Interest/Maturity Gap and Sensitivity

Interest/Maturity Gap G & K Chp. 5 G & K Chp. 5 Why Gap? Manage on- or off-balance sheet Why Gap? Manage on- or off-balance sheet Off-Balance Sheet (Futures, Options, later….) Off-Balance Sheet (Futures, Options, later….) Economic Environment Economic Environment Maturity Gap Maturity Gap Duration Gap Duration Gap

Why Gap? Maturity Pattern and Interest Rate Sensitivity of Assets and Liabilities differ. Maturity Pattern and Interest Rate Sensitivity of Assets and Liabilities differ. Fixed Rate Investment funded by Floating Rates can create Spread Squeezes. Fixed Rate Investment funded by Floating Rates can create Spread Squeezes. Want to create stable Spread, and force maximum funds through…… Want to create stable Spread, and force maximum funds through…… Changes in interest rates compound spread management by imparting value management in addition. Changes in interest rates compound spread management by imparting value management in addition.

Business Cycle and Interest Rates Trough: Low economic activity; low demand for funds, high demand for safe, liquid investments  Low relative rates, + - curve Trough: Low economic activity; low demand for funds, high demand for safe, liquid investments  Low relative rates, + - curve Growth to Peak: Increasing economic activity; high demand for funds, low demand for interest-rate investments  Higher relative rates, + - to – flattening curve Growth to Peak: Increasing economic activity; high demand for funds, low demand for interest-rate investments  Higher relative rates, + - to – flattening curve Slowdown  Trough; Slowing economic activity, early high demand for funds gives rise to drop off  High rates drop, with inverted-curve returning to positive slope Slowdown  Trough; Slowing economic activity, early high demand for funds gives rise to drop off  High rates drop, with inverted-curve returning to positive slope

Maturity Gap Repricing of Book Values of Assets vs. Liabilities in common time periods Repricing of Book Values of Assets vs. Liabilities in common time periods Pg. 5 of any output Pg. 5 of any output Rate Sensitive Assets (RSAs) and Rate Sensitive Liabilities (RSLs) Rate Sensitive Assets (RSAs) and 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:(Gap = RSA – RSL)  NII = Gap *  R Idea is:(Gap = RSA – RSL)  NII = Gap *  R

Maturity Gap Rates Go Up Rates Go Up Positive Gap  Increase NII Positive Gap  Increase NII Negative Gap  Decrease NII Negative Gap  Decrease NII Rates Go Down Rates Go Down Positive Gap  Decrease NII Positive Gap  Decrease NII Negative Gap  Increase NII Negative Gap  Increase NII Problems: Problems: Ignores Market Value Changes Ignores Market Value Changes Ignores variation in intra-bucket value changes Ignores variation in intra-bucket value changes Concentrates on single-period CF, not MV Concentrates on single-period CF, not MV

Maturity Gap Y1Q4: Y1Q4: 3 month Assets: month Assets: month Liabilities: month Liabilities: RSA – RSL = 3 month Gap = RSA – RSL = 3 month Gap = month Interest Rates go up.25% 3 month Interest Rates go up.25% NII should jump (0.0025*979.45) $2.45 mill NII should jump (0.0025*979.45) $2.45 mill

Duration Gap Duration Weighted Assets and Liabilities Duration Weighted Assets and Liabilities Managing the Change in Equity (Value) from a change in interest rates and their effect on Assets and Liabilities Managing the Change in Equity (Value) from a change in interest rates and their effect on Assets and Liabilities Remember:  Price = - D *  r / (1 + YTM) * Price Remember:  Price = - D *  r / (1 + YTM) * Price Applied to Assets and Liabilities:  A = - D *  R / (1 + R) * A  L = - D *  R / (1 + R) * L Applied to Assets and Liabilities:  A = - D A *  R / (1 + R) * A  L = - D L *  R / (1 + R) * L

Duration Gap Then:  E =  A -  L Then:  E =  A -  L  E = -[ D A - D L (L/A)] * [  R/(1+R)] * A  E = -[ D A - D L (L/A)] * [  R/(1+R)] * A Change in Equity is negative of difference in durations multiplied by interest rate change multiplied by asset base

Duration Gap Rates Go Up Rates Go Up Positive Duration Gap  Decrease Value Positive Duration Gap  Decrease Value Negative Duration Gap  Increase Value Negative Duration Gap  Increase Value Rates Go Down Rates Go Down Positive Duration Gap  Increase Value Positive Duration Gap  Increase Value Negative Duration Gap  Decrease Value Negative Duration Gap  Decrease Value

Duration Gap From 1.4 Output: From 1.4 Output: Assets: Duration = 0.427, Value = $4.897 bill Assets: Duration = 0.427, Value = $4.897 bill Liabs: Duration = 1.103, Value = $4.609 bill Liabs: Duration = 1.103, Value = $4.609 bill Notice……Negatively Gapped! Notice……Negatively Gapped! Assume R=7%  7.05% Assume R=7%  7.05%  E = -[ D A - D L (L/A)] * (  R/(1+R) * A = -[.427 – (4.609/4.897)]*(+.0005/1.07)*4.897 = -[.427 – (4.609/4.897)]*(+.0005/1.07)*4.897 = = +$ million = = +$ million