CASE STUDY PART 2
1. This is an individual assessment. You MUST produce and submit your own work.
2. Dataset: same company data and sample period as the one you have studied in Case Study
Part1.
3. Submission Deadline: Sun, 26 Nov, 22:00 (Week 11)
4. Total marks: 40.
5. There are two different sections: section 1 (35 marks) is a set of new analytic/computational
questions related to the same data you used in case study part 1, section 2 (5 marks) is reflection
on (group) work/analysis done in Case Study part 1.
6. Attach your Jupiter Notebook (Python) code for section 1 only. There is no need to produce any
additional analysis for reflection section 2.
7. Rules on open book assessment: You have access to all resources to work on the case study
questions. However, any use of external resources MUST be cited and referenced in your
answer paper (any style is fine, you may use Harvard style). This includes any
textbook(s)/journal articles material and any other internet resources. You do not have to
cite course notes/course textbook.
You cannot use someone else’s (any third party) work as your own.
The UNSW rules and policies on Academic Integrity and Plagiarism apply.
8. Show all the necessary derivations of the analytical results. Your discussion and answers
should be to the point.
9. In terms of presentations, keep it tidy and accurate, but there is no need to produce full-
blown business-style report. Number your answers so that it is clear to a marker which
question you answer.
10. Do not include full Python output in the answers. Only report the information required to
answer the specific questions. The Python output should be put at the end as an Appendix
(outside of page limit).
11. I know typing formal math in a text editor may be hard. As an alternative, you may
• use https://snip.mathpix.com/ which helps to convert handwritten math to word/tex
• take a snapshot with your camera and insert your handwritten math in your text
• write on the document (pdf) with a stylus.
Whatever method you decide to use make sure that what you intended is inserted, it looks
reasonably neat and most importantly it is readable.
12. Keep your report up to 6 pages long.
2
Section 1. Analytic/computational questions [35 marks]
In this application you will use daily closing price data on your company together with the
S&P500 index and 13-week (3-month) U.S. Treasury bill over the last 10 years ending on
November 9, 2023.
Note: some companies may have shorter periods of data available, use all available data in this
case.
Transform closing prices to (log)returns×100 (we will refer to them simply as returns).
1. Split your data into in-sample (training) set and out-of-sample (forecast evaluation) set.
Use the last 100 return observations for your forecast evaluation set. Use all remaining
observations for in-sample (training) set. You are given the following 4 models:
(i) Naive (Random walk model for prices with mean zero innovations; no drift)
(ii) AR(1) for your company return
(iii) AR(1)-X: AR(1) for your company return with the lag-1 S&P index return added.
(iv) CAPM model
(a) Report and discuss the parameter estimates (if any) for each of these model
specifications.
(b) Generate (using Python) dynamic h-step-ahead forecasts (h=1..100) for returns for each
observation in the forecast sample conditional on the observations in in-sample set.
Show the plots of forecasts against the out-sample realizations. Assess the accuracy of
these forecasting methods using plots, RMSE. Which model do you prefer and why?
(c) Analytically derive and compute the long-run forecast for each model. Use sample
estimates (on in-sample set) of unconditional mean for exogenous variables (Xs).
Compares these with unconditional samples means of returns (on in-sample) set and
with the 100-th step ahead forecast generated in (b). Explain your findings.
2. Given the AR(1) model for your company asset return series, assume normally distributed
errors and fit the following conditional volatility models: (i) GARCH(1,1), (ii) GJR-
GARCH(1,1) using the in-sample data.
Define conditional volatility as the square root of conditional variance.
(a) Report and comment on the variance equations parameter estimates. Do they satisfy
GARCH parameter restriction? What are usually observed values with GARCH
parameters? Do you observe these values?
(b) Draw the news impact curves (NIC) from the two conditional volatility models above.
Comment on the shapes of the NICs.
(c) Conditional on the in-sample data, generate h-step-ahead forecasts of volatility, for
(h=1..100) the volatility models GARCH(1,1) and GJR-GARCH(1,1).
(d) Conditional on the in-sample data, generate h-step-ahead forecasts of volatility, for
(h=1..100), generate volatility forecast using the AR(1) – exponentially weighted
moving average (EWMA) model with λ = 0.94
(e) Compare the plots of these volatility forecasts and comment.
3
(f) For GARCH(1,1) and GJR-GARCH(1,1) analytically derive and compute the long-run
volatility forecasts and compare these with sample standard deviations of residuals
(from AR(1) model) estimated using in-sample data and 100-th step forecast. What do
you conclude. Can you generate long-term forecast for EWMA model? Why so?
(g) Plot out-of-sample data together with generated AR(1) forecasts with 95%CIs based
on GJR-GARCH(1,1) model volatility estimates. How many actual observations do
you expect to see outside of the CIs? Comment.
(h) Using AR(1)-GJR-GARCH(1,1) model and using empirical distribution of in-sample
standardsed residuals, compute 95% Value-at-Risk (VaR) for the first day of the
forecast evaluation set. Assume that all investments of 10,000$ are in a single share of
the company you analyse. Explain the meaning behind the VaR and how it may be
used by regulators.
3. Conditional volatility is unobservable which makes a direct comparison between forecasted
volatility and actual volatility impossible. GARCH forecasts can be evaluated using
observable proxies for conditional volatility.
(a) Use the absolute values of return for each day in the evaluation set to compute a proxi
for volatility in this day.
(b) Using RMSE assess the accuracy of GARCH(1,1), GJR-GARCH(1,1) and EWMA
model’s forecasts using the volatility proxy. Which models did best overall using this
criterion?
(c) Is there a better proxy for volatility that you could use? If so, describe what it is and
how you would use it? Why can’t you use get the data you need for this proxy with
yfinance?
Section 2. Reflection on group work in Case Study part 1 [5 marks]
1. Looking back on Part 1 what could be improved about your analysis. You do not have to
write equations but be specific. Use bullet points for each point of improvement. There is
always some room for improvement even if have got a perfect score in Part 1.
2. Have you learnt anything new when you worked on this assignment in the group? It can
be anything not even directly related to the course. Use bullet points to answer.
3. Have experienced any issues when working in a group? If so, how have you addressed the
issues? If there were no issues, what in your view made your group work coherent and
collaborative.