Chapter Twelve

Asset-Liability Management: Determining and Measuring Interest Rates and Controlling

Interest-Sensitive and Duration Gaps

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

Historical View of Asset-Liability Management

• Asset Management Strategy• Liability Management Strategy• Funds Management Strategy

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

Yield to Maturity (YTM)

n

1tt

t

YTM) (1

CF PriceMarket

Bank Discount Rate (DR)

Maturity toDays #

360*

FV

Price Purchase- FV DR

Where: FV equals Face Value

Yield to Maturity

Maturity toDays #

365*

Price Purchase

Price Purchase- 100 YTM

Market Interest Rates

Function of:• Risk-Free Real Rate of Interest• Various Risk Premiums– Default Risk– Inflation Risk– Maturity Risk– Liquidity Risk– Call Risk

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

The Maturity Gap and the Yield Curve• Maturity Gap between the Average Maturity

of Assets and the Average Maturity of Liabilities

• Positive Maturity Gap and Upward-Sloping Yield Curve Lead to a Positive Net Interest Margin

Net Interest Margin

Assets Earnings Total

ExpensesInterest - IncomeInterest NIM

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

Interest-Sensitive Gap Measurements

Dollar Interest-Sensitive Gap

Interest-Sensitive Assets – Interest Sensitive Liabilities=

Relative Interest-

Sensitive Gap SizeBank

Gap ISDollar

Interest Sensitivity

Ratio sLiabilitie SensitiveInterest

Assets SensitiveInterest

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

Interest-Sensitive Liabilities

• Borrowings from Money Markets• Short-Term Savings Accounts• Money-Market Deposits• Variable-Rate Deposits

Asset-Sensitive Bank Has:

• Positive Dollar Interest-Sensitive Gap• Positive Relative Interest-Sensitive Gap• Interest Sensitivity Ratio Greater Than

One

Liability Sensitive Bank Has:

• Negative Dollar Interest-Sensitive Gap• Negative Relative Interest-Sensitive Gap• Interest Sensitivity Ratio Less Than One

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

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

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

NIM Influenced By:

• Changes in Interest Rates Up or Down• Changes in the Spread Between Asset Yields

and Liability Costs (Shape of Yield Curve)• Changes in the Volume of Interest-Bearing

Assets and Liabilities• Changes in the Mix of Assets and Liabilities

Cumulative Gap

• The Total Difference in Dollars Between Those Bank Assets and Liabilities Which Can be Repriced over a Designated Time Period• Changes in NIM=Overall Change in

Interest Rate * Size of the Cumulative Gap

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

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 and the Choice of Planning Periods is Highly Arbitrary

• Interest-Sensitive Gap Does Not Consider the Impact of Changing Interest Rates on Equity Position

The Concept of Duration

Duration is the Weighted Average Maturity of a Promised Stream of Future Cash Flows

To Calculate Duration

n

1tt

t

n

1tt

t

YTM) (1CFYTM) (1CF *t

D

Price Sensitivity of a Security

27

r

rD

P

P

10

0

r

Ddr

r

dr

r

CFr

tCF

P

dP

r

dr

r

nCF

r

CF

r

CF

r

CF

PP

dP

drr

nCF

r

CF

r

CF

r

CFdP

r

CF

r

CF

r

CF

r

CFP

tt

t

ttt

nn

nn

nn

111

1

111

3

1

2

1

1

11

3

1

2

1

1111

n

1

n

1

0

0

33

22

11

00

0

143

32

21

0

33

221

0

Modified Duration

r

DDm

1

rDP

Ptherefore m

0

0,

ConvexityThe Rate of Change in an Asset’s Price or Value Varies with the Level of Interest Rates or Yields

r

p

Factors Influencing Convexity

• Duration ( Maturity)• Coupon Rate

• Asset Values Change Differently According to Their Duration, Coupon Rates and Market Interest Rates

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

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

Duration Gap

TA

TL * D - D DG LA

r

rD

A

LD

A

NW

Lr

rDA

r

rDNW

r

rD

L

Lr

rD

A

A

LA

LA

L

A

1

11

1

1

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

PositiveGap

Interest Rate Rise

NW Decrease

Interest Rate Fall NW Increase

NegativeGap

Interest Rate Rise

NW Increase

Interest Rate Fall NW Decrease

ZeroGap

Interest Rate Rise

No Change

Interest Rate Fall No Change

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