1. McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved Chapter Seven Asset-Liability Management: Determining and Measuring Interest Rates and Controlling Interest-Sensitive and Duration Gaps

2. 7-2 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Key Topics Asset, Liability, and Funds Management Market Rates and Interest Rate Risk The Goals of Interest Rate Hedging Interest Sensitive Gap Management Duration Gap Management Limitations of Hedging Techniques

3. 7-3 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Asset-Liability Management The Purpose of Asset-Liability Management is to Control a Bank’s Sensitivity to Changes in Market Interest Rates and Limit its Losses in its Net Income or Equity

4. 7-4 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Historical View of Asset-Liability Management First :Asset Management Strategy –Refers to a strategy where it is assumed that management has control over the allocation of bank assets (loans) but little or no control over funds sources (deposits) Then: Liability Management Strategy –Strategy that focuses on new sources of funds and managing the mix of deposit and non deposit sources of funds by varying the price or interest rates offered Now: Funds Management Strategy –The concept of planning and control over both sides of the balance sheet – assets and liabilities

5. 7-5 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest rates Base (risk free) interest rates are determined by market forces not by individual banks. They are determined by the collective borrowing and lending decisions of thousands of participants in the money and capital markets Lending interest rates are determined by additional risk factors such as default risk, maturity risk and liquidity risk

6. 7-6 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Yield to Maturity (YTM) An interest rate measure

7. 7-7 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Bank Discount Rate (DR) Another interest rate measure Where: FV equals Face Value

8. 7-8 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rates Function of: Risk-Free Real Rate of Interest Various Risk Premiums –Default Risk –Inflation Risk –Liquidity Risk –Call Risk –Maturity Risk

9. 7-9 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Yield Curves Graphical Picture of Relationship Between Yields and Maturities on Securities Generally Created with Treasury Securities to Keep Default Risk Constant Shape of the Yield Curve determines the spread between long term and short term interest rates. Has profound influence on bank’s NIM –Upward – Long-Term Rates Higher than Short-Term Rates –Downward – Short-Term Rates Higher than Long- Term Rates –Horizontal – Short-Term and Long-Term Rates the Same

10. 7-10 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Market Risk Price Risk –When Interest Rates Rise, the Market Value of the Bond or Asset Falls Interest rate risk ( Reinvestment Risk/Refinancing Risk) –When Interest Rates Fall, the Coupon Payments on a Bond or maturing loans are Reinvested at Lower Rates –When interest rates rise the refinancing costs rise

11. 7-11 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest rate risk Financial institutions can lose income or value no matter which way interest rates go Rising rates can lead to losses on security instruments and fixed rate loans as the value of these instruments fall. Rising rates can also cause a loss to income if the bank has more rate sensitive liabilities than assets Falling interest rates can lead to capital gains but could lead to losses if there are more interest rate sensitive assets than liabilities

12. 7-12 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Net Interest Margin

13. 7-13 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Goal of Interest Rate Hedging One Important Goal of Interest Rate Hedging is to Insulate the Bank from the Damaging Effects of Fluctuating Interest Rates on Profits (NIM)

14. 7-14 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Problem If interest revenues are $63 million, interest costs are $42 million, earning assets are 700 million. What is the NIM. If interest costs and interest revenues double while its earning assets increase by 50% what will happen to NIM

15. 7-15 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Solution NIM = 63-42/700 = 3% New NIM = (63-42)*2/700*1.5 = 4%

16. 7-16 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Concept of Gap management Gap management involves the determining the maturity distribution and the repricing schedule for a bank’s assets and liabilities. When more assets are subject to repricing or will reach maturity in a given period than liabilities or vice versa, the Bank has a gap between assets and liabilities and is exposed to loss from an adverse movement in rates based on the gap’s size and direction and period

17. 7-17 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Maturity profile used to identify, measure, manage and control risk MaturityAssetsliabilitiesGap size Cumulative gap Next day$40-$50-10 1 week120-160-40-50 1 month65-105- 40-90 2 months280-250+30-60 3 months455-395+600

18. 7-18 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest-Sensitive Gap Measurements Dollar Interest- Sensitive Gap Interest-Sensitive Assets – Interest Sensitive Liabilities =

19. 7-19 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest-Sensitive Assets Short-Term Securities Issued by the Government and Private Borrowers Short-Term Loans Made by the Bank to Borrowing Customers Variable-Rate Loans Made by the Bank to Borrowing Customers

20. 7-20 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest-Sensitive Liabilities Borrowings from Money Markets Short-Term Savings Accounts Money-Market Deposits Variable-Rate Deposits

21. 7-21 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Asset-Sensitive Bank Has: Positive Dollar Interest-Sensitive Gap

22. 7-22 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Liability Sensitive Bank Has: Negative Dollar Interest-Sensitive Gap

23. 7-23 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Gap Positions and the Effect of Interest Rate Changes on the Bank Asset-Sensitive Bank –Interest Rates Rise NIM Rises –Interest Rates Fall NIM Falls Liability-Sensitive Bank –Interest Rates Rise NIM Falls –Interest Rates Fall NIM Rises

24. 7-24 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Zero Interest-Sensitive Gap Dollar Interest-Sensitive Gap is Zero –When Interest Rates Change in Either Direction - NIM is Protected and Will Not Change

25. 7-25 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Important Decision Regarding IS Gap Management Must Choose the Time Period Over Which NIM is to be Managed Management Must Choose a Target NIM To Increase NIM Management Must Either: –Develop Correct Interest Rate Forecast –Reallocate Assets and Liabilities to Increase Spread Management Must Choose Volume of Interest-Sensitive Assets and Liabilities

26. 7-26 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. NIM Influenced By: Changes in Interest Rates Up or Down Changes in the Spread Between Assets and Liabilities Changes in the Volume of Interest- Sensitive Assets and Liabilities Changes in the Mix of Assets and Liabilities

