Question

Assuming you are the Head of Credit Administration at your Financial Institution and your manager is concerned with the exposure due to the Interest Rate Risk caused by the mismatching of assets. To this end your manager asks you to review the two models for measuring Interest Rate Risk, “The Repricing model and the Maturity model” and advise which methodology is the best to be implemented.

Answer 1

Modelling Interest Rate Risk

Repricing Model

• The repricing model is the difference between those assets whose interest rates will be re-priced or changed over some future period and liabilities whose interest rates will be re-priced or changed over some future period.
• Quarterly reporting of commercial bank assets and liabilities in various maturity buckets         (or bin):
  • One day
  • More than one day to 3 months
  • More than 3 months to 6 months
  • More than 6 months to 12 months
  • More than 1 year to 5 years
  • More than 5 years

• The gap in each bucket or bin is measured as the difference between the rate-sensitive assets (RSAs) and the rate-sensitive liabilities (RSLs)

• Rate-sensitivity measures the time to re-pricing of an asset or liability

The cumulative gap (CGAP) is the sum of the individual maturity bucket gaps

The cumulative gap effect is the relation between changes in interest rates and changes in net interest income

• The change in net interest income for any given bucket i (?NIIi) is measured as:
• NIIi = (GAPi)?Ri = (RSAi – RSLi)?Ri, Where GAPi = the dollar size of the gap between the book value of rate-sensitive assets and rate-sensitive liabilities in maturity bucket I, ?Ri = the change in the level of interest rates impacting assets and liabilities in the ith maturity bucket

The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has on net interest income as interest rates change ?NIIi = (RSAi x ?RRSA) – (RSLi x ?RRSL)

Maturity Model

• Duration measures the interest rate sensitivity of an asset or liability’s value to small changes in interest rates
• The duration gap is a measure of overall interest rate risk exposure for an FI
• To find the duration of the total portfolio of assets (DA) (or liabilities (DL)) for an FI
  • First determine the duration of each asset (or liability) in the portfolio
  • Then calculate the market value weighted average of the duration of the assets (or liabilities) in the portfolio
• The change in the market value of the asset portfolio for a change in interest rates is:

• Similarly, the change in the market value of the liability portfolio for a change in interest rates is:

• Finally, the change in the market value of equity of an FI given a change in interest rates is determined from the basic balance sheet equation:

• By substituting and rearranging, the change in net worth is given as:

where k is L/A = a measure of the FI’s leverage

• The effect of interest rate changes on the market value of equity or net worth of an FI breaks down to three effects:
  • The leverage adjusted duration gap = (D_A – kD_L)
    • measured in years
    • reflects the duration mismatch on an FI’s balance sheet
    • the larger the gap, the more exposed the FI to interest rate risk
  • The size of the FI
  • The size of the interest rate shock