 8, 12, 24 and 36 over a common sample of your choice (remember that this is affected by the point at
which the data start AND the value of h) so that all the regressions use exactly the same sample, using a HAC correction of your choice, eg Newey-West. Examine and
discuss the values of ?, their significance and the R2 in each case, explaining and relating this to what is expected in long-horizon predictive regressions.
In this section we will try to forecast US inflation, which is a difficult task to do well. The Excel file unrate_cpi_iprod.xls contains monthly data from 1948 to 2018 on
CPI: Consumer Price Index for All Urban Consumers: All Items, Index 1982- 1984=100, Monthly, Seasonally Adjusted
INDPRO: Industrial Production Index, Index 2012=100, Monthly, Seasonally Adjusted
UNRATE: Civilian Unemployment Rate, Percent, Monthly, Seasonally Adjusted First define monthly inflation as pdot=log(CPI/CPI(-1)). This is what we aim to
Next define the no-change or RW forecast simply pdotfrw = pdot(-1). This will be your benchmark.
Construct the growth rate of INDPRO idot: the growth rate on unemployment udot: and the log of UNRATE lu.
Chose a sample period to estimate the forecasting equations not the whole sample and keep back 36 observations after the sample for evaluation.
1) Then estimate
i. An AR(p) where you choose the order by some criteria (explaining your
choice) with forecast pdotf1:
Then using your chosen value of p from (i),
ii. The AR(p) plus 4 lags of idot with forecast pdotf2:
iii. The AR(p) plus 4 lags of udot with forecast pdotf3:
iv. The AR(p) plus 4 lags of lu with forecast pdotf4
generating the forecasts for each over the forecast evaluation sample. EViews will generate those forecasts for you. Make sure you pick static forecasts to generate the
required one-step ahead results.
Calculate (you can let EViews do this for you) the RMSE for these forecasts and also calculate the RMSE for pdotfrw.
Which is the best forecast? Perform a Diebold Mariano test against the RW benchmark. Explain what the DM test does.
2) Now calculate the simple average of the forecast. Why might this be a good idea? How does it compare to the other forecasts?
3) Now for each of the three models (ii), (iii) and (iv) create in-sample forecasts and save them as pdotf2is, pdotf3is and pdotf4is. Perform an in-sample Bates- Granger
regression and use the estimated coefficients as weights in an average of the forecast evaluation period forecasts pdotf2, pdotf3 and pdotf4 resulting in
pdotfbg. Explain what the Bates-Granger regression does. Evaluate the RMSE of pdotfbg and comment.
[25 marks] [Total 60 marks]
Section 2 (40%)
In this section you have an opportunity to demonstrate technical ability and understanding.
Carefully explain why low-order ARCH models may fail to capture time series properties of returns volatility, and how GARCH models can succeed at this using a small
number of parameters.
Tests for market efficiency are often constructed on the basis that prices have a unit root. Explain what justifies this, and show in detail how this can be operationalised
using portmanteau autocorrelation tests and the variance ratio.
Explain how to generate a probability density forecast. Explain how you may evaluate such a forecast. Explain how you may test the hypothesis that one forecast is better
[16 marks] [Total 40 marks]
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. 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