McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights

McGraw-Hill/Irwin©2008 The McGraw-Hill

Companies, All Rights Reserved

Chapter SevenChapter Seven

Asset-Liability Management: Determining and Measuring

Interest Rates and Controlling Interest-Sensitive and Duration

Gaps

Asset-Liability Management: Determining and Measuring

Interest Rates and Controlling Interest-Sensitive and Duration

Gaps

7-2McGraw-Hill/IrwinBank Management and Financial Services, 7/e

© 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.

Key TopicsKey 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



Asset-Liability ManagementAsset-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

Historical View of Asset-Liability Management

• First :Asset Management Strategy– Refers to a strategy where it is assumed that

management has control over the allocation of bank assets (loans) but little or no control over funds sources (deposits)

• Then: Liability Management Strategy– Strategy that focuses on new sources of funds

and managing the mix of deposit and non deposit sources of funds by varying the price or interest rates offered

• Now: Funds Management Strategy– The concept of planning and control over both

sides of the balance sheet – assets and liabilities



Interest ratesInterest rates

• Base (risk free) interest rates are determined by market forces not by individual banks. They are determined by the collective borrowing and lending decisions of thousands of participants in the money and capital markets

• Lending interest rates are determined by additional risk factors such as default risk, maturity risk and liquidity risk



Yield to Maturity (YTM)An interest rate measureYield to Maturity (YTM)

An interest rate measure

n

1tt

t

YTM) (1

CF PriceMarket



Bank Discount Rate (DR)Another interest rate measure

Bank Discount Rate (DR)Another interest rate measure

Maturity toDays #

360*

FV

Price Purchase- FV DR

Where: FV equals Face Value



Interest Rates Interest Rates

Function of:• Risk-Free Real Rate of Interest• Various Risk Premiums

– Default Risk– Inflation Risk– Liquidity Risk– Call Risk– Maturity Risk



Yield CurvesYield 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 determines the spread between long term and short term interest rates. Has profound influence on bank’s NIM– 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



Market RiskMarket Risk

• Price Risk– When Interest Rates Rise, the Market Value of the

Bond or Asset Falls• Interest rate risk ( Reinvestment Risk/Refinancing

Risk) – When Interest Rates Fall, the Coupon Payments

on a Bond or maturing loans are Reinvested at Lower Rates

– When interest rates rise the refinancing costs rise



Interest rate riskInterest rate risk

• Financial institutions can lose income or value no matter which way interest rates go

• Rising rates can lead to losses on security instruments and fixed rate loans as the value of these instruments fall. Rising rates can also cause a loss to income if the bank has more rate sensitive liabilities than assets

• Falling interest rates can lead to capital gains but could lead to losses if there are more interest rate sensitive assets than liabilities



Net Interest MarginNet Interest Margin

Assets Earnings Total

ExpensesInterest - IncomeInterest NIM



Goal of Interest Rate Hedging

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 (NIM)



Problem Problem

• If interest revenues are $63 million, interest costs are $42 million, earning assets are 700 million. What is the NIM. If interest costs and interest revenues double while its earning assets increase by 50% what will happen to NIM



SolutionSolution

• NIM = 63-42/700 = 3%• New NIM = (63-42)*2/700*1.5 = 4%



Concept of Gap management

Concept of Gap management

• Gap management involves the determining the maturity distribution and the repricing schedule for a bank’s assets and liabilities.

• When more assets are subject to repricing or will reach maturity in a given period than liabilities or vice versa, the Bank has a gap between assets and liabilities and is exposed to loss from an adverse movement in rates based on the gap’s size and direction and period



Maturity profile used to identify, measure, manage and

control risk

Maturity profile used to identify, measure, manage and

control riskMaturity Asset

sliabilities

Gap size

Cumulative gap

Next day

$40 -$50 -10 -10

1 week 120 -160 -40 -50

1 month 65 -105 - 40 -90

2 months

280 -250 +30 -60

3 months

455 -395 +60 0



Interest-Sensitive Gap Measurements

Interest-Sensitive Gap Measurements

Dollar Interest-Sensitive Gap

Interest-Sensitive Assets – Interest Sensitive Liabilities=



Interest-Sensitive AssetsInterest-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 LiabilitiesInterest-Sensitive Liabilities

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



Asset-Sensitive Bank Has:Asset-Sensitive Bank Has:

• Positive Dollar Interest-Sensitive Gap



Liability Sensitive Bank Has:Liability Sensitive Bank Has:

• Negative Dollar Interest-Sensitive Gap



Gap Positions and the Effect of Interest Rate Changes on the

Bank

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 GapZero Interest-Sensitive Gap

• Dollar Interest-Sensitive Gap is Zero– When Interest Rates Change in Either

Direction - NIM is Protected and Will Not Change



Important Decision Regarding IS Gap

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: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



