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Asset and Liability Management Interest Rate Risk Management

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Asset and Liability Management Managing Interest Rate Risk Unexpected changes in interest rates can significantly alter a bank’s profitability and market value of equity.

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Figure 8-1 Interest Rate (Percent) Monthly Average Rates Fed Funds 10-Year Treasury 198019811982198319841985198619871988198919901991199219931994 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2

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Interest Rate Risk Reinvestment rate risk - Cost of funds vrs return on assets. => Funding GAP, impact on NII. Price Risk - Change in interest rates will cause a change in the value (price) of assets and liabilities. -Longer maturity (duration) -- > larger change in value for a given change in interest rates. =>Duration GAP, impact on market value of equity.

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Funding GAP: Focus on managing NII in the short run. Method Group assets and liabilities into time "buckets" according to when they mature or re-price. Calculate GAP for each time bucket Funding GAP t = $ Value RSA t - $ Value or RSL t where t = time bucket; e.g., 0-3 months.

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Factors Affecting NII. Changes in the level of i-rates. NII = (GAP) * ( i exp. ) Changes in the volume of assets and liab. Change in the composition of assets and liab. Changes in the relationship between asset yields and liab. cost of funds.

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Exhibit 8.3 Expected Balance Sheet for Hypothetical Bank AssetsYieldLiabilitiesCost Rate sensitive5008.0%6004.0% Fixed rate35011.0%2206.0% Non earning150100 920 Equity 80 Total1000 NII =(0.08x500+0.11x350)-(0.04x600+0.06x220) 78.5-37.2=41.3 NIM =41.3 / 850=4.86% GAP =500-600=-100

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Exhibit 8.4 1% increase in the level of all short-term rates. 1% decrease in spread between assets yields and interest cost. RSA increase to 8.5% RSL increase to 5.5% Proportionate doubling in size. Increase in RSAs and decrease in RSL’s RSA = 540, fixed rate = 310 RSL = 560, fixed rate = 260.

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1% Increase in Short-Term Rates Expected Balance Sheet for Hypothetical Bank AssetsYieldLiabilitiesCost Rate sensitive5009.0%6005.0% Fixed rate35011.0%2206.0% Non earning150100 920 Equity 80 Total1000 NII =(0.09x500+0.11x350)-(0.05x600+0.06x220) 83.5-43.2=40.3 NIM =40.3 / 850=4.74% GAP =500-600=-100

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1% Decrease in Spread Expected Balance Sheet for Hypothetical Bank AssetsYieldLiabilitiesCost Rate sensitive5008.5%6005.5% Fixed rate35011.0%2206.0% Non earning150100 920 Equity 80 Total1000 NII =(0.085x500+0.11x350)-(0.055x600+0.06x220) 81-46.2=34.8 NIM =34.8 / 850=4.09% GAP =500-600=-100

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Proportionate Doubling in Size Expected Balance Sheet for Hypothetical Bank AssetsYieldLiabilitiesCost Rate sensitive10008.0%12004.0% Fixed rate70011.0%4406.0% Non earning300200 1840 Equity 160 Total2000 NII =(0.08x1000+0.11x700)-(0.04x1200+0.06x440) 157-74.4=82.6 NIM =82.6 / 1700=4.86% GAP =1000-1200=-200

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Increase in RSAs and Decrease in RSLs Expected Balance Sheet for Hypothetical Bank AssetsYieldLiabilitiesCost Rate sensitive5408.0%5604.0% Fixed rate31011.0%2606.0% Non earning150100 920 Equity 80 Total1000 NII =(0.08x540+0.11x310)-(0.04x560+0.06x260) 77.3-38=39.3 NIM =39.3 / 850=4.62% GAP =540-560=-20

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Rate Sensitivity Reports Periodic GAP Gap for each time bucket. Measures the timing of potential income effects from interest rate changes. Cumulative GAP Sum of periodic GAP's. Measures aggregate interest rate risk over the entire period. Examine Exhibit 8.5:

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Break Even Analysis Focus on repriceable assets and calculate a break-even yield required to maintain stable NII after a rate change. Method: 1.Calculate repriceable assets and liab. for the desired period. 2.Calculate funding GAP for the period. 3.Calculate interest income for the period Int Inc. = r RSA x (n/365) x $RSA 4.Calculate interest expense for the period. 5.Calculate NII.

