1. Managing Interest Rate Risk: GAP and Earnings Sensitivity
Chapter 7
Managing Interest Rate Risk: GAP and Earnings Sensitivity

2. Managing 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

3. Managing 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

4. Managing Interest Rate Risk
Banks typically focus on either:
Net interest income or
The market value of stockholders' equity
GAP Analysis
A static measure of risk that is commonly associated with net interest income (margin) targeting
Earnings Sensitivity Analysis
Earnings sensitivity analysis extends GAP analysis by focusing on changes in bank earnings due to changes in interest rates and balance sheet composition

5. Managing 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

6. Measuring Interest Rate Risk with GAP
Three general factors potentially cause a bank’s net interest income to change.
Rate Effects
Unexpected changes in interest rates
Composition (Mix) Effects
Changes in the mix, or composition, of assets and/or liabilities
Volume Effects
Changes in the volume of earning assets and interest-bearing liabilities

7. 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?

8. 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)

9. Measuring Interest Rate Risk with GAP
Traditional Static Gap Analysis
Steps in GAP Analysis
Develop an interest rate forecast
Select a series of “time buckets” or time intervals for determining when assets and liabilities will reprice
Group assets and liabilities into these “buckets”
Calculate the GAP for each “bucket ”
Forecast the change in net interest income given an assumed change in interest rates

10. 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

11. 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

12. 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

13. 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.

14. 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

15. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Rate, Composition (Mix) and Volume Effects
All affect net interest income

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
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

17. 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

18. 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

19. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income

20. 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

21. 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

22. 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 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%. What is the bank’s 1-year GAP?

23. 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

24. 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 T-Bill at rate of 4.80%. The bank’s initial spread is 1.05%. What is the bank’s 6-month GAP?

25. 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

26. 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)

27. 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

28. 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

31. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.0

32. 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
$ $37.20 = $41.30

33. 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

34. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.1
What if all rates increase by 1%?

35. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.1
What if all rates increase by 1%?
With a negative GAP, interest income increases by less than the increase in interest expense. Thus, both NII and NIM fall.

36. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.2
What if all rates fall by 1%?

37. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.2
What if all rates fall by 1%?
With a negative GAP, interest income decreases by less than the decrease in interest expense. Thus, both NII and NIM increase.

38. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.3
What if rates rise but the spread falls by 1%?

39. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.3
What if rates rise but the spread falls by 1%?
Both NII and NIM fall with a decrease in the spread. Why the larger change?
Note: ∆NIIEXP ≠ GAP x ∆iEXP Why?

40. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.4
What if rates fall but the spread falls by 1%?

41. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.4
What if rates fall and the spread falls by 1%?
Both NII and NIM fall with a decrease in the spread.
Note: ∆NIIEXP ≠ GAP x ∆iEXP

42. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.5
What if rates rise and the spread rises by 1%?

43. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.5
What if rates rise and the spread rises by 1%?
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 3.6
What if rates fall and the spread rises by 1%?

45. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.6
What if rates fall and the spread rises by 1%?
Both NII and NIM increase with an increase in the spread.
Note: ∆NIIEXP ≠ GAP x ∆iEXP

46. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.7
What if the bank proportionately doubles in size?

47. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 3.7
What if the bank proportionately doubles in size?
Both NII doubles but NIM stays the same. Why? What has happened to the bank’s risk?

48. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.0

49. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.0
Bank has a positive GAP

50. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.1
What if rates increase by 1%?

51. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.1
What if rates increase by 1%?
With a positive GAP, interest income increases by more than the increase in interest expense. Thus, both NII and NIM rise.

52. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.2
What if rates decrease by 1%?

53. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.2
What if rates decrease by 1%?
With a positive GAP, interest income decreases by more than the decrease in interest expense. Thus, both NII and NIM fall.

54. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.3
What if rates rise but the spread falls by 1%?

55. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.3
What if rates rise but the spread falls by 1%?
Both NII and NIM fall with a decrease in the spread. Why the larger change?
Note: ∆NIIEXP ≠ GAP x ∆iEXP Why?

56. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.4
What if rates fall and the spread falls by 1%?

57. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.4
What if rates fall and the spread falls by 1%?
Both NII and NIM fall with a decrease in the spread.
Note: ∆NIIEXP ≠ GAP x ∆iEXP

58. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.5
What if rates rise and the spread rises by 1%?

59. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.5
What if rates rise and the spread rises by 1%?
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 4.6
What if rates fall and the spread rises by 1%?

61. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.6
What if rates fall and the spread rises by 1%?
Both NII and NIM increase with an increase in the spread.
Note: ∆NIIEXP ≠ GAP x ∆iEXP

62. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.7
What if the bank proportionately doubles in size?

63. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 4.7
What if the bank proportionately doubles in size?
Both NII doubles but NIM stays the same. Why? What has happened to the bank’s risk?

64. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 5.0

65. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 5.0
Bank has zero GAP

66. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 5.1
What if rates increase by 1%?

67. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 5.1
What if rates increase by 1%?
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!

68. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 5.2
What if rates fall and the spread falls by 1%?

69. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 5.2
What if rates fall and the spread falls by 1%?
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

70. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 5.3
What if rates rise and the spread rises by 1%?

71. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Example 5.3
What if rates rise and the spread rises by 1%?
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

72. Measuring Interest Rate Risk with GAP
Factors Affecting Net Interest Income
Summary of Base Cases
If a Negative GAP gives the largest NII and NIM, why not plan for a Negative GAP?

73. 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

75. 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

76. 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

77. 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

79. 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

80. 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

81. 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

82. 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-earning-asset 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

83. 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

84. Earnings Sensitivity Analysis
Steps to Earnings Sensitivity Analysis
Forecast interest rates.
Forecast balance sheet size and composition given the assumed interest rate environment
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

85. Earnings Sensitivity Analysis
Steps to Earnings Sensitivity Analysis
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

86. 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

87. 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

88. 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

89. 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

90. 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

94. 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 Earnings-at-Risk Simulation or Net Interest Income Simulation

95. 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.

96. 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

97. 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

98. Income Statement GAP Beta GAP
The adjusted GAP figure in a basic earnings sensitivity analysis derived from multiplying the amount of rate-sensitive assets by the associated beta factors and summing across all rate-sensitive assets, and subtracting the amount of rate-sensitive liabilities multiplied by the associated beta factors summed across all rate-sensitive liabilities

99. Income Statement GAP Balance Sheet GAP Earnings Change Ratio (ECR)
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

101. 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 non-interest-bearing liabilities
Use off-balance sheet transactions to hedge

102. Managing the GAP and Earnings Sensitivity Risk
How to Adjust the Effective GAP or Earnings Sensitivity Profile

103. Managing Interest Rate Risk: GAP and Earnings Sensitivity
Chapter 7
Managing Interest Rate Risk: GAP and Earnings Sensitivity