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Measuring Interest Rate Risk
Static Gap Analysis
• Calculate the gap between rate sensitive assets
and rate sensitive liabilities over a given horizon
(i.e. 0-90 days, 1 year)
• Assets or Liabilities are rate sensitive if:
– It is an interest paying demand deposit.
– It matures within the horizon or there is partial or
interim principal payment
– Interest Rate changes by contractual terms
– Interest Rate changes according to some base rate
Static GAP
• Difference between dollar value of risk
sensitive assets and risk sensitive
liabilities within some time bucket.
• Cumulative GAP measures the GAP for a
time horizon of today until the end of some
date.
• Cumulative GAP measures the effect of a
permanent change in interest rates on
income over that horizon.
∆NII = GAP*∆i
Example
Assets Yield Liabilities Yield
Rate Sensitive 500 8.00% 600 4.00%
Fixed Rate 350 11.00% 220 6.00%
Nonearning 150 100
/Nonpaying Equity
80
1000 1000
GAP -100
NII 41.3
NIM 4.86%
Assets Yield Liabilities Yield
Rate Sensitive 500 9.00% 600 5.00%
∆NII = Fixed Rate 350 11.00% 220 6.00%
GAP*∆I Nonearning/ 150 100
Nonpaying Equity
80
=-100*.01 1000 1000
GAP -100
=1 NII 40.3
NIM 4.74%
Steps for GAP Analysis
• Make Interest Rate Forecast
• Select a series of Time Buckets – Specific
periods of time in the future
• Allocate all rate sensitive assets and
liabilities into time buckets
• Calculate periodic GAP and cumulative
GAP for each time bucket.
• Calculate effect of change in interest rate
on net income.
Rate sensitivity reports
…classifies a bank’s assets and liabilities into time
intervals according to the minimum number of
days until each instrument can be repriced.
Hang Seng Bank 2005
Less than 3-6 Months6Months- More than Nonearning/ Trading
Assets 3 months 1 Year 1 Year Nonpaying Book Total
Cash& Short-term Funds 56807 3505 5539 2347 68198
Placings w/ Banks 11211 3101 1919 16231
CD's Held 20539 2366 4318 6348 19 33590
Investment Securities 63977 7027 11253 53821 1947 1866 139891
Advances to Customers 222916 14781 6182 5349 2546 99 251873
Other Assets 1857 896 97 313 33984 1695 38842
Total Assets 377307 28171 27274 65831 44016 6026 548625
Liabilities & Equity
Deposit Accounts 417652 5617 3242 7476 29429 463416
Deposts from Banks 8018 514 99 8631
Other Liabilities 3446 18 21954 7123 32541
Minority Interests 852 852
Shareholders Funds 43185 43185
Internal Funding of the Trading Book 1196 -1196 0
Total Liabilites 430312 5635 3242 7476 95934 6026 548625
GAP -53005 22536 24032 58355 -51918
Cumulative GAP -53005 -30469 -6437 51918 0
Weakness of GAP
• Cannot capture interest rate risk within buckets.
• Focuses on small interest rate changes in short-
run.
• May be changes in spreads between different
base rates and asset/liability rates.
• Does not allow composition of assets and
liabilities to change
– Non-interest paying liabilities may disappear if rates
rise.
– Debtors typically have an option to repay funds early.
Earnings Sensitivity Analysis
• Forecast different interest rate scenarios.
• Forecast changes in volume and
composition effects of interest rate
scenarios.
Cumulative Gap only measures interest risk if
changes in interest rate have even effects across
assets and liabilities
• Because interest rates changes may be temporary, they may affect of
the shape of the yield curve. If rate sensitive assets and liabilities
have different maturity structures, cumulative gap may not
• Consider the case where short-term interest rates go up by 2% for 6
months and return to previous level for subsequent 6 months.
Assets Yield Liabilities Yield
Rate Sensitive 500 600
Demand 200 9.00% 600 5.00%
6 Months 300 8.00%
Fixed Rate 350 11.00% 220 6.00%
Nonearning/ 150 100
Nonpaying Equity
80
1500 1600
GAP -100
NII 37.3
NIM 2.76%
Managing the GAP
• Calculate periodic GAPs and match rate
sensitive assets and liabilities at certain
intervals.
• Match long-term assets with non-bearing
liabilities
• Use off-balance sheet transactions to
hedge interest risk.
Present Value of a Stream of Income is
equal to the sum of the present value of
each component
• Examples
1. Coupon Bond C C C C FACE
PRICE ....
C BOND (1 y ) (1 y ) 2 (1 y )3 (1 y)T (1 y)T
2. Fixed Payment Loan
PAY PAY PAY PAY
....
(1 y ) (1 y ) (1 y )
2 3
(1 y )T
3. General
T
Xt
PVt
1 y
t
t 1
Changes in interest rates, change in
bond prices
• Bond prices are inverse to interest rates
which determine bond yields. A rise in
interest rates reduces bond prices. A fall in
interest rates increases bond prices.
• % effect of a permanent change in interest
rates results in a change in price/present
value proportional to T.
1 Par
log(1 y ) log( )
T P0
y 1
log P0
1 y T
How does a change in the discount
factor affect present value?
PV T 1
Xt yt
y 1 y t
t 1
T
Xt 1
t
1 y 1 y
t
t 1
PV T PVX t y Xt
t PVX t
PV t 1 PV 1 y
1 y
t
T PVX t
duration t
A way to measure the maturity structure of t 1 PV
an income stream is to calculate what PV
PV duration
percentage of the present value of an y
income stream comes from different 1 y
maturity dates
Duration also
To sum up this measure, calculate a measures the
weighted sum of the years until final sensitivity of the
maturity using these percentages as income stream to
weights. changes in the interest
This measure is called DURATION of the rate.
income stream.
Duration Gap
• Market Value of equity should be the gap
between the present value of assets and
the present value of liabilities
NWMV = APV – LPV
NW A L A L L
NW A L
A A A A L A
• Use the duration of assets to calculate the
y
effect of a change in interest rates 1 y
NW L
duration A duration L DGAP
A A
Immunization
• Banks may deal with interest rate risk by
structuring assets and liabilities so as to
close the duration gap as much as
possible.
• Firms conduct simulation series to
calculate the effect of different interest rate
scenarios on balance sheets.
