Topics Interest Rate Risk-8 and 9[1]

8/6/2019 Topics Interest Rate Risk-8 and 9[1]

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interest rate risk management, Skvde,D071 1

Topics 1: Interest rateTopics 1: Interest rate

riskriskHow to manage interest rate riskHow to manage interest rate risk in financialin financial

institutionsinstitutions

2008020820080208


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2interest rate risk management, Skvde,

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The magic of continuous growthThe magic of continuous growth

The compound average growth rate (CAGR)The compound average growth rate (CAGR)

determines how fast a country can catch up withdetermines how fast a country can catch up with

anoth

er. It is th

e continuous compoundedanoth

er. It is th

e continuous compoundedgrowth that exhibits fastest speed. Volatilitygrowth that exhibits fastest speed. Volatility(variability) in growth rate slows down the total(variability) in growth rate slows down the total

rate of growth.rate of growth.

Where V(t0) = the start value, V(t) = the finish value and t-t0 is the time span.


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The power of Compound rate ofThe power of Compound rate of

growthgrowth Ex: Growth rate of income per capita in Japan is 2,6Ex: Growth rate of income per capita in Japan is 2,6

%, it will take about 28 years to double the income%, it will take about 28 years to double the income

per capita. But if the growth rate is 5,8 % a year, itper capita. But if the growth rate is 5,8 % a year, it

will only take approx. 12,4 years to double thewill only take approx. 12,4 years to double the

income. If, one country has a pattern of growthincome. If, one country has a pattern of growthevery other year with 5,8% and 0% in the in betweenevery other year with 5,8% and 0% in the in between

years, then, it will take 24 years to double, whichyears, then, it will take 24 years to double, which

would have had 3,87 times the income, had it grownwould have had 3,87 times the income, had it grown

with a continuous growth rate of 5,8 every year.with a continuous growth rate of 5,8 every year.

(1+0,058)(1+0,058)12,412,4 =2,0119=2,0119

(1+0,058)(1+0,058)24,824,8 =4,048=4,048 Yrn

!1


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Calculating Interest Rate RiskCalculating Interest Rate Risk

This section discusses theThis section discusses the interest rate riskinterest rate riskassociated with financial intermediation:associated with financial intermediation: thetheorigins oforigins ofassetasset--liability management and toliability management and toidentify effective ways of measuring andidentify effective ways of measuring andmanagingmanaging interestinterest raterate riskrisk

Interest risk in a financial institution is aInterest risk in a financial institution is aspecial case of market risk.special case of market risk.

A standard measure of interest rate exposureA standard measure of interest rate exposure

is the Gap in the balance sheet. It quantifiesis the Gap in the balance sheet. It quantifiesthe earnings volatility that resulted from thethe earnings volatility that resulted from themismatch between the assets and liabilities.mismatch between the assets and liabilities.


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Managing interest rate riskManaging interest rate risk

Factors should be considered when calculating theFactors should be considered when calculating the

interest rate risk:interest rate risk:

The size of t

he gap and t

he time it takes to close

The size of t

he gap and t

he time it takes to close

up the gap are important factors.up the gap are important factors.

The worst case loss that can occur over the timeThe worst case loss that can occur over the time

the gap is closed up.the gap is closed up.

Time to restructure the balance sheetTime to restructure the balance sheet

How liquid the market for hedging activities is.How liquid the market for hedging activities is.


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6interest rate risk management, Skvde,D071

Models of interest riskModels of interest risk

Repricing modelRepricing model

Maturity modelMaturity model

Duration modelDuration model **Term structure of interest rate riskTerm structure of interest rate risk

**Theories of the term structure of interestTheories of the term structure of interest

ratesrates


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Central bank makes interest rateCentral bank makes interest rate

decisionsdecisionsThe central banks monetary policy strategyThe central banks monetary policy strategy

underlies the movement of interest rates,underlies the movement of interest rates,

that effects an financial institutions cost ofthat effects an financial institutions cost of

funds and return on assets (ROA).funds and return on assets (ROA).

Central banks have shifted their targetingCentral banks have shifted their targeting

regime from Nonborrowed Reservesregime from Nonborrowed Reserves

targeting to Interest Rate targeting.targeting to Interest Rate targeting.

Resulting in much more stable interest ratesResulting in much more stable interest rates

in recent decades. (see figure 8in recent decades. (see figure 8--1, 19651, 1965--2003)2003)


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Repricing ModelRepricing Model

Repricing gapRepricing gap isis the differencethe difference between the interestbetween the interest

rate sensitivity of assets and the interest rate sensitivityrate sensitivity of assets and the interest rate sensitivityof liabilities: RSAof liabilities: RSA -- RSL.RSL. Repricing (funding gap) modelRepricing (funding gap) model is based onis based on bookbook

value accounting cash flow analysis of the reprising gapvalue accounting cash flow analysis of the reprising gap..

