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**Re-pricing Model & Maturity Model**

Chapter 8 Re-pricing Model & Maturity Model

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**Interest Rate Risk Models**

Re-pricing model Maturity model Duration model In-house models Proprietary Commercial

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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.

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Short-Term Rates

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Short-Term Rates

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Short-Term Rates

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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

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**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).

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**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

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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 Note the cut-off levels**

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

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**Re-pricing Gap Example**

Assets Liabilities Gap Cum. Gap 1-day $ $ 30 $ $-10 >1day-3mos >3mos.-6mos >6mos.-12mos >1yr.-5yrs >5 years

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**Balance Sheet $Millions Repricing Buckets 0 to 1 yr 1 yr to 2 yrs **

IRR Commercial Bank Balance Sheet $Millions Repricing Buckets 0 to 1 yr 1 yr to 2 yrs 2 yrs to 5 yrs 5 yrs to 10 yrs >10 yrs Assets: Rate: Amount: 5 Year Prime-based Commercial Loans 6.0% 70 3 Year Auto Loans (3) 60 7/1 Adjustable Rate Mortgages(1) 6.5% 50 9 Year Treasury Notes 5.5% 30 30 Year Fixed Rate Mortgages 8.0% 190 Total 400 80 Liabilities Demand Deposits (2) 0.0% 21 9 18 Month CDs, interest paid annually 4.0% 150 36 Month CDs, interest paid annually 4.5% 72 Month CDs, interest paid annually 5.0% 20 Fed Funds Borrowed 2.0% 90 Equity (4) 111 89 (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 Cum Gap -191 -220 -160

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**Re-pricing Gap Example**

Assets Liabilities Gap Cum. Gap 1-day $ $ 30 $ $-10 >1day-3mos >3mos.-6mos >6mos.-12mos >1yr.-5yrs >5 years 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**

DNIIi = (GAPi) DRi = (RSAi - RSLi) DRi Example: In the one day bucket, gap is -$10 million. If rates rise by 1%, DNII(1) = (-$10 million) × .01 = -$100,000.

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**Applying the Re-pricing Model**

Example II: If we consider the cumulative 1-year gap, DNII = (CGAPone year) DR = (-$15 million)(.01) = -$150,000.

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**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.

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**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 overnight Text assumes that they do not re-price at all

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**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 = , or -5.8 percent.

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**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

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**Re-pricing Gap Example**

Assets Liabilities Gap Cum. Gap 1-day $ $ 30 $ $-10 >1day-3mos >3mos.-6mos >6mos.-12mos >1yr.-5yrs >5 years

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**Repricing Gap Example Assets Liabilities Gap Cum. Gap**

1-day $ $ 30 $ $-10 >1day-3mos >3mos.-6mos >6mos.-12mos >1yr.-5yrs >5 years

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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

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**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 )

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**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

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**Unequal Rate Change Example**

Spread effect example: RSA rate rises by 1.2% and RSL rate rises by 1.0% NII = interest revenue - interest expense = ($210 million × 1.2%) - ($225 million × 1.0%) = $2,520,000 -$2,250,000 = $270,000

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**Unequal Rate Change Example**

Spread effect example: RSA rate rises by 1.0% and RSL rate rises by 1.2% NII = interest revenue - interest expense = ($210 million × 1.0%) - ($225 million × 1.2%) = $2,100,000 -$2,700,000 = -$600,000

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**Re-pricing Model – 1 Year Cum Gap Analysis**

Simple Bank Repricing Maturity Balance 0 to 1 >1 Securities 0.75 9,000 Consumer Loans 0.5 10,000 1.5 15,000 3 16,000 Prime-Based Loans 50,000 Total Assets 100,000 69,000 Demand Deposits - Fixed 5 Demand Deposits - Variable 0.01 35,000 CDs 30,000 5,000 2 Equity NA Total Liabilities & NW 70,000 1 year Cum Gap -1,000 Change In Mkt Rates 1% Change in NII -10 Chang in NII/ Assets -.01%

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**Re-pricing Model – 1 Year Cum Gap Analysis**

Simple Bank Repricing Maturity Balance 0 to 1 >1 Securities 0.75 9,000 Consumer Loans 0.5 10,000 1.5 15,000 3 16,000 Mortgage Loans 50,000 Total Assets 100,000 19,000 Demand Deposits - Fixed 5 Demand Deposits - Variable 0.01 35,000 CDs 30,000 5,000 2 Equity NA Total Liabilities & NW 70,000 1 year Cum Gap -51,000 Change In Mkt Rates 1% Change in NII -510 Chang in NII/ Assets -.51%

