1. Re-pricing Model & Maturity Model
Chapter 8
Re-pricing Model & Maturity Model

2. Interest Rate Risk Models
Re-pricing model
Maturity model
Duration model
In-house models
Proprietary
Commercial

3. 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.

4. Short-Term Rates

5. Short-Term Rates

6. Short-Term Rates

7. 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

8. 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).

9. 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

10. 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

11. 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

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

13. 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

14. 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

15. 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.

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

17. 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.

18. 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

19. 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.

20. 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

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

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

23. 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

24. 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 )

25. 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

26. 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

27. 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

28. 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%

29. 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%

30. 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

31. 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

32. Prime Rate Vs Fed Funds 1955-2009

33. Prime Rate Vs Fed Funds 1997-2009

34. Prime Rate Vs Fed Funds 2007-2009

35. 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%

36. 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%

37. 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%

38. 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%

39. 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%

40. 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%

41. 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”

42. 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.

43. 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

44. *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.

45. 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.

46. *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.

47. *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)

48. *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.

49. Modified Maturity Model
Correct for leverage
to immunize, change:
MA - ML = 0 to
MA – ML& E = 0 with ME = 0
(not in text)