1. finance
2. bank
3. bank account

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
Interest rate risk
…the potential variability in a bank's net
interest income and market value of equity due
to changes in the level of market interest rates.
Example:
$10,000 Car loan
4 year Car loan at
8.5%
1 year CD at
4.5%
Spread
4.0%
But for How long?
Funding GAP
GAP = $RSA - $RSL,
where $RSA = $ amount of assets which will
mature or reprice in a give period of time.
In this example:
GAP1y = $0.00 - $10,000 = - $10,000
This is a negative GAP.
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.
What determines rate sensitivity?
 In general, an asset or liability is normally
classified as rate-sensitive with a time
frame if:
1.
2.
3.
4.
It matures
It represents and interim, or partial, principal
payment
The interest rate applied to outstanding
principal changes contractually during the
interval
The outstanding principal can be repriced
when some base rate of index changes and
management expects the base rate / index to
change during the interval
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% increase in the level of all short-term rates
 1% decrease in spread between assets yields
and interest cost

RSA increase to 8.5%

RSL increase to 5.5%
 Proportionate doubling in size.
 Increase in RSA’s and decrease in RSL’s

RSA = 540, fixed rate = 310

RSL = 560, fixed rate = 260.
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.
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
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
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
Rate volume, and mix analysis
 Many banks publish a summary of how
net interest income has changed over
time.
 They separate changes over time to
shifts in assets and liability composition
and volume from changes associated
with movements in interest rates.
 The purpose is to assess what factors
influence shifts in net interest income
over time.
2001 Compared to 2000
Change Due to *
Yield/
Net
Rate Change
Volume
Rate/Volume Analysis For Synovus Bank
Interest earned on:
Taxable loans, net
Tax-exempt loans, net t
Taxable investment securities
Tax-exempt investment securities t
Interest earning deposits with
Federal funds sold
Mortgage loans held for sale
Total interest income
Interest paid on:
Interest bearing demand deposits
Money market accounts
Savings deposits
Time deposits
Federal funds purchased and
Other borrowed funds
Total interest expense
Net interest income
$ 149,423 -117,147
1,373
-586
32,276
787
161,222
1,108
36,390
-450
197,612
658
-916
74
-6,229
2,622
4,507
2,026
2,570
-206
7,077
1,820
223
-176
406
-1,745
7,801
-1,680
156,461 -122,176
47
-1,339
6,121
34,285
28
1,447
-113
170,225
48
1,410
549
40,311
76
2,857
436
210,536
6,074 -12,517
21,380 -36,244
-369
-3,307
32,015 -22,545
-6,165 -29,744
21,318
-4,272
74,253 -108,629
$82,208 ($13,547)
-6,443
-14,864
-3,676
9,470
-35,909
17,046
-34,376
$68,661
1,537
5,433
4,654
13,888
-660
-67
38,824
32,812
23,148
15,870
21,960
3,361
89,463
71,297
$80,762 ($30,986)
6,970
18,542
-727
71,636
39,018
25,321
160,760
$49,776
-5,313
2,548
$
2000 Compared to 1999
Change Due to *
Yield/
Net
Rate Change
Volume
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.
 A rate sensitivity report shows GAP values
on a periodic and cumulative basis for each
time interval.

Periodic GAP
… measures the timing of potential income
effects from interest rate changes


Gap for each time bucket
Cumulative GAP
… measures aggregate interest rate risk over
the entire period