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**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 % re-pricing immediately/duration = 0 Passbook Accounts Treat as 20% re-pricing over 5 years/duration = 5 years % 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

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**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

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**Prime Rate Vs Fed Funds 1955-2009**

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**Prime Rate Vs Fed Funds 1997-2009**

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**Prime Rate Vs Fed Funds 2007-2009**

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**Re-pricing Model – 1 Year Cum Gap Analysis**

Simple Bank Repricing Maturity Balance 0 to 1 >1 Securities 0.75 9,000 Consumer Loans 0.5 10,000 1.5 15,000 3 16,000 Prime-Based Loans 50,000 Total Assets 100,000 69,000 Demand Deposits - Fixed 5 Demand Deposits - Variable 0.01 35,000 CDs 30,000 5,000 2 Equity NA Total Liabilities & NW 70,000 1 year Cum Gap -1,000 Change In Mkt Rates 2% Change in NII -20 Chang in NII/ Assets -.02%

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**Re-pricing Model – 1 Year Cum Gap Analysis**

Simple Bank Repricing Maturity Balance 0 to 1 >1 Securities 0.75 9,000 Consumer Loans 0.5 10,000 1.5 15,000 3 16,000 Prime-Based Loans 50,000 Total Assets 100,000 69,000 Demand Deposits - Fixed 5 Demand Deposits - Variable 0.01 35,000 CDs 30,000 5,000 2 Equity NA Total Liabilities & NW 70,000 1 year Cum Gap -1,000 Change In Mkt Rates 6% Change in NII -60 Chang in NII/ Assets -.07%

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**Re-pricing Model – 1 Year Cum Gap Analysis**

Simple S&L Repricing Maturity Balance 0 to 1 >1 Securities 0.75 12,000 Consumer Loans 0.5 2,000 1.5 3 Fixed Rate Mortgages 30 82,000 Total Assets 100,000 14,000 Demand Deposits - Fixed 5 NOW Accounts 0.01 20,000 CDs 61,000 10,000 2 5,000 Equity NA 4,000 Total Liabilities & NW 91,000 1 year Cum Gap -77,000 Change In Mkt Rates 1% Change in NII -770 Chang in NII/ Assets -.77%

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**Re-pricing Model – 1 Year Cum Gap Analysis**

Simple S&L Repricing Maturity Balance 0 to 1 >1 Securities 0.75 12,000 Consumer Loans 0.5 2,000 1.5 3 Fixed Rate Mortgages 30 82,000 Total Assets 100,000 14,000 Demand Deposits - Fixed 5 NOW Accounts 0.01 20,000 CDs 61,000 10,000 2 5,000 Equity NA 4,000 Total Liabilities & NW 91,000 1 year Cum Gap -77,000 Change In Mkt Rates 6% Change in NII -4,620 Chang in NII/ Assets -4.62%

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**Comparison of 1980 Bank vs S&L**

No Change in Rates Simple Bank Yield Balance Interest Simple S&L Assets 6.5% 100,000 6,500 7.0% 7,000 Liabilities 2.5% 90,000 -2,250 4.9% 96,000 -4,704 Equity 10,000 4,000 NII 4,250 2,296 Operating Expenses -2,000 -1,400 Pre-tax income 2,250 896 Taxes at 35% -788 -314 Net income 1,463 582 ROA 1.46% 0.58% ROE 14.6%

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**Comparison of 1980 Bank vs S&L**

Rates Up 6% Simple Bank Yield Balance Interest Simple S&L Assets 10.6% 100,000 10,640 7.8% 7,840 Liabilities 7.3% 90,000 -6,570 96,000 -10,176 Equity 10,000 4,000 NII 4,070 -2,336 Operating Expenses -2,000 -1,400 Pre-tax income 2,070 -3,736 Taxes at 35% -725 1,308 Net income 1,346 -2,428 ROA 1.35% -2.43% ROE 13.5% -60.7%

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**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”

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**Weaknesses of Re-pricing Model**

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 runoffs Bank continuously originates and retires consumer and mortgage loans and demand deposits/passbook account balances can vary. Runoffs may be rate-sensitive.

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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

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***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.

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**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.

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***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.

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***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)

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*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.

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**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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Copyright 2002, A.S. Cebenoyan1 Finance 208 Seminar in Financial Institutions Professor A. Sinan Cebenoyan Frank G. Zarb School of Business Hofstra University.

Copyright 2002, A.S. Cebenoyan1 Finance 208 Seminar in Financial Institutions Professor A. Sinan Cebenoyan Frank G. Zarb School of Business Hofstra University.

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