$1.$ A financial institution has the following assets: $$ A portfolio of $18-$year zero$-$coupon bonds with a face value of $$22$ million and currently yielding $7\mathrm{.}3\%$

$$ A $19$ million trading position in spot euros, with the current exchange rate of $$1\mathrm{.}05/$

$$ A $$14$ million trading position in equities

a$.$ Calculate the daily earnings at risk $($DEAR$)$ for the bonds, assuming a $62$ basis point potential adverse move in yields.

b$.$ Calculate the dollar DEAR for the position in euros, assuming a volatility of the daily percentage changes in the $/$$ of $43$ basis points and $99\%$ confidence that an adverse move will not exceed this amount.

c$.$ Calculate the DEAR for the equity position, assuming the standard deviation of daily returns on the equities is $342$ basis points and $99\%$ confidence that an adverse move will not exceed this amount.

d$.$ Calculate the $9-$day value at risk $($VAR$)$ for $($i$)$ the bonds, $($ii$)$ the euro position and $($iii$)$ the equity position.

e$.$ Calculate the DEAR for a portfolio of these three assets. The correlation coefficients are $0\mathrm{.}24$ for the bonds and the euros, $-0\mathrm{.}29$ for the bonds and the equities, and $0\mathrm{.}43$ for the equities and the euros.