1. Copyright 2002, A.S. Cebenoyan1 Finance 208 Seminar in Financial Institutions Professor A. Sinan Cebenoyan Frank G. Zarb School of Business Hofstra University Overview – Risks Set two

2. Copyright 2002, A.S. Cebenoyan2 Risks of Financial Intermediation Interest Rate Risk: The risk incurred by an FI when the maturity of its assets and liabilities are mismatched. 0 Liabilities 1 0 12 Assets Suppose the cost of Funds (liabilities) is 9 %, and interest return on assets is 10%. Profit spread of 1%. But there is Refinancing Risk - The Risk that the cost of rolling over or reborrowing funds will rise above the returns being earned on asset investments.

3. Copyright 2002, A.S. Cebenoyan3 Reinvestment Risk - The risk that the returns on funds to be reinvested will fall below the cost of funds 0 1 2 Liabilities 0 1 Assets FI borrows at 9%, and invests in an asset yielding 10%. But at what rate will reinvestment take place? Market Value Risk: As interest rates rise market value of assets or liabilities will fall. Moreover, mismatching maturities by holding longer term assets than liabilities implies when rates rise asset MVs fall more than liabilities. This could lead to economic loss and insolvency.

4. Copyright 2002, A.S. Cebenoyan4 Market Risk - The Risk incurred in the trading of assets and liabilities due to changes in interest rates, exchange rates, and other asset prices. –Barings Bank lost $1.2 billion on its trading position (buying Futures on the Nikkei index and betting the index would rise) Credit Risk - The risk that the promised cash flows from loans and securities held by FIs may not be paid in full. Virtually, all types of FIs face this risk. However, those that make loans or buy bonds with long- maturities are more exposed (banks, thrifts, and life insurance co.s). Default of a borrower puts both the principal and the interest payments at risk. –Diversification helps. Firm Specific Credit Risk is reduced, while the FI is still exposed to Systematic Credit Risk

5. Copyright 2002, A.S. Cebenoyan5 Off-Balance-Sheet Risk - The Risk incurred by an FI due to activities related to contingent assets. While all FIs, to some extent, engage in Off-Balance-Sheet activities, mostly larger banks have drawn attention. –For example: A letter of Credit which is a guaranty issued by an FI for a fee (makes it attractive) on which payment is contingent on the default of the agent that purchases the letter of credit. Nothing appears on the B/S but the fee appears on the income statement. Technology and Operational Risk –Purpose of technology is to lower operating costs, increase profits and capture new markets for the FI. –Economies of Scale: The degree to which an FI’s average unit costs of producing financial services fall as its output of services increase –Economies of Scope:The degree to which an FI can generate cost synergies by producing multiple financial service products. –Technology Risk occurs when technological investments do not produce the anticipated cost savings.

6. Copyright 2002, A.S. Cebenoyan6 - Operational Risk : The risk that existing technology or support systems may malfunction or break down. Foreign Exchange Risk: The risk that exchange rate changes can affect the value of an FI’s assets and liabilities located abroad. If a U.S. FI is net long in foreign currency denominated assets, any depreciation of the foreign currency against the US dollar would lead to a loss for the U.S. FI. If a net short position prevails, then an appreciation of the foreign currency would lead to a loss. - Even if we match the amounts of the assets and liabilities, we would still not be fully hedged if we have exposure to foreign interest rate risk from a maturity mismatch (simple maturity matching does not lead to a good hedge either, we need to match durations, but more on that later). Country or Sovereign Risk: The risk that repayments from foreign borrowers may be interrupted because of interference from foreign governments. RUNLiquidity Risk : The risk that a sudden surge in liability withdrawals may leave an FI in a position of having to liquidate assets in a very short period of time and at low prices. ( Fire-Sale ) (RUN!) Insolvency Risk: Not having enough capital to offset a decline in asset values.

7. Copyright 2002, A.S. Cebenoyan7 Interest Rate Risk The Repricing Model Also called the funding gap model. A book value accounting cash flow analysis of the repricing gap between the interest revenue earned on an FI’s assets and the interest paid on its liabilities over some particular period. Repricing Gap:The difference between those assets whose interest rates will be repriced or changed over some future period (Rate sensitive assets) and liabilities whose interest rates will be repriced or changed over some future period (Rate sensitive liabilities).

8. Copyright 2002, A.S. Cebenoyan8 AssetsLiabilities Gaps ____________________________________________ __ 1 day$20$30$-10 1day-3mos 30 40 -10 3mos-6mos 70 85 -15 6mos-12mos 90 70 +20 1yr-5yrs 40 30 +10 over 5yrs 10 5 +5 ___________________ $260 $260 0 The above breakdown in maturities has been required by the Fed from all banks in the form of repricing gaps.

