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FINANCIAL ECONOMETRICS
PRACTICAL WORK 3
This is group work. Groups of three or four are permitted.
Groups with less than three or more than four are not permitted.
All solutions must be submitted by the due date and time.
Do not write the names of members of your group on your submission.
Groups should answer all questions.
Required Submission
Your group will be assessed based on:
• A set of up to content 10 pages, and
• A 10 minute video presentation.
Recommendation
The recommendation is to write a 3–5 page technical report to answer problem 1. Use the remaining page count to answer problem 2 as a slide presentation.
Written Submission
You may submit either:
• One pdf document with both the technical report and the presentation, or
• Two pdf documents.
Presentation
You do not need to present the technical report, only the teaching material in problem 2.
Assessment
Each problem carries 50% weight towards the overall mark.
Problem 1
1. Complete these setup steps. They do not need to be reported as part of your submission:
(a) Download daily returns on the US Value-weighted-market from Ken French’s site. Use returns from July 1, 1963.
(b) Reconstruct the “as-if” price series for the VWM assuming the initial price, P0 = 1. Hint: Use numpy.cumprod.
(c) Construct monthly RV time series by squaring the daily log return series (computed using the “as-if” price series from the previous step) and summing up within a month. Hint: If you set a
DatetimeIndex, you can use resample.
(d) Get the count of the number of days in the month.
(e) Using the “as-if” VWM price, compute end-of-month returns using the log-difference.
2. Using at most the first 50% of the observations, build:
(a) An ARCH-family (ARCH, GARCH, TARCH, GJR-GARCH, EGARCH) model for end-of-month returns. Hint: arch.arch_model(...) simplified specifying the models needed for this assign ment.
(b) An ARCH-family (technically a Multiplicative Error Model) model for monthly RV. Hint: Use the transformation highlighted in the lectures to transform RV to a pseudo return that can be used with an ARCH-family model.
(c) A HAR-type model for monthly RV (decide whether you wish to log or not, as well as the specifi cation of the lags included)
You should also decide whether you want to use an expanding or a rolling scheme to update parameters when making forecasts. Explain how you ended up with the specifications chosen and the estimation scheme used.
3. Assess the objective and relative accuracy of the models using the second half of the data following best practices. Use both the monthly RV and the end-of-month returns as proxies for volatility. For simplicity, retain the same specifications selected in the previous step. Provide a justification for the choices you make in the assessment.
4. Which method works best when volatility is high? Which works best when it is low? You should specify how you choose your volatility regimes. Keep in mind that any information you use to identify the regime for an observation must be in-sample when making the prediction.
5. Draw conclusions and summarize what your team found.
Problem 2
Research the Du and Escanciano (2017) (SSRN Link) test for Expected Shortfall. Prepare a set of teaching slides and presentation where you explain the test to your peers – that is, students who have taken the Hilary Term financial econometrics course and have understood the material presented in class. There are many approaches to this problem and a fully successful presentation will leave the viewer feeling like they really understand the method. When considering approaches, think about what helped you understand new concepts. The slides submitted for this part of the assignment should be appropriate for teaching in a large lecture setting (like the MFE).
References
Du, Zaichao and Juan Carlos Escanciano (2017). “Backtesting Expected Shortfall: Accounting for Tail Risk”.
In: Management Science 63 (4), pp. 940–958. URL: https://pubsonline.informs.org/doi/ 10.1287/mnsc.2015.2342.