# Question: Values for the NASDAQ composite index during the 1 500 days

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

(c) The volatility-updating procedures in Section 13.3 with = 0.94. (Assume that the initial 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.

(a) The basic historical simulation approach.

(b) The exponential weighting scheme in Section 13.3 with = 0.995.

(c) The volatility-updating procedures in Section 13.3 with = 0.94. (Assume that the initial 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.

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