Chapter Seven
Asset-Liability Management:
Determining and Measuring Interest
Rates and Controlling Interest-Sensitive
and Duration Gaps
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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
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Historical View of Asset-Liability
Management
• Asset Management Strategy
• Liability Management Strategy
• Funds Management Strategy
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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
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Yield to Maturity (YTM)
n
CFt
Market Price  
t
t 1 (1  YTM)
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Bank Discount Rate (DR)
FV - Purchase Price
360
DR 
*
FV
# Days to Maturity
Where: FV equals Face Value
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Market Interest Rates
Function of:
• Risk-Free Real Rate of Interest
• Various Risk Premiums
–
–
–
–
–
Default Risk
Inflation Risk
Liquidity Risk
Call Risk
Maturity Risk
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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 LongTerm Rates
– Horizontal – Short-Term and Long-Term Rates the
Same
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Net Interest Margin
Interest Income - Interest Expenses
NIM 
Total Earnings Assets
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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
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Interest-Sensitive Gap Measurements
Interest-Sensitive Assets –
Dollar InterestSensitive Gap = Interest Sensitive Liabilities
Relative
Dollar IS Gap
Interest
Bank Size
Sensitive Gap
Interest
Interest Sensitive Assets
Sensitivity 
Interest
Sensitive
Liabilitie
s
Ratio
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Interest-Sensitive Assets
• Short-Term Securities Issued by the
Government and Private Borrowers
• Short-Term Loans Made by the Bank
to Borrowing Customers
• Variable-Rate Loans Made by the
Bank to Borrowing Customers
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Interest-Sensitive Liabilities
• Borrowings from Money Markets
• Short-Term Savings Accounts
• Money-Market Deposits
• Variable-Rate Deposits
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Asset-Sensitive Bank Has:
• Positive Dollar Interest-Sensitive Gap
• Positive Relative Interest-Sensitive
Gap
• Interest Sensitivity Ratio Greater
Than One
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Liability Sensitive Bank Has:
• Negative Dollar Interest-Sensitive
Gap
• Negative Relative Interest-Sensitive
Gap
• Interest Sensitivity Ratio Less Than
One
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Gap Positions and the Effect of
Interest Rate Changes on the Bank
• Liability-Sensitive
Bank
• Asset-Sensitive
Bank
– Interest Rates Rise
•NIM Rises
– Interest Rates Fall
•NIM Falls
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– Interest Rates Rise
•NIM Falls
– Interest Rates Fall
•NIM Rises
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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
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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
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NIM Influenced By:
• Changes in Interest Rates Up or Down
• Changes in the Spread Between Assets
and Liabilities
• Changes in the Volume of InterestSensitive Assets and Liabilities
• Changes in the Mix of Assets and
Liabilities
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Cumulative Gap
The Total Difference in Dollars
Between Those Bank Assets and
Liabilities Which Can be Repriced
over a Designated Time Period
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Aggressive Interest-Sensitive Gap
Management
Expected Change
in Interest Rates
Best InterestSensitive Gap
Position
Aggressive
Management’s
Likely Action
Rising Market
Interest Rates
Positive IS Gap
Falling Market
Interest Rates
Negative IS Gap
Increase in IS
Assets
Decrease in IS
Liabilities
Decrease in IS
Assets
Increase in IS
Liabilities
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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
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The Concept of Duration
Duration is the Weighted Average
Maturity of a Promised Stream of
Future Cash Flows
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To Calculate Duration
n
t * CFt

t
t 1 (1  YTM)
D n
CFt

t
t 1 (1  YTM)
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Price Sensitivity of a Security
P
i
 -D*
P
(1  i)
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Convexity
The Rate of Change in an Asset’s
Price or Value Varies with the Level
of Interest Rates or Yields
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Duration of an Asset portfolio
n
D A   w i * D Ai
i 1
Where:
wi = the dollar amount of the ith asset divided by total assets
DAi = the duration of the ith asset in the portfolio
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Duration of a Liability Portfolio
n
D L   w i * D Li
i 1
Where:
wi = the dollar amount of the ith liability divided by total liabilities
DLi = the duration of the ith liability in the portfolio
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Duration Gap
TL
D  DA - DL *
TA
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Change in the Value of a Bank’s
Net Worth

 

i
i
NW  - D A *
* A - - D L *
* L
(1  i)
(1  i) 

 
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Impact of Changing Interest Rates
on a Bank’s Net Worth
Positive
Interest Rate Rise
NW Decrease
Gap
Interest Rate Fall
NW Increase
Negative
Interest Rate Rise
NW Increase
Gap
Interest Rate Fall
NW Decrease
Zero
Interest Rate Rise
No Change
Gap
Interest Rate Fall
No Change
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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
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