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## Managing Interest Rate Risk: GAP and Earnings Sensitivity

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**Managing Interest Rate Risk**• Interest Rate Risk • The potential loss from unexpected changes in interest rates which can significantly alter a bank’s profitability and market value of equity**Managing Interest Rate Risk**• Interest Rate Risk • When a bank’s assets and liabilities do not reprice at the same time, the result is a change in net interest income • The change in the value of assets and the change in the value of liabilities will also differ, causing a change in the value of stockholder’s equity**Managing Interest Rate Risk**• Interest Rate Risk • Banks typically focus on either: • Net interest income or • The market value of stockholders' equity • GAP Analysis • A static measure of risk that is commonly associated with net interest income (margin) targeting • Earnings Sensitivity Analysis • Earnings sensitivity analysis extends GAP analysis by focusing on changes in bank earnings due to changes in interest rates and balance sheet composition**Managing Interest Rate Risk**• Interest Rate Risk • Asset and Liability Management Committee (ALCO) • The bank’s ALCO primary responsibility is interest rate risk management. • The ALCO coordinates the bank’s strategies to achieve the optimal risk/reward trade-off**Measuring Interest Rate Risk with GAP**• Three general factors potentially cause a bank’s net interest income to change. • Rate Effects • Unexpected changes in interest rates • Composition (Mix) Effects • Changes in the mix, or composition, of assets and/or liabilities • Volume Effects • Changes in the volume of earning assets and interest-bearing liabilities**Measuring Interest Rate Risk with GAP**• Consider a bank that makes a $25,000 five-year car loan to a customer at fixed rate of 8.5%. The bank initially funds the car loan with a one-year $25,000 CD at a cost of 4.5%. The bank’s initial spread is 4%. • What is the bank’s risk?**Measuring Interest Rate Risk with GAP**• Traditional Static Gap Analysis • Static GAP Analysis GAPt = RSAt- RSLt • RSAt • Rate Sensitive Assets • Those assets that will mature or reprice in a given time period (t) • RSLt • Rate Sensitive Liabilities • Those liabilities that will mature or reprice in a given time period (t)**Measuring Interest Rate Risk with GAP**• Traditional Static Gap Analysis • Steps in GAP Analysis • Develop an interest rate forecast • Select a series of “time buckets” or time intervals for determining when assets and liabilities will reprice • Group assets and liabilities into these “buckets” • Calculate the GAP for each “bucket ” • Forecast the change in net interest income given an assumed change in interest rates**Measuring Interest Rate Risk with GAP**• What Determines Rate Sensitivity • The initial issue is to determine what features make an asset or liability rate sensitive**Measuring Interest Rate Risk with GAP**• Expected Repricing versus Actual Repricing • In general, an asset or liability is normally classified as rate sensitive within a time interval if: • It matures • It represents an interim or partial principal payment • The interest rate applied to the outstanding principal balance changes contractually during the interval • The interest rate applied to the outstanding principal balance changes when some base rate or index changes and management expects the base rate/index to change during the time interval**Measuring Interest Rate Risk with GAP**• What Determines Rate Sensitivity • Maturity • If any asset or liability matures within a time interval, the principal amount will be repriced • The question is what principal amount is expected to reprice • Interim or Partial Principal Payment • Any principal payment on a loan is rate sensitive if management expects to receive it within the time interval • Any interest received or paid is not included in the GAP calculation**Measuring Interest Rate Risk with GAP**• What Determines Rate Sensitivity • Contractual Change in Rate • Some assets and deposit liabilities earn or pay rates that vary contractually with some index • These instruments are repriced whenever the index changes • If management knows that the index will contractually change within 90 days, the underlying asset or liability is rate sensitive within 0–90 days.**Measuring Interest Rate Risk with GAP**• What Determines Rate Sensitivity • Change in Base Rate or Index • Some loans and deposits carry interest rates tied to indexes where the bank has no control or definite knowledge of when the index will change. • For example, prime rate loans typically state that the bank can contractually change prime daily • The loan is rate sensitive in the sense that its yield can change at any time • However, the loan’s effective rate sensitivity depends on how frequently the prime rate actually changes**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Rate, Composition (Mix) and Volume Effects • All affect net interest income**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • The sign of GAP (positive or negative) indicates the nature of the bank’s interest rate risk • A negative (positive) GAP, indicates that the bank has more (less) RSLs than RSAs. When interest rates rise (fall) during the time interval, the bank pays higher (lower) rates on all repriceable liabilities and earns higher (lower) yields on all repriceable assets**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • The sign of GAP (positive or negative) indicates the nature of the bank’s interest rate risk • If all rates rise (fall) by equal amounts at the same time, both interest income and interest expense rise (fall), but interest expense rises (falls) more because more liabilities are repriced • Net interest income thus declines (increases), as does the bank’s net interest margin**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • If a bank has a zero GAP, RSAs equal RSLs and equal interest rate changes do not alter net interest income because changes in interest income equal changes in interest expense • It is virtually impossible for a bank to have a zero GAP given the complexity and size of bank balance sheets**Measuring Interest Rate Risk with GAP**Factors Affecting Net Interest Income**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • GAP analysis assumes a parallel shift in the yield curve**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • If there is a parallel shift in the yield curve then changes in Net Interest Income are directly proportional to the size of the GAP: ∆NIIEXP = GAP x ∆iEXP • It is rare, however, when the yield curve shifts parallel. If rates do not change by the same amount and at the same time, then net interest income may change by more or less**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • Example 1 • Recall the bank that makes a $25,000 five-year car loan to a customer at fixed rate of 8.5%. The bank initially funds the car loan with a one-year $25,000 CD at a cost of 4.5%. What is the bank’s 1-year GAP?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • Example 1 • RSA1 YR = $0 • RSL1 YR = $10,000 • GAP1 YR = $0 - $25,000 = -$25,000 • The bank’s one year funding GAP is -$25,000 • If interest rates rise (fall) by 1% in 1 year, the bank’s net interest margin and net interest income will fall (rise) • ∆NIIEXP = GAP x ∆iEXP = -$10,000 x 1% = -$100**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • Example 2 • Assume a bank accepts an 18-month $30,000 CD deposit at a cost of 3.75% and invests the funds in a $30,000 6-month T-Bill at rate of 4.80%. The bank’s initial spread is 1.05%. What is the bank’s 6-month GAP?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Level of Interest Rates • Example 2 • RSA6 MO = $30,000 • RSL6 MO = $0 • GAP6 MO = $30,000 – $0 = $30,000 • The bank’s 6-month funding GAP is $30,000 • If interest rates rise (fall) by 1% in 6 months, the bank’s net interest margin and net interest income will rise (fall) • ∆NIIEXP = GAP x ∆iEXP = $30,000 x 1% = $300**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in the Relationship Between Asset Yields and Liability Costs • Net interest income may differ from that expected if the spread between earning asset yields and the interest cost of interest-bearing liabilities changes • The spread may change because of a nonparallel shift in the yield curve or because of a change in the difference between different interest rates (basis risk)**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in Volume • Net interest income varies directly with changes in the volume of earning assets and interest-bearing liabilities, regardless of the level of interest rates • For example, if a bank doubles in size but the portfolio composition and interest rates remain unchanged, net interest income will double because the bank earns the same interest spread on twice the volume of earning assets such that NIM is unchanged**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Changes in Portfolio Composition • Any variation in portfolio mix potentially alters net interest income • There is no fixed relationship between changes in portfolio mix and net interest income • The impact varies with the relationships between interest rates on rate-sensitive and fixed-rate instruments and with the magnitude of funds shifts**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.0**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.0 • Interest Income • ($500 x 8%) + ($350 x 11%) = $78.50 • Interest Expense • ($600 x 4%) + ($220 x 6%) = $37.20 • Net Interest Income • $78.50 - $37.20 = $41.30**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.0 • Earning Assets • $500 + $350 = $850 • Net Interest Margin • $41.3/$850 = 4.86% • Funding GAP • $500 - $600 = -$100**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.1 • What if all rates increase by 1%?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.1 • What if all rates increase by 1%? • With a negative GAP, interest income increases by less than the increase in interest expense. Thus, both NII and NIM fall.**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.2 • What if all rates fall by 1%?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.2 • What if all rates fall by 1%? • With a negative GAP, interest income decreases by less than the decrease in interest expense. Thus, both NII and NIM increase.**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.3 • What if rates rise but the spread falls by 1%?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.3 • What if rates rise but the spread falls by 1%? • Both NII and NIM fall with a decrease in the spread. Why the larger change? • Note:∆NIIEXP ≠ GAP x ∆iEXP Why?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.4 • What if rates fall but the spread falls by 1%?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.4 • What if rates fall and the spread falls by 1%? • Both NII and NIM fall with a decrease in the spread. • Note:∆NIIEXP ≠ GAP x ∆iEXP**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.5 • What if rates rise and the spread rises by 1%?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.5 • What if rates rise and the spread rises by 1%? • Both NII and NIM increase with an increase in the spread. • Note:∆NIIEXP ≠ GAP x ∆iEXP**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.6 • What if rates fall and the spread rises by 1%?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.6 • What if rates fall and the spread rises by 1%? • Both NII and NIM increase with an increase in the spread. • Note:∆NIIEXP ≠ GAP x ∆iEXP**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.7 • What if the bank proportionately doubles in size?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 3.7 • What if the bank proportionately doubles in size? • Both NII doubles but NIM stays the same. Why? What has happened to the bank’s risk?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 4.0**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 4.0 • Bank has a positive GAP**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 4.1 • What if rates increase by 1%?**Measuring Interest Rate Risk with GAP**• Factors Affecting Net Interest Income • Example 4.1 • What if rates increase by 1%? • With a positive GAP, interest income increases by more than the increase in interest expense. Thus, both NII and NIM rise.