Managing Interest Rate
Risk: GAP and
Earnings Sensitivity
1
Managing 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
2
Managing Interest Rate Risk
 Interest Rate Risk
 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
3
Managing Interest Rate Risk
 Interest Rate Risk

Banks typically focus on either:



GAP Analysis


Net interest income or
The market value of stockholders' equity
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
4
Managing Interest Rate Risk
 Interest Rate Risk
 Asset
and Liability Management
Committee (ALCO)
The bank’s ALCO primary
responsibility is interest rate risk
management.
 The ALCO coordinates the bank’s
strategies to achieve the optimal
risk/reward trade-off

5
Measuring Interest Rate Risk with
GAP
 Three general factors potentially cause a
bank’s net interest income to change.

Rate Effects


Composition (Mix) Effects


Unexpected changes in interest rates
Changes in the mix, or composition, of
assets and/or liabilities
Volume Effects

Changes in the volume of earning assets
and interest-bearing liabilities
6
Measuring Interest Rate Risk with
GAP
 Consider a bank that makes a $25,000
five-year car loan to a customer at
fixed rate of 8.5%. The bank initially
funds the car loan with a one-year
$25,000 CD at a cost of 4.5%. The
bank’s initial spread is 4%.
 What
is the bank’s risk?
7
Measuring Interest Rate Risk with
GAP
 Traditional Static Gap Analysis
 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)
8
Measuring Interest Rate Risk with
GAP
 Traditional Static Gap Analysis
 Steps in GAP Analysis
1.
Develop an interest rate forecast
2.
Select a series of “time buckets” or time
intervals for determining when assets
and liabilities will reprice
3.
Group assets and liabilities into these
“buckets”
4.
Calculate the GAP for each “bucket ”
5.
Forecast the change in net interest
income given an assumed change in
interest rates
9
Measuring Interest Rate Risk with
GAP
 What Determines Rate Sensitivity
 The initial issue is to determine what
features make an asset or liability rate
sensitive
10
Measuring Interest Rate Risk with
GAP

Expected Repricing versus Actual
Repricing

In general, an asset or liability is normally
classified as rate sensitive within a time
interval if:
 It matures
 It represents an interim or partial principal
payment
 The interest rate applied to the outstanding
principal balance changes contractually during
the interval
 The interest rate applied to the outstanding
principal balance changes when some base
rate or index changes and management
expects the base rate/index to change during
the time interval
11
Measuring Interest Rate Risk with
GAP
 What Determines Rate Sensitivity
 Maturity
 If any asset or liability matures within a
time interval, the principal amount will be
repriced
 The question is what principal amount is
expected to reprice

Interim or Partial Principal Payment

Any principal payment on a loan is rate
sensitive if management expects to
receive it within the time interval
 Any interest received or paid is not included in
the GAP calculation
12
Measuring Interest Rate Risk with
GAP
 What Determines Rate Sensitivity
 Contractual
Change in Rate
Some assets and deposit liabilities earn
or pay rates that vary contractually with
some index
 These instruments are repriced
whenever the index changes

 If management knows that the index will
contractually change within 90 days, the
underlying asset or liability is rate
sensitive within 0–90 days.
13
Measuring Interest Rate Risk with
GAP
 What Determines Rate Sensitivity
 Change in Base Rate or Index
 Some loans and deposits carry interest
rates tied to indexes where the bank has
no control or definite knowledge of when
the index will change.
 For example, prime rate loans typically
state that the bank can contractually
change prime daily
 The loan is rate sensitive in the sense that its
yield can change at any time
 However, the loan’s effective rate sensitivity
depends on how frequently the prime rate
actually changes
14
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Rate,
Composition (Mix) and Volume
Effects

All affect net interest income
15
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes

in the Level of Interest Rates
The sign of GAP (positive or negative)
indicates the nature of the bank’s
interest rate risk
 A negative (positive) GAP, indicates that
the bank has more (less) RSLs than RSAs.
When interest rates rise (fall) during the
time interval, the bank pays higher (lower)
rates on all repriceable liabilities and earns
higher (lower) yields on all repriceable
assets
16
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income

Changes in the Level of Interest Rates

The sign of GAP (positive or negative)
indicates the nature of the bank’s interest
rate risk
 If all rates rise (fall) by equal amounts at the
same time, both interest income and interest
expense rise (fall), but interest expense rises
(falls) more because more liabilities are
repriced
 Net interest income thus declines (increases),
as does the bank’s net interest margin
17
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes
in the Level of Interest Rates
If a bank has a zero GAP, RSAs equal
RSLs and equal interest rate changes
do not alter net interest income
because changes in interest income
equal changes in interest expense
 It is virtually impossible for a bank to
have a zero GAP given the complexity
and size of bank balance sheets

18
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
19
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes

in the Level of Interest Rates
GAP analysis assumes a parallel shift
in the yield curve
20
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income

Changes in the Level of Interest Rates

If there is a parallel shift in the yield curve
then changes in Net Interest Income are
directly proportional to the size of the
GAP:
∆NIIEXP = GAP x ∆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
21
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes

in the Level of Interest Rates
Example 1
 Recall the bank that makes a $25,000 fiveyear car loan to a customer at fixed rate of
8.5%. The bank initially funds the car loan
with a one-year $25,000 CD at a cost of
4.5%. What is the bank’s 1-year GAP?
22
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes in the Level of Interest Rates
 Example 1
 RSA1 YR = $0
 RSL1 YR = $10,000
 GAP1 YR = $0 - $25,000 = -$25,000
 The bank’s one year funding GAP is $25,000
 If interest rates rise (fall) by 1% in 1 year,
the bank’s net interest margin and net
interest income will fall (rise)
 ∆NIIEXP = GAP x ∆iEXP = -$10,000 x 1% = $100
23
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes

in the Level of Interest Rates
Example 2
 Assume a bank accepts an 18-month
$30,000 CD deposit at a cost of 3.75% and
invests the funds in a $30,000 6-month TBill at rate of 4.80%. The bank’s initial
spread is 1.05%. What is the bank’s 6month GAP?
24
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes in the Level of Interest Rates
 Example 2
 RSA6 MO = $30,000
 RSL6 MO = $0
 GAP6 MO = $30,000 – $0 = $30,000
 The bank’s 6-month funding GAP is $30,000
 If interest rates rise (fall) by 1% in 6
months, the bank’s net interest margin and
net interest income will rise (fall)
 ∆NIIEXP = GAP x ∆iEXP = $30,000 x 1% =
$300
25
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income

Changes in the Relationship Between
Asset Yields and Liability Costs
Net interest income may differ from that
expected if the spread between earning
asset yields and the interest cost of
interest-bearing liabilities changes
 The spread may change because of a
nonparallel shift in the yield curve or
because of a change in the difference
between different interest rates (basis risk)

26
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes in Volume
 Net interest income varies directly with
changes in the volume of earning assets
and interest-bearing liabilities, regardless
of the level of interest rates
 For example, if a bank doubles in size but
the portfolio composition and interest
rates remain unchanged, net interest
income will double because the bank
earns the same interest spread on twice
the volume of earning assets such that
NIM is unchanged
27
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Changes
in Portfolio Composition
Any variation in portfolio mix
potentially alters net interest income
 There is no fixed relationship between
changes in portfolio mix and net
interest income

 The impact varies with the relationships
between interest rates on rate-sensitive
and fixed-rate instruments and with the
magnitude of funds shifts
28
29
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example
Rate sensitive
Fixed rate
Non earning
Total
3.0
Balance Sheet
Assets
Yield
$
500
8.0%
$
350
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
4.0%
6.0%
30
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

3.0
Interest Income
 ($500 x 8%) + ($350 x 11%) = $78.50

Interest Expense
 ($600 x 4%) + ($220 x 6%) = $37.20

Net Interest Income
 $78.50 - $37.20 = $41.30
31
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

