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Chapter 4
Asset-Liability Management
(ALM)Required Readings: Peter S.Rose, Chapter 6, 7, 8
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Chapter Contents ALMs purpose
How interest rate risk impact banks income?
Interest rate risk: GAP and using GAP to
measure interest rate risk to banks income
Using Duration forALM
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Asset-Liability Management
Whats ALM?
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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!
Trong : FV equals Face Value
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Conversion of DR into YTM YTM equivalent yield =
(100 purchase price)/Purchase Price *
(365/days to maturity)
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Example Suppose, a 100$ security is now sold on the
market at price of $96 with days to maturity
of 90 days. Whats DR, the YTM equivalent yield?
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Example DR = (100 96)/100 * 360/90 = 0.16
Equivalent YTM = (100 96)/96 *365/90 =
0.1690
Actual YTM =
PV = -96, FV = 100, N = 90/365, I = ?
I = 18%
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Thu nhp t li rng (NII) v Thu nhp
t li cn bin (NIM)
exp
as
Interestincome Interest ensesNIMTotalearning sets
!
NII: Net interest income
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Interest Rate Risk
Price Risk
When Interest Rates Rise, the Market
Value of the Bond orAsset 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:
Reinvestment Rate Risk If interest rates change, the bank will have to
reinvest the cash flows from assets or refinance
rolled-over liabilities at a different interest rate inthe future.
An increase in rates, ceteris paribus, increases a banks
interest income but also increases the banks interestexpense.
Static GAPAnalysis considers the impact ofchanging rates on the banks net interest income.
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Interest Rate Risk:
Price Risk If interest rates change, the market values of
assets and liabilities also change.
The longer is duration, the larger is the change invalue for a given change in interest rates.
Duration GAP considers the impact of
changing rates on the market value of equity.
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Interest Rate Risk Banks typically focus on either:
Net interest income or
The market value of stockholders' equity
GAPAnalysis A static measure of risk that is commonly associated with
net interest income (margin) targeting
Earnings Sensitivity Analysis Earnings sensitivity analysis extends GAP analysis by
focusing on changes in bank earnings due to changes ininterest rates and balance sheet composition
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Rate sensitive Asset/Liabilities (RSAs
vs RSLs) and Non rate sensitive (NRS) RSAs/ RSLs are assets or liabilities whose interest return or
cost vary with interest rate movements over the same timehorizon. E.g; short term securities.
RSAt Rate Sensitive Assets
Those assets that will mature or reprice in a given time period (t)
RSLt Rate Sensitive Liabilities
Those liabilities that will mature or reprice in a given time period (t)
Non rate sensitive (NRS) are assets or liabilities whoseinterest return or cost vary with interest rate movements overthe same time horizon. E.g; Vault cash
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What Determines Rate Sensitivity? An asset or liability is considered rate sensitivity if
during the time interval:
It matures It represents and interim, or partial, principal payment
It can be repriced
The interest rate applied to the outstanding principal changes
contractually during the interval
The outstanding principal can be repriced when some base rate
of index changes and management expects the base rate / index
to change during the interval
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Example on RSAs/RSLs
Assets Liabilities
1. Short term consumer loans (1 year
maturity) 50 Equity Capital (Fixed) 20
2. Long term consumer loans (2 year
maturity) 25 Demand deposits 40
3.Three-month Treasury Bills 30 Passbook savings 30
4. Six-month Treasury Notes 35 Three month CDs 40
5. Three year Treasury Bonds 70
Three month Banker
acceptances 20
6. 10 year, fixed rate mortgages 20 Six month CP 60
7. 30 year, floating rate mortgages
(rate adjusted every nine months)
40One year time deposits 20
Two year time deposits 40
270 270
Within 1 year, Determine the RSAs =? RSLs = ? Hows about NRS for assets and liabilities?
