chapter 7

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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

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
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2

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
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3

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
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4

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
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5

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
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6

McGraw
-
Hill/Irwin

Bank Management and Financial Services, 7/e

© 2008 The McGraw
-
Hill Companies, Inc., All Rights Reserved.

Yield to Maturity (YTM)





n
1
t
t
t
YTM)


(1
CF


Price
Market
7
-
7

McGraw
-
Hill/Irwin

Bank Management and Financial Services, 7/e

© 2008 The McGraw
-
Hill Companies, Inc., All Rights Reserved.

Bank Discount Rate (DR)

Maturity

to
Days

#
360
*
FV
Price

Purchase
-

FV


DR

Where: FV equals Face Value of a Security,
such as Treasury Bills

7
-
8

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

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
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10

McGraw
-
Hill/Irwin

Bank Management and Financial Services, 7/e

© 2008 The McGraw
-
Hill Companies, Inc., All Rights Reserved.

Net Interest Margin

Assets

Earnings

Total
Expenses
Interest

-

Income
Interest


NIM

7
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11

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
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12

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
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13

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

Size
Bank
Gap

IS
Dollar


Interest
Sensitivity
Ratio

s
Liabilitie

Sensitive
Interest
Assets

Sensitive
Interest


7
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14

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

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
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16

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
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17

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

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
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19

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

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

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
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22

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
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23

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

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
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25

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
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26

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
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27

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

Price
or

Value
Market
Current
YTM)


(1
CF

*
t
YTM)


(1
CF
YTM)


(1
CF

*
t


D
n
1
t
t
t
n
1
t
t
t
n
1
t
t
t











7
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28

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
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29

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
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30

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
1


i
A
i
A
i
D

*
w


D
Where:

w
i

= the dollar amount of the ith asset divided by total assets

D
Ai

= the duration of the ith asset in the portfolio

7
-
31

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
1
i
L
i
L
i
D

*

w


D
Where:

w
i

= the dollar amount of the ith liability divided by total liabilities

D
Li

= the duration of the ith liability in the portfolio

7
-
32

McGraw
-
Hill/Irwin

Bank Management and Financial Services, 7/e

© 2008 The McGraw
-
Hill Companies, Inc., All Rights Reserved.

Duration Gap

TA
TL

*

D

-

D


D
L
A

7
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33

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
L
A
7
-
34

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
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35

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

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?

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