Bank Management, 5th edition.
Timothy W. Koch and S. Scott MacDonald
Copyright © 2003 by South-Western, a division of Thomson Learning
MANAGING INTEREST
RATE RISK: GAP AND
EARNINGS SENSITIVITY
Chapter 8
Asset and liability management
… managing a bank's entire balance sheet
as a dynamic system of interrelated accounts
and transactions.
 The phrase, asset – liability
management has generally; however,
come to refer to managing interest rate
risk
 Interest
rate risk
… unexpected changes in interest
rates which can significantly alter a
bank’s profitability and market value of
equity.
Asset and liability management
committee (ALCO)
 A bank's asset and liability
management committee (ALCO)
coordinates all policy decisions and
strategies that determine a bank's risk
profit and profit objectives.
 Interest rate risk management is the
primary responsibility of this
committee.
Net interest income or the market value of
stockholders' equity?
 Banks typically focus on either:
 net interest income or
 the market value of stockholders' equity
as a target measure of performance.
 GAP models are commonly associated with net
interest income (margin) targeting.
 Earnings sensitivity analysis or net interest
income simulation, or “what if” forecasting
…provides information regarding how much NII
changes when rates are assumed to increase
or fall by various amounts.
Interest rate risk
 Reinvestment rate risk
... the risk that a bank can not reinvest cash flows
from assets or refinance rolled over or new
liabilities at a certain rate in the future
Cost of funds versus the return on assets
  Funding GAP, impact on NII
 Price Risk
… changes in interest rates will also cause a
change in the value (price) of assets and liabilities
Longer maturity (duration)
  larger change in value for a given change in
interest rates
  Duration GAP, impact on market value of
equity
Funding GAP
… focuses on managing NII in the short run.
 Method
 Group
assets and liabilities into time
"buckets” according to when they
mature or are expected to re-price
 Calculate GAP for each time bucket
 Funding GAPt
= $ Value RSAt - $ Value or RSLt

where t = time bucket; e.g., 0-3 months
Traditional static GAP analysis
…basic steps to static gap analysis
Management develops an interest rate forecast
Management selects a series of “time buckets”
(intervals) for determining when assets and liabilities
are rate-sensitive
3. Group assets and liabilities into time "buckets"
according to when they mature or re-price

The effects of any off-balance sheet positions
(swaps, futures, etc.) are added to the balance
sheet position

Calculate GAP for each time bucket

Funding GAPt = $ Value RSAt - $ Value or RSLt

where t = time bucket; e.g., 0-3 months
4. Management forecasts NII given the interest rate
environment
1.
2.
Rate sensitive assets and liabilities
… those assets and liabilities
management expects to be repriced
within a fixed time interval.
 They include:
 maturing instruments,
 floating and variable rate instruments, and
 any full or partial principal payments.
 A bank's GAP is defined as the difference
between a bank's rate sensitive assets and
rate sensitive liabilities.
 It is a balance sheet figure measured in
dollars for U.S. banks over a specific period
of time.
Factors affecting NII.
 Changes in the level of i-rates.
 NII = (GAP) * (iexp.)
 Note: this assumes a parallel shift in the
yield curve which rarely occurs
 Changes in the slope of the yield curve
or the relationship between asset yields
and liability cost of funds
 Changes in the volume of assets and
liabilities
 Change in the composition of assets and
liabilities
Expected balance sheet for hypothetical bank
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
500
8.0%
600
4.0%
Fixed rate
350
11.0%
220
6.0%
Non earning
150
100
920
Equity
80
Total
1000
1000
NII = (0.08 x 500 + 0.11 x 350) - (0.04 x 600 + 0.06 x 220)
NII = 78.5 - 37.2 = 41.3
NIM = 41.3 / 850 = 4.86%
GAP = 500 - 600 = -100
Factors affecting net interest income
 1)1% increase in the level of all short-term
rates
 2)1% decrease in spread between assets yields
and interest cost (เดิม spread 4%กลายเป็ น 3%)

RSA increase to 8.5%

RSL increase to 5.5%
 3)Proportionate doubling in size.
 4)Increase in RSA’s and decrease in RSL’s

