Values for the NASDAQ composite index during the 1,500 days preceding March 10, 2006, can be downloaded from the author’s website. Calculate the one-day 99% VaR 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 14.3 with  = 0.995.

(c) The volatility-updating procedure in Section 14.3 with  = 0.94. (Assume that the volatility is initially equal to the standard deviation of daily returns calculated from the whole sample.)

(d) Extreme value theory with u = 300.

(e) A model where daily returns are assumed to be normally distributed. (Use both an equally weighted 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.

AppendixLO1