Chapter 8 Re-pricing Model & Maturity Model. Interest Rate Risk Models –Re-pricing model –Maturity model –Duration model –In-house models Proprietary.

Chapter 8

Re-pricing Model & Maturity Model

Interest Rate Risk Models

– Re-pricing model– Maturity model– Duration model– In-house models

ProprietaryCommercial

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Central Bank and Interest Rates

Target is primarily short term rates– Focus on Fed Funds Rate in particular

Interest rate changes and volatility increasingly transmitted from country to country– Statements by Ben Bernanke can have

dramatic effects on world interest rates.

Short-Term Rates 1954-2009

0

5

10

15

20

25

Fed Funds Rate

3 Mo T-bill

3Mo CD

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Fed Funds

3Mo T-Bill

3Mo CD


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3Mo T-Bill

3Mo CD

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Rate Changes Can Vary by Market

Note that there have been significant differences in recent years

If your asset versus liability rates change by different amounts, that is called “basis risk”– May not be accounted for in your

interest rate risk model

Re-pricing Model

Re-pricing or funding gap model based on book value.

Contrasts with market value-based maturity and duration models recommended by the Bank for International Settlements (BIS).

Re-pricing Model

Rate sensitivity means time to re-pricing. Re-pricing gap is the difference between

the rate sensitivity of each asset and the rate sensitivity of each liability: RSA - RSL.

Refinancing risk (typical for banks) Reinvestment risk

Re-pricing Model

We are interested in the Re-pricing Model as an introduction to the importance of Net Interest Income– Variability of NII is really what we are

trying to protect– NII is the lifeblood of banks/thrifts

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Maturity Buckets

Commercial banks must report re-pricing gaps for assets and liabilities with maturities of:– One day.– More than one day to three months.– More than 3 three months to six months.– More than six months to twelve months.– More than one year to five years.– Over five years.

Note the cut-off levels

Re-pricing Gap Example

Assets Liabilities Gap Cum. Gap 1-day $ 20 $ 30 $-10 $-10>1day-3mos. 30 40 -10 -20>3mos.-6mos. 70 85 -15 -35>6mos.-12mos. 90 70 +20 -15>1yr.-5yrs. 40 30 +10 -5>5 years 10 5 +5 0

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IRR Commercial BankBalance Sheet $Millions Repricing Buckets

0 to 1 yr 1 yr to 2 yrs2 yrs to 5

yrs 5 yrs to 10 yrs >10 yrsAssets: Rate: Amount:

5 Year Prime-based Commercial Loans 6.0% 70 70 3 Year Auto Loans (3) 6.0% 60 60 7/1 Adjustable Rate Mortgages(1) 6.5% 50 50 9 Year Treasury Notes 5.5% 30 30 30 Year Fixed Rate Mortgages 8.0% 190 190 Total 400 70 0 60 80 190

Liabilities

Demand Deposits (2) 0.0% 30 21 9 18 Month CDs, interest paid annually 4.0% 150 150 36 Month CDs, interest paid annually 4.5% 80 80 72 Month CDs, interest paid annually 5.0% 20 20 Fed Funds Borrowed 2.0% 90 90 Equity (4) 0 30 Total 400 111 150 89 20 0

(1) 30 year term. Rate is fixed for first seven years and then adjusts annually.

(2) Assume for this exercise that 30% of demand deposits have a maturity and

duration of 5 years and the remaining 70% mature overnight.

(3) Auto loans are fully amortizing. For simplicity assume annual payments.

(4) for purposes of the repricing model, do not enter the amount of equiity

anywhere, so you will have a cumulative gap in cell J33 = +equity. Gap -41 -150 -29 60 190Cum Gap -41 -191 -220 -160 30

Re-pricing Gap Example Assets Liabilities Gap Cum. Gap

1-day $ 20 $ 30 $-10 $-10>1day-3mos. 30 40 -10 -20>3mos.-6mos. 70 85 -15 -35>6mos.-12mos. 90 70 +20 -15>1yr.-5yrs. 40 30 +10 -5>5 years 10 5 +5 0

Note this example is not realistic because asset = liabilities Usually assets > liabilities, final CGAP will be + Equity

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Applying the Re-pricing Model

NIIi = (GAPi) Ri = (RSAi - RSLi) Ri

Example: In the one day bucket, gap is -$10

million. If rates rise by 1%, NII(1) = (-$10 million) × .01 = -

$100,000.

Applying the Re-pricing Model

Example II: If we consider the cumulative 1-year

gap,

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

= -$150,000.

Rate-Sensitive Assets Examples from hypothetical balance

sheet:– Short-term consumer loans. If re-priced at

year-end, would just make one-year cutoff.– Three-month T-bills re-priced on maturity

every 3 months.– Six-month T-notes re-priced on maturity

every 6 months.– 30-year floating-rate mortgages re-priced

(rate reset) every 12 months.

Rate-Sensitive Liabilities

RSLs bucketed in same manner as RSAs. Demand deposits and passbook savings

accounts warrant special mention.– Generally considered rate-insensitive

(act as core deposits), but there are arguments for their inclusion as rate-sensitive liabilities.