3.0
Earning Assets
 $500 + $350 = $850

Net Interest Margin
 $41.3/$850 = 4.86%

Funding GAP
 $500 - $600 = -$100
32
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if all rates increase by 1%?
Rate sensitive
Fixed rate
Non earning
Total
3.1
Balance Sheet
Assets
Yield
$
500
9.0%
$
350
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
5.0%
6.0%
33
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 3.1
 What if all rates increase by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP
∆NIIEXP

$ 83.50
$ 43.20
$ 40.30
4.74%
$ (100)
$ (1.00)
With a negative GAP, interest income
increases by less than the increase in
interest expense. Thus, both NII and NIM
fall.
34
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if all rates fall by 1%?
Rate sensitive
Fixed rate
Non earning
Total
3.2
Balance Sheet
Assets
Yield
$
500
7.0%
$
350
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
3.0%
6.0%
35
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 3.2
 What if all rates fall by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP
∆NIIEXP

$ 73.50
$ 31.20
$ 42.30
4.98%
$ (100)
$ 1.00
With a negative GAP, interest income
decreases by less than the decrease in
interest expense. Thus, both NII and NIM
increase.
36
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

3.3
What if rates rise but the spread falls by
1%?
Rate sensitive
Fixed rate
Non earning
Total
Balance Sheet
Assets
Yield
$
500
8.5%
$
350
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
5.5%
6.0%
37
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 3.3
 What if rates rise but the spread falls by
1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 81.00
$ 46.20
$ 34.80
4.09%
$ (100)
Both NII and NIM fall with a decrease in the
spread. Why the larger change?
 Note: ∆NIIEXP ≠ GAP x ∆iEXP Why?
38
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

3.4
What if rates fall but the spread falls by
1%?
Rate sensitive
Fixed rate
Non earning
Total
Balance Sheet
Assets
Yield
$
500
6.5%
$
350
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
3.5%
6.0%
39
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 3.4
 What if rates fall and the spread falls by
1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 71.00
$ 34.20
$ 36.80
4.33%
$ (100)
Both NII and NIM fall with a decrease in the
spread.
 Note: ∆NIIEXP ≠ GAP x ∆iEXP
40
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates rise and the spread rises
by 1%?
Rate sensitive
Fixed rate
Non earning
Total
3.5
Balance Sheet
Assets
Yield
$
500
10.0%
$
350
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
5.0%
6.0%
41
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 3.5
 What if rates rise and the spread rises by
1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 88.50
$ 43.20
$ 45.30
5.33%
$ (100)
Both NII and NIM increase with an increase
in the spread.
 Note: ∆NIIEXP ≠ GAP x ∆iEXP
42
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates fall and the spread rises
by 1%?
Balance Sheet
Rate sensitive
Fixed rate
Non earning
Total
3.6
Assets
$
500
$
350
$
150
$ 1,000
Yield
7.0%
11.0%
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
2.0%
6.0%
43
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 3.6
 What if rates fall and the spread rises by
1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 73.50
$ 25.20
$ 48.30
5.68%
$ (100)
Both NII and NIM increase with an increase
in the spread.
 Note: ∆NIIEXP ≠ GAP x ∆iEXP
44
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if the bank proportionately
doubles in size?
Rate sensitive
Fixed rate
Non earning
Total
3.7
Balance Sheet
Assets
Yield
$ 1,000
8.0%
$
700
11.0%
$
300
$ 2,000
Liabilities
$ 1,200
$
440
$
200
$ 1,840
Equity
$
160
$ 2,000
Cost
4.0%
6.0%
45
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 3.7
 What if the bank proportionately doubles
in size?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 157.00
$ 74.40
$ 82.60
4.86%
$ (200)
Both NII doubles but NIM stays the same.
Why? What has happened to the bank’s
risk?
46
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example
Rate sensitive
Fixed rate
Non earning
Total
4.0
Balance Sheet
Assets
Yield
$
600
8.0%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
450
$
370
$
100
$
920
Equity
$
80
$ 1,000
Cost
4.0%
6.0%
47
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example
4.0
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 75.50
$ 40.20
$ 35.30
4.15%
$
150
Bank has a positive GAP
48
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates increase by 1%?
Rate sensitive
Fixed rate
Non earning
Total
4.1
Balance Sheet
Assets
Yield
$
600
9.0%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
450
$
370
$
100
$
920
Equity
$
80
$ 1,000
Cost
5.0%
6.0%
49
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 4.1
 What if rates increase by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP
∆NIIEXP

$ 81.50
$ 44.70
$ 36.80
4.33%
$
150
$ 1.50
With a positive GAP, interest income
increases by more than the increase in
interest expense. Thus, both NII and NIM
rise.
50
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates decrease by 1%?
Rate sensitive
Fixed rate
Non earning
Total
4.2
Balance Sheet
Assets
Yield
$
600
7.0%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
450
$
370
$
100
$
920
Equity
$
80
$ 1,000
Cost
3.0%
6.0%
51
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 4.2
 What if rates decrease by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP
∆NIIEXP

$ 69.50
$ 35.70
$ 33.80
3.98%
$
150
$ (1.50)
With a positive GAP, interest income
decreases by more than the decrease in
interest expense. Thus, both NII and NIM
fall.
52
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates rise but the spread falls by
1%?
Balance Sheet
Rate sensitive
Fixed rate
Non earning
Total
4.3
Assets
$
600
$
250
$
150
$ 1,000
Yield
8.5%
11.0%
Liabilities
$
450
$
370
$
100
$
920
Equity
$
80
$ 1,000
Cost
5.5%
6.0%
53
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 4.3
 What if rates rise but the spread falls by
1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 78.50
$ 46.95
$ 31.55
3.71%
$
150
Both NII and NIM fall with a decrease in
the spread. Why the larger change?
 Note: ∆NIIEXP ≠ GAP x ∆iEXP Why?
54
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates fall and the spread falls by
1%?
Rate sensitive
Fixed rate
Non earning
Total
4.4
Balance Sheet
Assets
Yield
$
600
6.5%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
450
$
370
$
100
$
920
Equity
$
80
$ 1,000
Cost
3.5%
6.0%
55
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 4.4
 What if rates fall and the spread falls by
1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP
$ 66.50
$ 37.95
$ 28.55
3.36%
$
150
Both NII and NIM fall with a decrease in the
spread.
 Note: ∆NIIEXP ≠ GAP x ∆iEXP

56
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates rise and the spread rises
by 1%?
Rate sensitive
Fixed rate
Non earning
Total
4.5
Balance Sheet
Assets
Yield
$
600
10.0%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
450
$
370
$
100
$
920
Equity
$
80
$ 1,000
Cost
5.0%
6.0%
57
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 4.5
 What if rates rise and the spread rises
by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP
$ 87.50
$ 44.70
$ 42.80
5.04%
$
150
Both NII and NIM increase with an
increase in the spread.
 Note: ∆NIIEXP ≠ GAP x ∆iEXP

58
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates fall and the spread rises
by 1%?
Rate sensitive
Fixed rate
Non earning
Total
4.6
Balance Sheet
Assets
Yield
$
600
7.0%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
450
$
370
$
100
$
920
Equity
$
80
$ 1,000
Cost
2.0%
6.0%
59
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 4.6
 What if rates fall and the spread rises
by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP
$ 69.50
$ 31.20
$ 38.30
4.51%
$
150
Both NII and NIM increase with an
increase in the spread.
 Note: ∆NIIEXP ≠ GAP x ∆iEXP

60
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if the bank proportionately
doubles in size?
Rate sensitive
Fixed rate
Non earning
Total
4.7
Balance Sheet
Assets
Yield
$ 1,200
8.0%
$
500
11.0%
$
300
$ 2,000
Liabilities
$
900
$
740
$
200
$ 1,840
Equity
$
160
$ 2,000
Cost
4.0%
6.0%
61
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 4.7
 What if the bank proportionately doubles
in size?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 151.00
$ 80.40
$ 70.60
4.15%
$
300
Both NII doubles but NIM stays the same.
Why? What has happened to the bank’s
risk?
62
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example
Rate sensitive
Fixed rate
Non earning
Total
5.0
Balance Sheet
Assets
Yield
$
600
8.0%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
4.0%
6.0%
63
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example
5.0
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 75.50
$ 37.20
$ 38.30
4.51%
$
-
Bank has zero GAP
64
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates increase by 1%?
Rate sensitive
Fixed rate
Non earning
Total
5.1
Balance Sheet
Assets
Yield
$
600
9.0%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
5.0%
6.0%
65
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 5.1
 What if rates increase by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 81.50
$ 43.20
$ 38.30
4.51%
$
-
With a zero GAP, interest income
increases by the amount as the increase in
interest expense. Thus, there is no
change in NII or NIM!
66
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates fall and the spread falls by
1%?
Rate sensitive
Fixed rate
Non earning
Total
5.2
Balance Sheet
Assets
Yield
$
600
6.5%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
3.5%
6.0%
67
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example 5.2
 What if rates fall and the spread falls by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 66.50
$ 34.20
$ 32.30
3.80%
$
-
Even with a zero GAP, interest income
falls by more than the decrease in interest
expense. Thus, both NII and NIM fall with
a decrease in the spread. Note: ∆NIIEXP ≠
GAP x ∆iEXP
68
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Example

What if rates rise and the spread rises
by 1%?
Rate sensitive
Fixed rate
Non earning
Total
5.3
Balance Sheet
Assets
Yield
$
600
10.0%
$
250
11.0%
$
150
$ 1,000
Liabilities
$
600
$
220
$
100
$
920
Equity
$
80
$ 1,000
Cost
5.0%
6.0%
69
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income

Example 5.3

What if rates rise and the spread rises by 1%?
Interest Income
Interest Expense
Net Interest Income
Net Interest Margin
Funding GAP

$ 87.50
$ 43.20
$ 44.30
5.21%
$
-
Even with a zero GAP, interest income rises
by more than the increase in interest expense.
Thus, both NII and NIM increase with an
increase in the spread. Note: ∆NIIEXP ≠ GAP x
∆iEXP
70
Measuring Interest Rate Risk with
GAP
 Factors Affecting Net Interest Income
 Summary
NII
NIM

of Base Cases
Positive
$35.30
4.15%
GAP
Zero
Negative
$38.20
$41.30
4.51%
4.86%
If a Negative GAP gives the largest NII
and NIM, why not plan for a Negative
GAP?
71
Measuring Interest Rate Risk with
GAP
 Rate, Volume, and Mix Analysis
 Many
financial institutions publish a
summary in their annual report of how
net interest income has changed over
time
 They separate changes attributable to
shifts in asset and liability composition
and volume from changes associated
with movements in interest rates
72
73
Measuring Interest Rate Risk with
GAP
 Rate Sensitivity Reports
 Many
managers monitor their bank’s
risk position and potential changes in
net interest income using rate
sensitivity reports

These report classify a bank’s assets
and liabilities as rate sensitive in
selected time buckets through one year
74
Measuring Interest Rate Risk with
GAP
 Rate Sensitivity Reports
 Periodic

GAP
The Gap for each time bucket and
measures the timing of potential
income effects from interest rate
changes
75
Measuring Interest Rate Risk with
GAP
 Rate Sensitivity Reports
 Cumulative
GAP
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

76
77
Measuring Interest Rate Risk with
GAP
 Strengths and Weaknesses of Static
GAP Analysis
 Strengths
Easy to understand
 Works well with small changes in
interest rates

78
Measuring Interest Rate Risk with
GAP
 Strengths and Weaknesses of Static GAP
Analysis

Weaknesses
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

79
Measuring Interest Rate Risk with
GAP
 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

80
Measuring Interest Rate Risk with
GAP
 GAP Divided by Earning Assets as a Measure
of Risk
 An alternative risk measure that relates the
absolute value of a bank’s GAP to earning
assets
 The greater this ratio, the greater the interest
rate risk
 Banks may specify a target GAP-to-earningasset ratio in their ALCO policy statements
 A target allows management to position the
bank to be either asset sensitive or liability
sensitive, depending on the outlook for
interest rates
81
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
82
Earnings Sensitivity Analysis
 Steps to Earnings Sensitivity Analysis
1. Forecast interest rates.
2. Forecast balance sheet size and
composition given the assumed interest
rate environment
3. Forecast when embedded options in
assets and liabilities will be exercised
such that prepayments change,
securities are called or put, deposits are
withdrawn early, or rate caps and rate
floors are exceeded under the assumed
interest rate environment
83
Earnings Sensitivity Analysis
 Steps to Earnings Sensitivity Analysis
4.
5.
6.
Identify when specific assets and liabilities
will reprice given the rate environment
Estimate net interest income and net
income under the assumed rate
environment
Repeat the process to compare forecasts of
net interest income and net income across
different interest rate environments versus
the base case

The choice of base case is important because
all estimated changes in earnings are
compared with the base case estimate
84
Earnings Sensitivity Analysis
 The key benefits of conducting earnings sensitivity
analysis are that managers can estimate the impact
of rate changes on earnings while allowing for the
following:





Interest rates to follow any future path
Different rates to change by different amounts at
different times
Expected changes in balance sheet mix and volume
Embedded options to be exercised at different times
and in different interest rate environments
Effective GAPs to change when interest rates change
 Thus, a bank does not have a single static GAP, but
instead will experience amounts of RSAs and RSLs
that change when interest rates change
85
Earnings Sensitivity Analysis
 Exercise of Embedded Options in Assets and
Liabilities
 The most common embedded options at
banks include the following:








Refinancing of loans
Prepayment (even partial) of principal on
loans
Bonds being called
Early withdrawal of deposits
Caps on loan or deposit rates
Floors on loan or deposit rates
Call or put options on FHLB advances
Exercise of loan commitments by borrowers
86
Earnings Sensitivity Analysis
 Exercise of Embedded Options in Assets and
Liabilities
 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
87
Earnings Sensitivity Analysis
 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
88
Earnings Sensitivity Analysis
 Earnings Sensitivity: An Example
 Consider the rate sensitivity report for
First Savings Bank (FSB) as of year-end
2008 that is presented on the next slide
 The report is based on the most likely
interest rate scenario
 FSB is a $1 billion bank that bases its
analysis on forecasts of the federal funds
rate and ties other rates to this overnight
rate
 As such, the federal funds rate serves as
the bank’s benchmark interest rate
89
90
91
92
Earnings Sensitivity Analysis
 Explanation of Sensitivity Results
 This example demonstrates the
importance of understanding the impact
of exercising embedded options and the
lags between the pricing of assets and
liabilities.
 The framework uses the federal funds
rate as the benchmark rate such that rate
shocks indicate how much the funds rate
changes
 Summary results are known as Earningsat-Risk Simulation or Net Interest Income
Simulation
93
Earnings Sensitivity Analysis
 Explanation of Sensitivity Results
 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.
94
Earnings Sensitivity Analysis
 Explanation of Sensitivity Results
 FSB’s earnings sensitivity results reflect
the impacts of rate changes on a bank
with this profile
 There are two basic causes or drivers
behind the estimated earnings changes
 First, other market rates change by
different amounts and at different times
relative to the federal funds rate
 Second, embedded options potentially
alter cash flows when the options go in
the money
95
Income Statement GAP
 Income Statement GAP
 An
interest rate risk model which
modifies the standard GAP model to
incorporate the different speeds and
amounts of repricing of specific assets
and liabilities given an interest rate
change
96
Income Statement GAP
 Beta GAP
 The adjusted GAP figure in a basic
earnings sensitivity analysis derived
from multiplying the amount of ratesensitive assets by the associated beta
factors and summing across all ratesensitive assets, and subtracting the
amount of rate-sensitive liabilities
multiplied by the associated beta
factors summed across all ratesensitive liabilities
97
Income Statement GAP
 Balance Sheet GAP
 The effective amount of assets that
reprice by the full assumed rate change
minus the effective amount of liabilities
that reprice by the full assumed rate
change.
 Earnings Change Ratio (ECR)
 A ratio calculated for each asset or
liability that estimates how the yield on
assets or rate paid on liabilities is
assumed to change relative to a 1 percent
change in the base rate
98
99
Managing the GAP and Earnings
Sensitivity Risk
 Steps to reduce 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 to
hedge
100
Managing the GAP and Earnings
Sensitivity Risk
 How to Adjust the Effective GAP or
Earnings Sensitivity Profile
101
Managing Interest Rate
Risk: Economic Value
of Equity
102
Managing Interest Rate Risk:
Economic Value of Equity
 Economic Value of Equity (EVE)
Analysis
 Focuses
on changes in stockholders’
equity given potential changes in
interest rates
103
Managing Interest Rate Risk:
Economic Value of Equity
 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
104
Managing Interest Rate Risk:
Economic Value of Equity
 GAP and Earnings Sensitivity versus
Duration GAP and EVE Sensitivity
105
Managing Interest Rate Risk:
Economic Value of Equity
 Recall from Chapter 6
 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
106
Managing Interest Rate Risk:
Economic Value of Equity
 Market Value Accounting Issues

