N1577
Principles of Banking
Seminar 4
GAP and DGAP analyses
Exercise 1
Consider a bank that accepts a 18-month $30,000 Certificate of Deposit and invests the funds in a $30,000 6-month T-Bill .
a) What is the bank’s 6-month GAP?
b) Calculate the change in NII if interest rates increase by 1 percentage point.
Exercise 2
If rate-sensitive assets equal £100 million and rate-sensitive liabilities equals £80 million, what is the expected change in net interest income if rates increase by 1 percentage point (Assume a parallel shift in the yield curve)?
Exercise 3
a) Consider the following bank balance sheet. Calculate NII, Earning Assets, NIM and GAP.
|
Balance Sheet
|
|
|
Assets
|
Yield
|
|
Liabilities
|
Cost
|
|
Rate sensitive
|
$
|
600
|
8.0%
|
|
$ 450
|
4.0%
|
|
Fixed rate
|
$
|
250
|
11.0%
|
|
$ 370
|
6.0%
|
|
Non earning
|
$
|
150
|
|
|
$ 100
|
|
|
|
|
|
|
|
$ 920
|
|
|
|
|
|
|
|
Equity
|
|
|
|
|
|
|
|
$ 80
|
|
|
Total
|
$
|
1,000
|
|
|
$ 1,000
|
|
For the following questions, also calculate NII, Earning Assets, NIM and GAP. Make necessary assumptions where appropriate.
b) What if interest rates increase by 1 percentage point?
c) What if interest rates decrease by 1 percentage point?
d) What if interest rates rise and at the same time the spread falls by 1 percentage point?
e) What if the bank proportionately doubles in size?
Exercise 4
You are provided with the following balance sheet of a bank:
|
Assets
|
Market Value
|
Rate
|
Duration
|
Liabilities & Equity
|
Market Value
|
Rate
|
Duration
|
|
Cash
|
£200
|
0%
|
0
|
Time Deposit
|
£1,100
|
3%
|
1
|
|
Treasury Bond
|
£600
|
5%
|
2.86
|
Certificates of Deposit (CD)
|
£700
|
5%
|
3.72
|
|
Commercial Loan
|
£1,200
|
11%
|
4.70
|
Equity
|
???
|
|
|
a. What is the bank’s Economic Value of Equity (EVE)?
b. Calculate the Interest Income from Assets.
c. Calculate the Interest Expense on Liabilities.
d. Calculate the value of the Net Interest Income.
e. Calculate the weighted duration of the assets?
f. Calculate the weighted duration of the liabilities?
g. Calculate the Duration GAP.
h. Based on the bank’s duration GAP, provide the possible strategies to reduce interest rate risk.
Exercise 5
Conduct duration GAP analysis using the following information:
|
Assets
|
Amount
|
Rate
|
Macaulay’s Duration (years)
|
|
Cash
|
£23,000
|
0%
|
0
|
|
Bonds
|
£102,000
|
7.2%
|
1.8
|
|
Commercial Loans
|
£375,000
|
11.0%
|
1.5
|
|
|
|
|
|
|
Liabilities & Equity
|
Amount
|
Rate
|
Macaulay’s Duration (years)
|
|
Small time deposits
|
£130,000
|
3.6%
|
4.0
|
|
Large CDs
|
£70,000
|
6.3%
|
1.0
|
|
Transaction accounts
|
£250,000
|
2.8%
|
3.3
|
|
Equity
|
£50,000
|
|
|
a. Calculate the bank’s duration GAP. Is this bank positioned to gain or lose if interest rates rise? What would be the change in EVE if all market interest rates fall by an average of 1.5 percentage points?
b. Provide a specific transaction that the bank could implement to immunise its interest rate risk. The transaction may be a new asset funded by a new liability or an asset sale and a simultaneous purchase of another asset.