LOOP GAP Bank, Inc. ($000)

ASSETS LIABILITIES/EQUITY ACCOUNT

Treasury Bills $90 Time Deposits $1,100

Treasury Notes $55 Short-term borrowings $230

Treasury Bonds $176 Demand Deposits $2,500

Loans $4,679 Equity $1,170

Notes: All Treasury bills have three months until maturity (hint: what is the duration of a zero coupon instrument such as this three-month Treasury bill). The Treasury notes portion of The Loop GAP Bank securities portfolio consists of 2-year bonds paying an annual coupon of 8 percent and selling at par (hint: dont worry about semi-annual compounding). Treasury 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 a one year duration, short-term borrowings have a 0.005 year duration, and demand deposits a zero year duration.

a. (Worth 5 points) What is the duration of the bank's Treasury notes?

b. (Worth 5 points) What is the duration of the bank's Treasury portfolio?

c. (Worth 10 points) What is the bank's duration gap?

d. (Worth 5 points) 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. (Worth 5 points) How much D_L must change to make the duration GAP =0?