1. Chapter Seven
Risk Management for Changing Interest
Rates: Asset-Liability Management and
Duration Techniques
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

2. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Key Topics
• Asset, Liability, and Funds Management
• Market Rates and Interest-Rate Risk
• The Goals of Interest-Rate Hedging
• Interest-Sensitive Gap Management
• Duration Gap Management
• Limitations of Hedging Techniques
7-2

3. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Asset-Liability Management
The Purpose of Asset-Liability
Management is to Control a Bank’s
Sensitivity to Changes in Market Interest
Rates and Limit its Losses in its Net
Income or Equity
7-3

4. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Historical View of Asset-Liability
Management
• Asset Management Strategy (control over
assets, no control over liabilities)
• Liability Management Strategy (control
over liabilities by changing rates and other
terms)
• Funds Management Strategy (work with
both strategies)
7-4

5. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Interest Rate Risk
• Price Risk
▫ When Interest Rates Rise, the Market Value of
the Bond or Asset Falls
• Reinvestment Risk
▫ When Interest Rates Fall, the Coupon
Payments on the Bond are Reinvested at
Lower Rates
7-5

6. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Interest Rate Risk: One of the Main
Challenges
• Forces Determining Interest Rates
▫ Loanable Funds Theory
• The Measurement of Interest Rates
▫ YTM
▫ Bank Discount
• Components of Interest Rates
7-6

7. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Yield to Maturity (YTM)
∑= +
=
n
1t
t
t
YTM)(1
CF
PriceMarket
7-7

8. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Bank Discount Rate (DR)
MaturitytoDays#
360
*
FV
PricePurchase-FV
DR =
Where: FV equals Face Value of a Security,
such as Treasury Bills
7-8

9. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Market Interest Rates
Function of:
• Risk-Free Real Rate of Interest
• Various Risk Premiums
▫ Default Risk
▫ Inflation Risk
▫ Liquidity Risk
▫ Call Risk
▫ Maturity Risk
7-9

10. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Yield Curves
• Graphical Picture of Relationship Between
Yields and Maturities on Securities
• Generally Created With Treasury Securities to
Keep Default Risk Constant
• Shape of the Yield Curve
▫ Upward – Long-Term Rates Higher than Short-Term
Rates
▫ Downward – Short-Term Rates Higher than Long-
Term Rates
▫ Horizontal – Short-Term and Long-Term Rates the
Same
• Shape of the Yield Curve and a Maturity Gap
7-10

11. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Net Interest Margin
AssetsEarningsTotal
ExpensesInterest-IncomeInterest
NIM =
7-11

12. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Goal of Interest Rate Hedging
One Important Goal of Interest Rate
Hedging is to Insulate the Bank from the
Damaging Effects of Fluctuating Interest
Rates on Profits
7-12

13. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Quick Quiz
• What forces cause interest rates to change?
• What makes it so difficult to correctly forecast
interest rate changes?
• What is the yield curve, and why is it important to
know about its shape and slope?
• What is the goal of hedging?
• First National Bank of Bannerville has posted interest
revenues of $63 million and interest costs from all of its
borrowings of $42 million. If this bank possesses $700 million
in total earning assets, what is First National’s net interest
margin? Suppose the bank’s interest revenues and interest
costs double, while its earning assets increase by 50%. What
will happen to its net interest margin?
7-13

14. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Interest-Sensitive Gap Measurements
Dollar Interest-
Sensitive Gap
Interest-Sensitive Assets –
Interest Sensitive Liabilities=
Relative
Interest-
Sensitive Gap SizeBank
GapISDollar
=
Interest
Sensitivity
Ratio
sLiabilitieSensitiveInterest
AssetsSensitiveInterest
=
7-14

15. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Examples of Repriceable (Interest Sensitive)
Assets and Liabilities
7-15

16. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Asset-Sensitive Bank Has:
• Positive Dollar Interest-Sensitive Gap
• Positive Relative Interest-Sensitive Gap
• Interest Sensitivity Ratio Greater Than
One
7-16

17. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Liability Sensitive Bank Has:
• Negative Dollar Interest-Sensitive Gap
• Negative Relative Interest-Sensitive Gap
• Interest Sensitivity Ratio Less Than One
7-17

18. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Computer-Based Techniques and Maturity
Buckets
7-18

19. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Gap Positions and the Effect of Interest
Rate Changes on the Bank
• Asset-Sensitive
Bank
▫ Interest Rates Rise
 NIM Rises
▫ Interest Rates Fall
 NIM Falls
• Liability-Sensitive
Bank
▫ Interest Rates Rise
 NIM Falls
▫ Interest Rates Fall
 NIM Rises
7-19

20. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Zero Interest-Sensitive Gap
• Dollar Interest-Sensitive Gap is Zero
• Relative Interest-Sensitive Gap is Zero
• Interest Sensitivity Ratio is One
▫ When Interest Rates Change in Either Direction -
NIM is Protected and Will Not Change
7-20

21. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Important Decision Regarding IS Gap
• Management Must Choose the Time Period
Over Which NIM is to be Managed
• Management Must Choose a Target NIM
• To Increase NIM Management Must Either:
▫ Develop Correct Interest Rate Forecast
▫ Reallocate Assets and Liabilities to Increase
Spread
• Management Must Choose Volume of Interest-
Sensitive Assets and Liabilities
7-21

22. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
NIM Influenced By:
• Changes in Interest Rates Up or Down
• Changes in the Spread Between Assets and
Liabilities
• Changes in the Volume of Interest-Sensitive
Assets and Liabilities
• Changes in the Mix of Assets and Liabilities
7-22

23. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Cumulative Gap
The Total Difference in Dollars Between
Those Bank Assets and Liabilities Which
Can be Repriced over a Designated Time
Period
7-23

24. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Aggressive Interest-Sensitive Gap
Management
7-24

25. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Problems with Interest-Sensitive Gap
Management
• Interest Paid on Liabilities Tend to Move Faster than
Interest Rates Earned on Assets
• Interest Rate Attached to Bank Assets and
Liabilities Do Not Move at the Same Speed as
Market Interest Rates
• Point at Which Some Assets and Liabilities are
Repriced is Not Easy to Identify
• Interest-Sensitive Gap Does Not Consider the
Impact of Changing Interest Rates on Equity
Position
7-25

26. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Quick Quiz
• Commerce National Bank reports interest-sensitive assets of $870
million and interest-sensitive liabilities of $625 million during the
coming month. Is the bank asset sensitive or liability sensitive?
What is likely to happen to the bank’s net interest margin if interest
rates rise? If they fall?
• People’s Savings Bank , a thrift institutions, has a cumulative gap
for the coming year of +$135 million, and interest rates are
expected to fall by two and a half percentage points. Calculate the
expected change in net interest income that this thrift institution
might experience. What will occur in net interest income if interest
rates rise by one and a quarter percentage points?
7-26

27. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
The Concept of Duration
Duration is the Weighted Average Maturity
of a Promised Stream of Future Cash
Flows
7-27

28. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
To Calculate the Instrument’s Duration
PriceorValueMarketCurrent
YTM)(1
CF*t
YTM)(1
CF
YTM)(1
CF*t
D
n
1t
t
t
n
1t
t
t
n
1t
t
t
∑
∑
∑ =
=
=
+
=
+
+
=
7-28

29. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Price Sensitivity of a Security
i)(1
i
*D-
P
P
+
∆
≈
∆
7-29

30. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Convexity
The Rate of Change in an Asset’s Price or
Value Varies with the Level of Interest
Rates or Yields
7-30

31. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Dollar-Weighted Duration of Asset Portfolio
∑=
=
n
1i
AiA i
D*wD
Where:
wi = the dollar amount of the ith asset divided by total assets
DAi = the duration of the ith asset in the portfolio
7-31

32. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Dollar-Weighted Duration of a Liability
Portfolio
∑=
=
n
1i
LiL i
D*wD
Where:
wi = the dollar amount of the ith liability divided by total liabilities
DLi = the duration of the ith liability in the portfolio
7-32

33. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Duration Gap
TA
TL
*D-DD LA=
7-33

34. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Change in the Value of a Bank’s Net Worth






+
∆






+
∆
=∆ L*
i)(1
i
*D--A*
i)(1
i
*D-NW LA
7-34

35. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Impact of Changing Interest Rates on a
Bank’s Net Worth
7-35

36. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Limitations of Duration Gap Management
• Finding Assets and Liabilities of the Same
Duration Can be Difficult
• Some Assets and Liabilities May Have Patterns of
Cash Flows that are Not Well Defined
• Customer Prepayments May Distort the Expected
Cash Flows in Duration
• Customer Defaults May Distort the Expected
Cash Flows in Duration
• Convexity Can Cause Problems
7-36

37. McGraw-Hill/Irwin
Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Quick Quiz
• What is duration? How is a financial institution’s
duration gap determined?
• What are the advantages of using duration as
opposed to interest-sensitive gap analysis?
• Suppose that a thrift institution has an average
asset duration of 2.5 years and an average liability
duration of 3.0 years. If the thrift holds total assets
of $560 million and total liabilities of $467 million,
does it have a significant leverage-adjusted duration
gap? If interest rates rise, what will happen to the
value of its net worth?
7-37