Use the data provided for a bank to answer the questions.

Assets (in millions)		Liabilities and Equity (in millions)
Cash	$ 30	Core deposits	$ 20
Federal funds	20	Federal funds	50
Loans (floating)	105	Euro CDs	130
Loans (fixed)	65	Equity	20
Total assets	$ 220	Total liabilities and equity	$ 220

•Assume that the fed funds rate is 8.5 percent. Variable-rate loans are priced at 4 percent over LIBOR (currently at 11 percent). Fixed-rate loans are selling at par and have five-year maturities with 12 percent interest paid annually. Assume that fixed rate loans are non-amortizing. Core deposits are all fixed rate for two years at 8 percent paid annually. Euro CDs currently yield 9 percent.

a. What is the duration of the fixed-rate loan portfolio if the loans are priced at par?
b. If the average duration of the floating-rate loans (including fed fund assets) is 0.36 year, what is the duration of the bank’s assets? (Note that the duration of cash is zero.)
c. What is the duration of the core deposits if they are priced at par?
d. If the duration of Euro CDs and fed fund liabilities is 0.401 year, what is the duration of the bank’s liabilities?
e-1. What is the bank’s duration gap?
e-2. What is the expected change in equity value if all yields increase by 100 basis points?
e-3. Given the equity change in e-2, what is the expected new market value of equity after the interest rate change?