Chapter 8

1. 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 1954-2009

5. Short-Term Rates 1997-2009

6. Short-Term Rates 2007-2009

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 • 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 AssetsLiabilitiesGapCum. 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

14. Re-pricing Gap Example AssetsLiabilitiesGapCum. 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

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 = -0.058, 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 AssetsLiabilitiesGapCum. 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

22. Repricing Gap Example AssetsLiabilitiesGapCum. 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 210225 >1yr.-5yrs. 40 30 +10 -5 >5 years 10 5 +5 0

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

29. Re-pricing Model – 1 Year Cum Gap Analysis

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 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

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

36. Re-pricing Model – 1 Year Cum Gap Analysis

37. Re-pricing Model – 1 Year Cum Gap Analysis

38. Re-pricing Model – 1 Year Cum Gap Analysis

39. Comparison of 1980 Bank vs S&L

40. Comparison of 1980 Bank vs S&L

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 • 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 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)