Bank Management, 6th edition.
Timothy W. Koch and S. Scott MacDonald
Copyright © 2006 by South-Western, a division of Thomson Learning
Managing Interest Rate Risk:
GAP and Earnings Sensitivity
Chapter 5
Interest Rate Risk
 Interest Rate Risk
 The
potential loss from unexpected
changes in interest rates which can
significantly alter a bank’s profitability
and market value of equity.
Interest Rate Risk: GAP & Earnings
Sensitivity
 When a bank’s assets and liabilities do
not reprice at the same time, the result
is a change in net interest income.
 The
change in the value of assets and
the change in the value of liabilities will
also differ, causing a change in the
value of stockholder’s equity
Interest Rate Risk
 Banks typically focus on either:
 Net interest income or
 The market value of stockholders' equity
 GAP Analysis
 A static measure of risk that is commonly
associated with net interest income (margin)
targeting
 Earnings Sensitivity Analysis
 Earnings sensitivity analysis extends GAP
analysis by focusing on changes in bank
earnings due to changes in interest rates and
balance sheet composition
Asset and Liability Management
Committee (ALCO)
 The ALCO’s primary responsibility is
interest rate risk management.
 The ALCO coordinates the bank’s
strategies to achieve the optimal
risk/reward trade-off.
Two Types of Interest Rate Risk
 Spread Risk (reinvestment rate risk)
 Changes
in interest rates will change
the bank’s cost of funds as well as the
return on their invested assets. They
may change by different amounts.
 Price Risk
 Changes
in interest rates may change
the market values of the bank’s assets
and liabilities by different amounts.
Interest Rate Risk:
Spread (Reinvestment Rate) Risk
 If interest rates change, the bank will have
to reinvest the cash flows from assets or
refinance rolled-over liabilities at a different
interest rate in the future.

An increase in rates, ceteris paribus,
increases a bank’s interest income but also
increases the bank’s interest expense.
 Static GAP Analysis considers the impact of
changing rates on the bank’s net interest
income.
Interest Rate Risk:
Price Risk
 If interest rates change, the market
values of assets and liabilities also
change.
 The
longer is duration, the larger is the
change in value for a given change in
interest rates.
 Duration GAP considers the impact of
changing rates on the market value of
equity.
Measuring Interest Rate Risk with GAP
 Example:
A
bank makes a $10,000 four-year car
loan to a customer at fixed rate of
8.5%. The bank initially funds the car
loan with a one-year $10,000 CD at a
cost of 4.5%. The bank’s initial spread
is 4%.
4 year Car Loan
1 Year CD
 What
8.50%
4.50%
4.00%
is the bank’s risk?
Measuring Interest Rate Risk with GAP
 Traditional Static GAP Analysis
GAPt = RSAt -RSLt
 RSAt

Rate Sensitive Assets
 Those assets that will mature or reprice in
a given time period (t)
 RSLt

Rate Sensitive Liabilities
 Those liabilities that will mature or reprice
in a given time period (t)
Measuring Interest Rate Risk with GAP
 Traditional Static GAP Analysis
 What
is the bank’s 1-year GAP with the
auto loan?
RSA1yr = $0
 RSL1yr = $10,000
 GAP1yr = $0 - $10,000 = -$10,000

 The bank’s one year funding GAP is -10,000
 If interest rates rise in 1 year, the bank’s
margin will fall. The opposite is also true
that if rates fall, the margin will rise.
Measuring Interest Rate Risk with GAP
 Traditional Static GAP Analysis
 Funding
GAP
Focuses on managing net interest
income in the short-run
 Assumes a ‘parallel shift in the yield
curve,’ or that all rates change at the
same time, in the same direction and by
the same amount.
Does this ever happen?

Traditional Static GAP Analysis
Steps in GAP Analysis
 Develop an interest rate forecast
 Select a series of “time buckets” or
intervals for determining when assets
and liabilities will reprice
 Group assets and liabilities into these
“buckets ”
 Calculate the GAP for each “bucket ”
 Forecast the change in net interest
income given an assumed change in
interest rates
What Determines Rate Sensitivity (Ignoring
Embedded Options)?
 An asset or liability is considered rate
sensitivity if during the time interval:



It matures
It represents and interim, or partial, principal
payment
It can be repriced


The interest rate applied to the 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
What are RSAs and RSLs?
 Considering a 0-90 day “time bucket,” RSAs and
RSLs include:
 Maturing instruments or principal payments
 If an asset or liability matures within 90 days,
the principal amount will be repriced
 Any full or partial principal payments within
90 days will be repriced
 Floating and variable rate instruments
 If the index will contractually change within
90 days, the asset or liability is rate sensitive
 The rate may change daily if their base rate
changes.
 Issue: do you expect the base rate to
change?
Factors Affecting Net Interest Income
 Changes in the level of interest rates
 Changes in the composition of assets
and liabilities
 Changes in the volume of earning
assets and interest-bearing liabilities
outstanding
 Changes in the relationship between
the yields on earning assets and rates
paid on interest-bearing liabilities
Factors Affecting Net Interest Income:
An Example
 Consider the following balance sheet:
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
$ 1,000
$ 1,000
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
Examine the impact of the following changes
 A 1% increase in the level of all short-term
rates?
 A 1% decrease in the spread between assets
yields and interest costs such that the rate
on RSAs increases to 8.5% and the rate on
RSLs increase to 5.5%?
 Changes in the relationship between shortterm asset yields and liability costs
 A proportionate doubling in size of the bank.
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
$ 1,000
$
1,000
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%
With a negative GAP, more
GAP = 500 - 600 = -100
liabilities than assets reprice
higher; hence NII and NIM fall
1% decrease in the spread
Expected Balance
Assets
Rate sensitive $ 500
Fixed rate
$ 350
Non earning
$ 150
Total
$ 1,000
Sheet for Hypothetical Bank
Yield
Liabilities
Cost
8.5%
$
600
5.5%
11.0%
$
220
6.0%
$
100
$
920
Equity
$
80
$ 1,000
NII = (0.085 x 500 + 0.11 x 350) - (0.055 x 600 + 0.06 x 220)
NII = 81 - 46.2 = 34.8
NII and NIM fall (rise) with a
NIM = 34.8 / 850 = 4.09%
decrease (increase) in the
GAP = 500 - 600 = -100
spread.
Why the larger change?
Changes in the Slope of the Yield Curve
 If liabilities are short-term and assets
are long-term, the spread will
 widen
as the yield curve increases in
slope
 narrow when the yield curve
decreases in slope and/or inverts
Proportionate doubling in size
Expected Balance
Assets
Rate sensitive $ 1,000
Fixed rate
$ 700
Non earning
$ 300
Total
$ 2,000
Sheet for Hypothetical Bank
Yield
Liabilities
Cost
8.0%
$ 1,200
4.0%
11.0%
$
440
6.0%
$
200
$ 1,840
Equity
$
160
$ 2,000
NII = (0.08 x 1000 + 0.11 x 700) - (0.04 x 1200 + 0.06 x 440)
NII = 157 - 74.4 = 82.6
NII and GAP double, but
NIM = 82.6 / 1700 = 4.86%
GAP = 1000 - 1200 = -200
stays the same.
NIM
What has happened to risk?
Changes in the Volume of Earning Assets and
Interest-Bearing Liabilities
 Net interest income varies directly with
changes in the volume of earning
assets and interest-bearing liabilities,
regardless of the level of interest rates
RSAs increase to $540 while fixed-rate assets
decrease to $310 and RSLs decrease to $560
while fixed-rate liabilities increase 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
$ 1,000
$ 1,000
NII = (0.08 x 540 + 0.11 x 310) - (0.04 x 560 + 0.06 x 260)
NII = 77.3 - 38 = 39.3
Although the bank’s GAP
NIM = 39.3 / 850 = 4.62%
(and hence risk) is lower,
GAP = 540 - 560 = -20
NII is also lower.
Changes in Portfolio Composition and Risk
 To reduce risk, a bank with a negative
GAP would try to increase RSAs
(variable rate loans or shorter
maturities on loans and investments)
and decrease RSLs (issue relatively
more longer-term CDs and fewer fed
funds purchased)
 Changes in portfolio composition also
raise or lower interest income and
expense based on the type of change
Changes in Net Interest Income are directly
proportional to the size of the GAP
 If there is a parallel shift in the yield
curve:
ΔNII exp  GAP  iexp
 It is rare, however, when the yield
curve shifts parallel
 If
rates do not change by the same
amount and at the same time, then net
interest income may change by more
or less.
 We can figure out how much. How?
Summary of GAP and the Change in NII
GAP Summary
Change in
Interest
Income
Increase
>
Decrease
>
Positive
Positive
Change in
Interest
Income
Increase
Decrease
Negative
Negative
Increase
Decrease
Increase
Decrease
<
<
Increase
Decrease
Decrease
Increase
Zero
Zero
Increase
Decrease
Increase
Decrease
=
=
Increase
Decrease
None
None
GAP
Change in
Interest
Expense
Increase
Decrease
Change in
Net Interest
Income
Increase
Decrease
Rate, Volume, and Mix Analysis
 Banks often 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
 changes associated with movements in
interest rates.


The purpose is to assess what factors
influence shifts in net interest income over
time.
Measuring Interest Rate Risk: Synovus
Interest earned on:
Taxable loans, net
Tax-exempt loans, net†
Taxable investment securities
Tax-exempt investment securities†
Interest earning deposits with banks
Federal funds sold and securities
purchased under resale agreements
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 securities
sold under repurchase agreements
Other borrowed funds
Total interest expense
Net interest income
2004 Compared to 2003
2003 Compared to 2002
Change Due to *
Change Due to *
Volume Yield/Rate Net Change Volume Yield/Rate Net Change
$ 149,423 (117,147)
32,276 161,222
36,390
197,612
1,373
(586)
787
1,108
(450)
658
(5,313)
(916)
(6,229)
4,507
2,570
7,077
2,548
74
2,622
2,026
(206)
1,820
223
(176)
47
28
48
76
406
(1,745)
(1,339)
7,801
156,461
(1,680)
(122,176)
6,121
34,285
6,074
21,380
(369)
32,015
(12,517)
(36,244)
(3,307)
(22,545)
(6,165)
21,318
74,253
82,208
1,447
1,410
2,857
(113)
170,225
549
40,311
436
210,536
(6,443)
(14,864)
(3,676)
9,470
1,537
4,654
(660)
38,824
5,433
13,888
(67)
32,812
6,970
18,542
(727)
71,636
(29,744)
(35,909)
23,148
15,870
39,018
(4,272)
(108,629)
(13,547)
17,046
(34,376)
68,661
21,960
89,463
80,762
3,361
71,297
(30,986)
25,321
160,760
49,776
Interest Rate-Sensitivity Reports
Classifies a bank’s assets and liabilities into time intervals
according to the minimum number of days until each
instrument is expected to be repriced.
 GAP values are reported a periodic and
cumulative basis for each time interval.


Periodic GAP
 Is the Gap for each time bucket and
measures the timing of potential income
effects from interest rate changes
Cumulative GAP
 It is the sum of periodic GAP's and
measures aggregate interest rate risk over
the entire period
 Cumulative GAP is important since it
directly measures a bank’s net interest
sensitivity throughout the time interval.
Measuring Interest Rate Risk with GAP
1-7
Days
Assets
U.S. Treas & ag
MM Inv
Municipals
FF & Repo's
Comm loans
Install loans
Cash
Other assets
Total Assets
0.7
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
Periodic GAP
Cumulative GAP
8-30
Days
1.3
1.3
13.8
0.5
15.0
31-90 91-180 181-365 Over Not Rate
Days Days
Days 1 year Sensitive
3.6
1.2
0.7
1.2
1.8
1.0
0.3
3.7
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
9.5
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
Total
Advantages and Disadvantages of
Static GAP Analysis
 Advantages
 Easy to understand
 Works well with small changes in interest
rates
 Disadvantages
 Ex-post measurement errors
 Ignores the time value of money
 Ignores the cumulative impact of interest rate
changes
 Typically considers demand deposits to be
non-rate sensitive
 Ignores embedded options in the bank’s
assets and liabilities
Measuring Interest Rate Risk with
the GAP Ratio
 GAP Ratio = RSAs/RSLs
A
GAP ratio greater than 1 indicates a
positive GAP
 A GAP ratio less than 1 indicates a
negative GAP
What is the ‘Optimal GAP’
 There is no general optimal value for a
bank's GAP in all environments.
 Generally, the farther a bank's GAP is
from zero, the greater is the bank's
risk.
 A bank must evaluate its overall risk
and return profile and objectives to
determine its optimal GAP
GAP and Variability in Earnings
 Neither the GAP nor GAP ratio provide
direct information on the potential variability
in earnings when rates change.

Consider two banks, both with $500 million
in total assets.



Bank A: $3 mil in RSAs and $2 mil in RSLs.
GAP = $1 mil and GAP ratio = 1.5 mil
Bank B: $300 mil in RSAs and $200 mil RSLs.
GAP equals $100 mill and 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.
Link Between GAP and Net Interest Margin
 Many banks will specify a target GAP
to earning asset ratio in the ALCO
policy statements
Target Gap
(Allowable % Change in NIM)(Expec ted NIM)

Earning assets
Expected % change in interest rates
Establishing a Target GAP: An 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
 Hence,
6%.
NIM should fall between 4% and
Establishing a Target GAP: An Example
(continued)
 If 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.
Speculating on the GAP
 Many bank managers attempt to adjust
the interest rate risk exposure of a
bank in anticipation of changes in
interest rates.
 This is speculative because it assumes
that management can forecast rates
better than the market.
Can a Bank Effectively Speculate on the GAP?
 Difficult to vary the GAP and win as
this requires consistently accurate
interest rate forecasts
 A bank has limited flexibility in
adjusting its GAP; e.g., loan and
deposit terms
 There is no adjustment for the timing
of cash flows or dynamics of the
changing GAP position
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.
Steps to Earnings Sensitivity Analysis
 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
 Repeat the process to compare forecasts of
net interest income and net income across
different interest rate environments.
Earnings Sensitivity Analysis and the
Exercise of Embedded Options
 Many bank assets and liabilities
contain different types of options, both
explicit and implicit:
 Option
to refinance a loan
 Call option on a federal agency bond
the bank owns
 Depositors have the option to withdraw
funds prior to maturity
 Cap (maximum) rate on a floating-rate
loan
Earnings Sensitivity Analysis
Recognizes that Different Interest
Rates Change by Different Amounts at
Different Times
 It is well recognized that banks are
quick to increase base loan rates but
are slow to lower base loan rates when
rates fall.
Recall the our example from before:
4 year Car Loan
1 Year CD
8.50%
4.50%
4.00%
 GAP1Yr = $0 - $10,000 = -$10,000
 What if rates increased?
1 year GAP Position
Change in Rates
-3
-2
-1,000
-2,000
-1
Base
GAP1yr
Change in Rates
+1
+2
+3
-8,000 -10,000 -10,000 -10,000 -10,000
Re-finance the auto loans
All CD’s will mature
What about the 3 Month GAP Position?
 Base GAP3m = $10,000 - $10,000 = 0
3 Month GAP Position
Change in Rates
-3
-2
-1
Base
GAP3m
+8,000 +6,000 +2,000
0
Re-finance auto loans, and
less likely to “pull” CD’s
Change in Rates
+1
+2
+3
-1,000 -3,000
-6,000
People will “pull” the CD’s
for higher returns
The implications of embedded options
 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?

This is often determined by the
economic and interest rate environment
 Static GAP analysis ignores these
embedded options
Earnings Sensitivity Analysis (Base Case)
Example
 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 (Base Case)
Example
 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
30,000
-25,000
-25,000
50,000
-20,252 -6,249
-20,252 -26,501
11,053
-15,448
43,582
28,134
50,000
0
30,000
65,000
261,000
49,200 71,748 51,918 -201,000
77,334 149,082 201,000
0
Interest Rate
Forecasts
Fed Funds Forecast vs. Implied Forward Rates
4.50
Market Implied Rates
4.25
%
e
ta4.00
R
s3.75
d
n
u
F3.50
d
e
F3.25
3.00
1
Most LikelyForecast
3 5 7 9 11 13 15 17 19 21 23
Time (month)
Most LikelyForecast and Rate Ramps Dec. 2005
6
5
t
n4
e
c
r3
e
P
2
0
11 1 3 5 7 9 11 1 3 5 7 9 12
2006
2007
1.0
.5
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
Change in NII ($MM)
.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 Sensitivity Analysis Results
 For the bank:
 The
embedded options can potentially
alter the bank’s cash flows
 Interest rates change by different
amounts at different times
 Summary results are known as
Earnings-at-Risk or Net Interest
Income Simulation
Earnings Sensitivity Analysis
 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 , or
 The greater is the maximum loss, the
greater is risk
Income Statement GAP
 Income Statement GAP
 Forecasts
the change in net interest
income given a 1% rise or fall in the
bank’s benchmark rate over the next
year.
 It converts contractual GAP data to
figures evidencing the impact of a 1%
rate movement.
 Income statement GAP is also know in
the industry as Beta GAP analysis
Income Statement GAP Adjusts the
Balance Sheet GAP to Incorporate the
Earnings Change Ratio
 The Earnings Change Ratio
 This
ratio indicates how the yield on
each asset and rate paid on each
liability is assumed to change relative
to a 1 percent move in the benchmark
rate.
Income Statement GAP
Amounts In Thousands
Rate-Sensitive Assets
Loans
Fixed Rate
Floating Rate
Securities
Principal Cash Flows
Agencies
Agy Callables
CMO Fixed
Fed Funds Sold
Floating Rate
Total Rate-Sensitive Assets
Rate-Sensitive Liabilities
Savings
Money Mkt Accts
NOW
Fed Funds Purch/Repo
CDs - IOOM
CDs < 100M
Total Rate-Sensitive
Liabilities
Rate Sensitivity Gap (AssetsLiab)
Total Assets
GAP as a Percent of Total
Assets
Change in Net Interest
Change in Net Interest
Net Interest Margin
Percentage Change in Net
Prime Down 100bp
Prime Up 100bp
Balance
Income Balance
Income
Sheet
Statement Sheet
Statement
t
t
GAP* ECR
GAP
GAP* ECR
GAP
A
B
AXB
C
D
CxD
$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
$1,925
11,001
2,196
0
3,468
4,370
$22,960
($7,466)
$29,909
-24.96%
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 $29,909
-6.94% -34.71%
($20.8)
0.07%
5.20%
1.34%
$12,274
5%
40%
20%
96%
85%
84%
$96
4,400
439
0
2,948
3,671
$11,554
$719
$29,909
2.40%
$7.2
0.02%
5.20%
0.46%
Managing the GAP and Earnings Sensitivity
Risk
 Steps to reduce risk
 Calculate
periodic GAPs over short
time intervals.
 Fund repriceable assets with matching
repriceable liabilities so that periodic
GAPs approach zero.
 Fund long-term assets with matching
noninterest-bearing liabilities.
 Use off-balance sheet transactions to
hedge.
Adjust the Effective Rate Sensitivity of a
Bank’s Assets and Liabilities
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, 6th edition.
Timothy W. Koch and S. Scott MacDonald
Copyright © 2006 by South-Western, a division of Thomson Learning
Managing Interest Rate Risk:
Duration GAP and Economic Value
of Equity
Chapter 6
Measuring Interest Rate Risk with Duration
GAP
 Economic Value of Equity Analysis
 Focuses
on changes in stockholders’
equity given potential changes in
interest rates
 Duration GAP Analysis
 Compares
the price sensitivity of a
bank’s total assets with the price
sensitivity of its total liabilities to
assess the impact of potential changes
in interest rates on stockholders’
equity.
Recall from Chapter 4
 Duration is a measure of the effective
maturity of a security.
 Duration
incorporates the timing and
size of a security’s cash flows.
 Duration measures how price sensitive
a security is to changes in interest
rates.

