# Gap Reports: Measuring Risk to NII and Economic Value

Measuring Risk to Net Interest Income

After a bank has stratified the bank’s assets, liabilities, and off- balance sheet instruments into time bands and determined how it will treat embedded options, it must measure net interest income (NII) at risk. The formula to translate gaps into the amount of net interest at risk, measuring exposure over several periods, is:

Change in NII = (Periodic gap) x (Change in rate) x (Time over which the periodic gap is in effect)

This formula can be illustrated by applying it to the gap report shown in the table and calculating change in the bank’s net interest income for an immediate 200 basis point increase in rates. For example, the bank has a negative gap of $20 million in the one-month to three-month time band. This means more liabilities than assets will reprice or mature during this time frame. Hence, for the remaining 10 months of the bank’s 12 month time horizon, the bank will have$20 million more of liabilities than assets that have repriced at higher (20 basis points higher) rates. As shown in table the increase in rates reduces the bank’s earnings effect of the banks repricing imbalances over the 12-month horizon is a reduction in net interest income of approximately $362,500. Sample Net Interest Income Sensitivity Calculation  Time Band Size of Gap (in millions of dollars) Basis Point Change Part of Year Gap is in Effect Impact on Annualized NII (In thousand of Dollars) <1 month$5 200 11.5/12 $95.8 1-3 months -$20 200 10/12 -$333.3 3-6 months -$20 200 7.5/12 -$250.0 6-12 months$25 200 3/12 $125.0 Total -$362.5

*assumes all repricings occur at midpoint of time band

It is important to stress that this to stress that this method of measuring a bank’s net interest income at risk is very crude and employs numerous simplifying assumptions, including the following:

• All repricing and maturities within a time band occurs simultaneously (as in the above formula), typically at the beginning, middle, or end of the period.

• All maturing assets and liabilities are reinvested at overnight rates.

• No other new business is booked.

• There is an instantaneous change in the overnight rate to a new and constant level.

• All interest rates move the same amount. The sensitivity of the results to these assumptions can be tested by using simulation models.

Measuring Risk to Economic Value

Gap reports may be used to measure the exposures of a bank’s net economic value to a change in interest rates. To do so, a bank multiplies the balances in each time band by a price sensitivity factor that approximates, for a given change in interest rates, the percentage in the present value of an instrument with similar cash flow and maturity characteristics. For example, consider a bank that approximates, for a given change in interest rates, the percentage change in the present value of an instrument with similar cash flow and maturity characteristics. For example, consider a bank that has $10 million of two-year Treasury notes slotted in the time band covering from two years to three years in its gap report. To estimate the market value sensitivity of those balances to a 200-basis-point increase in market, a banker would multiply those balances by a factor that approximates the change in the present value of a two-year Treasury note for a 200 –basis –point movement in rates. The present value of a note with 7.5% coupon would decline 3.6% for such a rate movement. Hence, the estimated decline in the market value of the bank’s$10million two-year Treasury note would be approximately $360,000 ($10 million times negative 3.6%).

Similar price sensitivity factors can be applied to other types instruments and time bands .The exposure of the banks net economic value would be the sum of the weighted balances.

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