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Interest rate GAP/ Dollar GAP/
Funding GAP/Maturity GAP) GAP = RSAs RSLs
Cummulative GAP(CGAP): measures the
difference between RSA
and RSL over a more
extended period
( ) ( )i i i i i iNII GAP R RSA RSL R( ! ( ! (
( )i i NII CGAP R( ! (
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Example on Interest sensitive GAP
Days
Assets maturing
or Repricing
within
Liabilities
maturing
or Repricing
within
Increme
ntal
Gap
Cummul
ative
Gap
1 day 20 30 -10 -102-30 days 30 40 -10 -20
31-90 days 70 85 -15 -35
91-180 days 90 70 20 -15
181-365 40 30 10 -5
1 year -5
years 10 5 5 0
260 260
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Example A bank makes a $10,000 four-year car loan to a
customer at fixed rate of 8.5%. The bank initially funds
the car loan with a one-year $10,000 CD at a cost of
4.5%. The banks initial spread is 4%.
What is the banks one year gap?
4 year Car Loan 8.50%
1 Year CD 4.50%
4.00%
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Example Traditional Static GAPAnalysis
What is the banks 1-year GAP with the auto
loan? RSA1yr= $0
RSL1yr = $10,000
GAP1yr= $0 - $10,000 = -$10,000
The banks one year funding GAP is -10,000
If interest rates rise (fall) in 1 year, the banks margin will
fall (rise)
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Other Gap Measurements
Relative
Interest-
Sensitive Gap SizeBank
GapISDollar!
Interest
SensitivityRatio
sLiabilitieSensitiveInterest
AssetsSensitiveInterest
!
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Asset-Sensitive Bank Has:
Positive Dollar Interest-Sensitive Gap
Positive Relative Interest-Sensitive Gap
Interest Sensitivity Ratio GreaterThan
One
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Liability Sensitive Bank Has:
Negative Dollar Interest-Sensitive Gap
Negative Relative Interest-Sensitive Gap
Interest Sensitivity Ratio Less Than One
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Factors Affecting Net Interest
Income Changes in the level of interest rates
Changes in the composition of assets and
liabilities
Changes in the volume of earning assets and
interest-bearing liabilities outstanding
Changes in the relationship between the yieldson earning assets and rates paid on interest-
bearing liabilities
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Example Consider the following balance sheet:
Assets Yield Liabilities Cost
Rate sensitive 500$ 8.0% 600$ 4.0%Fixed rate 350$ 11.0% 220$ 6.0%
Non earning 150$ 100$
920$
Equity
80$
Total 1,000$ 1,000$
GAP = 500 - 600 = -100
NII = (0.08 x 500 + 0.11 x 350) - (0.04 x 600 + 0.06 x 220)
NIM = 41.3 / 850 = 4.86%
NII = 78.5 - 37.2 = 41.3
Expected Balance Sheet for Hypothetical Bank
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Examine the impact of the following
changes A 1% increase in the level of all short-term
rates?
A 1% decrease in the spread between assetsyields and interest costs such that the rate on
RSAs increases to 8.5% and the rate on RSLs
increase to 5.5%? A proportionate doubling in size of the bank?
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1% increase in short-term ratesAssets Yield Liabilities Cost
Rate sensitive 500$ 9.0% 600$ 5.0%
Fixed rate 350$ 11.0% 220$ 6.0%
Non earning 150$ 100$
920$
Equity
80$
Total 1,000$ 1,000$
GAP = 500 - 600 = -100
NII = (0.09 x 500 + 0.11 x 350) - (0.05 x 600 + 0.06 x 220)
NIM = 40.3 / 850 = 4.74%
NII = 83.5 - 43.2 = 40.3
Expected Balance Sheet for Hypothetical Bank
With a negative GAP, more
liabilities than assets reprice
higher; hence NII and NIM fall
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1% decrease in the spreadAssets Yield Liabilities Cost
Rate sensitive 500$ 8.5% 600$ 5.5%
Fixed rate 350$ 11.0% 220$ 6.0%
Non earning 150$ 100$920$
Equity
80$
Total 1,000$ 1,000$
GAP = 500 - 600 = -100
NII = (0.085 x 500 + 0.11 x 350) - (0.055 x 600 + 0.06 x 220)
NIM = 34.8 / 850 = 4.09%
NII = 81 - 46.2 = 34.8
Expected Balance Sheet for Hypothetical Bank
NII and NIM fall (rise) with a
decrease (increase) in the
spread.