The greater (shorter) the duration, the
greater (lesser) the price sensitivity.
Duration and Price Volatility
 Duration as an Elasticity Measure
 Duration
versus Maturity
Consider the cash flows for these two
securities over the following time line
0
5
10
15
20

01
900
5
10
15
$1,000
20
$100
Duration versus Maturity
 The maturity of both is 20 years

Maturity does not account for the differences in
timing of the cash flows
 What is the effective maturity of both?

The effective maturity of the first security is:


(1,000/1,000) x 20 = 20 years
The effective maturity of the second security is:

[(900/1,000) x 1]+[(100/1,000) x 20] = 2.9 years
 Duration is similar, however, it uses a weighted
average of the present values of the cash flows
Duration versus Maturity
Duration is an approximate measure of
the price elasticity of demand
% Change in Quantity Demanded
Price Elasticity of Demand  % Change in Price
Duration versus Maturity
 The longer the duration, the larger the
change in price for a given change in
interest rates.
P
Duration  - P
i
(1  i)
 i 
P  - Duration 
P

 (1  i) 
Measuring Duration
 Duration is a weighted average of the
time until the expected cash flows
from a security will be received,
relative to the security’s price
 Macaulay’s
k
Duration
n
CFt (t)
CFt (t)


t
t
(1
+
r)
(1
+
r)
t =1
D = t=k1

CFt
Price of the Security

t
t =1 (1 + r)
Measuring Duration
 Example
 What
is the duration of a bond with a
$1,000 face value, 10% annual coupon
payments, 3 years to maturity and a
12% YTM? The bond’s price is $951.96.
100  1 100  2 100  3 1,000  3
+
+
+
1
2
3
2,597.6
(1.12)
(1.12)
(1.12)
(1.12) 3
D

= 2.73 years
3
100
1000
951.96
+

t
(1.12) 3
t =1 (1.12)
Measuring Duration
 Example
 What
is the duration of a bond with a
$1,000 face value, 10% coupon, 3 years
to maturity but the YTM is 5%?The
bond’s price is $1,136.16.
100 * 1 100 * 2 100 * 3 1,000 * 3
+
+
+
1
2
3
3,127.31
(1.05)
(1.05)
(1.05)
(1.05) 3
D

= 2.75 years
1136.16
1,136.16
Measuring Duration
 Example
 What
is the duration of a bond with a
$1,000 face value, 10% coupon, 3 years
to maturity but the YTM is 20%?The
bond’s price is $789.35.
100 * 1 100 * 2 100 * 3 1,000 * 3
+
+
+
1
2
3
2,131.95
(1.20)
(1.20)
(1.20)
(1.20) 3
D

= 2.68 years
789.35
789.35
Measuring Duration
 Example
 What
is the duration of a zero coupon
bond with a $1,000 face value, 3 years
to maturity but the YTM is 12%?
1,000 * 3
2,135.34
(1.12) 3
D

= 3 years
1,000
711.78
(1.12) 3

By definition, the duration of a zero
coupon bond is equal to its maturity
Duration and Modified Duration
 The greater the duration, the greater
the price sensitivity
 Modified Duration gives an estimate of
price volatility:
Macaulay' s Duration
Modified Duration 
(1  i)
P
 - Modified Duration  i
P
Effective Duration
 Effective Duration
 Used
to estimate a security’s price
sensitivity when the security contains
embedded options.
 Compares a security’s estimated price in
a falling and rising rate environment.
Effective Duration
Pi- - Pi
Effective Duration 

P0 (i - i )
 Where:
Pi- = Price if rates fall
Pi+ = Price if rates rise
P0 = Initial (current) price
i+ = Initial market rate plus the increase in rate
i- = Initial market rate minus the decrease in rate
Effective Duration
 Example
 Consider
a 3-year, 9.4 percent semiannual coupon bond selling for $10,000
par to yield 9.4 percent to maturity.
 Macaulay’s Duration for the option-free
version of this bond is 5.36 semiannual
periods, or 2.68 years.
 The Modified Duration of this bond is
5.12 semiannual periods or 2.56 years.
Effective Duration
 Example
 Assume,
instead, that the bond is
callable at par in the near-term .
If rates fall, the price will not rise much
above the par value since it will likely
be called
 If rates rise, the bond is unlikely to be
called and the price will fall

Effective Duration
 Example
 If
rates rise 30 basis points to 5%
semiannually, the price will fall to
$9,847.72.
 If rates fall 30 basis points to 4.4%
semiannually, the price will remain at
par
$10,000 - $9,847.72
Effective Duration 
 2.54
$10,000( 0.05 - 0.044)
Duration GAP
 Duration GAP Model
 Focuses
on either managing the
market value of stockholders’ equity

The bank can protect EITHER the
market value of equity or net interest
income, but not both

Duration GAP analysis emphasizes the
impact on equity
Duration GAP
 Duration GAP Analysis
 Compares
the duration of a bank’s
assets with the duration of the bank’s
liabilities and examines how the
economic value stockholders’ equity
will change when interest rates
change.
Two Types of Interest Rate Risk
 Reinvestment Rate Risk
 Changes
in interest rates will change
the bank’s cost of funds as well as the
return on invested assets
 Price Risk
 Changes
in interest rates will change
the market values of the bank’s assets
and liabilities
Reinvestment Rate Risk
 If interest rates change, the bank will
have to reinvest the cash flows from
assets or refinance rolled-over
liabilities at a different interest rate in
the future
 An
increase in rates increases a bank’s
return on assets but also increases the
bank’s cost of funds
Price Risk
 If interest rates change, the value of
assets and liabilities also change.
 The
longer the duration, the larger the
change in value for a given change in
interest rates
 Duration GAP considers the impact of
changing rates on the market value of
equity
Reinvestment Rate Risk and Price Risk
 Reinvestment Rate Risk
 If
interest rates rise (fall), the yield from
the reinvestment of the cash flows
rises (falls) and the holding period
return (HPR) increases (decreases).
 Price risk
 If
interest rates rise (fall), the price falls
(rises). Thus, if you sell the security
prior to maturity, the HPR falls (rises).
Reinvestment Rate Risk and Price Risk
 Increases in interest rates will increase
the HPR from a higher reinvestment
rate but reduce the HPR from capital
losses if the security is sold prior to
maturity.
 Decreases in interest rates will
decrease the HPR from a lower
reinvestment rate but increase the
HPR from capital gains if the security
is sold prior to maturity.
Reinvestment Rate Risk and Price Risk
 An immunized security or portfolio is
one in which the gain from the higher
reinvestment rate is just offset by the
capital loss.
 For an individual security,
immunization occurs when an
investor’s holding period equals the
duration of the security.
Steps in Duration GAP Analysis
 Forecast interest rates.
 Estimate the market values of bank assets,
liabilities and stockholders’ equity.
 Estimate the weighted average duration of
assets and the weighted average duration of
liabilities.

Incorporate the effects of both on- and offbalance sheet items. These estimates are
used to calculate duration gap.
 Forecasts changes in the market value of
stockholders’ equity across different
interest rate environments.
Weighted Average Duration of Bank Assets
 Weighted Average Duration of Bank
Assets (DA)
n
DA   w iDai
 Where
i
wi = Market value of asset i divided by
the market value of all bank assets
 Dai = Macaulay’s duration of asset i
 n = number of different bank assets

Weighted Average Duration of Bank Liabilities
 Weighted Average Duration of Bank
Liabilities (DL)
m
DL   z jDlj
 Where
j
zj = Market value of liability j divided by
the market value of all bank liabilities
 Dlj= Macaulay’s duration of liability j
 m = number of different bank liabilities

Duration GAP and Economic Value of Equity
 Let MVA and MVL equal the market values of
assets and liabilities, respectively.
 If: ΔEVE  ΔMVA  ΔMVL
and
Duration GAP
DGAP  DA - (MVL/MVA)D L
 Then:
 y 
ΔEVE  - DGAP 
MVA

 (1  y) 

where y = the general level of interest
rates
Duration GAP and Economic Value of Equity
 To protect the economic value of
equity against any change when rates
change , the bank could set the
duration gap to zero:
 y 
ΔEVE  - DGAP 
MVA