Rate sensitivityRate sensitivitymeans asset or liability is repriced atmeans asset or liability is repriced atcurrent market interest rate within a certain timecurrent market interest rate within a certain timehorizon.horizon.

Contrasts withContrasts withmarket valuemarket value--basedbasedmaturity and durationmaturity and durationmodels recommended by the Bank for Internationalmodels recommended by the Bank for InternationalSettlements (BIS).Settlements (BIS).


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RepricingModel (cont.)RepricingModel (cont.)

Refinancing risk:Refinancing risk: the riskthe risk that the cost of rolling overthat the cost of rolling overor reor re--borrowing funds will rise above the returnsborrowing funds will rise above the returns

being earned on asset investment due to interestbeing earned on asset investment due to interest

rate changes.rate changes.


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Repricing Gap Example: table 1Repricing Gap Example: table 1

AssetsAssets LiabilitiesLiabilities GapGap Cum. GapCum. Gap

11--dayday $ 20$ 20 $ 30$ 30 $$--1010 $$--1010

>1day>1day--3mos. 30 403mos. 30 40 --1010 --2020

>3mos.>3mos.--6mos. 70 856mos. 70 85 --1515 --3535

>6mos.>6mos.--12mos. 90 70 +2012mos. 90 70 +20 --1515

>1yr.>1yr.--5yrs. 40 30 +105yrs. 40 30 +10 --55>5 years>5 years 10 5 +5 010 5 +5 0


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Applying the Repricing ModelApplying the Repricing Model

((NIINIIii = (GAP= (GAPii)) ((RRii = (RSA= (RSAii -- RSLRSLii)) ((rrii

ExampleExample::In the one day bucket (see table 1), gap isIn the one day bucket (see table 1), gap is --

$10 million. If rates rise by 1%,$10 million. If rates rise by 1%,

((N

IIN

II(1)(1) = (= (--$10 million)$10 million) .01 =.01 = --$100,000.$100,000.


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Applying the Repricing ModelApplying the Repricing Model

Example II:Example II:

If we consider the cumulative 1If we consider the cumulative 1--year gap,year gap,

((NII = (CGAPNII = (CGAPone yearone year)) ((R = (R = (--$15 million)(.01)$15 million)(.01)

== --$150,000.$150,000.

NII Net interest incomeNII Net interest income


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Equal Rate Changes on RSAs, RSLsEqual Rate Changes on RSAs, RSLs

Example: Suppose rates riseExample: Suppose rates rise 1%1% for both RSAsfor both RSAs

and RSLs. Expected annual change in Net Interestand RSLs. Expected annual change in Net InterestIncome (NII) is,Income (NII) is,

((NII = CGAPNII = CGAP (( RR

= $15 million= $15 million .01.01= $150,000= $150,000

Conclusion:Conclusion:

With

positive CGAP, rates ch

ange andN

II moveWith

positive CGAP, rates ch

ange andN

II movein the same direction, vice versa.in the same direction, vice versa.

Changes proportional to CGAP assuming noChanges proportional to CGAP assuming nospread effectspread effect


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Cumulative GAP Ratio (CGAP)Cumulative GAP Ratio (CGAP)

It is useful to express CGAP in ratio form as,It is useful to express CGAP in ratio form as,

CGAP/Total Assets.CGAP/Total Assets.

Provides direction of exposure andProvides direction of exposure and Scale of the exposure.Scale of the exposure.

Example:Example:

CGAP/A = $15 million / $270 million = 0.56, orCGAP/A = $15 million / $270 million = 0.56, or5.6 percent.5.6 percent.


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Unequal Changes in RatesUnequal Changes in Rates If changes in rates on RSAs and RSLs are notIf changes in rates on RSAs and RSLs are not

equal, the spread changes. In this case,equal, the spread changes. In this case,

((NII = (RSANII = (RSA (( RRRSARSA)) -- (RSL(RSL (( RRRSLRSL))

Spread effect: the effect a change in the spreadSpread effect: the effect a change in the spread

between the rates on RSAs and RSLs has on netbetween the rates on RSAs and RSLs has on net

interest income as interest rate ch

anges.interest income as interest rate ch

anges.


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Unequal Rate Change ExampleUnequal Rate Change Example

Spread effectSpread effect example:example:

RSA rate rises by 1.2% and RSL rate rises by 1.0%RSA rate rises by 1.2% and RSL rate rises by 1.0%

((NII =NII = (( interest revenueinterest revenue -- (( interest expenseinterest expense= ($155 million= ($155 million 1.2%)1.2%) -- ($155 million($155 million 1.0%)1.0%)

= $310,000= $310,000


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Restructuring Assets &Restructuring Assets &

LiabilitiesLiabilities The Financial Institution (FI) can restructure itsThe Financial Institution (FI) can restructure its

assets and liabilities, on or off the balance sheet,assets and liabilities, on or off the balance sheet,to benefit from projected interest rate changes.to benefit from projected interest rate changes.