9. Copyright 2002, A.S. Cebenoyan9 Bank calculates the gaps in each bucket, by looking at rate sensitivity of each asset and liability (time to repricing).  NII i = (GAP i )  R i = (RSA i - RSL i )  R i The above applies to any i bucket. This can also be extended to incorporate cumulative gaps Look at cumulative gap for the one-year repricing gap CGAP= -10 + -10 + -15 + 20 = -$15 If the interest rates that apply to this bucket rise by 1 percent  NII 1-yr = (-$15million)(.01) = -$150,000

10. Copyright 2002, A.S. Cebenoyan10 AssetsLiabilities ____________________________________________ _____ ST consumer loans$50Equity Capital $20 (1-yr mat.) LT consumer loans 25Demand deposits 40 (2-yr mat.) 3 mos. T-bills 30Passbook svngs 30 6 mos T notes 353 mos CDs 40 3yr T bonds 703 mos BA’s 20 10yr,fixed-rt mtgs 206 mos Comm.P. 60 30yr floating-rt mtgs 401yr Time deps 20 (rate adj. Every 9mos) 2yr time deps 40 -------------- $270$270

11. Copyright 2002, A.S. Cebenoyan11 Rate Sensitive Assets----One year –ST consumer loans$50 –3 month T-bills 30 –6 month T-notes 35 –30 year floating mtgs 40 $155 Rate sensitive Liabilities----One year –3 month CDs$40 –3 month BA’s 20 –6 month Comm. Paper 60 –1 year Time deps. 20 $140 CGAP =RSA - RSL = 155-140 =$15 million If the rates rise by 1 percent >>>  NII=15(.01)=$150,000

12. Copyright 2002, A.S. Cebenoyan12 Arguments against inclusion of DD: –explicit interest rate on DD is zero –transaction accounts (NOW), rates sticky –Many DD are core deps, meaning longterm Arguments for inclusion of DD: –implicit interest rates (not charging fully for checks) –if rates rise, deposits are drawn down, forcing bank to replace them with higher- yield rate-sensitive funds Similar arguments for passbook savings accounts

13. Copyright 2002, A.S. Cebenoyan13 Weaknesses of The Repricing Model Market Value effects (true exposure not captured) Overaggregation (mismatches within buckets) liabilities may be repriced at different times than assets in the same bucket. Runoffs : are periodic cash flows of interest and principal amortization payments on long-term assets such as conventional mortgages that can be reinvested at market rates. AssetsRunoffsLiabilities Runoffs _________________ 1 yr______________________ 1yr______ ST consumer loans $50Equity Capital$20 LT consumer loans 520Demand deposits 30 10 3 mos. T-bills 30Passbook svngs 15 15 6 mos T notes 353 mos CDs 40 3yr T bonds 10 603 mos BA’s 20 10yr,fixed-rt mtgs 2 186 mos Comm.P. 60 30yr floating-rt mtgs 401yr Time deps 20 2yr time deps 20 20 ---------------------------- $172 98$$205$65

14. Copyright 2002, A.S. Cebenoyan14 Interest Rate Risk The Maturity Model Market Value Accounting: The assets and liabilities of the FI are revalued according to the current level of interest rates. Examples: –How interest rate changes affect bond value: 1 year bond, 10% coupon, $100 face value, R=10% –Sells at par, $100 –if interest rates go up, R=11%, sells at 99.10 –capital loss (  P 1 ) = $0.90 per $100 value –(  P  R)< 0 –Rising interest rates generally lower the market values of both assets and liabilities of an FI.

15. Copyright 2002, A.S. Cebenoyan15 Show the effect of the same interest rate change if the bond is a two-year bond, all else equal. –At R=10%, still sells at par –At R=11%, P 2 = $98.29 –But  P 2 = 98.29 - 100 = -1.71% –Thus, the longer the maturity of a fixed-income asset or liability, the greater its fall in price and market value for any given increase in the level of market interest rates. But, this increase in the fall of value happens at a diminishing rate as time to maturity goes up. Maturity Model with a Portfolio of Assets & Liabilities –M A or M L designates the weighted average of assets and liabilities. –If bank has $100 in 3 year, 10% coupon bonds, and had raised $90 with 1-year deposits paying 10%, Show effects of a 1% rise in R. –Show effects of a 7% rise

16. Copyright 2002, A.S. Cebenoyan16 Original B/S ___A________L_____ _ A=100L=90 (1 year) ( 3 year) E=10 1% rise in Int. rates ___A________L_____ _ A=97.56L=89.19 E=8.37  E  L -1.63 = (-2.44) - (- 0.81) 7% rise in Int. rates ___A________L_____ _ A=84.53L=84.62 E=-0.09  E  L -10.09 = -15.47 - (- 5.38) Bank is insolvent. The situation is tragic if bank has extreme Asset Liability mismatch