Why the larger change?
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Proportionate doubling in sizeAssets Yield Liabilities Cost
Rate sensitive 1,000$ 8.0% 1,200$ 4.0%
Fixed rate 700$ 11.0% 440$ 6.0%
Non earning 300$ 200$1,840$
Equity
160$
Total 2,000$ 2,000$
GAP = 1000 - 1200 = -200
NII = (0.08 x 1000 + 0.11 x 700) - (0.04 x 1200 + 0.06 x 440)
NIM = 82.6 / 1700 = 4.86%
NII = 157 - 74.4 = 82.6
Expected Balance Sheet for Hypothetical Bank
NII and GAP double, but NIM
stays the same.
What has happened to risk?
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RSAs increase to $540 while fixed-rate assets decrease to$310 and RSLs decrease to $560 while fixed-rateliabilities increase to $260
Assets Yield Liabilities Cost
Rate sensitive 540$ 8.0% 560$ 4.0%
Fixed rate 310$ 11.0% 260$ 6.0%Non earning 150$ 100$
920$
Equity
80$
Total 1,000$ 1,000$
GAP = 540 - 560 = -20
NII = (0.08 x 540 + 0.11 x 310) - (0.04 x 560 + 0.06 x 260)
NIM = 39.3 / 850 = 4.62%
NII = 77.3 - 38 = 39.3
Expected Balance Sheet for Hypothetical Bank
Although the banks GAP
(and hence risk) is lower,
NII is also lower.
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Changes in Portfolio Composition and
Risk To reduce risk, a bank with a negative GAP
would try to increase RSAs (variable rate
loans or shorter maturities on loans andinvestments) and decrease RSLs (issue
relatively more longer-term CDs and fewer
fed funds purchased)
Changes in portfolio composition also raise or
lower interest income and expense based on
the type of change
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Summary of GAP and the Change
in NII
GAP
Change in
Interest
Income
Change in
Interest
Income
Change in
Interest
Expense
Change in
Net Interest
Income
Positive Increase Increase > Increase IncreasePositive Decrease Decrease > Decrease Decrease
Negative Increase Increase < Increase Decrease
Negative Decrease Decrease < Decrease Increase
Zero Increase Increase = Increase NoneZero Decrease Decrease = Decrease None
GAP Summary
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Exercise on IS GAP, NIIAssets Liabilities and Equities
Rate sensitive 200 (12%)
Non rate sensitive 400 (11%) Non earning 100
Total 700
Rate sensitive 300 (6%)
Non rate sensitive 300 (5%)Equity 100
Total 700
Q: Determining the GAP? Net interest income? Net interest margin? How
much will net interest income change if interest rates fall by 2%?
What changes in portfolio composition would you recommend to management
if you expected interest rates to increase?
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Three problems with IS GAP Time Horizon
Market value effects
Focus on Net interest income
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Duration GAP analysis What is Duration and its measurement?
Networth of the bank (NW)
Duration GAP and hedging interest rate riskwith duration
Weaknesses of duration GAP
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Duration and its measurement
1
1
*
(1 )
(1 )
n
tt
n
tt
ExpectedCF t
YTMD
ExpectedCFYTM
!
!
!
A loan with annual interest
payment @10% for 5 years,
the loan principal is $1000.
What is the Duration of theloan if the current market price
is $1000?
How is the loan price vary if
the interest rates increase by
1%?
1
P iDx
P i
( (!
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Net Worth of the bank
NW A L!
NW A L( ! ( (
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Duration GAP Duration GAP =
Duration of asset
portfolio Duration of
bank liabilities
The bank tries to
manage duration gap
approaching zero Positive duration gap
Negative duration gap
1
n
i
Durationofeachassetxmarketvalue
AssetportfolioDurationTotalmarketvalueofallassets
!!
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Weaknesses of duration GAP?