Positive gap: increase in rates increases NIIPositive gap: increase in rates increases NII

Negative gap: increase in rates decreases NIINegative gap: increase in rates decreases NII


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Weaknesses of Repricing ModelWeaknesses of Repricing Model

Weaknesses:Weaknesses:

Ignores market value effects and offIgnores market value effects and off--balance sheetbalance sheet

(OBS) cash

flows(OBS) cash

flows OveraggregativeOveraggregative

Distribution of assets & liabilities within individualDistribution of assets & liabilities within individual

buckets is not considered. Mismatches within buckets canbuckets is not considered. Mismatches within buckets can

be substantial.be substantial. Ignores effects of runoffsIgnores effects of runoffs

Bank continuously originates and retires consumer andBank continuously originates and retires consumer andmortgage loans. Runoffs may be ratemortgage loans. Runoffs may be rate--sensitive.sensitive.


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interest rate risk management, Skvde,

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The Maturity ModelThe Maturity Model

Explicitly incorporates market value effects.Explicitly incorporates market value effects. For fixedFor fixed--income assets and liabilities:income assets and liabilities:

Rise (fall) in interest rates leads to fall (rise) in marketRise (fall) in interest rates leads to fall (rise) in marketprice.price.

The longer the maturity, the greater the effect ofThe longer the maturity, the greater the effect ofinterest rate changes on market price.interest rate changes on market price.

Fall in value of longerFall in value of longer--term securities increases atterm securities increases at

diminishing rate for given increase in interest rates.diminishing rate for given increase in interest rates.


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Maturities and Interest Rate ExposureMaturities and Interest Rate Exposure

If MIf MAA -- MMLL = 0, is the FI immunized?= 0, is the FI immunized?Extreme example:Extreme example:

Suppose liabilities consist of 1Suppose liabilities consist of 1--year zero couponyear zero coupon

bond with face value $100. Assets consist of 1bond with face value $100. Assets consist of 1--year loan, which pays back $99.99 shortly afteryear loan, which pays back $99.99 shortly afterorigination, and 1 at the end of the year. Bothorigination, and 1 at the end of the year. Bothhave maturities of 1 year.have maturities of 1 year.

NotNot immunized, although maturity gap equalsimmunized, although maturity gap equalszero.zero.

Reason: Differences inReason: Differences in duration*duration*

**(See Chapter 9)(See Chapter 9)


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Maturity ModelMaturity Model

Leverage also affects ability to eliminate interestLeverage also affects ability to eliminate interestrate risk using maturity modelrate risk using maturity modelExample:Example:

Assets: $100 million in oneAssets: $100 million in one--year 10year 10--percentpercent

bonds, funded with $90 million in onebonds, funded with $90 million in one--year 10year 10--percent deposits (and equity)percent deposits (and equity)

Maturity gap is zero but exposure to interestMaturity gap is zero but exposure to interestrate risk is not zero. Reason: it is durationrate risk is not zero. Reason: it is duration

(duration is a weighted average of the maturities(duration is a weighted average of the maturitiesof the cash payments), also called effectiveof the cash payments), also called effectivematurity.maturity.


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DurationDuration

The average life of an asset or liability (sameThe average life of an asset or liability (sameas financial instruments such as bonds,as financial instruments such as bonds,

deposits)deposits)

Th

e weigh

tedTh

e weigh

ted--average time to maturity usingaverage time to maturity usingpresent value of the cash flows, relative to thepresent value of the cash flows, relative to the

total present value of the asset or liability astotal present value of the asset or liability asweights.weights.

!! !

n

t

t

t

n

t

t

t

i

CP

i

CPtDUR

11 11


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*Term Structure of Interest*Term Structure of Interest

RatesRatesYTMYTM

Time to Maturity

Time to Maturity

Time to Maturity

Time to Maturity

YTM


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*Unbiased Expectations Theory*Unbiased Expectations Theory

Yield curve reflects marketsYield curve reflects markets

expectations of future shortexpectations of future short--term rates.term rates.

LongLong--term rates are geometric averageterm rates are geometric averageof current and expected shortof current and expected short--termterm

rates.rates.

? A 1r~E1r~E1R1R1

N21NN~!


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*Liquidity Premium Theory*Liquidity Premium Theory

Allows for future uncertainty.Allows for future uncertainty.

Risk Premium required to hold longRisk Premium required to hold long--term.term.

Liquidity premium theory of term structure ofLiquidity premium theory of term structure ofinterest rates explains the shape of the yield curveinterest rates explains the shape of the yield curveincluding the downward sloping yield curve whereincluding the downward sloping yield curve whereshort term interest rate is higher than longer termshort term interest rate is higher than longer terminterest rate with the same risk profile.interest rate with the same risk profile.


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*Market Segmentation Theory*Market Segmentation Theory

Investors have specific needs in terms ofInvestors have specific needs in terms of

maturity.maturity. Yield curve reflects intersection of demand andYield curve reflects intersection of demand and

supply of individual maturities.supply of individual maturities.

Topics Interest Rate Risk-8 and 9[1]

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