Interest/Maturity Gap and SensitivityInterest/Maturity GapWhy Gap?Business Cycle and Interest RatesMaturity GapSlide 6Slide 7Duration GapSlide 9Slide 10Slide 11Interest/Maturity Interest/Maturity GapGapandandSensitivitySensitivityInterest/Maturity GapInterest/Maturity GapG & K Chp. 5G & K Chp. 5Why Gap? Manage on- or off-balance Why Gap? Manage on- or off-balance sheetsheetOff-Balance Sheet (Futures, Options, Off-Balance Sheet (Futures, Options, later….)later….)Economic EnvironmentEconomic EnvironmentMaturity GapMaturity GapDuration GapDuration GapWhy Gap?Why Gap?Maturity Pattern and Interest Rate Maturity Pattern and Interest Rate Sensitivity of Assets and Liabilities Sensitivity of Assets and Liabilities differ.differ.Fixed Rate Investment funded by Fixed Rate Investment funded by Floating Rates can create Spread Floating Rates can create Spread Squeezes.Squeezes.Want to create stable Spread, and force Want to create stable Spread, and force maximum funds through……maximum funds through……Changes in interest rates compound Changes in interest rates compound spread management by imparting value spread management by imparting value management in addition.management in addition.Business Cycle and Business Cycle and Interest RatesInterest RatesTrough: Low economic activity; low Trough: Low economic activity; low demand for funds, high demand for safe, demand for funds, high demand for safe, liquid investments liquid investments  Low relative rates, + Low relative rates, + - curve- curveGrowth to Peak: Increasing economic Growth to Peak: Increasing economic activity; high demand for funds, low activity; high demand for funds, low demand for interest-rate investments demand for interest-rate investments  Higher relative rates, + - to – flattening Higher relative rates, + - to – flattening curvecurveSlowdownSlowdownTrough; Slowing economic Trough; Slowing economic activity, early high demand for funds activity, early high demand for funds gives rise to drop off gives rise to drop off  High rates drop, High rates drop, with inverted-curve returning to positive with inverted-curve returning to positive slopeslopeMaturity GapMaturity GapRepricing of Repricing of Book ValuesBook Values of Assets of Assets vs. Liabilities in common time vs. Liabilities in common time periodsperiodsPg. 5 of any outputPg. 5 of any outputRate Sensitive Assets (RSAs) andRate Sensitive Assets (RSAs) and Rate Sensitive Liabilities (RSLs) Rate Sensitive Liabilities (RSLs)3, 6, 9 mo., 1 yr., 1-3 yrs., Over 3 yrs.3, 6, 9 mo., 1 yr., 1-3 yrs., Over 3 yrs.Idea is:Idea is:(Gap = RSA – RSL)(Gap = RSA – RSL)NII NII = Gap * = Gap *  R RMaturity GapMaturity GapRates Go UpRates Go UpPositive Gap Positive Gap  Increase NII Increase NIINegative Gap Negative Gap  Decrease NII Decrease NIIRates Go DownRates Go DownPositive Gap Positive Gap  Decrease NII Decrease NIINegative Gap Negative Gap  Increase NII Increase NIIProblems:Problems:Ignores Market Value ChangesIgnores Market Value ChangesIgnores variation in intra-bucket value Ignores variation in intra-bucket value changeschangesConcentrates on single-period CF, not Concentrates on single-period CF, not MVMVMaturity GapMaturity GapY1Q4:Y1Q4:3 month Assets: 3596.963 month Assets: 3596.963 month Liabilities: 2617.513 month Liabilities: 2617.51RSA – RSL = 3 month Gap = 979.45RSA – RSL = 3 month Gap = 979.453 month Interest Rates go up .3 month Interest Rates go up .25%25%NII should jump (0.0025*979.45) NII should jump (0.0025*979.45) $2.45 mill$2.45 millDuration GapDuration GapDuration Weighted Assets and Duration Weighted Assets and LiabilitiesLiabilitiesManaging the Change in Equity Managing the Change in Equity (Value) from a change in interest (Value) from a change in interest rates and their effect on Assets and rates and their effect on Assets and LiabilitiesLiabilitiesRemember:Remember: Price = - D * Price = - D * r / (1 r / (1 + YTM) * Price+ YTM) * PriceApplied to Assets and Liabilities:Applied to Assets and Liabilities: A = - DA = - DA * * R / (1 + R) * A R / (1 + R) * A L = - DL = - DL * * R / (1 + R) * LR / (1 + R) * LDuration GapDuration GapThen:Then: E = E = A - A - LLE = -[ DE = -[ DAA - D - DLL (L/A)] * [ (L/A)] * [R/(1+R)] * R/(1+R)] * AAChange in Equity is negative of Change in Equity is negative of difference in durations multiplied by difference in durations multiplied by interest rate change multiplied by interest rate change multiplied by asset baseasset baseDuration GapDuration GapRates Go UpRates Go UpPositive Duration Gap Positive Duration Gap  Decrease Decrease ValueValueNegative Duration Gap Negative Duration Gap  Increase Increase ValueValueRates Go DownRates Go DownPositive Duration Gap Positive Duration Gap  Increase Value Increase ValueNegative Duration Gap Negative Duration Gap  Decrease Decrease ValueValueDuration GapDuration GapFrom 1.4 Output:From 1.4 Output:Assets: Duration = 0.427 , Value = $4.897 Assets: Duration = 0.427 , Value = $4.897 billbillLiabs: Duration = 1.103, Value = $4.609 billLiabs: Duration = 1.103, Value = $4.609 billNotice……Negatively Gapped!Notice……Negatively Gapped!Assume R=7% Assume R=7% 7.05%7.05%E = -[ DE = -[ DAA - D - DLL (L/A)] * ( (L/A)] * (R/(1+R) * AR/(1+R) * A = -[.427 – 1.103 = -[.427 – 1.103 (4.609/4.897)]*(+.0005/1.07)*4.897(4.609/4.897)]*(+.0005/1.07)*4.897 = +0.00139846 = +$ 1.39846 million= +0.00139846 = +$ 1.39846