Question $1$

Consider a bank whose asset and liability both consist of bonds only. The asset consists of

a $20-$year coupon bond with face value $$120$ million, coupon rate $7\mathrm{.}5\%,$ and its coupons

are paid once per year. The liability consists of a $6-$year zero coupon bond with face value

$$190$ million. The current yield for all these bonds are $6\mathrm{.}5\%.$

$($a$)(5$ marks$)$ What is the bank's current market value of equity $($expressed in million

dollars$)?$

$($b$)(5$ marks$)$ What is the bank's current leverage$-$adjusted modified duration gap?

$($c$)(5$ marks$)$ Assume parallel yield shift. Based on the prediction from the duration

model, how much would the market value of equity change $($expressed in million

dollars$),$ for a $10$ basis points increase in the yield?

$($d$)(5$ marks$)$ Assume parallel yield shift. Based on the prediction from the duration

model, what is the range of the yield change $($expressed in basis points$)$ for which

the market value of equity would become negative?