EVE sensitivity analysis is linked with the
debate concerning whether market value
accounting is appropriate for financial
institutions


Recently many large commercial and
investment banks reported large write-downs
of mortgage-related assets, which depleted
their capital
Some managers argued that the write-downs
far exceeded the true decline in value of the
assets and because banks did not need to sell
the assets they should not be forced to
recognize the “paper” losses
107
108
Measuring Interest Rate Risk with
Duration GAP
 Duration GAP Analysis
 Compares
the price sensitivity of a
bank’s total assets with the price
sensitivity of its total liabilities to
assess whether the market value of
assets or liabilities changes more
when rates change
109
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 Macaulay’s
Duration (D)
 Cashflow t 
t 
t

n
(1  i )
D  t 

P*




where P* is the initial price, i is the
market interest rate, and t is equal to
the time until the cash payment is made
110
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 Macaulay’s

Duration (D)
Macaulay’s duration is a measure of
price sensitivity where P refers to the
price of the underlying security:
ΔP
D

 Δi
P
(1  i)
111
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 Modified

Duration
Indicates how much the price of a
security will change in percentage
terms for a given change in interest
rates
Modified Duration = D/(1+i)
112
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 Example

Assume that a ten-year zero coupon
bond has a par value of $10,000,
current price of $7,835.26, and a market
rate of interest of 5%. What is the
expected change in the bond’s price if
interest rates fall by 25 basis points?
113
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 Example

Since the bond is a zero-coupon bond,
Macaulay’s Duration equals the time to
maturity, 10 years. With a market rate
of interest, the Modified Duration is
10/(1.05) = 9.524 years. If rates change
by 0.25% (.0025), the bond’s price will
change by approximately 9.524 × .0025
× $7,835.26 = $186.56
114
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
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

115
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and Effective
Duration

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
the rate
i- = Initial market rate minus the decrease
in the rate
116
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 Effective

Duration
Example
 Consider a 3-year, 9.4 percent semi-annual
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
117
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 Effective

Duration
Example
 Assume 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
118
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 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
119
Measuring Interest Rate Risk with
Duration GAP
 Duration, Modified Duration, and
Effective Duration
 Effective

Duration
Example
$10,000 - $9,847.72
Effective Duration 
 2.54
$10,000(0.05 - 0.044)
120
Measuring Interest Rate Risk with
Duration GAP
 Duration GAP Model
 Focuses
on 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 and focuses on price
sensitivity

121
Measuring Interest Rate Risk with
Duration GAP
 Duration GAP Model

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 off-balance
sheet items. These estimates are used to calculate
duration gap

Forecasts changes in the market value of
stockholders’ equity across different interest
rate environments
122
Measuring Interest Rate Risk with
Duration GAP
 Duration GAP Model
 Weighted
Average Duration of Bank
Assets (DA):
n
DA   w i Da i
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

123
Measuring Interest Rate Risk with
Duration GAP
 Duration GAP Model
 Weighted
Average Duration of Bank
Liabilities (DL):
m
where
DL   z jDl j
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

124
Measuring Interest Rate Risk with
Duration GAP
 Duration GAP Model
 Let MVA and MVL equal the market values
of assets and liabilities, respectively
 If ΔEVE = ΔMVA – ΔMVL
and
 Duration GAP = DGAP = DA –
(MVL/MVA)DL
then
 ΔEVE = -DGAP[Δy/(1+y)]MVA
where y is the interest rate
125
Measuring Interest Rate Risk with
Duration GAP
 Duration GAP Model
 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) 
126
Measuring Interest Rate Risk with
Duration GAP
 Duration GAP Model

DGAP as a Measure of Risk

The sign and size of DGAP provide
information about whether rising or falling
rates are beneficial or harmful and how much
risk the bank is taking
 If DGAP is positive, an increase in rates will lower
EVE, while a decrease in rates will increase EVE
 If DGAP is negative, an increase in rates will
increase EVE, while a decrease in rates will lower
EVE
 The closer DGAP is to zero, the smaller is the
potential change in EVE for any change in rates
127
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
128
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 Implications of DGAP
 The value of DGAP at 1.42 years indicates
that the bank has a substantial mismatch
in average durations of assets and
liabilities
 Since the DGAP is positive, the market
value of assets will change more than the
market value of liabilities if all rates
change by comparable amounts
 In this example, an increase in rates will cause
a decrease in EVE, while a decrease in rates
will cause an increase in EVE
129
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 Implications of DGAP > 0

A positive DGAP indicates that assets are more price
sensitive than liabilities
 When interest rates rise (fall), assets will fall
proportionately more (less) in value than
liabilities and EVE will fall (rise) accordingly.

Implications of DGAP < 0

A negative DGAP indicates that liabilities
are more price sensitive than assets
 When interest rates rise (fall), assets will fall
proportionately less (more) in value that
liabilities and the EVE will rise (fall)
130
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
131
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 Duration
GAP Summary
132
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 DGAP

As a Measure of Risk
DGAP measures can be used to
approximate the expected change in
economic value of equity for a given
change in interest rates
ΔEVE  - DGAP[
y
]MVA
(1  y)
133
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 DGAP

As a Measure of Risk
In this case:
.01
ΔEVE  - 1.42[
]$1,000  $12.91
1.10

The actual decrease, as shown in
Exhibit 8.3, was $12
134
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 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
or
 a combination of both
135
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
136
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 An

Immunized Portfolio
With a 1% increase in rates, the EVE
did not change with the immunized
portfolio versus $12.0 when the
portfolio was not immunized
137
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 An Immunized Portfolio
 If DGAP > 0, reduce interest rate risk by:
 shortening asset durations
 Buy short-term securities and sell longterm securities
 Make floating-rate loans and sell fixed-rate
loans
 lengthening liability durations
 Issue longer-term CDs
 Borrow via longer-term FHLB advances
 Obtain more core transactions accounts
from stable sources
138
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks

An Immunized Portfolio

If DGAP < 0, reduce interest rate risk by:
 lengthening asset durations
 Sell short-term securities and buy long-term
securities
 Sell floating-rate loans and make fixed-rate
loans
 Buy securities without call options
 shortening liability durations
 Issue shorter-term CDs
 Borrow via shorter-term FHLB advances
 Use short-term purchased liability funding from
federal funds and repurchase agreements
139
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 Banks
may choose to target variables
other than the market value of equity in
managing interest rate risk
 Many banks are interested in
stabilizing the book value of net
interest income