Cumulative GapCumulative Gap

The Total Difference in Dollars Between Those Bank Assets and Liabilities Which Can be Repriced over a Designated Time Period



Aggressive Interest-Sensitive Gap Management

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



ProblemProblem

• If interest rate sensitive assets are $870 and interest sensitive liabilities are $625 during the next month. Is the bank asset sensitive or liability sensitive. What happens to NIM if rate rise? What happens to NIM if rates fall



Solution Solution

• As assets sensitive assets are larger the bank is asset sensitive by $245

• If rates rise NI increases. If rates fall NIM decreases



Problem Problem

• If the gap for the one year period is + 135 million and rates fall by 2.5% then calculate the expected change in NII. What would happen if rates rise by 1.25%



solutionsolution

• 135 million * - .025 = - 3.38 million• 135 million* .0125 = + 1.69



Definitions Definitions

• Dollar interest sensitive gap = interest sensitive assets - interest rate sensitive liabilities over asset planning period



ProblemProblem

• Suppose interest sensitive assets are 570 million and interest rate sensitive liabilities are 685 million. What is the dollar interest sensitive gap?



Solution Solution

• Dollar interest– sensitive gap = 570 – 685 = -115



Problems with Interest-Sensitive Gap Management

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



The Concept of DurationThe Concept of Duration

Duration is the Weighted Average Maturity of a Promised Stream of Future Cash Flows. It is a direct measure of price risk.



Duration gap measurementDuration gap measurement

• It is the difference between the duration of a bank’s assets and the duration of its liabilities

• The duration of the banks assets can be determined by taking the weighted average of the duration of all assets in the portfolio

• The weight is the dollar amount of a particular type of asset out of the total amount of assets

• The duration of liabilities can be determined in a similar way



Interest rate sensitive gap versus duration

Interest rate sensitive gap versus duration

• Gap only looks at impact of changes in interest rates on net income

• Duration takes into account the impact of interest rate changes on the market value of the bank’s equity position



To Calculate DurationTo Calculate Duration

n

1tt

t

n

1tt

t

YTM) (1CFYTM) (1CF *t

D



Duration of a bank loan calculation

Duration of a bank loan calculation

• Loan term 5 years. Annual interest rate payment is 10% (similar to coupon rate on a bond). The face value of the loan is also its current value because the yield to maturity on the loan is also 10%. What is the loan’s duration



Duration (con’t)Duration (con’t)

CF period

CF expected

PV @10%

Time period

PV x t

1 100 90.91 1 90.91

2 100 82.64 2 165.29

3 100 75.13 3 225.39

4 100 68.30 4 273.21

5 100 62.09 5 310.4

5 1000 620.92

5 3104.61

Dur. =

4,169.87/1000=4.17 years



Price Sensitivity of a Security

Price Sensitivity of a Security

i) (1

i * D-

P

P



Price sensitivity of a security

Price sensitivity of a security

• Duration= 4, and interest rates go up from 10 to 11 pct

• Change in price % = -D x Δ i/1+I• -4 x .01/1+.10 = - 3.64%• If rate go down from 10 to 9 pct then• -4 x -.01/1+.10 = + 3.64%



Duration GapDuration Gap

TA

TL * D - D D LA



Duration gap calculationDuration gap calculation

• Asset duration is 2.5 years, liability duration is 3 years, total assets = $560 million and total liabilities = $467 million

• Duration gap = Da –DL* Liabilities/assets = 2.5 yrs – 3 yrs * (467/560) = 2.5 – 2.5018 = - .018 years

• Slight duration gap. If rates rise the value of liabilities will fall by more than the value of assets resulting in a small increase in net worth

• Net worth = assets - liabilities



Duration of an Asset portfolio

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

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



Change in the Value of a Bank’s Net Worth

Change in the Value of a Bank’s Net Worth

L * i) (1

i * D- - A *

i) (1

i * D- NW LA



Duration gap calculationDuration gap calculation

• Asset duration is 3.25 years and liability duration is 1.75 years. The liabilities amount to $485 million while assets total $512 million. Interest rates rise form 7 to 8 per cent. What happens to the net worth.



solutionsolution

• First calculate duration gap.• Duration gap = 3.25 yrs – 1.75 yrs

*485/512 = + 1.5923• The change in net worth due to the

increase in interest rates is = {-3.25yrsx .01/(1+.07) x $512} – {-1.75 yrs x .01/(1+.07) x $485 mill } = -7.62



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

Positive Interest Rate Rise

NW Decrease

D. Gap Interest Rate Fall NW IncreaseNegative Interest Rate

RiseNW Increase

D. Gap Interest Rate Fall NW Decrease

Zero Interest Rate Rise

No Change

D. Gap Interest Rate Fall No Change



Limitations of Duration Gap Management

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

Documents

McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights