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**Measuring Interest Rate Risk**

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Static Gap Analysis Calculate the gap between rate sensitive assets and rate sensitive liabilities over a given horizon (i.e days, 1 year) Assets or Liabilities are rate sensitive if: It is an interest paying demand deposit. It matures within the horizon or there is partial or interim principal payment Interest Rate changes by contractual terms Interest Rate changes according to some base rate

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Static GAP Difference between dollar value of risk sensitive assets and risk sensitive liabilities within some time bucket. Cumulative GAP measures the GAP for a time horizon of today until the end of some date. Cumulative GAP measures the effect of a permanent change in interest rates on income over that horizon. ∆NII = GAP*∆i

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Example ∆NII = GAP*∆I =-100*.01 = 1

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**Steps for GAP Analysis Make Interest Rate Forecast**

Select a series of Time Buckets – Specific periods of time in the future Allocate all rate sensitive assets and liabilities into time buckets Calculate periodic GAP and cumulative GAP for each time bucket. Calculate effect of change in interest rate on net income.

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Rate sensitivity reports …classifies a bank’s assets and liabilities into time intervals according to the minimum number of days until each instrument can be repriced. Hang Seng Bank 2005

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**Weakness of GAP Cannot capture interest rate risk within buckets.**

Focuses on small interest rate changes in short-run. May be changes in spreads between different base rates and asset/liability rates. Does not allow composition of assets and liabilities to change Non-interest paying liabilities may disappear if rates rise. Debtors typically have an option to repay funds early.

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**Earnings Sensitivity Analysis**

Forecast different interest rate scenarios. Forecast changes in volume and composition effects of interest rate scenarios.

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Cumulative Gap only measures interest risk if changes in interest rate have even effects across assets and liabilities Because interest rates changes may be temporary, they may affect of the shape of the yield curve. If rate sensitive assets and liabilities have different maturity structures, cumulative gap may not Consider the case where short-term interest rates go up by 2% for 6 months and return to previous level for subsequent 6 months.

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Managing the GAP Calculate periodic GAPs and match rate sensitive assets and liabilities at certain intervals. Match long-term assets with non-bearing liabilities Use off-balance sheet transactions to hedge interest risk.

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**Present Value of a Stream of Income is equal to the sum of the present value of each component**

Examples Coupon Bond Fixed Payment Loan General

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**Changes in interest rates, change in bond prices**

Bond prices are inverse to interest rates which determine bond yields. A rise in interest rates reduces bond prices. A fall in interest rates increases bond prices. % effect of a permanent change in interest rates results in a change in price/present value proportional to T.

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**How does a change in the discount factor affect present value?**

A way to measure the maturity structure of an income stream is to calculate what percentage of the present value of an income stream comes from different maturity dates To sum up this measure, calculate a weighted sum of the years until final maturity using these percentages as weights. This measure is called DURATION of the income stream. Duration also measures the sensitivity of the income stream to changes in the interest rate.

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Duration Gap Market Value of equity should be the gap between the present value of assets and the present value of liabilities NWMV = APV – LPV Use the duration of assets to calculate the effect of a change in interest rates

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Immunization Banks may deal with interest rate risk by structuring assets and liabilities so as to close the duration gap as much as possible. Firms conduct simulation series to calculate the effect of different interest rate scenarios on balance sheets.

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