Use the following balance sheet (in millions of dollars) for a bank and assume that 20% of fixed-rate mortgages, 10 % of checkable deposits, and 10% of savings deposits are rate-sensitive. Assume all variable-rate mortgages are rate-sensitive. DUR stands for duration.

Assets Liabilities (and capital)

Reserves 15 DUR = 0 Checkable deposits 125 DUR = 1.5

Securities

<1 year 35 DUR = .3 Savings deposits 50 DUR = 2.5

>1 year 70 DUR = 2 CDs

Mortgages < 1 year 70 DUR = .5

Variable-rate 20 DUR = .5 > 1 year 60 DUR = 1.5

Fixed-rate 75 DUR = 4 Borrowings

Commercial loans < 1 year 25 DUR = .25 < 1 year 45 DUR = .8 Capital 20

> 1 year 90 DUR = 1.75

Total assets 350 Total liabilities plus capital 350

Consider assets and liabilities of less than a year to maturity to be rate-sensitive (one-year maturity bucket).

a) Calculate the repricing (funding) gap for a one-year maturity bucket.

b) Calculate the change in net interest income in the first year for a decrease in interest rate from 5% to 4% (be sure to note whether income increases or decreases).

c) Calculate the average duration of assets.

d) Calculate the average duration of liabilities.

e) Calculate the leverage-adjusted duration gap.

f) Calculate the change in net worth (capital) if the interest rate decreases from 5% to 4%?