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Break Even Analysis (Cont.) Forecast Break-Even yield on assets 5.Calculate NII. 6.Calculate new interest expense on RSL that rolled over. Int exp. = r RSL forcasted x (n/365) x $RSL 7.Calculate interest expense on "new money" Int exp. on new money = r new money x (n/365) x $amt of new money 8.Calculate required interest income = 5.) + 6.) + 7.) 9.Calculate break even asset yield for the use of new money. Break even rate = [8.) net new money] x (365/n)

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Break Even Analysis (Cont.) Calculate Break Even Asset YieldAnnualized Average Rate Rollover of RSA and RSL's$ amount Rates Unchanged Repriceable assets21,300,000 14.10% Repriceable liabilities28,300,000 9.50% GAP(7,000,000) Interest income (next 30 days)246,847 =21.3mx0.141x(30/360) Interest expense (next 30days)220,973 =28.3mx0.095x(30/360) Net interest return25,874 Forecasted Break-even Yield on Assets "New" Int exp. on existing RSL-2.00%216,321 9.30% Int exp on new money1.00 mill8,548 10.40% Target net spread on repriceables25,874 Required interest income250,742 Break even asset yield (annualied)250,742x(30/365) =13.70% 21300000+1000000(1-0.03)

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Speculating on the GAP. NII = (GAP) * ( i exp ) Speculating on the GAP 1.Difficult to vary the GAP and win. 2.Requires accurate interest rate forecast on a consistent basis. 3.Usually only look short term. 4.Only limited flexibility in adjusting the GAP, customers and depositors. 5.No adjustment for timing of cash flows or dynamics of the changing GAP position.

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Duration GAP Focus on managing NII or the market value of equity, recognizing the timing of cash flows Interest rate risk is measured by comparing the weighted average duration of assets with liab. Asset duration > Liability duration interest rates Market value of equity falls

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Duration vrs maturity 1.)1000 loan, principal + interest paid in 20 years. 2.)1000 loan, 900 principal in 1 year, 100 principal in 20 years. 1000 + int |------------------------------|--------------------------- -| 0 10 20 900+int 100 + int |---|--------------------------|--------------------------- -| 0 10 20 What is the maturity of each? What is the "effective" maturity? 1.)= 20 years 2.) = [(900/100) x 1]+[(100/1000) x 20] = 2.9 yrs Duration, however, uses a weighted average of the present values.

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Duration Approximate measure of the market value of interest elasticity Price (value) changes Longer maturity/duration larger changes in price for a given change in i-rates. Larger coupon smaller change in price for a given change in i-rates.

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Calculate Duration Examples: 1000 face value, 10% coupon, 3 year, 12% YTM

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Calculate Duration Examples: 1000 face value, 10% coupon, 3 year, 12% YTM

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If YTM = 5% 1000 face value, 10% coupon, 3 year, 5% YTM

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If YTM = 20% 1000 face value, 10% coupon, 3 year, 20% YTM

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If YTM = 12% and Coupon = 0 1000 face value, 0% coupon, 3 year, 12% YTM 1000 |-------|-------|-------| 0 1 2 3

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If YTM = 12% and Coupon = 0 1000 face value, 0% coupon, 3 year, 12% YTM 1000 |-------|-------|-------| 0 1 2 3 = 3 by definition

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Relate Two Types of Interest Rate Risk Reinvestment rate risk Price risk. If i-rate YTM from reinvestment of the cash flows and holding period return (HPR) increases. If you sell the security prior to maturity then the price or value falls, hence HPR falls. Increases in i-rates will improve HPR from a higher reinvestment rate but reduce HPR from capital losses if the security is sold prior to maturity. An immunized security is one in which the gain from the higher reinvestment rate is just offset by the capital loss. This point is where your holding period equals the duration of the security.

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Duration GAP at the Bank The bank can protect either the market value of equity (MVE) or the book value of NII, but not both. To protect the MVE the bank would set DGAP to zero: DGAP = DA - u x DL. whereDA= weighted average duration of assets, DL= weighted average duration of liabs,

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Exhibit 8.8 click for other examples

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Exhibit 8.8

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Calculating DGAP In exhibit 8.8: DA = (700 / 1000) * 2.65 + (200 / 1000) * 5.97 = 3.05 DA = (520 / 920) * 1.00 + (400 / 920) * 3.48 = 2.08 DGAP = 3.00 - (920 / 1000) * 2.06 = 1.14 years What does 1.14 mean? The average duration of assets > liabilities, hence asset values change by more than liability values.

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What is the minimum risk position? To eliminate the risk of changes in the MVE, what do they have to change DA or DL by? Change DA = -1.14 Change DL = +1.14/u = 1.24

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Exhibit 8.9

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Calculating DGAP In exhibit 8.9: DA = (684 / 974) * 2.64 + (189 / 974) * 5.89 = 3.00 DA = (515 / 903) * 1.00 + (387 / 903) * 3.48 = 2.06 DGAP = 3.00 - (903 / 974) * 2.06 = 1.09 years What does 1.09 mean? The average duration of assets > liabilities, hence asset values change by more than liability values.

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Change in the Market Value of Equity Using the relationship:

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Change in the Market Value of Equity Using the relationship: We can define the change in the MVE as: In our case: MVE = (-1.14) x [+0.01 / (1.1356)] x 1,000 = -$10.04

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