 (1  y) 
Hypothetical Bank Balance Sheet
1
Assets
Cash
Earning assets
3-yr Commercial loan
6-yr Treasury bond
84 1
Total Earning Assets
Non-cash earning(1
assets
.12)1
Total assets D 
Liabilities
Interest bearing liabs.
1-yr Time deposit
3-yr Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
Par
$1,000 % Coup
Years
Mat.
$100
$
$ 700 12.00%
3
$ 200
8.00%
6
84

2
84

3
$ 900 2 
$ (1-.12)
(1.12)3
$ 1,000
700
$ 620
$ 300
$ 920
$ $ 920
$
80
$ 1,000
YTM
Market
Value
5.00%
7.00%
1
3

Dur.
100
12.00% $ 700
8.00% $ 200
700
3
11.11% $ 900
(1.12)3 $ 10.00% $ 1,000
2.69
4.99
5.00% $ 620
7.00% $ 300
5.65% $ 920
$ 5.65% $ 920
$
80
$ 1,000
1.00
2.81
2.88
1.59
Calculating DGAP
 DA

($700/$1000)*2.69 + ($200/$1000)*4.99 = 2.88
 DL

($620/$920)*1.00 + ($300/$920)*2.81 = 1.59
 DGAP

2.88 - (920/1000)*1.59 = 1.42 years

What does this tell us?
 The average duration of assets is greater than the
average duration of liabilities; thus asset values
change by more than liability values.
1 percent increase in all rates.
1
Par
$1,000 % Coup
Years
Mat.
YTM
Market
Value
Assets
Cash
$ 100
$
Earning assets
3-yr Commercial loan
$ 700 12.00%
3
13.00% $
6-yr Treasury bond
$ 200
8.00%
6
9.00% $
Total Earning Assets
$ 900
12.13% $
3
84
700 $
Non-cash earning assets
$
PV 

t
t

1
Total assets
$ 1,000
10.88%3 $
1.13
1.13

Liabilities
Interest bearing liabs.
1-yr Time deposit
3-yr Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
$ 620
$ 300
$ 920
$ $ 920
$
80
$ 1,000
5.00%
7.00%
1
3
6.00% $
8.00% $
6.64% $
$
6.64% $
$
$
Dur.
100
683
191
875
975
2.69
4.97
614
292
906
906
68
975
1.00
2.81
2.86
1.58
Calculating DGAP
 DA

($683/$974)*2.68 + ($191/$974)*4.97 = 2.86
 DA

($614/$906)*1.00 + ($292/$906)*2.80 = 1.58
 DGAP

2.86 - ($906/$974) * 1.58 = 1.36 years

What does 1.36 mean?
 The average duration of assets is greater than the
average duration of liabilities, thus asset values
change by more than liability values.
Change in the Market Value of Equity
y
ΔEVE  - DGAP[
]MVA
(1  y)
 In this case:
.01
ΔEVE  - 1.42[
]$1,000  $12.91
1.10
Positive and Negative Duration GAPs
 Positive DGAP

Indicates that assets are more price sensitive
than liabilities, on average.

Thus, when interest rates rise (fall), assets will
fall proportionately more (less) in value than
liabilities and EVE will fall (rise) accordingly.
 Negative DGAP

Indicates that weighted liabilities are more
price sensitive than weighted assets.

Thus, when interest rates rise (fall), assets will
fall proportionately less (more) in value that
liabilities and the EVE will rise (fall).
DGAP Summary
DGAP Summary
Positive
Positive
Change in
Interest
Rates
Increase
Decrease
Decrease > Decrease → Decrease
Increase > Increase → Increase
Negative
Negative
Increase
Decrease
Decrease < Decrease → Increase
Increase < Increase → Decrease
Zero
Zero
Increase
Decrease
Decrease = Decrease →
Increase = Increase →
DGAP
Assets
Liabilities
Equity
None
None
An Immunized Portfolio
 To immunize the EVE from rate
changes in the example, the bank
would need to:
 decrease
the asset duration by 1.42
years or
 increase the duration of liabilities by
1.54 years
 DA / ( MVA/MVL)
= 1.42 / ($920 / $1,000)
= 1.54 years
Immunized Portfolio
1
Par
Years
$1,000 % Coup Mat.
Assets
Cash
$ 100
Earning assets
3-yr Commercial loan
$ 700
6-yr Treasury bond
$ 200
Total Earning Assets $ 900
Non-cash earning assets$ Total assets
$ 1,000
Liabilities
Interest bearing liabs.
1-yr Time deposit
$ 340
3-yr Certificate of deposit$ 300
6-yr Zero-coupon CD* $ 444
Tot. Int Bearing Liabs. $ 1,084
Tot. non-int. bearing
$ Total liabilities
$ 1,084
Total equity
$ 80
YTM
Market
Value
$
12.00%
8.00%
5.00%
7.00%
0.00%
3
6
1
3
6
100
12.00% $ 700
8.00% $ 200
11.11% $ 900
$ 10.00% $ 1,000
5.00%
7.00%
8.00%
6.57%
$
$
$
$
$
6.57% $
$
DGAP = 2.88 – 0.92 (3.11) ≈ 0
Dur.
340
300
280
920
920
80
2.69
4.99
2.88
1.00
2.81
6.00
3.11
Immunized Portfolio with a 1% increase in rates
1
Par
$1,000
Assets
Cash
$ 100.0
Earning assets
3-yr Commercial loan
$ 700.0
6-yr Treasury bond
$ 200.0
Total Earning Assets $ 900.0
Non-cash earning assets$
Total assets
$ 1,000.0
Liabilities
Interest bearing liabs.
1-yr Time deposit
$ 340.0
3-yr Certificate of deposit$ 300.0
6-yr Zero-coupon CD* $ 444.3
Tot. Int Bearing Liabs. $ 1,084.3
Tot. non-int. bearing
$
Total liabilities
$ 1,084.3
Total equity
$ 80.0
Years
% Coup Mat.
YTM
Market
Value
Dur.
$ 100.0
12.00%
8.00%
5.00%
7.00%
0.00%
3
6
1
3
6
13.00% $ 683.5
9.00% $ 191.0
12.13% $ 874.5
$ 10.88% $ 974.5
6.00%
8.00%
9.00%
7.54%
$ 336.8
$ 292.3
$ 264.9
$ 894.0
$ 7.54% $ 894.0
$ 80.5
2.69
4.97
2.86
1.00
2.81
6.00
3.07
Immunized Portfolio with a 1% increase in rates
 EVE changed by only $0.5 with the
immunized portfolio versus $25.0
when the portfolio was not immunized.
Stabilizing the Book Value of Net Interest Income
 This can be done for a 1-year time horizon,
with the appropriate duration gap measure

DGAP* MVRSA(1- DRSA) - MVRSL(1- DRSL)
where:



MVRSA = cumulative market value of RSAs
MVRSL = cumulative market value of RSLs
DRSA = composite duration of RSAs for the
given time horizon
 Equal to the sum of the products of each asset’s
duration with the relative share of its total asset
market value

DRSL = composite duration of RSLs for the
given time horizon
 Equal to the sum of the products of each liability’s
duration with the relative share of its total liability
market value.
Stabilizing the Book Value of Net Interest Income
 If DGAP* is positive, the bank’s net interest
income will decrease when interest rates
decrease, and increase when rates increase.

If DGAP* is negative, the relationship is
reversed.
 Only when DGAP* equals zero is interest
rate risk eliminated.

Banks can use duration analysis to stabilize
a number of different variables reflecting
bank performance.
Economic Value of Equity Sensitivity Analysis
 Effectively involves the same steps as
earnings sensitivity analysis.
 In EVE analysis, however, the bank
focuses on:
 The
relative durations of assets and
liabilities
 How much the durations change in
different interest rate environments
 What happens to the economic value of
equity across different rate environments
Embedded Options
 Embedded options sharply influence the
estimated volatility in EVE
 Prepayments
that exceed (fall short of)
that expected will shorten (lengthen)
duration.
 A bond being called will shorten duration.
 A deposit that is withdrawn early will
shorten duration.
 A deposit that is not withdrawn as
expected will lengthen duration.
Assets
First Savings Bank Economic Value of Equity
Market Value/Duration Report as of 12/31/04
Most Likely Rate Scenario-Base Strategy
Book Value
Market Value Book Yield Duration*
$ 100,000
$
25,000
$ 170,000
$
55,000
$ 250,000
$ 100,000
$
25,000
$ 725,000
$ (15,000)
$ 710,000
$
$
$
$
$
$
$
$
$
$
102,000
25,500
170,850
54,725
245,000
100,500
25,000
723,575
11,250
712,325
9.00%
8.75%
7.50%
6.90%
7.60%
8.00%
14.00%
8.03%
0.00%
8.03%
1.1
0.5
6.0
1.9
1.0
2.6
8.0
2.5
Loans
Prime Based Ln
Equity Credit Lines
Fixed Rate > I yr
Var Rate Mtg 1 Yr
30-Year Mortgage
Consumer Ln
Credit Card
Total Loans
Loan Loss Reserve
Net Loans
Investments
Eurodollars
CMO Fix Rate
US Treasury
Total Investments
$
$
$
$
80,000 $
35,000 $
75,000 $
190,000 $
80,000
34,825
74,813
189,638
5.50%
6.25%
5.80%
5.76%
0.1
2.0
1.8
1.1
Fed Funds Sold
Cash & Due From
Non-int Rel Assets
Total Assets
$
$
$
$
25,000 $
15,000 $
60,000 $
100,000 $
25,000
15,000
60,000
100,000
5.25%
0.00%
0.00%
6.93%
6.5
8.0
2.6
First Savings Bank Economic Value of Equity
Liabilities
Market Value/Duration Report as of 12/31/04
Most Likely Rate Scenario-Base Strategy
Book Value
Market Value Book Yield Duration*
MMDA
Retail CDs
Savings
NOW
DDA Personal
Comm'l DDA
Total Deposits
TT&L
L-T Notes Fixed
Fed Funds Purch
NIR Liabilities
Total Liabilities
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
232,800
400,000
33,600
38,800
52,250
58,200
815,650
25,000
50,250
28,500
919,400
Equity
Total Liab & Equity
$
65,000 $
$ 1,000,000 $
82,563
1,001,963
Deposits
$
$
Off Balance Sheet
lnt Rate Swaps
Adjusted Equity
$
240,000
400,000
35,000
40,000
55,000
60,000
830,000
25,000
50,000
30,000
935,000
- $
1,250
65,000 $
83,813
2.25%
5.40%
4.00%
2.00%
5.00%
8.00%
5.25%
1.1
1.9
1.9
8.0
4.8
1.6
5.9
8.0
2.0
9.9
2.6
6.00%
Notional
2.8 50,000
7.9
Duration Gap for First Savings Bank EVE
 Market Value of Assets
 $1,001,963
 Duration of Assets
 2.6
years
 Market Value of Liabilities
 $919,400
 Duration of Liabilities
 2.0
years
Duration Gap for First Savings Bank EVE
 Duration Gap
2.6 – ($919,400/$1,001,963)*2.0
= 0.765 years
=
 Example:
A
1% increase in rates would reduce
EVE by $7.2 million
= 0.765 (0.01 / 1.0693) * $1,001,963