This can be done for a one-year time
horizon, with the appropriate duration
gap measure
140
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks
 DGAP* = MVRSA(1 − DRSA) − MVRSL(1 −
DRSL)
 where
 MVRSA = cumulative market value of ratesensitive assets (RSAs)
 MVRSL = cumulative market value of ratesensitive liabilities (RSLs)
 DRSA = composite duration of RSAs for
the given time horizon
 DRSL = composite duration of RSLs for
the given time horizon
141
Measuring Interest Rate Risk with
Duration GAP
 A Duration Application for Banks

DGAP* > 0


DGAP* < 0


Net interest income will decrease (increase)
when interest rates decrease (increase)
Net interest income will decrease (increase)
when interest rates increase (decrease)
DGAP* = 0

Interest rate risk eliminated
 A major point is that duration analysis can be used
to stabilize a number of different variables
reflecting bank performance
142
Economic Value of Equity
Sensitivity Analysis
 Involves the comparison of changes in
the Economic Value of Equity (EVE)
across different interest rate
environments
 An
important component of EVE
sensitivity analysis is allowing
different rates to change by different
amounts and incorporating projections
of when embedded customer options
will be exercised and what their values
will be
143
Economic Value of Equity
Sensitivity Analysis
 Estimating the timing of cash flows
and subsequent durations of assets
and liabilities is complicated by:
 Prepayments
that exceed (fall short of)
those expected
 A bond being
 A deposit that is withdrawn early or a
deposit that is not withdrawn as
expected
144
Economic Value of Equity
Sensitivity Analysis
 EVE Sensitivity Analysis: An Example
 First
Savings Bank
Average duration of assets equals 2.6
years
 Market value of assets equals
$1,001,963,000
 Average duration of liabilities equals 2
years
 Market value of liabilities equals
$919,400,000

145
146
Economic Value of Equity
Sensitivity Analysis
 EVE Sensitivity Analysis: An Example

First Savings Bank

Duration Gap
 2.6 – ($919,400,000/$1,001,963,000) × 2.0 = 0.765
years

Example:
 A 1% increase in rates would reduce EVE by $7.2
million
 ΔMVE = -DGAP[Δy/(1+y)]MVA
 ΔMVE = -0.765 (0.01/1.0693) × $1,001,963,000
= -$7,168,257
 Recall that the average rate on assets is
6.93%
 The estimate of -$7,168,257 ignores the impact of
interest rates on embedded options and the
effective duration of assets and liabilities
147
Economic Value of Equity
Sensitivity Analysis
 EVE Sensitivity Analysis: An Example
148
Economic Value of Equity
Sensitivity Analysis
 EVE Sensitivity Analysis: An Example

First Savings Bank

The previous slide shows that FSB’s EVE
will fall by $8.2 million if rates are rise by
1%
 This differs from the estimate of -$7,168,257
because this sensitivity analysis takes into
account the embedded options on loans and
deposits
 For example, with an increase in interest rates,
depositors may withdraw a CD before maturity
to reinvest the funds at a higher interest rate
149
Economic Value of Equity
Sensitivity Analysis
 EVE Sensitivity Analysis: An Example
 First

Savings Bank
Effective “Duration” of Equity
 Recall, duration measures the percentage
change in market value for a given change
in interest rates
 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 = $8,200 /
$82,563 = 9.9 years
150
Earnings Sensitivity Analysis
versus EVE Sensitivity Analysis
 Strengths and Weaknesses: DGAP and
EVE-Sensitivity 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
151
Earnings Sensitivity Analysis
versus EVE Sensitivity Analysis
 Strengths and Weaknesses: DGAP and EVE-
Sensitivity 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
152
A Critique of Strategies for Managing
Earnings and EVE Sensitivity
 GAP and DGAP Management
Strategies
 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
changing GAP and DGAP
153
A Critique of Strategies for Managing
Earnings and EVE Sensitivity
 Interest Rate Risk: An Example
 Consider
the case where a bank has
two alternatives for funding $1,000 for
two years
A 2-year security yielding 6 percent
 Two consecutive 1-year securities, with
the current 1-year yield equal to 5.5
percent

 It is not known today what a 1-year
security will yield in one year
154
A Critique of Strategies for Managing
Earnings and EVE Sensitivity
 Interest Rate Risk: An Example
 Consider
the case where a bank has
two alternative for funding $1,000 for
two years
0
1
2
Two-Year Security
$60
0
$60
1
2
One-Year Security & then
another One-Year Security
$55
?
155
A Critique of Strategies for Managing
Earnings and EVE Sensitivity
 Interest Rate Risk: An Example

Consider the case where a bank has two
alternative for funding $1,000 for two
years

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 of
:
 6% + 6% = 5.5% + x so x must = 6.5%
156
A Critique of Strategies for Managing
Earnings and EVE Sensitivity
 Interest Rate Risk: An Example
 Consider the case where a bank has two
alternative for investing $1,000 for two
years
 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%
 By choosing one or the other, the depositor
and the bank “place a bet” that the actual rate
in one year will differ from the forward rate of
6.5 percent
157
Yield Curve Strategies
 When the U.S. economy hits its peak, the
yield curve typically inverts, with shortterm 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 rates to fall and the
yield curve to return to its “normal”
shape.
158
Yield Curve Strategies
 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
 Follow strategies to become more liability
sensitive and/or lengthen the duration of
assets versus the duration of liabilities

159
160
Using Derivatives to
Manage Interest Rate
Risk
161
Using Derivatives to Manage
Interest Rate Risk
 Derivative
 Any
instrument or contract that derives
its value from another underlying
asset, instrument, or contract
162
Using Derivatives to Manage
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

163
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
164
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
165
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
166
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
167
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

168
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

169
Characteristics of Financial
Futures
 A Brief Example
 Assume you want to invest $1 million in
10-year T-bonds in six months and
believe that rates will fall
 You would like to “lock in” the 4.5% 10year yield prevailing today
 If such a contract existed, you would buy a
futures contract on 10-year T-bonds with
an expiration date just after the six-month
period
 Assume that such a contract is priced at a
4.45% rate
170
Characteristics of Financial
Futures
 A Brief Example
 If
10-year Treasury rates actually fall
sharply during the six months, the
futures rate will similarly fall such that
the futures price rises
An increase in the futures price
generates a profit on the futures trade
 You will eventually sell the futures
contract to exit the trade

171
Characteristics of Financial
Futures
 A Brief Example
 You will eventually sell the futures
contract to exit the trade
 Your effective yield will be determined
by the prevailing 10-year Treasury rate
and the gain (or loss) on the futures
trade
 In this example, the decline in 10-year
rates will be offset by profits on the
long futures position
172
Characteristics of Financial
Futures
 A Brief Example
 The
10-year Treasury rate falls by
0.80%, which represents an
opportunity loss
However, buying a futures contract
generates a 0.77% profit
 The effective yield on the investment
equals the prevailing 3.70% rate at the
time of investment plus the 0.77%
futures profit, or 4.47%

173
Characteristics of Financial
Futures
 A Brief Example
174
Characteristics of Financial
Futures
 Types of Future Traders
 Commission

Brokers
Execute trades for other parties
 Locals
Trade for their own account
 Locals are speculators

175
Characteristics of Financial
Futures
 Types of Future 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

176
Characteristics of Financial
Futures
 Types of Future Traders
 Scalper

A speculator who tries to time price
movements over very short time
intervals and takes positions that
remain outstanding for only minutes
177
Characteristics of Financial
Futures
 Types of Future 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
178
Characteristics of Financial
Futures
 Types of Future Traders
 Position

Trader
A speculator who holds a position for a
longer period in anticipation of a more
significant, longer-term market moves
179
Characteristics of Financial
Futures
 Types of Future 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
180
Characteristics of Financial
Futures
 Types of Future 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
181
Characteristics of Financial
Futures
 Types of Future 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
182
Characteristics of Financial
Futures
 Types of Future 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
183
Characteristics of Financial
Futures
 The Mechanics of Futures Trading
 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

