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Central Bank & Interest Rate Risk. Federal Reserve Bank: U.S. central bank Open market operations influence money supply, inflation, and interest rates Oct-1979 to Oct-1982, nonborrowed reserves target regime – did not work Implications of reserves target policy:

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Central Bank & Interest Rate Risk

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Central bank interest rate risk

Central Bank & Interest Rate Risk

  • Federal Reserve Bank: U.S. central bank

    • Open market operations influence money supply, inflation, and interest rates

  • Oct-1979 to Oct-1982, nonborrowed reserves target regime – did not work

  • Implications of reserves target policy:

    • Increases importance of measuring and managing interest rate risk.

  • Effects of interest rate targeting.

    • Lessens interest rate risk

  • Greenspan view: Risk Management

    • Focus on Federal Funds Rate

    • Simple announcement of Fed Funds increase, decrease, or no change.

Repricing model

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.

  • Refinancing risk

Maturity buckets

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.

Repricing gap example

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

>1yr.-5yrs. 40 30 +10 -5

>5 years 10 5 +5 0

Repricing gap

Repricing Gap

Applying the repricing model

Applying the Repricing Model

  • DNIIi = (GAPi) DRi = (RSAi - RSLi) Dri


    In the one day bucket, gap is -$10 million. If rates rise by 1%,

    DNII(1) = (-$10 million) × .01 = -$100,000.

Applying the repricing model1

Applying the Repricing Model

  • Example II:

    If we consider the cumulative 1-year gap,

    DNII = (CGAPone year) DR = (-$15 million)(.01)

    = -$150,000.

Repricing model1

Repricing Model

Cgap ratio

CGAP Ratio

  • May be useful to express CGAP in ratio form as,


    • Provides direction of exposure and

    • Scale of the exposure.

  • Example:

    • CGAP/A = $15 million / $270 million = .056, or 5.6 percent.

Unequal changes in rates

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 )

  • Spread effect example:

  • RSA=RSL=$155m

  • 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

Restructuring assets liabilities

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

    • Example: State Street Boston

      • Good luck?

      • Or Good Management?

Repricing model2

Repricing Model

  • Problems with model:

    • measures only short-term profit changes not shareholder wealth changes

    • maturity buckets are arbitrarily chosen

    • assets and liabilities within a bucket are considered equally rate sensitive

    • ignores runoffs

    • ignores prepayments

    • ignores CFs gnerated from off balance sheet activities

The maturity model

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 model example

Maturity Model Example

  • FI issues a one-year CD to a depositor that has a face value of $100 and an interest rate promised to depositors of 15%. (On maturity at year end, the FI has to repay $115.) Suppose FI lends $100 for one year to a corporate borrower at 15% annual interest (so $A=$L). However, the FI contractually requires half of the loan ($50) to be repaid after 6 months and the last half to be repaid at the end of the year. Note that although the maturity of the loan equals the maturity of the deposit and the loan is fully funded by the deposit liabilities, the CFs on the loan may be greater or less than the $115 required to pay off depositors, depending on what happens to interest rates over the one year period.

Maturities and interest rate exposure

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

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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