Financial Econometrics (EF5070)
Financial Econometrics (EF5070) 2023/2024 Semester A Assignment 4
• The assignment is to be done individually.
• Your solution should consist of one single pdf file and one single R file.
• Clearly state your name, SIS ID, and the course name on the cover page of your pdf file.
• In your pdf file, indicate how you solved each problem and show intermediate steps. It
is advised to show numerical results in the form of small tables. Make your R code easy- to-read. Use explanatory comments (after a # character) in your R file if necessary. Overly lengthy solutions will receive low marks.
• You need to upload your solution (i.e., the one pdf file and the one R file) on the Canvas page of the course (Assignments → Assignment 4). The deadline for uploading your solution is 13 December, 2023 (Wednesday), 11:59 p.m.
Financial Econometrics (EF5070) Dr. Ferenc Horvath
The file HSTRI.txt contains the Hang Seng Total Return Index (which is the major stock market index of the Hong Kong Stock Exchange) values from 3 January, 1990 to 22 September, 2023.
• Calculate the daily non-annualized continuously-compounded (n.a.c.c.) net returns.
• Consider a portfolio of $1,000,000 invested in the Hang Seng Total Return Index at the end of 22 September, 2023. From the perspective of 22 September, 2023, calculate the 1-day and 30-day 95%, 99%, and 99.9% Value at Risks and Expected Shortfalls using the approaches below. (I.e., you need to calculate 6 VaR and 6 ES values with each
approach.)
o The RiskMetrics method. (Note: on Slide 8/14 of Week 11, the ���������1−��� in the
ES formula is the Value at Risk of a standard normal distribution, not of the portfolio value or of the portfolio return. E.g., ���������0.95 ≈ 1.644854 in that formula.)
o AnARMA-GARCHmodelwithStudent-tdistribution.
▪ You do not have to consider potential seasonality effects.
▪ Hint: to calculate the 1-day VaR and ES, you need to simulate returns for
the next period using your fitted model. Then, the VaR can be obtained as the empirical quantile. The ES can be obtained as the mean of the simulated values which are lower than the VaR. (You can convert the simulated values into a vector using the as.vector function, then arrange them in ascending order using the sort function, then you can take the mean of the first some elements.) The 15-day VaR and ES can be calculated similarly, but you need to simulate the n.a.c.c. returns for the next 15 periods and sum up these 15 returns for each simulated outcome.
o Thesamplequantile(fortheVaR)andthesampleconditionalmean(fortheES). Note: with this approach, you need to calculate only the 1-day VaR and 1-day ES values. I.e., you do not need to calculate the 30-day VaR and 30-day ES values.