184
Characteristics of Financial
Futures
 The Mechanics of Futures Trading
 Maintenance

Margin
The minimum deposit required at the
end of each day
 Unlike margin accounts for stocks, futures
margin deposits represent a guarantee that
a trader will be able to make any
mandatory payment obligations
185
Characteristics of Financial
Futures
 The Mechanics of Futures Trading
 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
186
Characteristics of Financial
Futures
 The Mechanics of Futures Trading

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

187
Characteristics of Financial
Futures
 An 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

188
Characteristics of Financial
Futures
 An Example: 90-Day Eurodollar Time
Deposit Futures
 Contracts

trade according to an index:
100 – Futures Price = Futures Rate
 An index of 94.50 indicates a futures rate
of 5.5%
 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)
189
Characteristics of Financial
Futures
 An Example: 90-Day Eurodollar Time
Deposit Futures
 Over
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)

190
191
Characteristics of Financial
Futures
 An Example: 90-Day Eurodollar Time Deposit
Futures





OPEN
 The index price at the open of trading
HIGH
 The high price during the day
LOW
 The low price during the day
LAST
 The last price quoted during the day
PT CHGE
 The basis-point change between the last price
quoted and the closing price the previous day
192
Characteristics of Financial
Futures
 An Example: 90-Day Eurodollar Time
Deposit Futures
 SETTLEMENT

The previous day’s closing price
 VOLUME

The previous day’s volume of contracts
traded during the day
 OPEN

INTEREST
The total number of futures contracts
outstanding at the end of the day.
193
Characteristics of Financial
Futures
 Expectations Embedded in Future
Rates
 According
to the unbiased
expectations theory, an upward
sloping yield curve indicates a
consensus forecast that short-term
interest rates are expected to rise
 A flat yield curve suggests that rates
will remain relatively constant
194
Characteristics of Financial
Futures
 Expectations Embedded in Future
Rates
195
Characteristics of Financial
Futures
 Expectations Embedded in Future Rates
 The previous slide presents two yield
curves at the close of business on June 5,
2008
 There was a sharp decrease in rates from
one year prior.
 The yield curve in June 2008 was relatively
steep
 The difference between the one-month and 30year Treasury rates was 289 basis points

The yield curve in June 2007 was relatively
flat
196
Characteristics of Financial
Futures
 Expectations Embedded in Future Rates
One interpretation of futures rates is that
they provide information about
consensus expectations of future cash
rates
 When futures rates continually rise as the
expiration dates of the futures contracts
extend into the future, it signals an
expected increase in subsequent cash
market rates

197
Characteristics of Financial
Futures
 Daily Marking-To-Market
 Consider a trader trading on June 6, 2008
who buys one December 2008 threemonth Eurodollar futures contract at
$96.98 posting $1,100 in cash as initial
margin
 Maintenance margin is set at $700 per
contract
 The futures contract expires
approximately six months after the initial
purchase, during which time the futures
price and rate fluctuate daily
198
Characteristics of Financial
Futures
 Daily Marking-To-Market
 Suppose
that on June 13 the futures
rate falls fro 3.02% to 2.92%
 The trader could withdraw $250 (10
basis points × $25) from the margin
account, representing the increase in
value of the position
199
Characteristics of Financial
Futures
 Daily Marking-To-Market
 If
the futures rate increases to 3.08%
the next day, the trader’s long position
decreases in value

The 16 basis-point increase represents
a $400 drop in margin such that the
ending account balance would equal
$950
200
Characteristics of Financial
Futures
 Daily Marking-To-Market
 If the futures rate increases further to
3.23%, the trader must make a
variation margin payment sufficient to
bring the account up to $700
 In this case, the account balance would
have fallen to $575 and the margin
contribution would equal $125
 The exchange member may close the
account if the trader does not meet the
variation margin requirement
201
Characteristics of Financial
Futures
 Daily Marking-To-Market
 The

Basis
Basis = Cash Price – Futures Price
 or

Basis = Futures Rate – Cash 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
202
Characteristics of Financial
Futures
203
Speculation versus Hedging
 Speculators Take On Risk To Earn
Speculative Profits
Speculation is extremely risky
 Example


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
204
Speculation versus Hedging
 Hedgers Take Positions to Avoid or
Reduce Risk
A
hedger already has a position in the
cash market and uses futures to adjust
the risk of being in the cash market

The focus is on reducing or avoiding
risk
205
Speculation versus Hedging
 Hedgers Take Positions to Avoid or
Reduce Risk

Example

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
206
207
Speculation versus Hedging
 Steps in Hedging
1.
2.
3.
4.
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
208
Speculation versus Hedging
 Steps in Hedging
5.
6.
7.
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
209
Speculation versus Hedging
 A Long Hedge: Reduce Risk Associated
With A Decrease In Interest Rates
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

210
Speculation versus Hedging
 A Long Hedge: Reduce Risk Associated With
A Decrease In Interest Rates
 On June 6, 2008, your bank expects to
receive a $1 million payment on November
28, 2008, and anticipates investing the funds
in three-month Eurodollar time deposits


The cash market risk exposure is that the
bank would like to invest the funds at today’s
rates, but will not have access to the funds for
over five months
In June 2008, the market expected Eurodollar
rates to increase as evidenced by rising
futures rates.
211
Speculation versus Hedging
 A Long Hedge: Reduce Risk Associated
With A Decrease In Interest Rates

In order to hedge, the bank should buy
futures contracts
The best futures contract will generally be
the first contract that expires after the
known cash transaction date.
 This contract is best because its futures
price will generally show the highest
correlation with the cash price

 In this example, the December 2008 Eurodollar
futures contract is the first to expire after
November 2008
212
Speculation versus Hedging
 A Long Hedge: Reduce Risk
Associated With A Decrease In Interest
Rates
 The
time line of the bank’s hedging
activities:
213
Speculation versus Hedging
214
Speculation versus Hedging
 A Short Hedge: Reduce Risk Associated
With A Increase In Interest Rates
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

215
Speculation versus Hedging
 A Short Hedge: Reduce Risk Associated
With A Increase In Interest Rates

On June 6, 2008, your bank expects to
sell a six-month $1 million Eurodollar
deposit on August 17, 2008
The cash market risk exposure is that
interest rates may rise and the value of the
Eurodollar deposit will fall by August 2008
 In order to hedge, the bank should sell
futures contracts

216
Speculation versus Hedging
 A Long Hedge: Reduce Risk
Associated With A Decrease In Interest
Rates
 In
order to hedge, the bank should sell
futures contracts

In this example, the September 2008
Eurodollar futures contract is the first
to expire after September 17, 2008
217
Speculation versus Hedging
 A Long Hedge: Reduce Risk
Associated With A Decrease In Interest
Rates
 The
time line of the bank’s hedging
activities:
218
Speculation versus Hedging
219
Speculation versus Hedging
 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
220
Speculation versus Hedging
 Change in the Basis
 Effective
Return
= Initial Cash Rate – Change in Basis
= Initial Cash Rate – (B2 – B1)
where :
B1 is the basis when the hedge is opened
B2 is the basis when the hedge is closed
221
Speculation versus Hedging
 Change in the Basis
 Effective
Return: Long Hedge
= Initial Cash Rate – (B2 – B1)
= 2.68% - (0.10% - 0.34%) = 2.92%
 Effective
Return: Short Hedge
= Initial Cash Rate – (B2 – B1)
= 3.00% - (0.14% - -0.17%) = 2.69%
222
Speculation versus Hedging
 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
223
Speculation versus Hedging
 Basis Risk and Cross Hedging
 Cross

Hedge
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
224
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
225
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
 Some feel that such micro linkages force
microhedges that may potentially
increase a firm’s total risk because these
hedges ignore all other portfolio
components

