CHAPTER SIX Asset-Liability Management:

Determining and Measuring Interest Rates and Controlling a Bank’s

Interest-Sensitive And Duration GapsThe purpose of this chapter is to explore the options bankers have today for dealing with risk – especially the risk of loss due to changing interest rates – and to see how a bank’s management cancoordinate the management of its assets with the management of its liabilities in order to achieve the institution’s goals.

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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 RiskWhen Interest Rates Rise, the Market Value of the Bond or Asset Falls

Reinvestment RiskWhen Interest Rates Fall, the Coupon Payments on the Bond are Reinvested at Lower Rates

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Yield to Maturity (YTM)

n

1tt

t

YTM) (1

CF PriceMarket

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Bank Discount Rate (DR)

Maturity toDays #

360*

FV

Price Purchase- FV DR

Where: FV equals Face Value

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Market Interest Rates

Function of:Risk-Free Real Rate of InterestVarious Risk Premiums

Default RiskInflation RiskMarketability RiskCall RiskMaturity Risk

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Net Interest Margin

Assets Earnings Total

ExpensesInterest - IncomeInterest NIM

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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

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Interest-Sensitive Gap Measurements

Dollar Interest-Sensitive Gap

Interest-Sensitive Assets – Interest Sensitive Liabilities

=

Relative Interest-

Sensitive Gap SizeBank

Gap ISDollar

Interest Sensitivity

RatiosLiabilitie SensitiveInterest

Assets SensitiveInterest

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Interest-Sensitive Assets

Short-Term Securities Issued by the Government and Private BorrowersShort-Term Loans Made by the Bank to Borrowing CustomersVariable-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

Asset-Sensitive BankInterest Rates Rise

NIM Rises

Interest Rates FallNIM Falls

Liability-Sensitive BankInterest Rates Rise

NIM Falls

Interest Rates FallNIM Rises

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Zero Interest-Sensitive Gap

Dollar Interest-Sensitive Gap is ZeroRelative Interest-Sensitive Gap is ZeroInterest 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 ManagedManagement Must Choose a Target NIMTo Increase NIM Management Must Either:

Develop Correct Interest Rate ForecastReallocate Assets and Liabilities to Increase Spread

Management Must Choose Dollar 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 Interest-Sensitive 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 Interest-Sensitive Gap

Position

Aggressive Management’s Likely Action

Rising Market Interest Rates

Positive IS Gap Increase in IS Assets

Decrease in IS Liabilities

Falling Market Interest Rates

Negative IS Gap 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

1tt

t

n

1tt

t

YTM) (1CFYTM) (1CF *t

D

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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 Asset’s Price or Value Varies with the Level of Interest Rates or Yields

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Duration of an Asset portfolio

n

1 iAiA i

D *w D

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

1iLiL i

D * w D

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 - D D LA

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Change in the Value of a Bank’s Net Worth

L * i) (1

i * D- - A *

i) (1

i * D- NW LA

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Impact of Changing Interest Rates on a Bank’s Net Worth

Positive Rise Decrease

Gap Fall Increase

Negative Rise Increase

Gap Fall Decrease

Zero Rise No Change

Gap Fall No Change

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Limitations of Duration Gap Management

Finding Assets and Liabilities of the Same Duration Can be DifficultSome Assets and Liabilities May Have Patterns of Cash Flows that are Not Well DefinedCustomer Prepayments May Distort the Expected Cash Flows in DurationCustomer Defaults May Distort the Expected Cash Flows in DurationConvexity Can Cause Problems