RSA = 540, fixed rate = 310

RSL = 560, fixed rate = 260.
1) 1% increase in short-term rates
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
500
9.0%
600
5.0%
Fixed rate
350
11.0%
220
6.0%
Non earning
150
100
920
Equity
80
Total
1000
1000
NII = (0.09 x 500 + 0.11 x 350) - (0.05 x 600 + 0.06 x 220)
NII = 83.5 - 43.2 = 40.3
NIM = 40.3 / 850 = 4.74%
GAP = 500 - 600 = -100
Changes in NII are directly proportional to
the size of the GAP
 NIIexp = (GAP) * ( iexp)
 The larger is the GAP, the greater is
the dollar change in NII.
 *This applies only in the case of a
parallel shift in the yield curve, which
is rare.
 If
rates do not change by the same
amount, then the GAP may change by
more or less.
2) 1% decrease in spread
… non- parallel shift in the yield curve
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
500
8.5%
600
5.5%
Fixed rate
350
11.0%
220
6.0%
Non earning
150
100
920
Equity
80
Total
1000
1000
NII = (0.085 x 500 + 0.11 x 350) - (0.055 x 600 + 0.06 x 220)
NII = 81 - 46.2 = 34.8
NIM = 34.8 / 850 = 4.09%
GAP = 500 - 600 = -100
3) Proportionate doubling in size
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
1000
8.0%
1200
4.0%
Fixed rate
700
11.0%
440
6.0%
Non earning
300
200
1840
Equity
160
Total
2000
2000
NII = (0.08 x 1000 + 0.11 x 700) - (0.04 x 1200 + 0.06 x 440)
NII = 157 - 74.4 = 82.6
NIM = 82.6 / 1700 = 4.86%
GAP = 1000 - 1200 = -200
4) Increase in RSAs and decrease in RSLs
RSA increase to 540, fixed rate assets to 310;
RSL decrease to 560, fixed rate liabilities to 260.
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
540
8.0%
560
4.0%
Fixed rate
310
11.0%
260
6.0%
Non earning
150
100
920
Equity
80
Total
1000
1000
NII = (0.08 x 540 + 0.11 x 310) - (0.04 x 560 + 0.06 x 260)
NII = 77.3 - 38 = 39.3
NIM = 39.3 / 850 = 4.62%
GAP = 540 - 560 = -20
Positive and negative gap’s
 Positive GAP
…indicates a bank has more rate sensitive
assets than liabilities, and that net interest
income will generally rise (fall) when
interest rates rise (fall).
 Negative GAP
…indicates a bank has more rate sensitive
liabilities than rate sensitive assets, and that
net interest income will generally fall (rise)
when interest rates rise (fall).
Optimal value for a bank’s GAP?
 There is no general optimal value for a bank's
GAP in all environments.
 GAP is a measure of interest rate risk.
 The best GAP for a bank can be determined
only by evaluating a bank's overall risk and
return profile and objectives.
 Generally, the farther a bank's GAP is from
zero, the greater is the bank's risk.
 Many banks establish GAP policy targets to
control interest rate risk by specifying that
GAP as a fraction of earning assets should be
plus or minus 15%, or the ratio of RSAs to
RSLs should fall between 0.9 and 1.1.
Link between GAP and net interest margin
 Some ALM programs focus on the
GAP or GAP ratio when evaluating
interest rate risk:
GAP Ratio = RSAs / RSLs
 When
the GAP is positive, the GAP
ratio is greater than one.
 A negative GAP, in turn, is consistent
with a GAP ratio less than one.
GAP and potential variability in earnings
 Neither the GAP nor GAP ratio provide direct
information on the potential variability in
earnings when rates change.

The GAP ratio ignores size.
 Example: Consider two banks that have $500
million in total assets.



The first bank has $3 million in RSAs and $2
million in RSLs, its GAP = $1 million and its GAP
ratio = 1.5
The second bank has $300 million in RSAs and
$200 million in RSLs.
 Its GAP equals $100 million, yet it reports the
same 1.5 GAP ratio.
Clearly, the second bank assumes greater interest
rate risk because its net interest income will
change more when interest rates change.
Target NIM and GAP
 A better risk measure relates the absolute value
of a bank’s GAP to earning assets.



The greater is this ratio, the greater the interest
rate risk
The ratio of GAP to earning assets has the
additional advantage in that it can be directly
linked to variations in NIM.
In particular, management can determine a
target value for GAP in light of specific risk
objectives stated terms of a bank’s target NIM:
Target GAP
(Allowable % change in NIM)(Expected NIM)

Earning assets
Expected % change in interest rates
Example:
Consider a bank with $50 million in earning assets that
expects to generate a 5% NIM. The bank will risk changes
in NIM equal to plus or minus 20% during the year, NIM
should fall between 4 and 6%.
 Management expects interest rates to vary up
to 4 percent during the upcoming year
 The bank’s ratio of its 1-year cumulative GAP
(absolute value) to earning assets should not
exceed 25 percent.
Target GAP/Earning assets= (.20)(0.05) / 0.04 = 0.25
 Management’s willingness to allow only a 20
percent variation in NIM sets limits on the GAP
which would be allowed to vary+/- $12.5 million,
based on $50 million in earning assets.
สมมติท่านรักษา GAP ไว้ ที่ 25% คือมี rate sensitive
assets 50 ล้าน และ rate sensitive liabilities 37.5 ล้าน
GAP 12.5 ล้าน (positive gap)
 ท่ านจะสามารถ จากัด การเปลีย่ นแปลงของ NIM ไว้ ทไี่ ม่ เกิน 20% ได้ ตาม
นโยบายที่กาหนด Target NIM 5%-/+20% (4%-6%)
 หาก อัตราดอกเบีย้ ในตลาดเพิม่ ขึน้ 4% (parallel)


NII = GAP * I
= 12.5 * .04 = 0.5 ล้าน
 เดิม คาดว่ าจะได้ NIM 5 % จาก 50 ล้ าน แสดงว่ า NII เดิม เท่ ากับ 2.5
ล้าน (50*.05)
 ดังนั้น การทีด่ อกเบีย้ ขึน้ 4% ทาให้ NII เพิม่ ขึน้ เป็ น 2.5+0.5 = 3 ล้ าน
ซึ่งเมื่อคานวณเป็ น NIM จะได้ 6 % (3/50) นั่นคือ NIM เปลีย่ นแปลง
ตามนโยบาย คือ ไม่ เกิน20%