Problem $($Hull $12\mathrm{.}17).$ Values for the NASDAQ Composite index during the $1,500$ days preceding March $31,2022,$ can be downloaded from the author$$s website. Calculate the one$-$day $99\%$ VaR and one$-$day $99\%$ ES on March $31,2022,$ for a $$10$ million portfolio invexted in the index using:

$($a$)$ The The basic historical simulation approach, and

$($b$)$ The exponential weighting scheme in Section $12\mathrm{.}3\mathrm{.}1$ with $\backslash$lambda $=0\mathrm{.}995.$ Discuss the reasons for the differences between the results you get.