Sum of periodic GAP's
Rate sensitivity analysis for security bank
MM Inv
Municipals
FF & Repo's
Comm loans
Install loans
Cash
Other assets
Total Assets
5.0
1.0
0.3
6.3
Liabilities and Equity
MMDA
Super NOW
2.2
CD's < 100,000
0.9
CD's > 100,000
1.9
FF purchased
NOW
Savings
DD
Other liabilities
Equity
Total Liab & Eq.
5.0
GAP
Periodic GAP
1.3
Cumulative GAP
1.3
13.8
0.5
15.0
1.2
0.7
1.8
1.0
2.2
7.6
2.9
1.6
4.7
1.3
4.6
1.9
15.5
8.2
10.0
5.0
12.3
2.0
4.0
5.1
12.9
10.0
6.9
7.9
9.0
1.8
1.2
35.0
9.0
5.7
14.7
3.0
11.5
5.0
42.5
13.8
9.0
5.7
100.0
13.5
1.0
7.0
21.5
17.3
2.2
19.6
27.9
9.6
1.9
13.5
1.0
7.0
100.0
2.9
9.6
1.9
11.0
30.3
24.4
3.0
4.8
4.0
5.3
-20.3
-15.0
-14.4
-29.4
6.0
-23.4
30.2
6.8
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.
Speculating on the GAP.
NII = (GAP) * ( iexp)
 Many bank managers attempt to adjust the
interest rate risk exposure of a bank in
anticipation of changes in interest rates.

This activity is speculative because it assumes
that management can forecast rates better than
forward rates embedded in the yield curve.
 Speculating on the GAP
 Difficult to vary the GAP and win – requires
accurate interest rate forecast on a consistent
basis.
 Usually only look short term.
 Only limited flexibility in adjusting the GAP,
customers and depositors.
 No adjustment for timing of cash flows or
dynamics of the changing GAP position.
Advantages / disadvantages of GAP
 The primary advantage of GAP analysis
is its simplicity.
 The primary weakness is that it ignores
the time value of money.
 GAP further ignores the impact of
embedded options.
 For this reason, most banks conduct
earnings sensitivity analysis, or pro
forma analysis, to project earnings and
the variation in earnings under different
interest rate environments.
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 million.
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 from $12.5
million to $12.5 million, based on $50 million in
earning assets.
Earnings sensitivity analysis
…allows management to incorporate the
impact of different spreads between asset
yields and liability interest costs when rates
change by different amounts.
 Shifts in the yield curve are rarely
parallel!
 It is well recognized that banks are
quick to increase base loan rates but
are slow to lower base loan rates when
rates fall.
Exercise of embedded options in
assets and liabilities
 Customers have different types of
options, both explicit and implicit:
 Option
to refinance a loan
 Call option on a federal agency bond
the bank owns
 Depositors option to withdraw funds
prior to maturity
Interest rate risk and embedded options
…our previous example
Example:
$10,000 Car loan
4 year Car loan at
8.5%
1 year CD at
4.5%
Spread
4.0%
But for How long?
Funding GAP
GAP = $RSA - $RSL,
where $RSA = $ amount of assets which will
mature or reprice in a give period of time.
In this example:
GAP1y = $0.00 - $10,000 = - $10,000
This is a negative GAP.
Implied options:
10,000 4yr loan, financed by a 1 yr CD
 In the previous example, what if rates increased?
 1 year GAP position:
-3
-1,000
-2
-2,000
-1
base
+1
+2
+3
-8,000 -10,000 -10,000 -10,000 -10,000
Gap
All CD’s will mature
Re-finance the auto loans
 3 month GAP is zero by definition:
-3
-2
-1
base
+1
+2
+3
+8,000
+6,000
+2,000
0
Gap
-1,000
-3,000
-6,000
Re-finance the auto loans,
and less likely to “pull” CD’s
People will “pull” the CD’s
for higher returns
The implications of embedded options
 Is the bank the buyer or seller of the option

Does the bank or the customer determine when
the option is exercised?
 How and by what amount is the bank being
compensated for selling the option, or how
much must it pay to buy the option?
 When will the option be exercised?