27. 7-27 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Cumulative Gap The Total Difference in Dollars Between Those Bank Assets and Liabilities Which Can be Repriced over a Designated Time Period

28. 7-28 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Aggressive Interest-Sensitive Gap Management Expected Change in Interest Rates Best Interest- Sensitive Gap Position Aggressive Management’s Likely Action Rising Market Interest Rates Positive IS GapIncrease in IS Assets Decrease in IS Liabilities Falling Market Interest Rates Negative IS GapDecrease in IS Assets Increase in IS Liabilities

29. 7-29 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Problem If interest rate sensitive assets are $870 and interest sensitive liabilities are $625 during the next month. Is the bank asset sensitive or liability sensitive. What happens to NIM if rate rise? What happens to NIM if rates fall

30. 7-30 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Solution As assets sensitive assets are larger the bank is asset sensitive by $245 If rates rise NI increases. If rates fall NIM decreases

31. 7-31 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Problem If the gap for the one year period is + 135 million and rates fall by 2.5% then calculate the expected change in NII. What would happen if rates rise by 1.25%

32. 7-32 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. solution 135 million * -.025 = - 3.38 million 135 million*.0125 = + 1.69

33. 7-33 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Definitions Dollar interest sensitive gap = interest sensitive assets - interest rate sensitive liabilities over asset planning period

34. 7-34 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Problem Suppose interest sensitive assets are 570 million and interest rate sensitive liabilities are 685 million. What is the dollar interest sensitive gap?

35. 7-35 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Solution Dollar interest– sensitive gap = 570 – 685 = -115

36. 7-36 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Problems with Interest-Sensitive Gap Management Interest Paid on Liabilities Tend to Move Faster than Interest Rates Earned on Assets Interest Rate Attached to Bank Assets and Liabilities Do Not Move at the Same Speed as Market Interest Rates Point at Which Some Assets and Liabilities are Repriced is Not Easy to Identify Interest-Sensitive Gap Does Not Consider the Impact of Changing Interest Rates on Equity Position

37. 7-37 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. The Concept of Duration Duration is the Weighted Average Maturity of a Promised Stream of Future Cash Flows. It is a direct measure of price risk.

38. 7-38 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration gap measurement It is the difference between the duration of a bank’s assets and the duration of its liabilities The duration of the banks assets can be determined by taking the weighted average of the duration of all assets in the portfolio The weight is the dollar amount of a particular type of asset out of the total amount of assets The duration of liabilities can be determined in a similar way

39. 7-39 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest rate sensitive gap versus duration Gap only looks at impact of changes in interest rates on net income Duration takes into account the impact of interest rate changes on the market value of the bank’s equity position

40. 7-40 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. To Calculate Duration

41. 7-41 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration of a bank loan calculation Loan term 5 years. Annual interest rate payment is 10% (similar to coupon rate on a bond). The face value of the loan is also its current value because the yield to maturity on the loan is also 10%. What is the loan’s duration

42. 7-42 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration (con’t) CF period CF expected PV @10% Time period PV x t 110090.911 210082.642165.29 310075.133225.39 410068.304273.21 510062.095310.4 51000620.9253104.61 Dur. =4,169.87/1000 =4.17 years

43. 7-43 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Price Sensitivity of a Security

44. 7-44 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Price sensitivity of a security Duration= 4, and interest rates go up from 10 to 11 pct Change in price % = -D x Δ i/1+I -4 x.01/1+.10 = - 3.64% If rate go down from 10 to 9 pct then -4 x -.01/1+.10 = + 3.64%

45. 7-45 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Gap

46. 7-46 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration gap calculation Asset duration is 2.5 years, liability duration is 3 years, total assets = $560 million and total liabilities = $467 million Duration gap = Da –DL* Liabilities/assets = 2.5 yrs – 3 yrs * (467/560) = 2.5 – 2.5018 = -.018 years Slight duration gap. If rates rise the value of liabilities will fall by more than the value of assets resulting in a small increase in net worth Net worth = assets - liabilities

47. 7-47 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration of an Asset portfolio Where: w i = the dollar amount of the ith asset divided by total assets D Ai = the duration of the ith asset in the portfolio

48. 7-48 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration of a Liability Portfolio Where: w i = the dollar amount of the ith liability divided by total liabilities D Li = the duration of the ith liability in the portfolio

49. 7-49 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Change in the Value of a Bank’s Net Worth

50. 7-50 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration gap calculation Asset duration is 3.25 years and liability duration is 1.75 years. The liabilities amount to $485 million while assets total $512 million. Interest rates rise form 7 to 8 per cent. What happens to the net worth.

51. 7-51 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. solution First calculate duration gap. Duration gap = 3.25 yrs – 1.75 yrs *485/512 = + 1.5923 The change in net worth due to the increase in interest rates is = {-3.25yrsx.01/(1+.07) x $512} – {-1.75 yrs x.01/(1+.07) x $485 mill } = -7.62

52. 7-52 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Impact of Changing Interest Rates on a Bank’s Net Worth PositiveInterest Rate RiseNW Decrease D. GapInterest Rate FallNW Increase NegativeInterest Rate RiseNW Increase D. GapInterest Rate FallNW Decrease ZeroInterest Rate RiseNo Change D. GapInterest Rate FallNo Change

53. 7-53 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Limitations of Duration Gap Management Finding Assets and Liabilities of the Same Duration Can be Difficult Some Assets and Liabilities May Have Patterns of Cash Flows that are Not Well Defined Customer Prepayments May Distort the Expected Cash Flows in Duration Customer Defaults May Distort the Expected Cash Flows in Duration Convexity Can Cause Problems