Task $2$: Interest Rate Risk analysis based on the Duration Model

The market value of the assets of Bank COMM equals $$5,000($millions$).$ The composition of these assets $($in market values$)$ is as follows: $2\%$ Treasury bills, $5\%$ Treasury notes, $25\%$ bonds, $65\%$ commercial loans and the rest represents cash. These assets are funded by demand deposits $(70\%),$ equity $(5\%)$ and CDs$.$

Notes:

All Treasury bills have three months until maturity.

One$-$year Treasury notes are priced at par and have a coupon of $4$ percent paid semiannually.

Bonds: you noticed that the price of one bond rose from $$1020\mathrm{.}65$ to $$1030\mathrm{.}23$ when the yield to maturity fell from $6\mathrm{.}75$ percent to $6\mathrm{.}5$ percent.

Commercial loans are at par. The loans have an interest rate of $6$ percent, a maturity of four years, and annual payments of principal and interest that will exactly amortise the loan at maturity. $.$

$1-$year CDs are at par and have an annual foxed rate of $3$ percent.

a$)$ What is the bank's intered rate risk exposure based on the duration model? Show your analysis.

b$)$ What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire vield curve of