226
Microhedging Applications
 Creating a Synthetic Liability with a Short
Hedge

Example
Assume that on June 6, 2008, a bank
agreed to finance a $1 million six-month
loan
 Management wanted to match fund the
loan by issuing a $1 million, six-month
Eurodollar time deposit

 The six-month cash Eurodollar rate was 3%
 The three-month Eurodollar rate was 2.68%
 The three-month Eurodollar futures rate for
September 2008 expiration equaled 2.83%
227
Microhedging Applications
 Creating a Synthetic Liability with a Short
Hedge

Rather than issue a direct six-month
Eurodollar liability at 3%, the bank
created a synthetic six-month liability by
shorting futures

The objective was to use the futures
market to borrow at a lower rate than the
six-month cash Eurodollar rate
 A short futures position would reduce the risk
of rising interest rates for the second cash
Eurodollar borrowing
228
Microhedging Applications
 Creating a Synthetic Liability with a
Short Hedge
229
230
Microhedging Applications
 The Mechanics of Applying a
Microhedge
1.
2.
3.
Determine the bank’s interest rate
position
Forecast the dollar flows or value
expected in cash market transactions
Choose the appropriate futures
contract
231
Microhedging Applications
 The Mechanics of Applying a Microhedge
4. Determine the correct number of futures
contracts
A  Mc
NF 
b
F  Mf

Where




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
232
Microhedging Applications
 The Mechanics of Applying a
Microhedge
5.
6.
Determine the Appropriate Time
Frame for the Hedge
Monitor Hedge Performance
233
Macrohedging Applications
 Macrohedging
 Focuses
on reducing interest rate risk
associated with a bank’s entire
portfolio rather than with individual
transactions
234
Macrohedging Applications
 Hedging: GAP or Earnings Sensitivity
 If
a bank loses when interest rates fall
(the bank has a positive GAP), it
should 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

235
Macrohedging Applications
 Hedging: GAP or Earnings Sensitivity
 If
a bank loses when interest rates rise
(the bank has a negative GAP), it
should 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

236
Macrohedging Applications
 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)
237
Macrohedging Applications
 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
238
Macrohedging Applications
 Hedging: Duration GAP and EVE
Sensitivity
 Example:

With a positive duration gap, the EVE
will decline if interest rates rise
239
Macrohedging Applications
 Hedging: Duration GAP and EVE
Sensitivity
 Example:

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
240
Macrohedging Applications
 Hedging: Duration GAP and EVE
Sensitivity

Example:

If 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) 1.59($920) 0.25(MVF)


0
(1.10)
(1.06)
(1.049)
 MVF = $4,096.82, so the bank should sell four
Eurodollar futures contracts
241
Macrohedging Applications
 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
242
Using Forward Rate Agreements
to Manage Rate Risk
 Forward Rate Agreements
A
forward contract based on interest
rates based on a notional principal
amount at a specified future date

Similar to futures but differ in that they:
 Are negotiated between parties
 Do not necessarily involve standardized
assets
 Require no cash exchange until expiration
(i.e. there is no marking-to-market)
 No exchange guarantees performance 243
Using Forward Rate Agreements
to Manage Rate Risk
 Notional Principal
 Serves
as a reference figure in
determining cash flows for the two
counterparties to a forward rate
agreement agree
 “Notional” refers to the condition that
the principal does not change hands,
but is only used to calculate the value
of interest payments
244
Using Forward Rate Agreements
to Manage Rate Risk
 Buyer
 Agrees
to pay a fixed-rate coupon
payment and receive a floating-rate
payment against the notional principal
at some specified future date
245
Using Forward Rate Agreements
to Manage Rate Risk
 Seller
 Agrees
to pay a floating-rate payment
and receive the fixed-rate payment
against the same notional principal

The buyer and seller will receive or pay
cash when the actual interest rate at
settlement is different than the exercise
rate
246
Using Forward Rate Agreements
to Manage Rate Risk
 Forward Rate Agreements: An Example
Suppose that Metro Bank (as the seller)
enters into a receive fixed-rate/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 5%

247
Using Forward Rate Agreements
to Manage Rate Risk
 Forward Rate Agreements: An
Example
 Metro
Bank would refer to this as a “3
vs. 6” FRA at 5% on a $1 million
notional amount from County Bank
 The only cash flow will be determined
in six months at contract maturity by
comparing the prevailing 3-month
LIBOR with 5%
248
Using Forward Rate Agreements
to Manage Rate Risk
 Forward Rate Agreements: An Example
 Assume that in three months 3-month
LIBOR equals 6%
 In this case, Metro Bank would receive from
County Bank $2,463
 The interest settlement amount is $2,500:
 Interest = (.06 - .05)(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).06]=$2,463
249
Using Forward Rate Agreements
to Manage Rate Risk
 Forward Rate Agreements: An
Example
 If
instead, LIBOR equals 3% in three
months, Metro Bank would pay
County Bank:

The interest settlement amount is
$5,000
 Interest = (.05 -.03)(90/360) $1,000,000 =
$5,000
 Actual interest = $5,000 /[1 + (90/360).03] =
$4,963
250
Using Forward Rate Agreements
to Manage Rate Risk
 Forward Rate Agreements: An Example
 County Bank would pay fixed-rate/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
 Metro Bank would sell fixed-rate/receive
floating-rate as a hedge if it was exposed
to loss in a falling rate environment.
 This is analogous to a long futures
position
251
Using Forward Rate Agreements
to Manage Rate Risk
 Potential Problems with FRAs
 There
is no clearinghouse to
guarantee, so you might not be paid
when the counterparty owes you cash
 It is sometimes difficult to find a
specific counterparty that wants to
take exactly the opposite position
 FRAs are not as liquid as many
alternatives
252
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Basic
(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

253
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Basic (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
254
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Basic
(Plain Vanilla) Interest Rate Swap
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

255
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics

Plain Vanilla Example

Using data for a 2-year swap based on 3month 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

256
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Plan
Vanilla Example
257
258
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Plain Vanilla Example
 If the three-month LIBOR for the first
pricing interval equals 3%
 The fixed payment for Party FIX is $83,770 and
the floating rate receipt is $67,744
 Party FIX will have to pay the difference of
$16,026
 The floating-rate payment for Party FLT is
$67,744 and the fixed-rate receipt is$83,520
 Party FLT will receive the difference of
$15,776
 The dealer will net $250 from the spread
($16,026 -$15,776)
259
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Plain Vanilla Example
 At the second and subsequent pricing
intervals, only the applicable LIBOR is
unknown
 As LIBOR changes, the amount that both Party
FIX and Party FLT either pay or receive will
change
 Party FIX will only receive cash at any
pricing interval if three-month LIBOR
exceeds 3.36%
 Party FLT will similarly receive cash as
long as three-month LIBOR is less than
3.35%
260
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Convert
a Floating-Rate Liability to a
Fixed Rate Liability

Consider a bank that makes a $1
million, three-year fixed-rate loan with
quarterly interest at 8%
 It finances the loan by issuing a threemonth Eurodollar deposit priced at threemonth LIBOR
261
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics

Convert a Floating-Rate Liability to a Fixed
Rate Liability

By itself, this transaction exhibits
considerable interest rate
 The bank is liability sensitive and loses (gains) if
LIBOR rises (falls)

The bank can use a basic swap to microhedge
this transaction
 Using the data from Exhibit 9.8, the bank could
agree to pay 3.72% and receive three-month LIBOR
against $1 million for the three years
 By doing this, the bank locks in a borrowing cost of
3.72% because it will both receive and pay LIBOR
every quarter
262
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Convert a Floating-Rate Liability to a
Fixed Rate Liability
 The use of the swap enables the bank
to reduce risk and lock in a spread of
4.28 percent (8.00 percent − 3.72
percent) on this transaction while
effectively fixing the borrowing cost at
3.72 percent for three years
263
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Convert a Fixed-Rate Asset to a FloatingRate Asset
 Consider a bank that has a customer who
demands a fixed-rate loan
 The bank has a policy of making only floatingrate loans because it is liability sensitive and
will lose if interest rates rise
 Ideally, the bank wants to price the loan based
on prime