Often determined by the economic and interest
rate environment
 Static GAP analysis ignores these embedded
options
Earnings sensitivity analysis consists
of six general steps:
1.
2.
3.
4.
5.
6.
Forecast future interest rates,
Identify changes in the composition of assets
and liabilities in different rate environments,
Forecast when embedded options will be
exercised,
Identify when specific assets and liabilities
will reprice given the rate environment,
Estimate net interest income and net income,
and
Repeat the process to compare forecasts of
net interest income and net income across
rate environments.
Earnings sensitivity analysis
ABC rate-sensitivity report for most likely (base case)
Assets
Total
3 Months >3-6
>6-12
or Less Months Months
>1-3
Years
>3-5
Years
>5-10
Years
>10-20
Years
>20
Years
Loans
Prime Based
Equity Credit Lines
Fixed Rate >1 yr
Var Rate Mtg I Yr
30-Yr Fix Mortgage
Consumer
Credit Card
Investments
Eurodollars
CMOs FixRate
US Treasury
Fed Funds Sold
Cash & Due From Banks
Loan Loss Reserve
Non-earning Assets
Total Assets
100,000
25,000
170,000
55,000
250,000
100,000
25,000
100,000
25,000
18,000
13,750
5,127
6,000
3,000
80,000
35,000
75,000
25,000
80,000
2,871
15,000
-15,000
60,000
1,000,000
18,000
13,750
5,129
6,000
3,000
36,000
27,500
9,329
12,000
6,000
96,000
2,000
32,792
48,000
13,000
28,916 116,789
28,000
2,872
5,000
5,224
5,000
13,790
25,000
5,284
40,000
51,918
4,959
25,000
278,748
53,751 101,053 228,582 104,200 121,748
51,918
15,000
-15,000
60,000
60,000
Earnings sensitivity analysis
ABC rate-sensitivity report for most likely (base case)
Liabilities and GAP measures
Total
3 Months >3-6
>6-12
or Less Months Months
>1-3
Years
>3-5
Years
>5-10
Years
>10-20
Years
>20
Years
Deposits
MMDAs
Retail CDs
Savings
NOW
DDA Personal
Comm'l DDA
240,000
400,000
35,000
40,000
55,000
60,000
240,000
60,000
25,000
50,000
25,000
60,000
90,000 160,000
30,000
35,000
40,000
55,000
36,000
24,000
Borrowings
TT&L
L-T notes FR
Fed Funds Purch
NIR Liabilities
Capital
Tot Liab & Equity
Swaps- Pay Fixed
GAP
CUMULATIVE GAP
30,000
65,000
1,000,000
50,000
0
349,000
60,000
90,000 160,000
50,000
-20,252 -6,249 11,053
-20,252 -26,501 -15,448
30,000
50,000
0
30,000
65,000
261,000
-25,000 -25,000
43,582
28,134
49,200 71,748 51,918 -201,000
77,334 149,082 201,000
0
Fed Funds Rate %
Interest Rate
Forecasts
Fed Funds Forecast vs. Implied Forward Rates
6.50
Market Implied Rates
6.25
6.00
Most Likely Forecast
5.75
5.50
5.25
5.00
1
3
Most LikelyForecast and Rate Ramps Dec. 2001
10
8
t6
n
e
c
r4
e
P
2
0
11 1 3 5 7 9 11 1 3 5 7 9 12
2002
2003
5
7
9 11 13 15 17 19 21 23
Time (month)
1.0
Sensitivity of Earnings: Year One
Change in NII ($MM)
2
(.5)
(1.0)
(1.5)
ALCO Guideline
Board Limit
(2.0)
(2.5)
(3.0)
(3.5)
- 300
1.0
.5
Change in NII ($MM)
Earnings sensitivity over one and
two years versus most likely rate
scenario
.5
-200
-100
ML
+100
+200
Ramped Change in Rates from Most Likely (Basis Point)
+300
Sensitivity of Earnings: Year Two
2
(.5)
(1.0)
(1.5)
ALCO Guideline
Board Limit
(2.0)
(2.5)
(3.0)
- 300
-200
-100
ML
+100
+200
Ramped Change in Rates from Most Likely (Basis Points)
+300
Earnings at risk
…the potential variation in net interest income across
different interest rate environments, given different
assumptions about balance sheet composition, when
embedded options will be exercised, and the timing of
repricings.
 Demonstrates the potential volatility in
earnings across these environments.
 The greater is the potential variation in
earnings (earnings at risk), the greater
is the amount of risk assumed by a
bank.
Earnings-at-risk for PNC and Washington
Mutual for a gradual change in interest
rates, December 31, 2001
Gradual Change in Interest Rates*
PNC
Net interest income change
for next 1 year (2002)
Washington Mutual
Net interest income change
for next 1 year (2002)
Net income change for
next 1 year (2002)
-2%
-1%
1%
-2.80%
-0.30%
2%
1.47%
-5.18%
2.19%
-2.76%
Income statement gap
 For smaller banks with limited off-balance
sheet exposure, one procedure is to use
Income Statement GAP analysis, which is a
simplified procedure that takes some of the
factors into account.
 This model uses an all encompassing
Earnings Change Ratio (ECR).


This ratio attempts to incorporate information
on each asset and liability.
This ratio indicates how the yield on each asset,
and rate paid on each liability, is assumed to
change relative to a 1 percent drop in the prime
rate.
Prime Down 100bp
Prime Up 100bp
Balance
Income Balance
Income
Report data as of 09-30-02 Sheet
Statement Sheet
Statement
t
t
GAP* ECR
GAP
GAP* ECR
GAP
Rate-Sensitive Assets
A
B
AXB
C
D
CxD
Income statement GAP and earnings
variability
Amounts In Thousands
Loans
Fixed Rate
Floating Rate
Securities
Principal Cash Flows
Agencies
Agy Callables
CMO Fixed
Fed Funds Sold
Floating Rate
Total Rate-Sensitive Assets
$5,661
3,678
100%
100%
$5,661
3,678
$5,661
3,678
100%
100%
$5,661
3,678
200
2,940
315
2,700
71%
71%
58%
96%
142
2,087
183
2,592
200
300
41
2,700
71%
60%
51%
96%
142
180
21
2,592
$14,343
$12,580
$15,494
Rate-Sensitive Liabilities
Savings
$1,925
Money Mkt Accts
11,001
NOW
2,196
Fed Funds Purch/Repo
0
CDs - IOOM
3,468
CDs < 100M
4,370
Total Rate-Sensitive
$22,960
Liabilities
Rate Sensitivity Gap (Assets- ($7,466)
Liab)
Total Assets
$29,909
GAP as a Percent of Total
-24.96%
Assets
Change in Net Interest
Change in Net Interest
Net Interest Margin
Percentage Change in Net
75%
60%
80%
96%
85%
84%
$1,444
$1,925
6,601
11,001
1,757
2,196
0
0
2,948
3,468
3,671
4,370
$16,420 $22,960
($2,077) ($10,380)
$29,909
-6.94%
($20.8)
0.07%
5.20%
1.34%
$29,909
-34.71%
$12,274
5%
40%
20%
96%
85%
84%
$96
4,400
439
0
2,948
3,671
$11,554
$719
$29,909
2.41%
$7.2
0.02%
5.20%
0.46%
Steps that banks can take to reduce
interest rate risk
 Calculate periodic GAPs over short
time intervals.
 Match fund repriceable assets with
similar repriceable liabilities so that
periodic GAPs approach zero.
 Match fund long-term assets with
noninterest-bearing liabilities.
 Use off-balance sheet transactions,
such as interest rate swaps and
financial futures, to hedge.
Various ways to adjust the effective rate sensitivity
of a bank’s assets and liabilities on-balance sheet.
Objective
Approaches
Reduce asset
sensitivity
Buy longer-term securities.
Lengthen the maturities of loans.
Move from floating-rate loans to term loans.
Increase asset
sensitivity
Buy short-term securities.
Shorten loan maturities.
Make more loans on a floating-rate basis.
Reduce liability
sensitivity
Pay premiums to attract longer-term deposit
instruments.
Issue long-term subordinated debt.
Increase liability
sensitivity
Pay premiums to attract short-term deposit
instruments.
Borrow more via non-core purchased liabilities.
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