Recall that the average rate on assets
is 6.93%
Change in EVE (millions of dollars)
Sensitivity of EVE versus Most Likely (Zero Shock)
Interest Rate Scenario
20.0
10.0
13.6
8.8
8.2
2
(10.0)
ALCO Guideline
Board Limit
(20.0)
(8.2)
(20.4)
(30.0)
(36.6)
(40.0)
-300
-200
-100
0
+100
+200
+300
Shocks to Current Rates
Sensitivity of Economic Value of Equity measures the change in the economic value of
the corporation’s equity under various changes in interest rates. Rate changes are
instantaneous changes from current rates. The change in economic value of equity is
derived from the difference between changes in the market value of assets and changes
in the market value of liabilities.
Effective “Duration” of Equity
 By definition, duration measures the
percentage change in market value for
a given change in interest rates
 Thus,
a bank’s duration of equity
measures the percentage change in
EVE that will occur with a 1 percent
change in rates:

Effective duration of equity
9.9 yrs. = $8,200 / $82,563
Asset/Liability Sensitivity and DGAP
 Funding GAP and Duration GAP are NOT
directly comparable
 Funding
GAP examines various “time
buckets” while Duration GAP represents
the entire balance sheet.

Generally, if a bank is liability (asset)
sensitive in the sense that net interest
income falls (rises) when rates rise and
vice versa, it will likely have a positive
(negative) DGAP suggesting that assets
are more price sensitive than liabilities, on
average.
Strengths and Weaknesses: DGAP and EVESensitivity Analysis
 Strengths
 Duration analysis provides a
comprehensive measure of interest rate
risk
 Duration measures are additive
 This allows for the matching of total
assets with total liabilities rather than the
matching of individual accounts
 Duration analysis takes a longer term
view than static gap analysis
Strengths and Weaknesses: DGAP and EVESensitivity Analysis
 Weaknesses
 It is difficult to compute duration
accurately
 “Correct” duration analysis requires that
each future cash flow be discounted by a
distinct discount rate
 A bank must continuously monitor and
adjust the duration of its portfolio
 It is difficult to estimate the duration on
assets and liabilities that do not earn or
pay interest
 Duration measures are highly subjective
Speculating on Duration GAP
 It is difficult to actively vary GAP or
DGAP and consistently win
 Interest
rates forecasts are frequently
wrong
 Even if rates change as predicted,
banks have limited flexibility in vary
GAP and DGAP and must often
sacrifice yield to do so
Gap and DGAP Management Strategies
Example
 Cash flows from investing $1,000 either
in a 2-year security yielding 6 percent or
two consecutive 1-year securities, with
the current 1-year yield equal to 5.5
percent.
0
1
2
Two-Year Security
$60
0
$60
1
2
One-Year Security & then
another One-Year Security
$55
?
Gap and DGAP Management Strategies
Example
 It is not known today what a 1-year security
will yield in one year.
 For the two consecutive 1-year securities to
generate the same $120 in interest, ignoring
compounding, the 1-year security must
yield 6.5% one year from the present.
 This break-even rate is a 1-year forward
rate, one year from the present:

6% + 6% = 5.5% + x
so x must = 6.5%
Gap and DGAP Management Strategies
Example
 By investing in the 1-year security, a
depositor is betting that the 1-year
interest rate in one year will be greater
than 6.5%
 By issuing the 2-year security, the
bank is betting that the 1-year interest
rate in one year will be greater than
6.5%
Yield Curve Strategy
 When the U.S. economy hits its peak,
the yield curve typically inverts, with
short-term rates exceeding long-term
rates.
 Only
twice since WWII has a recession
not followed an inverted yield curve
 As the economy contracts, the Federal
Reserve typically increases the money
supply, which causes the rates to fall
and the yield curve to return to its
“normal” shape.
Yield Curve Strategy
 To take advantage of this trend, when
the yield curve inverts, banks could:
 Buy

long-term non-callable securities
Prices will rise as rates fall
 Make

fixed-rate non-callable loans
Borrowers are locked into higher rates
 Price
deposits on a floating-rate basis
 Lengthen the duration of assets
relative to the duration of liabilities
Interest Rates and the Business Cycle
The general level of interest rates and the shape of the yield curve
appear to follow the U.S. business cycle.
Peak
In expansionary
Short-TermRates
stages rates rise until
they reach a peak as
the Federal Reserve
Long-TermRates
tightens credit
availability.
)t
n
e
c
r
e
P
(
s
e
t
a
Contraction
R
t Expansion
s
In contractionary
e
rstages rates fall until
e
tthey reach a trough
n
Iwhen the U.S.
Expansion
The inverted yield curve has predicted the last
five recessions
DATE WHEN 1-YEAR RATE
LENGTH OF TIME UNTIL
FIRST EXCEEDS 10-YEAR RATE START OF NEXT RECESSION
Trough
economy falls into
recession.
Time
Apr. ’68
Mar. ’73
Sept. ’78
Sept. ’80
Feb. ’89
Dec. ’00
20 months (Dec. ’69)
8 months (Nov. ’73)
16 months (Jan. ’80)
10 months (July ’81)
17 months (July ’90)
15 months (March ’01)
Bank Management, 6th edition.
Timothy W. Koch and S. Scott MacDonald
Copyright © 2006 by South-Western, a division of Thomson Learning
Using Derivatives to Manage
Interest Rate Risk
Chapter 7
Derivatives
 A derivative is any instrument or
contract that derives its value from
another underlying asset, instrument,
or contract.
Managing Interest Rate Risk
 Derivatives Used to Manage Interest
Rate Risk
 Financial
Futures Contracts
 Forward Rate Agreements
 Interest Rate Swaps
 Options on Interest Rates
Interest Rate Caps
 Interest Rate Floors

Characteristics of Financial Futures
 Financial Futures Contracts
A
commitment, between a buyer and a
seller, on the quantity of a
standardized financial asset or index
 Futures Markets
 The
organized exchanges where
futures contracts are traded
 Interest Rate Futures
 When
the underlying asset is an
interest-bearing security
Characteristics of Financial Futures
 Buyers
 A buyer of a futures contract is said to
be long futures
 Agrees to pay the underlying futures
price or take delivery of the underlying
asset
 Buyers gain when futures prices rise
and lose when futures prices fall
 Note that prices and interest rates
move inversely, so buyers gain when
rates fall.
Characteristics of Financial Futures
 Sellers
A
seller of a futures contract is said to
be short futures
 Agrees to receive the underlying
futures price or to deliver the
underlying asset
 Sellers gain when futures prices fall
and lose when futures prices rise

The same for sellers, so they gain when
rates rise.
Characteristics of Financial Futures
 Cash or Spot Market
 Market
for any asset where the buyer
tenders payment and takes possession
of the asset when the price is set
 Forward Contract
 Contract
for any asset where the buyer
and seller agree on the asset’s price
but defer the actual exchange until a
specified future date
Characteristics of Financial Futures
 Forward versus Futures Contracts
 Futures

Contracts
Traded on formal exchanges
 Examples: Chicago Board of Trade and the
Chicago Mercantile Exchange
Involve standardized instruments
 Positions require a daily marking to
market
 Positions require a deposit equivalent
to a performance bond

Characteristics of Financial Futures
 Forward versus Futures Contracts
 Forward
contracts
Terms are negotiated between parties
 Do not necessarily involve
standardized assets
 Require no cash exchange until
expiration
 No marking to market

Types of Futures Traders
 Speculator
 Takes
a position with the objective of
making a profit
 Tries to guess the direction that prices
will move and time trades to sell (buy)
at higher (lower) prices than the
purchase price.
Types of Futures Traders
 Hedger



Has an existing or anticipated position in the
cash market and trades futures contracts to
reduce the risk associated with uncertain
changes in the value of the cash position
Takes a position in the futures market whose
value varies in the opposite direction as the
value of the cash position when rates change
Risk is reduced because gains or losses on
the futures position at least partially offset
gains or losses on the cash position.
Types of Futures Traders
 Hedger versus Speculator
 The
essential difference between a
speculator and hedger is the objective
of the trader.
A speculator wants to profit on trades
 A hedger wants to reduce risk
associated with a known or anticipated
cash position

