Chapter Seven

Risk Management for Changing Interest Rates: Asset-Liability Management and Duration

TechniquesCopyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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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 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 (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)

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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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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

CF PriceMarket

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Bank Discount Rate (DR)

Maturity toDays #

360*

FV

Price Purchase- FV DR

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

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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 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

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 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 $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?

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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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Examples of Repriceable (Interest Sensitive) 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 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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Computer-Based Techniques and Maturity Buckets

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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

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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 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

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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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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?

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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 the Instrument’s Duration

Priceor ValueMarket Current

YTM) (1

CF *t

YTM) (1

CF

YTM) (1

CF *t

D

n

1tt

t

n

1tt

t

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

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Dollar-Weighted Duration of 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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Dollar-Weighted 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

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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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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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