– FOR NOW, we will treat these as though they re-price overnightText assumes that they do not re-price

at all

CGAP Ratio

May be useful to express CGAP in ratio form as,

CGAP/Assets.– Provides direction of exposure and – Scale of the exposure.

Example- 12 month CGAP: – CGAP/A = -$15 million / $260 million = -

0.058, or -5.8 percent.

Equal Rate Changes on RSAs, RSLs

Example: Suppose rates rise 2% for RSAs and RSLs. Expected annual change in NII,

NII = CGAP × R= -$15 million × .02= -$300,000

With positive CGAP, rates and NII move in the same direction.

Change proportional to CGAP

Re-pricing Gap Example

Assets Liabilities Gap Cum. Gap 1-day $ 20 $ 30 $-10 $-10>1day-3mos. 30 40 -10 -20>3mos.-6mos. 70 85 -15 -35>6mos.-12mos. 90 70 +20 -15>1yr.-5yrs. 40 30 +10 -5>5 years 10 5 +5 0

Repricing Gap Example

Assets Liabilities Gap Cum. Gap 1-day $ 20 $ 30 $-10 $-10>1day-3mos. 30 40 -10 -20>3mos.-6mos. 70 85 -15 -35>6mos.-12mos. 90 70 +20 -15

210 225>1yr.-5yrs. 40 30 +10 -5>5 years 10 5 +5 0

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Equal Rate Changes on RSAs, RSLs

Example: Suppose rates rise 1% for RSAs and RSLs. Expected annual change in NII,

NII = CGAP × R= -$15 million × .01= -$150,000

With positive CGAP, rates and NII move in the same direction.

Change proportional to CGAP

Unequal Changes in Rates

If changes in rates on RSAs and RSLs are not equal, the spread changes. In this case, NII = (RSA × RRSA ) - (RSL × RRSL )

Unequal Rate Change Example

Spread effect example: RSA rate rises by 1.0% and RSL rate rises by 1.0%

NII = interest revenue - interest expense

= ($210 million × 1.0%) - ($225 million × 1.0%)

= $2,100,000 -$2,250,000 = -$150,000




= ($210 million × 1.2%) - ($225 million × 1.0%)

= $2,520,000 -$2,250,000 = $270,000

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= ($210 million × 1.0%) - ($225 million × 1.2%)

= $2,100,000 -$2,700,000 = -$600,000

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Simple Bank Repricing

Maturity Balance 0 to 1 >1

Securities 0.75 9,000 9,000

Consumer Loans 0.5 10,000 10,000


Consumer Loans 3 16,000 16,000

Prime-Based Loans 3 50,000 50,000

Total Assets 100,000 69,000

Demand Deposits - Fixed 5 15,000 15,000

Demand Deposits - Variable 0.01 35,000 35,000

CDs 0.5 30,000 30,000

CDs 0.75 5,000 5,000

CDs 2 5,000 5,000

Equity NA 10,000

Total Liabilities & NW 100,000 70,000

1 year Cum Gap -1,000

Change In Mkt Rates 1%

Change in NII -10

Chang in NII/ Assets -.01%

Re-pricing Model – 1 Year Cum Gap Analysis



Securities 0.75 9,000 9,000




Mortgage Loans 3 50,000 50,000




CDs 0.5 30,000 30,000

CDs 0.75 5,000 5,000

CDs 2 5,000 5,000

Equity NA 10,000




Change in NII -510



Difficult Balance Sheet Items Equity/Common Stock O/S

– Ignore for re-pricing model, duration/maturity = 0

Demand Deposits– Treat as 30% re-pricing over 5 years/duration = 5

years 70% re-pricing immediately/duration = 0

Passbook Accounts– Treat as 20% re-pricing over 5 years/duration = 5

years 80% re-pricing immediately/duration = 0

Amortizing Loans– We will bucket at final maturity, but really should be

spread out in buckets as principal is repaid. Not a problem for duration/market value methods

Difficult Balance Sheet Items Prime-based loans Adjustable rate mortgages

– Put in based on adjustment date– Re-pricing/maturity/duration models cannot

cope with life-time cap

Assets with options– Re-pricing model cannot cope– Duration model does not account for option– Only market value approaches have the

capability to deal with options– Mortgages are most important class– Callable corporate bonds also