Types of Futures Traders
 Commission Brokers
 Execute trades for other parties
 Locals
 Trade for their own account
 Locals are speculators
 Scalper
 A speculator who tries to time price
movements over very short time
intervals and takes positions that
remain outstanding for only minutes
Types of Futures Traders
 Day Trader
 Similar to a scalper but tries to profit
from short-term price movements
during the trading day; normally
offsets the initial position before the
market closes such that no position
remains outstanding overnight
 Position Trader
 A speculator who holds a position for a
longer period in anticipation of a more
significant, longer-term market move.
Types of Futures Traders
 Spreader versus Arbitrageur
 Both are speculators that take
relatively low-risk positions
 Futures Spreader
 May simultaneously buy a futures
contract and sell a related futures
contract trying to profit on anticipated
movements in the price difference
 The position is generally low risk
because the prices of both contracts
typically move in the same direction
Types of Futures Traders
 Arbitrageur



Tries to profit by identifying the same asset
that is being traded at two different prices in
different markets at the same time
Buys the asset at the lower price and
simultaneously sells it at the higher price
Arbitrage transactions are thus low risk and
serve to bring prices back in line in the sense
that the same asset should trade at the same
price in all markets
Margin Requirements
 Initial Margin
A
cash deposit (or U.S. government
securities) with the exchange simply
for initiating a transaction
 Initial margins are relatively low, often
involving less than 5% of the
underlying asset’s value
 Maintenance Margin
 The
minimum deposit required at the
end of each day
Margin Requirements
 Unlike margin accounts for stocks,
futures margin deposits represent a
guarantee that a trader will be able to
make any mandatory payment
obligations
 Same effect as a performance bond
Margin Requirements
 Marking-to-Market
 The
daily settlement process where at
the end of every trading day, a trader’s
margin account is:
Credited with any gains
 Debited with any losses

 Variation Margin
 The
daily change in the value of margin
account due to marking-to-market
Expiration and Delivery
 Expiration Date
 Every futures contract has a formal
expiration date
 On the expiration date, trading stops
and participants settle their final
positions
 Less than 1% of financial futures
contracts experience physical delivery
at expiration because most traders
offset their futures positions in
advance
Example
 90-Day Eurodollar Time Deposit
Futures
 The
underlying asset is a Eurodollar
time deposit with a 3-month maturity.
 Eurodollar rates are quoted on an
interest-bearing basis, assuming a 360day year.
 Each Eurodollar futures contract
represents $1 million of initial face
value of Eurodollar deposits maturing
three months after contract expiration.
Example
 90-Day Eurodollar Time Deposit
Futures
 Forty
separate contracts are traded at
any point in time, as contracts expire
in March, June, September and
December each year
 Buyers make a profit when futures
rates fall (prices rise)
 Sellers make a profit when futures
rates rise (prices fall)
Example
 90-Day Eurodollar Time Deposit
Futures
 Contracts
trade according to an index
that equals

100% - the futures interest rate
 An index of 94.50 indicates a futures rate
of 5.5 percent
 Each
basis point change in the futures
rate equals a $25 change in value of
the contract (0.001 x $1 million x
90/360)
Eurodollar Futures
 The first column indicates the




settlement month and year
Each row lists price and yield
data for a distinct futures
contract that expires
sequentially every three
months
The next four columns report
the opening price, high and
low price, and closing
settlement price.
The next column, the change
in settlement price from the
previous day.
The two columns under Yield
convert the settlement price to
a Eurodollar futures rate as:
100 - Settlement Price
= Futures Rate
Eurodollar (CME)-$1,000,000; pts of 100%
OPEN
INT
Mar
96.98 96.99 96.98
96.99
— 3.91
—
823,734
Apr
96.81 96.81 96.81
96.81
_.01 3.19
.01
19,460
June 96.53 96.55 96.52
96.54
— 3.46
— 1,409,983
Sept 96.14 96.17 96.13
96.15
_.01 3.05
.01 1,413,496
Dec
95.92 95.94 95.88
95.91
_.01 4.09
.01 1,146,461
Mr06 95.78 95.80 95.74
95.77
_.01 4.23
.01
873,403
June 95.64 95.60 95.62
95.64
_.01 4.34
.01
567,637
Sept 95.37 95.58 95.53
95.54
_.01 4.44
.01
434,034
Dec
95.47 95.50 95.44
95.47
— 4.53
—
300,746
Mr07 95.42 95.44 95.37
95.42
— 4.58
—
250,271
June 95.31 95.38 95.31
95.37
.01
4.63 _.01
211,664
Sept 95.27 95.32 95.23
95.31
.02
4.69 _.02
164,295
Dec
95.21 95.27 95.18
95.26
.03
4.74 _.03
154,123
Mr08 95.16 95.23 95.11
95.21
.04
4.79 _.04
122,800
June 95.08 95.17 95.07
95.14
.05
4.84 _.05
113,790
Sept 95.03 95.13 95.01
95.11
.06
4.89 _.06
107,792
Dec
94.95 95.06 94.94
95.05
.07
4.95 _.07
96,046
Mr09 94.91 95.02 94.89
95.01
.08
4.99 _.07
81,015
June 94.05 94.97 94.84
94.97
.08
5.03 _.08
76,224
Sept 94.81 94.93 94.79
94.92
.08
5.08 _.08
41,524
Dec
94.77 94.38 94.74
94.87
.08
5.15 _.08
40,594
Mr10 94.77 94.64 94.70
94.83
.09
5.27 _.09
17,481
Sept 94.66 94.76 94.62
94.75
.09
5.25 _.09
9,309
Sp11 94.58 94.60 94.47
94.60
.09
5.40 _.09
2,583
Dec
94.49 94.56 94.43
94.56
.09
5.44 _.09
2,358
Mr12 94.48 94.54 94.41
94.53
.09
5.47 _.09
1,392
Est vol 2,082,746; vol Wed 1,519,709; open int 8,631,643, _160,422.
OPEN HIGH LOW
SETTLE CHA YIELD CHA
The Basis
 The basis is the cash price of an asset
minus the corresponding futures price
for the same asset at a point in time
 For
financial futures, the basis can be
calculated as the futures rate minus
the spot rate
 It may be positive or negative,
depending on whether futures rates
are above or below spot rates
 May swing widely in value far in
advance of contract expiration
The Relationship Between Futures Rates and
Cash Rates - One Possible Pattern on March 10
Rate (Percent)
4.50
December 2005
Futures Rate
4.09
Cash Rate
3.00
1.76
Basis Futures Rate- Cash Rate
1.09
0
March 10, 2005
August 23, 2005
Expiration
December 20, 2005
Speculation versus Hedging
 A speculator takes on additional risk
to earn speculative profits
 Speculation
is extremely risky
 A hedger already has a position in the
cash market and uses futures to adjust
the risk of being in the cash market
 The
risk
focus is on reducing or avoiding
Speculation versus Hedging
 Example
 Speculating

You believe interest rates will fall, so
you buy Eurodollar futures
 If rates fall, the price of the underlying
Eurodollar rises, and thus the futures
contract value rises earning you a profit
 If rates rise, the price of the Eurodollar
futures contract falls in value, resulting in
a loss
Speculation versus Hedging
 Example
 Hedging

A bank anticipates needing to borrow
$1,000,000 in 60 days. The bank is
concerned that rates will rise in the
next 60 days
 A possible strategy would be to short
Eurodollar futures.
 If interest rates rise (fall), the short
futures position will increase (decrease)
in value. This will (partially) offset the
increase (decrease) in borrowing costs
Speculation versus Hedging
 With financial futures, risk often
cannot be eliminated, only reduced.
 Traders
normally assume basis risk in
that the basis might change adversely
between the time the hedge is initiated
and closed
 Perfect Hedge
 The
gains (losses) from the futures
position perfectly offset the losses
(gains) on the spot position at each
price
Profit Diagrams for the December 2005
Eurodollar Futures Contract: Mar 10, 2005
Steps in Hedging
 Identify the cash market risk exposure to reduce
 Given the cash market risk, determine whether a





long or short futures position is needed
Select the best futures contract
Determine the appropriate number of futures
contracts to trade.
Buy or sell the appropriate futures contracts
Determine when to get out of the hedge position,
either by reversing the trades, letting contracts
expire, or making or taking delivery
Verify that futures trading meets regulatory
requirements and the banks internal risk policies
A Long Hedge
 A long hedge (buy futures) is appropriate for
a participant who wants to reduce spot
market risk associated with a decline in
interest rates
 If spot rates decline, futures rates will
typically also decline so that the value of the
futures position will likely increase.
 Any loss in the cash market is at least
partially offset by a gain in futures
Long Hedge Example
 On March 10, 2005, your bank expects to
receive a $1 million payment on November
8, 2005, and anticipates investing the funds
in 3-month Eurodollar time deposits


The cash market risk exposure is that the
bank will not have access to the funds for
eight months.
In March 2005, the market expected
Eurodollar rates to increase sharply as
evidenced by rising futures rates.
Long Hedge Example
 In order to hedge, the bank should buy
futures contracts
 The
best futures contract will generally
be the December 2005, 3-month
Eurodollar futures contract, which is
the first to expire after November 2005.

