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## financial modelling essay assignment

Order ID# 45178248544XXTG457Plagiarism Level: 0-0.5%Writer Classification: PhD competentStyle: APA/MLA/Harvard/ChicagoDelivery: Minimum 3 HoursRevision: PermittedSources: 4-6Course Level: Masters/University CollegeGuarantee Status: 96-99%

InstructionsThe 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 different results.

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.

Part A

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) ?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) ?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) ?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) ?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) ?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.

[20 marks]

Part C

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

forecast.

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

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),

The AR(p) plus 4 lags of idot with forecast pdotf2:

The AR(p) plus 4 lags of udot with forecast pdotf3:

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.

Part A

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.

[12 marks]

Part B

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.

[12 marks]

Part C

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 than another.

[16 marks] [Total 40 marks]

RUBRIC

Excellent Quality95-100%

Introduction45-41 points

The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.

Literature Support91-84 points

The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.

Methodology58-53 points

Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.

Average Score50-85%

40-38 points

More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.

83-76 points

Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.

52-49 points

Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.

Poor Quality0-45%

37-1 points

The background and/or significance are missing. No search history information is provided.

75-1 points

Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.

48-1 points

There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met

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