Chicago State Bank holds assets and liabilities whose average duration and dollar amount are shown as below:

Asset and Liability Items Avg. Duration Dollar Amount

Cash reserves $0\mathrm{.}0$ yrs$.$ $$40$ mill.

Investment$-$grade bonds $8\mathrm{.}0$ yrs$.$ $$60$ mill.

Commercial loans $3\mathrm{.}6$ yrs$.$ $$320$ mill.

Consumer loans $4\mathrm{.}5$ yrs$.$ $$140$ mill.

Deposits $1\mathrm{.}1$ yrs$.$ $$490$ mill.

Non$-$deposit borrowings $0\mathrm{.}1$ yrs $$20$ mill.

It has equity of $$50$ million.

a$.$ What is the dollar$-$weighted duration of the bank$$s asset portfolio and liability portfolio?

b$.$ What is the leveraged$-$adjusted duration gap?

c$.$ If all interest rates rise by $2$ percent, calculate the impact on the bank's market value of equity using the duration approximation. $($For this part of the question assume that $\backslash$Delta R$/(1+$R$)=+0\mathrm{.}02)$

d$.$ Discuss how the bank$$s risk management manager could restructure its assets to reduce this interest rate risk exposure. Quantify how much it must change the duration of its assets. Using bullet points to identify and discuss shortcomings of this strategy.