The contract that expires immediately
after the known cash transactions date
is generally best because its futures
price will show the highest correlation
with the cash price.
Long Hedge Example
 The time line of the bank’s hedging
activities would look something like
this:
March 10, 2005
November 8, 2005
December 20, 2005
Cash: Anticipated investment
Futures: Buy a futures contract
Invest $1 million
Sell the futures contract
Expiration of Dec. 2005
futures contract
Long Hedge Example
Date
Cash Market
Futures Market
Basis
3/10/05
(Initial futures
position)
11/8/05
(Close futures
position)
Net effect
Bank anticipates investing $1 million
in Eurodollars in 8 months; current
cash rate = 3.00%
Bank invests $1 million in 3-month
Eurodollars at 3.93%
Bank buys one December 2005
Eurodollar futures contract at
4.09%; price = 95.91
Bank sells one December 2005
Eurodollar futures contract at
4.03%; price = 95.97%
Futures profit:
4.09% - 4.03% = 0.06%;
6 basis points worth
$25 each = $150
4.09% - 3.00% = 1.09%
Opportunity gain:
3.93% - 3.00% = 0.93%;
93 basis points worth
$25 each = $2,325
Cumulative
e investment income:
Interest at 3.93% = $1,000,000(.0393)(90/360) = $9,825
Profit from futures trades = $ 150
Total = $9,975
Effective return 
$9,975 360
 3.99%
$1,000,000 90
4.03% - 3.93% = 0.10%
Basis change: 0.10% - 1.09%
= -0.99%
A Short Hedge
 A short hedge (sell futures) is appropriate
for a participant who wants to reduce spot
market risk associated with an increase in
interest rates
 If spot rates increase, futures rates will
typically also increase so that the value of
the futures position will likely decrease.
 Any loss in the cash market is at least
partially offset by a gain in the futures
market
Short Hedge Example
 On March 10, 2005, your bank expects
to sell a six-month $1 million
Eurodollar deposit on August 15, 2005
 The
cash market risk exposure is that
interest rates may rise and the value of
the Eurodollar deposit will fall by
August 2005
 In order to hedge, the bank should sell
futures contracts
Short Hedge Example
 The time line of the bank’s hedging
activities would look something like
this:
March 10, 2005
August 17, 2005
Cash: Anticipated sale of
Sell $1 million Eurodollar
investment
Deposit
Futures: Sell a futures contract Buy the futures contract
September 20, 2005
Expiration of Sept. 2005
futures contract
Short Hedge Example
Date
3/10/05
8/17/05
Net result:
Cash Market
Bank anticipates selling
$1 million Eurodollar
deposit in 127 days;
current cash rate
= 3.00%
Bank sells $1 million
Eurodollar deposit at
4.00%
Opportunity loss.
4.00% - 3.00% = 1.00%;
100 basis points worth
$25 each = $2,500
Futures Market
Bank sells one Sept.
2005 Eurodollar futures
contract at 3.85%;
price = 96.15
Basis
3.85% - 3.00% = 0.85%
Bank buys one Sept.
2005 Eurodollar futures
contract at 4.14%;
price = 95.86
Futures profit:
4.14% - 3.85% 3 0.29%;
29 basis points worth
$25 each = $725
4.14% - 4.00% = 0.14%
Effective loss = $2,500 - $725 = $1,775
Effective rate at sale of deposit = 4.00% - 0.29% = 3.71%
or 3.00% - (0.71%) = 3.71%
Basis change: 0.14% - 0.85%
=-0.71%
Change in the Basis
 Long and short hedges work well if the
futures rate moves in line with the spot
rate
 The actual risk assumed by a trader in
both hedges is that the basis might
change between the time the hedge is
initiated and closed
 In
the long hedge position above, the
spot rate increased by 0.93% while the
futures rate fell by 0.06%. This caused
the basis to fall by 0.99% (The basis
fell from 1.09% to 0.10%, or by 0.99%)
Change in the Basis
 Effective Return from a Hedge
 Total
income from the combined cash
and futures positions relative to the
investment amount
 Effective return
 Initial

Cash Rate - Change in Basis
In the long hedge example:
 3.00% - (-0.99%) = 3.99%
Basis Risk and Cross Hedging
 Cross Hedge
 Where a trader uses a futures contract
based on one security that differs from
the security being hedged in the cash
market
 Example
 Using Eurodollar futures to hedge changes
in the commercial paper rate
 Basis
risk increases with a cross
hedge because the futures and spot
interest rates may not move closely
together
Microhedging Applications
 Microhedge
 The
hedging of a transaction
associated with a specific asset,
liability or commitment
 Macrohedge
 Taking
futures positions to reduce
aggregate portfolio interest rate risk
Microhedging Applications
 Banks are generally restricted in their
use of financial futures for hedging
purposes
 Banks
must recognize futures on a
micro basis by linking each futures
transaction with a specific cash
instrument or commitment

Many analysts feel that such micro
linkages force microhedges that may
potentially increase a firm’s total risk
because these hedges ignore all other
portfolio components
Creating a Synthetic Liability with a Short Hedge
Time Line
3/10/05
7/3/05
Six-Month Deposit
Synthetic
Six-Month Deposit
3.25%
3.00%
Three-Month Cash Eurodollar
3.88%
-0.48%
Profit = 3.40%
Three-Month Synthetic Eurodollar
All In Six-Month Cost = 3.20%
9/30/05
Creating a Synthetic Liability with a Short Hedge
Summary of Relevant Eurodollar Rates and Transactions
March 10, 2005
3-month cash rate = 3.00%; bank issues a $1 million, 91-day Eurodollar deposit
6-month cash rate = 3.25%
Bank sells one September 2005 Eurodollar futures; futures rate = 3.85%
July 3, 2005
3-month cash rate = 3.88%; bank issues a $1 million, 91-day Eurodollar deposit
Buy: One September 2005 Eurodollar futures; futures rate = 4.33%
Date
Cash Market
Futures Market
Basis
3/10/05
Bank issues $1 million, 91-day Eurodollar time deposit
at 3.00%; 3-mo. interest expense = $7,583.
Bank sells one September 2005
Eurodollar futures contract at 3.85%
0.85%
7/3/05
Bank issues $1 million, 91-day Eurodollar time deposit
at 3.88%; 3-mo. interest expense = $9,808 (increase
in interest expense over previous period = $2,225).
6-mo. interest expense = $17,391
Bank buys one September 2005
Eurodollar futures contract at 4.33%;
0.45%
Net effect:
Profit on futures = $1,200
$17,391- $1,200 360
 3.20%
$1,000,000 182
Interest on 6-month Eurodollar deposit issued March 10 = $13,144 at 3.25%; vs. 3.20% from synthetic liability
Effective borrowing cost 
The Mechanics of Applying a Microhedge
1. Determine the bank’s interest rate
position
2. Forecast the dollar flows or value
expected in cash market transactions
3. Choose the appropriate futures
contract
The Mechanics of Applying a Microhedge
4. Determine the correct number of futures
contracts

Where
A  Mc
NF 
b
F  Mf
NF = number of futures contracts

A = Dollar value of cash flow to be hedged

F = Face value of futures contract

Mc = Maturity or duration of anticipated cash
asset or liability

Mf = Maturity or duration of futures contract
 b  Expected rate movement on cash instrument
Expected rate movement on futures contract

The Mechanics of Applying a Microhedge
5. Determine the Appropriate Time
Frame for the Hedge
6. Monitor Hedge Performance
Macrohedging
 Macrohedging
 Focuses
on reducing interest rate risk
associated with a bank’s entire
portfolio rather than with individual
transactions
Macrohedging
 Hedging: GAP or Earnings Sensitivity
 If GAP is positive, the bank is asset sensitive
and its net interest income rises when
interest rates rise and falls when interest
rates fall
 If GAP is negative, the bank is liability
sensitive and its net interest income falls
when interest rates rise and rises when
interest rates fall

Positive GAP


Use a long hedge
Negative GAP

Use a short hedge
Hedging: GAP or Earnings Sensitivity
 Positive GAP
 Use
a long hedge
If rates rise, the bank’s higher net
interest income will be offset by losses
on the futures position
 If rates fall, the bank’s lower net
interest income will be offset by gains
on the futures position

Hedging: GAP or Earnings Sensitivity
 Negative GAP
 Use
a short hedge
If rates rise, the bank’s lower net
interest income will be offset by gains
on the futures position
 If rates fall, the bank’s higher net
interest income will be offset by losses
on the futures position

Hedging: Duration GAP and EVE Sensitivity
 To eliminate interest rate risk, a bank
could structure its portfolio so that its
duration gap equals zero
y
ΔEVE  - DGAP[
]MVA
(1  y)
Hedging: Duration GAP and EVE Sensitivity
 Futures can be used to adjust the
bank’s duration gap
 The
appropriate size of a futures
position can be determined by solving
the following equation for the market
value of futures contracts (MVF), where
DF is the duration of the futures
contract
DA(MVRSA) DL(MVRSL) DF(MVF)


0
1  ia
1  il
1  if
Hedging: Duration GAP and EVE Sensitivity
 Example:
A
bank has a positive duration gap of
1.4 years, therefore, the market value
of equity will decline if interest rates
rise. The bank needs to sell interest
rate futures contracts in order to hedge
its risk position
 The short position indicates that
the bank will make a profit if futures
rates increase
Hedging: Duration GAP and EVE Sensitivity
 Example:
 Assume
the bank uses a Eurodollar
futures contract currently trading at
4.9% with a duration of 0.25 years, the
target market value of futures
contracts (MVF) is:
2.88($900) 1.61($920) 0.25(MVF)


