Use the following balance sheet information to answer questions a$-$f:

Balance Sheet $($in Million Dollars$)$ and Duration $($in years$)$

Duration Amount

T$-$Bills $0\mathrm{.}590$

T$-$notes $0\mathrm{.}955$

T$-$Bonds X $176$

Loans $7\mathrm{.}02,724$

Deposits $1\mathrm{.}02,092$

Federal funds $0\mathrm{.}01238$

Equity $715$

Notes: Treasury Bonds are five year maturities paying $6\%$ semi$-$annually and selling at par.

Total assets $=90+55+176+2,724=3,045$

Total liability $=2092+238=2,330$

a$.$ What is the duration of the Treasury bonds portfolio? That is calculate $$X$$ in the above balance sheet.

b$.$ What is the average duration of the assets?

c$.$ What is the average duration of the liabilities?

d$.$ What is the bank$$s leverage adjusted duration gap? What is the bank interest rate risk exposure?

e$.$ If the entire yield curve shifted upward by $50$ basis points $($i$.$e$.,$R$/(1+$R$)=0\mathrm{.}0050),$ what is the impact on the bank$$s market value of equity?

f$.$ If the entire yield curve shifted downward by $25$ basis points $($i$.$e$.,$R$/(1+$R$)=-0\mathrm{.}0025),$ what is the impact on the bank$$s market value of equity