17. Copyright 2002, A.S. Cebenoyan17 In the case of Deep Discount (zero coupon) Bonds, the problem is extreme, and the implications are disastrous. –Show the effect on the same balance sheet, if the assets were 30-year deep-discount bonds. A 1% increase in interest rates, reduces the value of the 30-yr bond by -23.73% per $100. Thus the bank will have net worth of -12.92 completely and massively insolvent. Maturity matching, by setting M A = M L, and having a maturity gap of 0, seems like might help. Let’s see: Maturity Matching and Interest Rate Risk Exposure –Won’t work. Example: –Bank issues a one-year CD to a depositor, with a face value of $100, and 15% interest. So, $115 is due the depositor at year 1. –Same bank lends to borrower $100 for one year at 15%, But requires half to be repaid in six months, the other half at end of year (plus interest, of course).

18. Copyright 2002, A.S. Cebenoyan18 Maturities are matched, and if interest rates remain at 15% throughout the year: – at half-year, bank receives $50 + $7.5 in interest (100 x.5 x.15), $57.5 –at end-of-year, bank receives $50 + $3.75 in interest (50 x.5 x.15) plus the reinvestment income from the $57.5 received at half-year, (57.5 x.5 x.15), $4.3125, for a total of $58.06. –Bank pays off the CD at $115, and has made $0.5625 BUT, if interest rates fell to 12% in the middle of the year, this would not affect the 15% on the loan, nor the 15% on the CD, but reinvestment of the $57.5 will have to be at 12%, THUS: –at half-year bank still gets $57.50 –at end of year, bank receives $53.75 from loan, but $3.45 from reinvestment of the $57.50 (57.5 x.5 x.12), a total of $114.7. –Bank pays off CD at $115, and loses $0.3, despite maturity matching of assets and liabilities. DURATION next.

19. Copyright 2002, A.S. Cebenoyan19 Interest Rate Risk The Duration Model Duration and duration gap are more accurate measures of an FI’s interest rate risk exposure Interest elasticity - Interest sensitivity of an asset or liability’s value More complete measure as it takes into account time of arrival of all cash flows as well as maturity of asset or liability

20. Copyright 2002, A.S. Cebenoyan20 Same loan example as before: $57.5 at half-year, and $53.75 at 1-yr. Taking present values at 15%: PV at half-year = 57.5 / (1.075) = 53.49 PV at one-year = 53.75 / (1.075) 2 = 46.51 Notice Present Values add up to $100. Duration is the weighted-average time to maturity using the relative present values of the cash flows as weights. Relative present value at half year = 53.49 /100 =.5349 Relative present value at one-year = 46.51 /100 =.4651 D Loan =.5349 (1/2) +.4651 (1) =.7326 If financed by the one-year CD, D CD = 1, Negative Duration Gap!!!

21. Copyright 2002, A.S. Cebenoyan21 General Formula for Duration Examples: Duration of a Six-Year Eurobond. Show 4.993 years Duration of a 2-year Treasury Bond. Show 1.88 years Duration of Zero-coupons. Always equal to maturity. Duration of a Perpetuity = 1 + (1/R)

22. Copyright 2002, A.S. Cebenoyan22 Features of Duration: Maturity Yield Coupon Interest

23. Copyright 2002, A.S. Cebenoyan23 The Economic Meaning of Duration Start with price of a coupon-bond: We are after a measure of interest rate sensitivity, So:

24. Copyright 2002, A.S. Cebenoyan24 Remember the concept of elasticity from economics, such as income elasticity of demand: Remember also our definition of Duration: Notice that the denominator is just the price of the bond,

25. Copyright 2002, A.S. Cebenoyan25 Notice that the right hand side is identical to the term in brackets in the last equation on slide number 11. So substitute DP into that equation, we get: Interest elasticity of price?

26. Copyright 2002, A.S. Cebenoyan26 A further rearrangement allows us to measure price changes as a function of duration: Applications: The 6-year Eurobond with an 8% coupon and 8% yield, had a duration of D = 4.99 years. If yields rose 1 basis point, then: dP/P = -(4.99) [.0001/1.08] = -.000462 or -0.0462% To calculate the dollar change in value, rewrite the equation above = (1,000)(-4.99)(.0001/1.08)= $0.462 The bond price falls to $999.538 after a one basis point increase in yields.

