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Chapter Seven

Risk Management for ChangingInterest Rates: Asset-LiabilityManagement and Duration Techniques

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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

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Asset-Liability Management

The Purpose of Asset-Liability

Management is to Control a BanksSensitivity to Changes in MarketInterest Rates and Limit its Losses inits Net Income or Equity

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Historical View of Asset-Liability

Management Asset Management Strategy (controlover assets, no control over liabilities)

Liability Management Strategy (controlover liabilities by changing rates andother terms)

Funds Management Strategy (workwith both strategies)

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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 atLower Rates

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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

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Yield to Maturity (YTM)

n

1tt

t

YTM)(1

CFPriceMarket

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Bank Discount Rate (DR)

MaturitytoDays#

360*

FV

PricePurchase-FVDR

Where: FV equals Face Value of a Security,

such as Treasury Bills

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Market Interest RatesFunction 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 BetweenYields 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

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Net Interest Margin

AssetsEarningsTotal

ExpensesInterest-IncomeInterestNIM

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Goal of Interest Rate Hedging

One Important Goal of Interest RateHedging is to Insulate the Bank fromthe Damaging Effects of FluctuatingInterest Rates on Profits

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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 $700million in total earning assets, what is First Nationalsnet interest margin? Suppose the banks interestrevenues and interest costs double, while its earningassets increase by 50%. What will happen to its netinterest margin?

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Interest-Sensitive Gap Measurements

Dollar Interest-

Sensitive Gap

Interest-Sensitive Assets

Interest Sensitive Liabilities=

RelativeInterest-

Sensitive Gap SizeBank

GapISDollar

InterestSensitivity

RatiosLiabilitieSensitiveInterest

AssetsSensitiveInterest

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Examples of Repriceable (InterestSensitive) Assets and Liabilities

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Asset-Sensitive Bank Has:

Positive Dollar Interest-Sensitive Gap

Positive Relative Interest-Sensitive Gap

Interest Sensitivity Ratio Greater ThanOne

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Liability Sensitive Bank Has:

Negative Dollar Interest-Sensitive Gap

Negative Relative Interest-SensitiveGap

Interest Sensitivity Ratio Less ThanOne

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Computer-Based Techniques andMaturity Buckets

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Gap Positions and the Effect ofInterest Rate Changes on the Bank

Asset-SensitiveBank Interest Rates Rise

NIM Rises

Interest Rates Fall NIM Falls

Liability-

Sensitive Bank 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 EitherDirection - NIM is Protected and Will Not

Change

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Important Decision Regarding IS Gap

Management Must Choose the Time PeriodOver 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 ofInterest-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 Interest-Sensitive

Assets and Liabilities

Changes in the Mix of Assets and Liabilities

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Cumulative Gap

The Total Difference in DollarsBetween Those Bank Assets andLiabilities Which Can be Repriced overa Designated Time Period

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Aggressive Interest-Sensitive GapManagement

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Problems with Interest-Sensitive GapManagement

Interest Paid on Liabilities Tend to Move Fasterthan Interest Rates Earned on Assets

Interest Rate Attached to Bank Assets and

Liabilities Do Not Move at the Same Speed asMarket Interest Rates

Point at Which Some Assets and Liabilities areRepriced is Not Easy to Identify

Interest-Sensitive Gap Does Not Consider theImpact of Changing Interest Rates on EquityPosition

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Quick Quiz

Commerce National Bank reports interest-sensitive assets of$870 million and interest-sensitive liabilities of $625 millionduring the coming month. Is the bank asset sensitive orliability sensitive? What is likely to happen to the banks netinterest margin if interest rates rise? If they fall?

Peoples Savings Bank , a thrift institutions, has a cumulativegap for the coming year of +$135 million, and interest ratesare 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 netinterest income if interest rates rise by one and a quarterpercentage points?

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The Concept of Duration

Duration is the Weighted AverageMaturity of a Promised Stream ofFuture Cash Flows

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To Calculate the Instruments Duration

PriceorValueMarketCurrent

YTM)(1

CF*t

YTM)(1

CF

YTM)(1

CF*t

D

n

1tt

t

n

1t

tt

n

1tt

t

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Price Sensitivity of a Security

i)(1

i*D-

P

P

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Convexity

The Rate of Change in an Assets Price

or Value Varies with the Level of

Interest Rates or Yields

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Dollar-Weighted Duration of Asset

Portfolio

n

1i

AiA iD*wD

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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Dollar-Weighted Duration of a LiabilityPortfolio

n

1i

LiLi

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

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Duration Gap

TA

TL*D-DDLA

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Change in the Value of a Banks Net

Worth

L*

i)(1

i*D--A*

i)(1

i*D-NW

LA

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Impact of Changing Interest Rates on aBanks Net Worth

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Limitations of Duration Gap Management

Finding Assets and Liabilities of the SameDuration Can be Difficult

Some Assets and Liabilities May HavePatterns 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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Quick Quiz

What is duration? How is a financialinstitutions 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 averageliability duration of 3.0 years. If the thrift holdstotal assets of $560 million and total liabilitiesof $467 million, does it have a significantleverage-adjusted duration gap? If interestrates rise, what will happen to the value of itsnet worth?