0
(1.10)
(1.06)
(1.049)

MVF = $4,024.36, so the bank should
sell four Eurodollar futures contracts
Hedging: Duration GAP and EVE Sensitivity
 Example:
 If
all interest rates increased by 1%, the
profit on the four futures contracts
would total 4 x 100 x $25 = $10,000,
which partially offset the $12,000
decrease in the economic value of
equity associated with the increase in
cash rates

Recall from Exhibit 6.2, the unhedged
bank had a reduction in EVE of $12,000
Accounting Requirements and Tax Implications
 Regulators generally limit a bank’s use of
futures for hedging purposes



If a bank has a dealer operation, it can use
futures as part of its trading activities
In such accounts, gains and losses on these
futures must be marked-to-market, thereby
affecting current income
Microhedging

To qualify as a hedge, a bank must show that
a cash transaction exposes it to interest rate
risk, a futures contract must lower the bank’s
risk exposure, and the bank must designate
the contract as a hedge
Using Forward Rate Agreements to Manage
Interest Rate Risk
 Forward Rate Agreements
 A forward contract based on interest rates based on a
notional principal amount at a specified future date
 Buyer
 Agrees to pay a fixed-rate coupon payment (at the
exercise rate) and receive a floating-rate payment
 Seller
 Agrees to make a floating-rate payment and receive a
fixed-rate payment
 The buyer and seller will receive or pay cash when
the actual interest rate at settlement is different
than the exercise rate
Forward Rate Agreements (FRA)
 Similar to futures but differ in that
they:
 Are
negotiated between parties
 Do not necessarily involve
standardized assets
 Require no cash exchange until
expiration

There is no marking-to-market
 No
exchange guarantees performance
Notional Principal
 The two counterparties to a forward
rate agreement agree to a notional
principal amount that serves as a
reference figure in determining cash
flows.
 Notional

Refers to the condition that the
principal does not change hands, but is
only used to calculate the value of
interest payments.
Notional Principal
 Buyer
 Agrees to pay a fixed-rate coupon
payment and receive a floating-rate
payment against the notional principal
at some specified future date.
 Seller
 Agrees to pay a floating-rate payment
and receive the fixed-rate payment
against the same notional principal.
Example: Forward Rate Agreements
 Suppose that Metro Bank (as the
seller) enters into a receive fixedrate/pay floating-rating forward rate
agreement with County Bank (as the
buyer) with a six-month maturity
based on a $1 million notional
principal amount
 The floating rate is the 3-month LIBOR
and the fixed (exercise) rate is 7%
Example: Forward Rate Agreements
 Metro Bank would refer to this as a “3 vs. 6”
FRA at 7 percent on a $1 million notional
amount from County Bank
 The phrase “3 vs. 6” refers to a 3-month
interest rate observed three months from
the present, for a security with a maturity
date six months from the present
 The only cash flow will be determined in six
months at contract maturity by comparing
the prevailing 3-month LIBOR with 7%
Example: Forward Rate Agreements
 Assume that in three months 3-month
LIBOR equals 8%

In this case, Metro Bank would receive from
County Bank $2,451.

The interest settlement amount is $2,500:
 Interest = (.08 - .07)(90/360) $1,000,000 = $2,500.

Because this represents interest that would
be paid three months later at maturity of the
instrument, the actual payment is discounted
at the prevailing 3-month LIBOR:
 Actual interest = $2,500/[1+(90/360).08]=$2,451
Example: Forward Rate Agreements
 If instead, LIBOR equals 5% in three
months, Metro Bank would pay County
Bank:
 The


interest settlement amount is $5,000
Interest = (.07 -.05)(90/360) $1,000,000 = $5,000
Actual interest = $5,000 /[1 + (90/360).05] = $4,938
Example: Forward Rate Agreements
 The FRA position is similar to a futures
position
 County
Bank would pay fixedrate/receive floating-rate as a hedge if
it was exposed to loss in a rising rate
environment.

This is analogous to a short futures
position
Example: Forward Rate Agreements
 The FRA position is similar to a futures
position
 Metro
Bank would take its position as a
hedge if it was exposed to loss in a
falling (relative to forward rate) rate
environment.

This is analogous to a long futures
position
Basic Interest Rate Swaps
 Basic or Plain Vanilla Interest Rate
Swap
 An
agreement between two parties to
exchange a series of cash flows based
on a specified notional principal
amount
 Two parties facing different types of
interest rate risk can exchange interest
payments
Basic Interest Rate Swaps
 Basic or Plain Vanilla Interest Rate
Swap
 One
party makes payments based on a
fixed interest rate and receives floating
rate payments
 The other party exchanges floating rate
payments for fixed-rate payments
 When interest rates change, the party
that benefits from a swap receives a
net cash payment while the party that
loses makes a net cash payment
Basic Interest Rate Swaps
 Conceptually, a basic interest rate
swap is a package of FRAs
 As
with FRAs, swap payments are
netted and the notional principal never
changes hands
Basic Interest Rate Swaps
 Using data for a 2-year swap based on
3-month LIBOR as the floating rate
 This
swap involves eight quarterly
payments.
Party FIX agrees to pay a fixed rate
 Party FLT agrees to receive a fixed rate
with cash flows calculated against a
$10 million notional principal amount

Basic Interest Rate Swaps
Basic Interest Rate Swaps
 Firms with a negative GAP can reduce
risk by making a fixed-rate interest
payment in exchange for a floating-rate
interest receipt
 Firms with a positive GAP take the
opposite position, by making floatinginterest payments in exchange for a
fixed-rate receipt
Basic Interest Rate Swaps
 Basic interest rate swaps are used to:
 Adjust the rate sensitivity of an asset
or liability
 For example, effectively converting a
fixed-rate loan into a floating-rate loan
 Create a synthetic security
 For example, enter into a swap instead
of investing in a security
 Macrohedge
 Use swaps to hedge the bank’s
aggregate interest rate risk
Basic Interest Rate Swaps
 Swap Dealers
 Handle
most swap transactions
 Make a market in swap contracts
 Offer terms for both fixed-rate and
floating rate payers and earn a spread for
their services
Basic Interest Rate Swaps
 Comparing Financial Futures, FRAs,
and Basic Swaps
Objective
Profit If Rates Rise
Profit If Rates Fall
Financial Futures
Sell Futures
Buy Futures
Position
FRAs & Basic Swaps
Pay Fixed, Receive Floating
Pay Floating, Receive Fixed
 There is some credit risk with swaps in
that the counterparty may default on
the exchange of the interest payments
 Only
the interest payment exchange is
at risk, not the principal
Interest Rate Caps and Floors
 Interest Rate Cap
 An
agreement between two
counterparties that limits the buyer’s
interest rate exposure to a maximum
limit

Buying a interest rate cap is the same
as purchasing a call option on an
interest rate
Buying a Cap on 3-Month LIBOR at 4 percent
A. Cap 5 Long Call Option on Three-Month LIBOR
Dollar Payout
(Three-month LIBOR
- 4%) 3 Notional
Principal Amount
1C
Three-Month
LIBOR
4 Percent
B. Cap Payoff: Strike Rate 5 4 Percent*
Rate
Floating
Rate
4 Percent
Value
Date
Value
Date
Value
Date
Time
Value
Date
Value
Date
Interest Rate Caps and Floors
 Interest Rate Floor
 An
agreement between two
counterparties that limits the buyer’s
interest rate exposure to a minimum
rate

Buying an interest rate floor is the
same as purchasing a put option on an
interest rate
Buying a Floor on 3-Month LIBOR at 4 percent
A. Floor = Long Put Option on Three-Month LIBOR
Dollar Payout
(4% - Three-month
LIBOR) X Notional
Principal Amount
1P
Three-Month
LIBOR
4 Percent
B. Floor Payoff: Strike Rate = 4 Percent*
Rate
Floating
Rate
4 Percent
Value
Date
Value
Date
Value
Date
Time
Value
Date
Value
Date
Interest Rate Caps and Floors
 Interest Rate Collar
 The simultaneous purchase of an
interest rate cap and sale of an interest
rate floor on the same index for the
same maturity and notional principal
amount
 A collar creates a band within which
the buyer’s effective interest rate
fluctuates
 It protects a bank from rising interest
rates
Interest Rate Caps and Floors
 Zero Cost Collar
 A collar where the buyer pays no net
premium
 The premium paid for the cap equals
the premium received for the floor
 Reverse Collar
 Buying an interest rate floor and
simultaneously selling an interest rate
cap
 It protects a bank from falling interest
rates
Pricing Interest Rate Caps and Floors
 The size of the premiums for caps and
floors is determined by:
 The
relationship between the strike
rate an the current index

This indicates how much the index
must move before the cap or floor is inthe-money
 The
shape of yield curve and the
volatility of interest rates

With an upward sloping yield curve,
caps will be more expensive than floors
Pricing Interest Rate Caps and Floors
A. Caps/Floors
Term
Bid
Offer
Caps
4.00%
Bid
Offer
5.00%
Bid
Offer
6.00%
1 year
2 years
3 years
5 years
7 years
10 years
3
36
74
135
201
278
1
10
22
76
101
157
24
51
105
222
413
549
Floors
1 year
2 years
3 years
5 years
7 years
10 years
30
57
115
240
433
573
1.50%
1
1
7
24
38
85
2
6
16
39
60
115
7
43
84
150
324
308
2.00%
15
31
40
75
92
162
19
37
49
88
106
192
2
15
29
5
116
197
2.50%
57
84
128
190
228
257
55
91
137
205
250
287