# Commercial Bank Management

1. The balance sheet of XYZ Bank appears below. All figures in millions of US Dollars.

a. Calculate total one-year rate-sensitive assets.

b. Calculate total one-year rate-sensitive liabilities.

c. Calculate one-year repricing GAP for the bank.

d. Suppose that interest rates rise by 2 percent on both RSAs and RSLs. What would be the

expected annual change in net interest income of the bank?

2. A government bond currently carries a yield to maturity of 6 percent and a market price of

$1,168.49. If the bond promises to pay $100 in interest annually for five years, what is its current

duration?

3. Suppose that you purchase a bond that matures in five years and pays a 13.76% coupon rate

annually. The bond is priced to yield 10%. What’s the duration?

4. A $1,000 par value bond with five years left to maturity pays an interest payment semiannually

with a 6% coupon rate and is priced to have a 5% yield to maturity. If interest rates surprisingly

increase by 0.5%, by how much would the bond’s price change?

5. Suppose that a savings institution has an average asset duration of 2.5 years and an average

liability duration of 3.0 years. If the savings institution holds total assets of $560 million and total

liabilities of $467 million, does it have a significant leverage-adjusted duration gap? If interest

rates rise, what will happen to the value of its net worth?

6. Why do we need to make a convexity adjustment to estimate a bond’s percentage price change

with respect to a given change in interest rates?

7. Blue Moon National Bank holds assets and liabilities whose average durations and dollar

amounts are as shown in this table:

Asset and Liability Items

Avg. Duration

(years)

Dollar Amount

(millions)

Investment Grade Bonds 15.00 $65.00

Commercial Loans 3.00 $400.00

Consumer Loan 7.00 $250.00

Deposits 1.25 $600.00

Nondeposit Borrowings 0.50 $50.00

a. What is the weighted average duration of Blue Moon’s asset portfolio and liability portfolio,

respectively?

b. What is the leverage-adjusted duration gap?

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