Problem 4. (Hull 13.17) Values for the NASDAQ Composite index during the 1,500 days preceding March 10, 2006, can be downloaded from the authors website. Calculate the one-day 99% VaR, and one-day 99% ES on March 10, 2006, for a $10 million portfolio invested in the index using:

(a) The basic historical simulation approach.

(b) The exponential weighting scheme in Section 13.3.1 with = 0.995.

c) The volatility-scaling procedures in Sections 13.3.2 and 13.3.3 with = 0.94 (assume that the inital variance when EWMA is applied is the sample variance).

(d) Extreme value theory with u = 300 and equal weightings.

(e) A model where daily returns are assumed to be normally distributed with mean zero (use both an equally weighted approach and the EWMA approach with = 0.94 to estimate the standard deviation of daily returns.).

Discuss the reasons for the differences between the results you get.