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Chapter. 8. Interest Rate Risk I. Overview. This chapter discusses the interest rate risk associated with financial intermediation: Federal Reserve policy Repricing model Maturity model Duration model *Term structure of interest rate risk *Theories of term structure of interest rates.

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  1. Chapter 8 Interest Rate Risk I

  2. Overview • This chapter discusses the interest rate risk associated with financial intermediation: • Federal Reserve policy • Repricing model • Maturity model • Duration model • *Term structure of interest rate risk • *Theories of term structure of interest rates

  3. Central Bank Policy and Interest Rate Risk • Japan: March 2001 announced it would no longer target the uncollateralized overnight call rate. • New target: Outstanding current account balances at BOJ • Targeting of bank reserves in U.S. proved disastrous

  4. Central Bank and Interest Rate Risk • Effects of interest rate targeting. • Lessens interest rate risk • October 1979 to October 1982, nonborrowed reserves target regime. • Implications of return to reserves target policy: • Increases importance of measuring and managing interest rate risk.

  5. Web Resources • For information related to central bank policy, visit: Bank for International Settlements: www.bis.org Federal Reserve Bank: www.federalreserve.gov Bank of Japan: www.boj.or.jp Web Surf

  6. Repricing Model • Repricing 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). • Rate sensitivity means time to repricing. • Repricing gap is the difference between the rate sensitivity of each asset and the rate sensitivity of each liability: RSA - RSL.

  7. Maturity Buckets • Commercial banks must report repricing 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.

  8. Repricing Gap Example AssetsLiabilitiesGap 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

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

  10. Applying the Repricing Model • Example II: If we consider the cumulative 1-year gap, DNIIi = (CGAPi) DRi = (-$15 million)(.01) = -$150,000.

  11. Rate-Sensitive Assets • Examples from hypothetical balance sheet: • Short-term consumer loans. If repriced at year-end, would just make one-year cutoff. • Three-month T-bills repriced on maturity every 3 months. • Six-month T-notes repriced on maturity every 6 months. • 30-year floating-rate mortgages repriced (rate reset) every 9 months.

  12. 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.

  13. CGAP Ratio • May be useful to express CGAP in ratio form as, CGAP/Assets. • Provides direction of exposure and • Scale of the exposure. • Example: • CGAP/A = $15 million / $270 million = 0.56, or 5.6 percent.

  14. Equal Changes in Rates on RSAs and RSLs • Example: Suppose rates rise 2% 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.

  15. 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 )

  16. 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 = ($155 million × 1.2%) - ($155 million × 1.0%) = $310,000

  17. Restructuring Assets and 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

  18. Weaknesses of Repricing Model • Weaknesses: • Ignores market value effects and off-balance sheet cash flows • Overaggregative • 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. Runoffs may be rate-sensitive.

  19. 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.

  20. 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, MA - ML > 0 for most banks and thrifts.

  21. 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.

  22. Maturity Matching 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 maturities are equal. • Reason: Differences in duration.

  23. Duration • The average life of an asset or liability • The weighted-average time to maturity using present value of the cash flows, relative to the total present value of the asset or liability as weights.

  24. *Term Structure of Interest Rates YTM YTM Time to Maturity Time to Maturity Time to Maturity Time to Maturity

  25. *Unbiased Expectations Theory • Yield curve reflects market’s expectations of future short-term rates. • Long-term rates are geometric average of current and expected short-term rates. __~~ RN = [(1+R1)(1+E(r2))…(1+E(rN))]1/N - 1

  26. *Liquidity Premium Theory • Allows for future uncertainty. • Premium required to hold long-term. *Market Segmentation Theory • Investors have specific needs in terms of maturity. • Yield curve reflects intersection of demand and supply of individual maturities.

  27. Pertinent Websites Bank for International Settlements www.bis.org Federal Reserve www.federalreserve.gov Bank of Japan www.boj.or.jp Web Surf

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