A fund owns $$100-$million face amount of a $10-$year zero$-$coupon bond. The current

bond yield is $4\mathrm{.}00\%.$ The change in the bond yield is unknown, but is believed to be

normally distributed with a mean of $0\mathrm{.}0\%$ and a standard deviation of $0\mathrm{.}15\%.$

a$.(4$ points$)$ What is the fund$$s daily Value at Risk at a $95\%$ confidence level?

Assume the fund bought another $$100-$million face amount of a $20-$year zero$-$coupon

bond. The current bond yield is $3\mathrm{.}00\%.$ The change in the bond yield is unknown, but is

believed to be normally distributed with a mean of $0\mathrm{.}0\%$ and a standard deviation of $0\mathrm{.}11\%.$

b$.(6$ points$)$ Assume that the yield changes of these two bonds are independent with

each other. What is the fund$$s daily Value at Risk at a $95\%$ confidence level by

owning a portfolio of these two bonds?