Financial Econometrics (EF5070) 2023/2024 Semester A Assignment 2
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Financial Econometrics (EF5070) 2023/2024 Semester A
Assignment 2
• 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.
• 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 2). The deadline for uploading your solution is 25 October, 2023 (Wednesday), 11:59 p.m.
The file HSTRI.txt contains the Hang Seng Total Return Index (which is the major stock market indexof 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.
• Do you find evidence of autocorrelation in then.a.c.c. net returns?
• Do you find evidence of ARCH effects in the n.a.c.c. net returns?
• Fit an appropriate ARMA-GARCH model to the n.a.c.c. net returns with conditionally Gaussian shocks. Carefully check the model residuals for autocorrelation and ARCH effects.
• Extend your fitted ARMA-GARCH model into an ARMA-GARCH-M model by including the conditional variance itself in the mean equation. Is the risk premium statistically significantly different from zero? Is its sign in accordance with economic intuition (i.e., with the concept of ’’risk aversion’’)?
• Fit an appropriate ARMA-EGARCH model to the n.a.c.c. net returns, where the shocks conditionally follow a Gaussian distribution. Is the leverage effect statistically significant?
• Now, instead of an EGARCH, fit an appropriate TGARCH model to the n.a.c.c. net returns, where the shocks conditionally follow a Gaussian distribution. Is the leverage effect statistically significant in this model? Is the sign of the leverage coefficient in accordance with the stylized fact that negative shocks tend to increase the volatility more than positive shocks of the same magnitude?
• The file HSTRIsummer.txt contains a dummy variable for each trading day in the Hong Kong Stock Exchange from 3 January, 1990 to 22 September, 2023. This dummy variable takes the value of one if the trading day is during the summer, and zero otherwise. Using an appropriate ARMA-GARCH model with conditionally Gaussian shocks, test whether the conditional volatility of the n.a.c.c. daily net return is higher during summers than during non-summer periods.
• The file HSBC.txt contains the closing prices of the HSBC stock in the Hong Kong Stock Exchange from 3 January, 1990 to 22 September, 2023.1
o Calculate the daily n.a.c.c. net returns of the HSBC stock, and fit an appropriate ARMA-GARCH model to these daily returns.
o Then, using your fitted model, obtain the conditional variances of the daily n.a.c.c. net returns of the HSBC stock for each day.
o Fit an appropriate ARMA-GARCH model to the daily n.a.c.c. net return of the Hang Seng Total Return Index such that you use the conditional variance of the HSBC stock return obtained in the previous point as an external regressor in the volatility equation. Can the conditional variance of the HSBC stock return help explain the conditional variance of the Hang Seng Total Return Index return? Is the sign of the corresponding coefficient in accordance with economic intuition?
• Consider the daily n.a.c.c. net returns of the Hang Seng Total Return Index.
o Convert these daily n.a.c.c. net returns into monthly n.a.c.c. net returns. Fit an appropriate ARMA-GARCH model to these monthly returns.
o Using the daily n.a.c.c. net returns, calculate the realized variances of the monthly n.a.c.c. net returns.2
o Plot the calculated realized volatilities (i.e., the square roots of the realized variances). In a consistent figure, also plot the volatilities of the monthly n.a.c.c. net returns which you fitted via your ARMA-GARCH model. Compare the two conditional volatility series.
2023-10-25