![Change in the Market Value of
Equity
∆V
Using the relationship:
%∆ V
DUR ≅ V ≅
∆i % ∆i
1+i
We can define the change in ∆MVE as:
the
i
∆ ≅
MVE (− ) ×
DGAP ×
TA
+
(1 iearnassets )
In our case:
∆MVE = (-1.14) x [+0.01 / (1.1356)] x 1,000
= -$10.04](https://image.slidesharecdn.com/alminterestrateriskmanagement-120919124850-phpapp02/85/Alm-interest-rate-risk-management-38-320.jpg)
Alm interest rate risk management
- 1. Asset and Liability Management Interest Rate Risk Management
- 2. 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.
- 3. Figure 8-1 Interest Rate (Percent) 20 19 18 Fed Funds 17 10-Year Treasury 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 Monthly Average Rates
- 4. 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
- 5. 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 GAPt = $ Value RSAt - $ Value or RSLt where t = time bucket; e.g., 0-3 months.
- 6. Factors Affecting NII. Changes in the level of i-rates. ∆NII = (GAP) * (∆iexp.) 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.
- 7. Exhibit 8.3 Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive 500 8.0% 600 4.0% Fixed rate 350 11.0% 220 6.0% Non earning 150 100 920 Equity 80 Total 1000 1000 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
- 8. 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.
- 9. 1% Increase in Short-Term Rates Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive 500 9.0% 600 5.0% Fixed rate 350 11.0% 220 6.0% Non earning 150 100 920 Equity 80 Total 1000 1000 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
- 10. 1% Decrease in Spread Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive 500 8.5% 600 5.5% Fixed rate 350 11.0% 220 6.0% Non earning 150 100 920 Equity 80 Total 1000 1000 NII = (0.085x500+0.11x350) - (0.055x600+0.06x220) 81 - 46.2 = 34.8 NIM = 34.8 / 850 = 4.09% GAP = 500 - 600 = -100
- 11. Proportionate Doubling in Size Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive 1000 8.0% 1200 4.0% Fixed rate 700 11.0% 440 6.0% Non earning 300 200 1840 Equity 160 Total 2000 2000 NII = (0.08x1000+0.11x700) - (0.04x1200+0.06x440) 157 - 74.4 = 82.6 NIM = 82.6 / 1700 = 4.86% GAP = 1000 - 1200 = -200
- 12. Increase in RSAs and Decrease in RSLs Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive 540 8.0% 560 4.0% Fixed rate 310 11.0% 260 6.0% Non earning 150 100 920 Equity 80 Total 1000 1000 NII = (0.08x540+0.11x310) - (0.04x560+0.06x260) 77.3 - 38 = 39.3 NIM = 39.3 / 850 = 4.62% GAP = 540 - 560 = -20
- 13. 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:
- 14. Time Frame for Rate Sensitivity Assets 1-7 8-30 31-90 91-180 181-365 > 1 yr Not RS Total U.S. Treasury 0.7 3.6 1.2 0.3 3.7 9.5 MM Inv 1.2 1.8 3 Municipals 0.7 1 2.2 7.6 11.5 FF & Repo's 5 5 Comm loans 1 13.8 2.9 4.7 4.6 15.5 42.5 Install loans 0.3 0.5 1.6 1.3 1.9 8.2 13.8 Cash 9 9 Other assets 5.7 5.7 Total Assets 6.3 15 10 10 9 35 14.7 100 Liabilities and Equity MMDA 17.3 17.3 Super NOW 2.2 2.2 CD's < 100,000 0.9 2 5.1 6.9 1.8 2.9 19.6 CD's > 100,000 1.9 4 12.9 7.9 1.2 27.9 FF purchased 0 NOW 9.6 9.6 Savings 1.9 1.9 DD 13.5 13.5 Other liabilities 1 1 Equity 7 7 Total Liab & Eq. 22.3 6 18 24.4 3 4.8 21.5 100 GAP Periodic GAP -16 9 -8 -14.4 6 30.2 Cumulative GAP -16 -7 -15 -29.4 -23.4 6.8
- 15. 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. = rRSA x (n/365) x $RSA 4. Calculate interest expense for the period. 5. Calculate NII.
- 16. 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. = rRSL forcasted x (n/365) x $RSL 7. Calculate interest expense on "new money" Int exp. on new money = rnew 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
- 17. Break Even Analysis (Cont.) Calculate Break Even Asset Yield Annualized Average Rate Rollover of RSA and RSL's $ amount Rates Unchanged Repriceable assets 21,300,000 14.10% Repriceable liabilities 28,300,000 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 return 25,874 Forecasted Break-even Yield on Assets "New" Int exp. on existing RSL -2.00% 216,321 9.30% Int exp on new money 1.00 mill 8,548 10.40% Target net spread on repriceables 25,874 Required interest income 250,742 Break even asset yield (annualied) 250,742x(30/365) = 13.70% 21300000+1000000(1-0.03)
- 18. Speculating on the GAP. ∆NII = (GAP) * (∆ iexp) 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.
- 19. 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
- 20. 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
- 21. Duration Approximate measure of the market value of interest elasticity ∆V %∆ V DUR ≅ V ≅ ∆i % ∆i 1+i 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.