Now assume that the bank makes the
same $1 million, three-year fixed-rate loan
as in the “Convert a Floating-Rate Liability
to a Fixed Rate Liability” example
264
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Convert a Fixed-Rate Asset to a FloatingRate Asset
 The bank could enter into a swap,
agreeing to pay a 3.7% fixed rate and
receive prime minus 2.40% with quarterly
payments
 This effectively converts the fixed-rate loan
into a variable rate loan that floats with the
prime rate
265
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Create a Synthetic Hedge
 Some view basic interest rate swaps as
synthetic securities
 As such, they enter into a swap contract that
essentially replicates the net cash flows from a
balance sheet transaction
 Suppose a bank buys a three-year Treasury
yielding 2.73%, which it finances by issuing
a three-month deposit
 As an alternative, the bank could enter into
a three-month swap agreeing to pay threemonth LIBOR and receive a fixed rate
266
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Macrohedge
 Banks can also use interest rate swaps to
hedge their aggregate risk exposure
measured by earnings and EVE sensitivity
 A bank that is liability sensitive or has a
positive duration gap will take a basic swap
position that potentially produces profits when
rates increase
 With a basic swap, this means paying a
fixed rate and receiving a floating rate
 Any profits can be used to offset losses
from lost net interest income or
declining
267
Basic Interest Rate Swaps as a
Risk Management Tool
 Characteristics
 Macrohedge

In terms of GAP analysis, a liabilitysensitive bank has more rate-sensitive
liabilities than rate-sensitive assets
 To hedge, the bank needs the equivalent of
more RSAs
 A swap that pays fixed and receives
floating is comparable to increasing RSAs
relative to RSLs because the receipt
reprices with rate changes
268
Basic Interest Rate Swaps as a
Risk Management Tool
 Pricing Basic Swaps

The floating rate is based on some
predetermined money market rate or
index


The payment frequency is coincidentally
set at every six months, three months, or
one month, and is generally matched with
the money market rate
The fixed rate is set at a spread above the
comparable maturity fixed rate security
269
Basic Interest Rate Swaps as a
Risk Management Tool
 Comparing Financial Futures, FRAs and Basic
Swaps

Similarities



Each enables a party to enter an agreement,
which provides for cash receipts or cash
payments depending on how interest rates
move
Each allows managers to alter a bank’s
interest rate risk exposure
None requires much of an initial cash
commitment to take a position
270
Basic Interest Rate Swaps as a
Risk Management Tool
 Comparing Financial Futures, FRAs and Basic
Swaps

Differences
 Financial futures are standardized contracts
based on fixed principal amounts while with FRAs
and interest rate swaps, parties negotiate the
notional principal amount
 Financial futures require daily marking-to-market,
which is not required with FRAs and swaps
 Many futures contracts cannot be traded out more
than three to four years, while interest rate swaps
often extend 10 to 30 years
 The market for FRAs is not that liquid and most
contracts are short term
271
Basic Interest Rate Swaps as a
Risk Management Tool
 The Risk with Swaps
 Counterparty risk is extremely important
to swap participants
 Credit risk exists because the
counterparty to a swap contract may
default
 This is not as great for a single contract
since the swap parties exchange only net
interest payments
 The notional principal amount never changes
hands, such that a party will not lose that
amount
272
Interest Rate Caps and Floors
 Buying an Interest Rate Cap
 Interest

Rate Cap
An agreement between two
counterparties that limits the buyer’s
interest rate exposure to a maximum
rate
 Buying a cap is the same as purchasing a
call option on an interest rate
273
274
Interest Rate Caps and Floors
 Buying an Interest Rate Floor
 Interest

Rate Floor
An agreement between two
counterparties that limits the buyer’s
interest rate exposure to a minimum
rate
 Buying a floor is the same as purchasing a
put option on an interest rate
275
276
Interest Rate Caps and Floors
 Interest Rate Collar and Reverse Collar
 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
277
Interest Rate Caps and Floors
 Interest Rate Collar and Reverse Collar
 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
 Used to protect a bank against falling interest
rates
278
Interest Rate Caps and Floors
 Interest Rate Collar and Reverse Collar

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 in-the-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
279
Interest Rate Caps and Floors
280
Interest Rate Caps and Floors
 Protecting Against Falling Interest
Rates
 Assume
that a bank is asset sensitive
The bank holds loans priced at prime
plus 1% and funds the loans with a
three-year fixed-rate deposit at 3.75%
percent
 Management believes that interest
rates will fall over the next three years

281
Interest Rate Caps and Floors
 Protecting Against Falling Interest Rates
 It is considering three alternative
approaches to reduce risk associated with
falling rates:
1. Entering into a basic interest rate swap to
pay three-month LIBOR and receive a fixed
rate
2. Buying an interest rate floor
3. Buying a reverse collar
 Note that, initially, the bank holds assets
priced based on prime and deposits priced
based on a fixed rate of 3.75%
282
Interest Rate Caps and Floors
 Protecting Against Falling Interest
Rates
 Strategy:
Use a Basic Interest Rate
Swap: Pay Floating and Receive Fixed

As shown on the next slide, the use of
the swap effectively fixes the spread
near the current level, except for basis
risk
283
284
Interest Rate Caps and Floors
 Protecting Against Falling Interest
Rates
 Strategy:
Buy a Floor on the Floating
Rate

As shown on the next slide, the use of
the floor protects against loss from
falling rates while retaining the benefits
from rising rates
285
286
Interest Rate Caps and Floors
 Protecting Against Falling Interest Rates
 Strategy: Buy a Reverse Collar: Sell a Cap
and Buy a Floor on the Floating Rate
 As shown on the next slide, the use of the
reverse collar differs from a pure floor by
eliminating some of the potential benefits
in a rising-rate environment
 The bank actually receives a net premium up
front and while this is attractive up front, if
rates increase sufficiently, the bank does not
benefit
 The net result is that the bank’s spread will
vary within a band
287
288
Interest Rate Caps and Floors
 Protecting Against Rising Interest Rates

Assume that a bank is liability sensitive
That bank has made three-year fixed-rate
term loans at 7% funded with three-month
Eurodollar deposits for which it pays the
prevailing LIBOR minus 0.25%
 Management believes is concerned that
interest rates will rise over the next three
years

289
Interest Rate Caps and Floors
 Protecting Against Rising Interest
Rates

It is considering three alternative
approaches to reduce risk associated
with rising rates:
1. Entering into a basic interest rate swap to
pay a fixed rate and receive the threemonth LIBOR
2. Buying an interest rate cap
3. Buying a collar
290
Interest Rate Caps and Floors
 Protecting Against Rising Interest
Rates
 Strategy:
Use a Basic Interest Rate
Swap: Pay Fixed and Receive Floating

As shown on the next slide, the use of
the swap effectively fixes the spread
near the current level, except for basis
risk
291
292
Interest Rate Caps and Floors
 Protecting Against Rising Interest
Rates
 Strategy:
Buy a Cap on the Floating
Rate

As shown on the next slide, the use of
the cap protects against loss from
rising rates while retaining the benefits
from falling rates
293
294
Interest Rate Caps and Floors
 Protecting Against Rising Interest
Rates
 Strategy:
Buy a Collar: Buy a Cap and
Sell a Floor on the Floating Rate

As shown on the next slide, the use of
the collar differs from a pure cap by
eliminating some of the potential
benefits in a falling-rate environment
 The net result is that the collar effectively
creates a band within which the bank’s
margin will fluctuate
295
296
Using Derivatives to
Manage Interest Rate
Risk
297