The balance sheet for Gotbucks Bank, Inc. (GBI), is presented below ($ millions). Cash Federal funds Assets Liabilities and Equity $ 30 Core deposits 20 Federal funds 105 Euro CDs 65 Equity $220 Total liabilities and equity Loans (floating) Loans (fixed) Total assets $ 20 50 130 20 $220 Notes to the balance sheet: The fed funds rate is 8.5 percent, the floating loan rate is LIBOR + 4 per- cent, and currently LIBOR is 11 percent. Fixed-rate loans have five-year maturities, are priced at par, and pay 12 percent annual interest. The principal is repaid at maturity Core deposits are fixed rate for two years at 8 percent paid annually. The principal is repaid at maturity Euros currently yield 9 percent.

a. What is the duration of the fixed-rate loan portfolio of Gotbucks Bank?

b. If the duration of the floating-rate loans and fed funds is 0.36 year, what is the duration of GBI's assets?

c. What is the duration of the core deposits if they are priced at par?

d. If the duration of the Euro CDs and fed funds liabilities is 0.401 year, what is the duration of GBI's liabilities?

e. What is GBI's duration gap? What is its interest rate risk exposure?

f. What is the impact on the market value of equity if the relative change in all interest rates is an increase of 1 percent (100 basis points)? Note that the relative change in interest rates is AR/(1+ R) = 0.01. g. What is the impact on the market value of equity if the relative change in all interest rates is a decrease of 0.5 percent (-50 basis points)? h. What variables are available to GBI to immunize the bank? How much would each variable need to change to get DGAP to equal zero?