Prime Rate Vs Fed Funds 1955-2009

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Fed Funds Rate

Prime Rate


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Prime Rate


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Prime Rate



Securities 0.75 9,000 9,000








CDs 0.5 30,000 30,000

CDs 0.75 5,000 5,000

CDs 2 5,000 5,000

Equity NA 10,000




Change in NII -20





Securities 0.75 9,000 9,000








CDs 0.5 30,000 30,000

CDs 0.75 5,000 5,000

CDs 2 5,000 5,000

Equity NA 10,000




Change in NII -60




Simple S&L Repricing


Securities 0.75 12,000 12,000




Fixed Rate Mortgages 30 82,000 82,000


Demand Deposits - Fixed 5 0 0

NOW Accounts 0.01 20,000 20,000

CDs 0.5 61,000 61,000

CDs 0.75 10,000 10,000

CDs 2 5,000 5,000

Equity NA 4,000




Change in NII -770



Simple S&L Repricing


Securities 0.75 12,000 12,000




Fixed Rate Mortgages 30 82,000 82,000


Demand Deposits - Fixed 5 0 0

NOW Accounts 0.01 20,000 20,000

CDs 0.5 61,000 61,000

CDs 0.75 10,000 10,000

CDs 2 5,000 5,000

Equity NA 4,000




Change in NII -4,620

Chang in NII/ Assets -4.62%

Comparison of 1980 Bank vs S&L

No Change in Rates No Change in Rates

Simple Bank Yield Balance Interest Simple S&L Yield Balance Interest

Assets 6.5% 100,000 6,500 Assets 7.0% 100,000 7,000

Liabilities 2.5% 90,000 -2,250 Liabilities 4.9% 96,000 -4,704

Equity 0 10,000 Equity 0 4,000

NII 4,250 NII 2,296

Operating Expenses -2,000 Operating Expenses -1,400

Pre-tax income 2,250 Pre-tax income 896

Taxes at 35% -788 Taxes at 35% -314

Net income 1,463 Net income 582

ROA 1.46% ROA 0.58%

ROE 14.6% ROE 14.6%

Comparison of 1980 Bank vs S&L

Rates Up 6% Rates Up 6%

Simple Bank Yield Balance Interest Simple S&L Yield Balance Interest

Assets 10.6% 100,000 10,640 Assets 7.8% 100,000 7,840

Liabilities 7.3% 90,000 -6,570 Liabilities 10.6% 96,000 -10,176

Equity 0 10,000 Equity 0 4,000

NII 4,070 NII -2,336

Operating Expenses -2,000 Operating Expenses -1,400

Pre-tax income 2,070 Pre-tax income -3,736

Taxes at 35% -725 Taxes at 35% 1,308

Net income 1,346 Net income -2,428

ROA 1.35% ROA -2.43%

ROE 13.5% ROE -60.7%

Restructuring Assets & Liabilities

The FI can restructure its assets and liabilities, on or off the balance sheet, to benefit from projected interest rate changes.– Positive gap: increase in rates increases

NII– Negative gap: decrease in rates increases

NII The “simple bank” we looked at does not

appear to be subject to much interest rate risk.

Let’s try restructuring for the “Simple S&L”

Weaknesses of Re-pricing Model

Weaknesses:– Ignores market value effects and off-

balance sheet (OBS) cash flows– Over-aggregative

Distribution of assets & liabilities within individual buckets is not considered. Mismatches within buckets can be substantial.

– Ignores effects of runoffsBank continuously originates and retires

consumer and mortgage loans and demand deposits/passbook account balances can vary. Runoffs may be rate-sensitive.

A Word About Spreads

Text example: Prime-based loans versus CD rates

What about libor-based loans versus CD rates?

What about CMT-based loans versus CD rates

What about each loan type above versus wholesale funding costs?

This is why the industry spreads all items to Treasury or LIBOR

*The Maturity Model Explicitly incorporates market value

effects. For fixed-income assets and liabilities:

– Rise (fall) in interest rates leads to fall (rise) in market price.

– The longer the maturity, the greater the effect of interest rate changes on market price.

– Fall in value of longer-term securities increases at diminishing rate for given increase in interest rates.

Maturity of Portfolio*

Maturity of portfolio of assets (liabilities) equals weighted average of maturities of individual components of the portfolio.

Principles stated on previous slide apply to portfolio as well as to individual assets or liabilities.

Typically, maturity gap, MA - ML > 0 for most banks and thrifts.

*Effects of Interest Rate Changes

Size of the gap determines the size of interest rate change that would drive net worth to zero.

Immunization and effect of setting MA - ML = 0.

*Maturities and Interest Rate Exposure

If MA - ML = 0, is the FI immunized?– Extreme example: Suppose liabilities consist

of 1-year zero coupon bond with face value $100. Assets consist of 1-year loan, which pays back $99.99 shortly after origination, and 1¢ at the end of the year. Both have maturities of 1 year.

– Not immunized, although maturity gap equals zero.

– Reason: Differences in duration** **(See Chapter 9)

*Maturity Model

Leverage also affects ability to eliminate interest rate risk using maturity model– Example:

Assets: $100 million in one-year 10-percent bonds, funded with $90 million in one-year 10-percent deposits (and equity)

Maturity gap is zero but exposure to interest rate risk is not zero.

Modified Maturity Model

Correct for leverage

to immunize, change: MA - ML = 0 to

MA – ML& E = 0 with ME = 0

(not in text)

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Chapter 8 Re-pricing Model & Maturity Model. Interest Rate Risk Models –Re-pricing model –Maturity model –Duration model –In-house models Proprietary.

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