This document discusses various methods for measuring and managing interest rate risk, including interest rate sensitivity gap analysis and duration gap analysis. It defines interest rate sensitivity gap as the difference between interest rate sensitive assets and liabilities, and explains how a positive, negative, or zero gap impacts changes in net interest income from interest rate movements. It also introduces duration as a weighted measure of maturity that considers the timing of cash flows from assets and liabilities. The document provides examples of calculating weighted duration gaps for asset and liability portfolios, and the change in net worth from an interest rate increase. It notes limitations in using duration gap analysis for interest rate risk management.

1. 1
CHAPTER 7
ASSET-LIABILITY
MANAGEMENT
PART 2

2. INTEREST SENSITIVE GAP
MANAGEMENT - SUMMARY
Gap Change in
interest rate
Change in net
interest income
Positive ISA > ISL Increase Increase
Decrease Decrease
Negative ISA < ISL Increase Decrease
Decrease Increase
Zero ISA = ISL Increase No change
Decrease No change

3. How to Measure Interest Rate Risk
Exposure
1. Cumulative gap
2. Aggressive gap management
3. Weighted interest-sensitive gap

4. Cumulative gap
 The total difference in dollars between those assets and liabilities that can
be repriced over a designated period of time.
 Example: The bank has RM100 million in earning assets and RM200
million in liabilities subject to an interest rate change each month over the
next 6 months.
The cumulative gap:
(RM100 million per month x 6) – (RM200 million per month x 6) = - RM600
million.

5.  The cumulative gap is useful because, given any specific change in
market interest rates, we can calculate approximately how net interest
income will be affected by an interest rate change.
 Change in net interest income
= Overall change in interest rate (in percentage points) x size of the
cumulative gap (in dollars).
 Example: Suppose market interest rate rises by 1 percentage point.
The loss of net interest income will be:
 0.01 x –RM600 million = -RM6 million

6. Aggressive Gap Management
 Some banks shade their interest-sensitive gaps toward either asset
sensitivity or liability sensitivity, depending on their degree of
confidence in their own interest rate forecast.
 Example: If management believes interest rates are going to fall over
the current situation, it will probably allow interest-sensitive liabilities
to climb above interest-sensitive assets.
 If interest rates do fall as predicted, liability costs will drop by more
than revenues and the NIM will increase.

7. Weighted Interest-Sensitive Gap
 This approach takes into account the tendency of interest rates to
vary in speed and magnitude relative to each other and with the up
and down cycle of business activity.
 The interest rates on assets often change by different amounts and
by different speeds than interest rates on liabilities.
 Under this approach, all interest-sensitive assets and liabilities are
given weight based on their speed (sensitivity) relative to some
market interest rate.

8. Weighted Interest-Sensitive Gap
 For example, federal funds loans generally carry interest rates set in
the open market, so these loans have an interest rate sensitivity
weight of 1.0.
 On the other way, loans and leases are the most rate-volatile so its
weight is estimated to be 1.5.
 On the liability side, the bank can assume deposits have a rate-
sensitive weight of 0.86 because deposits rate may change more
slowly than market interest rates.

9. Weighted Interest-Sensitive Gap
 To determine the interest-sensitive gap, the dollar amount of each
type of assets or liability would be multiplied by its weight and added
to the rest of the interest-sensitive assets or liabilities.
 More rate-volatile assets and liabilities will weigh more heavily in the
refigured balance sheet.
 This weighted interest-sensitive gap should be more accurate than
the unweighted interest-sensitive gap.
 The interest-sensitive gap may change from negative to positive or
vice versa and may change significantly the interest rate strategy
pursued by the bank

10. 10

11. INTEREST SENSITIVE GAP
MANAGEMENT
Optimal value for a bank’s gap?
 There is NO general optimal value for a bank’s gap in all
environment.
 Gap is a measure of interest rate risk.
 The best gap for a bank can be determined only by evaluating a
bank’s overall risk and return profile and objectives.
 The farther the bank’s gap from zero, the greater the bank’s
risk.

12.  Bank managers try to adjust the interest rate exposure in
anticipation of changes in interest rates.
 Speculating on the gap:
* Difficult to vary the gap and win (requires accurate interest rate
forecast on a consistent basis).
* Usually only look short term.
* Limited flexibility in adjusting the gap, customers and depositors.
* No adjustment for timing of cash flows or dynamics of the
changing gap position.

13. INTEREST SENSITIVE GAP
MANAGEMENT
With positive gap The risk Possible
management
responses
Asset sensitive
ISA > ISL
If interest rate rises,
banks are fine.
BUT,
Losses if interest rate
fall because bank net
interest margin will be
reduced
Do nothing (maybe
interest rate will rise or
stable)
Extend asset
maturities or shorten
liability maturities
Increase ISL or
decrease ISA

14. With negative gap The risk Possible
management
responses
Liability sensitive
ISA < ISL
If interest rate falls,
banks are fine.
BUT,
Losses if interest
rate rise because
the bank’s net
interest margin will
be reduced
Do nothing (maybe
interest rate will fall
or stable)
Shorten asset
maturities or
lengthen liability
maturities
Decrease ISL or
increase ISA
INTEREST SENSITIVE GAP
MANAGEMENT

15. Problems with IS gap
management:
i. Interest paid on liabilities tend to move faster than interest rates
earned on assets.
ii. Interest rate attached to bank assets and liabilities do not move
at the same speed as market interest rates.
iii. Point at which some assets and liabilities are repriced is not
easy to identify.
iv. Interest sensitive gap does not consider the impact of changing
interest rates in equity position.

16. DURATION GAP MANAGEMENT
 Duration is a value and time-weighted measure of maturity that
considers the timing of all cash inflows from earning assets and all
cash outflows associated with liabilities.
 It measures the average maturity of a promised stream of future
cash payments.
 In effect, duration measures the average time needed to recover
the funds committed to an investment.

17. CONCEPT OF DURATION:
 How to calculate duration.
 How to calculate change in net worth if interest rate rises.
 How to calculate dollar-weighted asset portfolio duration.
 How to calculate dollar-weighted liability portfolio duration.
 How to calculate duration gap.

18. How to Calculate Duration
18
D= instrument’s duration in year
t= period of time in which flow of cash to be received
CF= expected cash flow for each time period
YTM= instrument’s current yield to maturity
Abbreviated formula

19. How to Calculate Duration
Example:
Suppose a commercial bank grants a loan to one of its customers for a term of 5
years. The customer promises the bank an annual interest payment of 10%. The par
value of the loan is RM1,000, which is also its current market value (price) because
the loan’s current yield to maturity is 10%. What is this loan’s duration?
years
4.17
RM1,000
RM4,169.87
000
,
1
)
10
.
0
1
/(
5
000
,
1
)
10
.
1
/(
100
D
5
1
t
5










RM
RM
t
RM t

20. 20

21. How to Calculate Change in Net
Worth if Interest Rate Rises
Example:
Suppose a commercial bank has an average duration in its assets
of 3 years, an average liability duration of 2 years, total liabilities of
RM100 million, and total assets of RM120 million. Interest rate was
originally 10%, but suddenly they rise to 12%. Find the change in
the value of net worth.

22. 
















 L
*
i)
(1
i
*
D
-
-
A
*
i)
(1
i
*
D
-
NW L
A
22
How to Calculate Change in Net
Worth if Interest Rate Rises

23. million
RM 91
.
2
100
*
0.10)
(1
02
.
0
*
2
-
-
120
*
)
10
.
0
(1
02
.
0
*
3
-
NW

















23
How to Calculate Change in Net
Worth if Interest Rate Rises

24. How to Calculate Ringgit-Weighted
Asset Portfolio Duration
Example:
Assets Held Market value (RM) Asset Durations
Treasury Bonds 90 mil 7.49 years
Commercial
Loans
100 mil 0.60 years
Consumer Loans 50 mil 1.2 years
Real Estate Loans 40 mil 2.25 years
Municipal Bonds 20 mil 1.5 years

25. 


n
1
i
A
i
A i
D
*
w
D
25
Where:
wi = the dollar amount of the ith asset divided by total assets
DAi = the duration of the ith asset in the portfolio
How to Calculate Ringgit-
Weighted Asset Portfolio Duration

26. years
3.05
300
914.10
20
40
50
100
90
20)
(1.5
40)
(2.25
50)
(1.20
100)
(0.60
90)
(7.49
assets
all
of
ue
market val
Total
asset
each
of
ue
Market val
asset
each
of
Duration
D
n
1
t
A




















26
How to Calculate Ringgit-
Weighted Asset Portfolio Duration

27. How to Calculate Ringgit-Weighted
Liability Portfolio Duration
Example:
Liabilities Held Market value (RM) Asset Durations
Deposit 78 mil 2.5 years
Other Non-deposit
borrowings
60 mil 3.0 years

28. How to Calculate Ringgit-
Weighted Liability Portfolio
Duration



n
1
i
L
i
L i
D
*
w
D
28
Where:
wi = the dollar amount of the ith liability divided by total liabilities
DLi = the duration of the ith liability in the portfolio

29. years
2.72
138
375
60
78
60)
(3.0
78)
(2.5
DL







29
How to Calculate Ringgit-
Weighted Liability Portfolio
Duration

30. How to Calculate Leverage-
Adjusted Duration Gap

31. How to Calculate Leverage-
Adjusted Duration Gap
TA
TL
*
D
-
D
D L
A

31

32. How to Calculate Leverage-
Adjusted Duration Gap
years
1.80
300
138
72
.
2
-
3.05
D









32

33. Limitations of Duration Gap
Management
33
1. Finding assets and liabilities of the same
duration can be difficult
2. Some assets and liabilities may have patterns of
cash flows that are not well defined
3. Customer prepayments may distort the expected
cash flows in duration
4. Customer defaults may distort the expected cash
flows in duration