27. Copyright 2002, A.S. Cebenoyan27 Obviously the higher the duration the higher will be the proportionate drop in prices as interest rates rise. A note on semiannual coupon adjustment to the duration - price relationship: Duration and Immunization FI needs to make a guaranteed payment to an investor in five years (in 2004) an amount of $1,469. If It invests in the market and hopes that the rates will not fall in the next five years it would be very risky (and stupid), after all the payment is guaranteed! What to do? Two alternatives: Buy five-year maturity Discount (Zero coupon) Bonds Buy five-year duration coupon bond

28. Copyright 2002, A.S. Cebenoyan28 If interest rates are 8%, $1,000 would be worth $1,469 in five years. Buy 1.469 five-year zeros at $680.58 for 1 bond, paying $1,000, and you are guaranteed $1,469 in five years. Duration and maturity are matched, no reinvestment risk. All OK. If on the other hand, FI buys the six-year maturity 8% coupon, 8% yield Eurobond with duration of 4.99 years, AND: Interest rates remain at 8%: Cash Flows: Coupons, 5x80$400 Reinvestment (80xFVAF)-400 69 Proceeds from sale of bond, end of year 5 1,000 $1,469

29. Copyright 2002, A.S. Cebenoyan29 If interest rates instantaneously fall to 7% Coupons$400 Reinvestment Income 60 Proceeds from sale of bond1,009 $1,469 If interest rates instantaneously rise to 9% Coupons$400 Reinvestment 78 Bond sale 991 $1,469 Matching the duration of any fixed income instrument to the FI’s investment horizon immunizes it against instantaneous interest rate shocks.

30. Copyright 2002, A.S. Cebenoyan30 Duration Gap for a Financial Institution Let D A be the weighted average duration of the asset portfolio of the FI, and D L be the weighted average duration of the liabilities portfolio, Then And since  E =  A -  L, Multiply both sides with 1/A, we get

31. Copyright 2002, A.S. Cebenoyan31 Where k = L / A,a measure of FI’s leverage. The above equation gives us the effect of interest rate changes on the market value of an FI’s equity or net worth, and it breaks down into three effects: 1.The leverage adjusted duration gap = [D A -D L k] the larger this gap in absolute terms, the more exposure 2.The size of the FI. The larger the scale of the FI the larger the dollar size of net worth exposure 3.Size of the interest rate shock. The larger the shock, the greater the exposure.

32. Copyright 2002, A.S. Cebenoyan32 Example: Suppose D A = 5 years, and D L = 3 years. For an FI with $100 million in assets and $90 million in liabilities (with a net worth of $10 million), the impact of an immediate 1 percent (  R =.01) increase in interest rates from a base of 10% on the equity of the FI would be:  E = -(5-(.9)(3)) x $100 million x.01/1.1 = -$2.09 million This is the reduction in equity : from $10 million to $7.91 million. Obviously assets and liabilities go down according to the duration formula (check the numbers please). As you can see the lower the leverage ratio, and/or the lower the duration of the liabilities, and/or the higher the duration of assets the higher the impact on equity. What to do? Get the leverage adjusted duration gap as close to 0 (zero) as possible.

33. Copyright 2002, A.S. Cebenoyan33 Some Difficulties in the Application of Duration Models Immunization is a dynamic problem Over time even if interest rates do not change, duration changes and not at the same rate as calendar time. The 6 year eurobond with 4.99 year duration (about the same as the investment horizon -five years), a year later will have a duration of 4.31 years. Remember you were only immunized for immediate interest rate changes. Now, a year later, you are facing a duration of 4.31 years with a 4 year horizon. Any interest rate changes now will no longer be applying to an immunized portfolio. Need to rebalance the portfolio ideally continuously, frequently in practice. Convexity What if interest rate changes are large? Duration assumes a linear relationship between bond price changes and interest rate changes.

34. Copyright 2002, A.S. Cebenoyan34 The actual price-yield relationship is nonlinear. Convexity is the degree of curvature of the price-yield curve around some interest rate level. A nice feature of convexity is that for rate increases the capital loss effect is smaller than the capital gain effect for rate decreases. Higher convexity generates a higher insurance effect against interest rate risk. Measuring convexity and offsetting errors in duration model After a Taylor’s series expansion and dropping the terms with third and higher order, we get: Where, MD is modified duration, D/(1+R). CX reflects the degree of curvature in the price-yield curve at the current yield level.

35. Copyright 2002, A.S. Cebenoyan35 The sum of the terms in the brackets gives us the degree to which the positive effect dominates the negative effect. The scaling factor normalizes this difference. A commonly used scaling factor is 10 8. Example: Convexity of the 8%, 6-year Eurobond: CX = 10 8 [{(999.53785-1000)/1000} + {(1000.46243-1000)/1000}] = 28 For a 2% rise in R, from 8% to 10% The relative change in price will be:  P/P = - [4.99/1.08].02 + (1/2)(28)(.02) 2 = -.0924 +.0056 =-.0868 or 8.68%. Notice how convexity corrects for the overestimation of duration