- 22. Calculate Duration n n n n Ctt(t) Ctt(t) ∑ (1 + r)tt ∑ (1 + r)tt DUR = t=1 t=1 n n = t=1 t=1 Ctt PV of the Sec. ∑ (1 + r)tt t=1 t=1 Examples: 1000 face value, 10% coupon, 3 year, 12% YTM
- 23. Calculate Duration n n n n Ctt(t) Ctt(t) ∑ (1 + r)tt ∑ (1 + r)tt DUR = t=1 t=1 n n = t=1 t=1 Ctt PV of the Sec. ∑ (1 + r)tt t=1 t=1 Examples: 100 * 1 100 * 2 100 * 3 1000 * 3 1000 face+value, 10% coupon, 3 year, (1.12)11 + (1.12)22 (1.12) 3 3 + (1.12)33 2597.6 D= = = 2.73 years 12% YTM100 3 3 1000 951.96 ∑ (1.12) tt + (1.12)3 3 t=1 t=1
- 24. If YTM = 5% 1000 face value, 10% coupon, 3 year, 5% YTM 100 * 1 100 * 2 100 * 3 1000 * 3 1 + 2 + 3 + (1.05) 1 (1.05) 2 (1.05) 3 (1.05)33 D= 1136.16 3127.31 D= = 2.75 years 1136.16
- 25. If YTM = 20% 1000 face value, 10% coupon, 3 year, 20% YTM 2131.95 D= = 2.68 years 789.35
- 26. If YTM = 12% and Coupon = 0 1000 face value, 0% coupon, 3 year, 12% YTM 1000 |-------|-------|-------| 0 1 2 3
- 27. If YTM = 12% and Coupon = 0 1000 face value, 0% coupon, 3 year, 12% YTM 1000 |-------|-------|-------| 0 1000 * 3 2 1 3 (1.12)3 3 D= 1000 (1.12)3 3 = 3 by definition
- 28. 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.
- 29. 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,
- 30. click for other 1 Exhibit 8.8 Exhib it 8.8 examples Par Years $1,000 % Coup Mat. YTM Market Value Dur. Assets Cash 100 100 Earning assets Commercial loan 700 14.00% 3 14.00% 700 2.65 Treasury bond 200 12.00% 9 12.00% 200 5.97 Total Earning Assets 900 13.56% 900 Non-cash earning assets 0 0 Total assets 1000 12.20% 1000 3.05 Liabilities Interest bearing liabs. Time deposit 520 9.00% 1 9.00% 520 1.00 Certificate of deposit 400 10.00% 4 10.00% 400 3.49 Tot. Int Bearing Liabs. 920 9.43% 920 Tot. non-int. bearing 0 0 Total liabilities 920 9.43% 920 2.08 Total equity 80 80 Total liabs & equity 1000 1000
- 31. 1 Exhibit 8.8 Par Years $1,000 % Coup Mat. YTM Market Value Dur. Assets Cash 100 100 Earning assets Commercial loan 700 14.00% 3 14.00% 700 2.65 Treasury bond 200 12.00% 9 12.00% 200 5.97 98 × 1 × 98 × 700 × 900 Total Earning Assets 989001 3 13.56%3 1 + 02 + 3 + 3 Non-cash earning assets 0 Total dur =.14) assets (1 (1.14) (1.14) 1000 (1.14) 1000 12.20% 3.05 Liabilities 700 Interest bearing liabs. Time deposit 520 9.00% 1 9.00% 520 1.00 Certificate of deposit 400 10.00% 4 10.00% 400 3.49 Tot. Int Bearing Liabs. 920 9.43% 920 Tot. non-int. bearing 0 0 Total liabilities 920 9.43% 920 2.08 Total equity 80 80 Total liabs & equity 1000 1000
- 32. 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.
- 33. 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
- 34. Exhibit 8.9 1 Par Years Market $1,000 % Coup Mat. YTM Value Dur. Assets Cash 100 100 Earning assets Commercial loan 700 14.00% 3 15.00% 684.02 2.64 Treasury bond 200 12.00% 9 13.00% 189.74 5.89 Total Earning Assets 900 14.57% 873.75 Non-cash earning assets 0 0 Total assets 1000 13.07% 973.75 3.00 Liabilities Interest bearing liabs. Time deposit 520 9.00% 1 10.00% 515.27 1.00 Certificate of deposit 400 10.00% 4 11.00% 387.59 3.48 Tot. Int Bearing Liabs. 920 10.43% 902.86 Tot. non-int. bearing 0 0 Total liabilities 920 10.43% 902.86 2.06 Total equity 80 70.891 Total liabs & equity 1000 973.75
- 35. Exhibit 8.9 1 Par Years Market $1,000 % Coup Mat. YTM Value Dur. Assets Cash 100 100 Earning assets Commercial loan 700 14.00% 3 15.00% 684.02 2.64 Treasury bond 200 12.00% 9 13.00% 189.74 5.89 Total Earning Assets 900 14.57% 873.75 Non-cash earning assets 3 0 0 98 1000700 Total assets = PV ∑ ) (1.15 + t (1.15)3 13.07% 973.75 3.00 Liabilities t= 1 Interest bearing liabs. Time deposit 520 9.00% 1 10.00% 515.27 1.00 Certificate of deposit 400 10.00% 4 11.00% 387.59 3.48 Tot. Int Bearing Liabs. 920 10.43% 902.86 Tot. non-int. bearing 0 0 Total liabilities 920 10.43% 902.86 2.06 Total equity 80 70.891 Total liabs & equity 1000 973.75
- 36. 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.
- 37. Change in the Market Value of Equity Using the relationship: ∆V V %∆ V DUR ≅ ≅ ∆i % ∆i 1+i
- 38. Change in the Market Value of Equity ∆V Using the relationship: %∆ V DUR ≅ V ≅ ∆i % ∆i 1+i We can define the change in ∆MVE as: the i ∆ ≅ MVE (− ) × DGAP × TA + (1 iearnassets ) In our case: ∆MVE = (-1.14) x [+0.01 / (1.1356)] x 1,000 = -$10.04