LOOP Gap Bank, Inc. ($000)

ASSETSLIABILITIES/EQUITY ACCOUNT

Government Bills $90Time Deposits$1,100

Government Notes $55Short-term borrowings$230

Government Bonds$176Demand Deposits$2,500

Loans$4,679Equity$1,170

Notes:All Government bills have three months until maturity.The Government notes portion of The Chicago GAP Bank securities portfolio consists of 2-year bonds paying an annual coupon of 8 percent and selling at par (hint: don't worry about semi-annual compounding). Government bond portion of the securities portfolio has a duration of 4.5 years and the loan portfolio has a duration of 7 years.Time deposits have an one year duration, short-term borrowings have a 0.005 year duration, and demand deposits a zero year duration.

a. What is the duration of the bank's Government note portfolio?

b. What is the duration of the bank's Government portfolio?

c. What is the bank's duration gap?

d. If all interest rates fall 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 R/(1+R) = -.02)

e. How much D_L must change to make the duration GAP =0?