Again, consider the position and data of Exercise 1. Apply the POT method to calculate risk measures for the position:

(a) Use threshold 2.5\%. Write down the estimates, including standard error, and compute the corresponding \(\mathrm{VaR}_{0.99}\) and \(\mathrm{ES}_{0.99}\).

(b) Use threshold \(2 \%\). Write down the estimates and their standard errors, obtain the QQ-plot of the data versus exponential quantiles, and compute the corresponding \(\mathrm{VaR}_{0.99}\) and \(\mathrm{ES}_{0.99}\).

(c) Are the risk measures sensitive to the choice of threshold? Why?

Data From Exercise 1:

Consider a long position of \(\$ 1\) million on the Apple stock. To assess the risk of the position, we employ daily returns of the stock from January 2, 2001 to September 30, 2011 for 2704 observations. The daily simple returns are obtained from CRSP and in the file d-aapl-0111.txt. Let the tail probability be \(p=0.01\). Compute the VaR and ES of the position for the next trading day and the next 10 trading days using the following methods: