1. Fixed Income Zvi Wiener 02-588-3049 http://www.tfii.org Fixed Income 4

2. http://www.tfii.org FI - 4 slide 2 Japanese Government Bonds JGB short term Treasury bills medium term bonds long term bonds super long term bonds (20 years)

3. http://www.tfii.org FI - 4 slide 3 German Government Bonds U-Schatze discount paper up to 2 years Kassens = federal government notes (2-6 y.) OBLEs = 5 year federal government notes Bunds = federal government bonds (6-30 y.) all coupon payments are annual

4. http://www.tfii.org FI - 4 slide 4 UK Government Bonds Gilts straights = bullet bonds (some callable) convertibles (option to holder to convert to longer gilts) index linked low coupon 2-2.5% irredeemable (perpetual)

5. http://www.tfii.org FI - 4 slide 5 Brady Bonds Argentina, Brazil, Costa Rica, Dominican Republic, Ecuador, Mexico, Uruguay, Venezuela, Bulgaria, Jordan, Nigeria, Philippines, Poland. Partially collateralized by US government securities

6. http://www.tfii.org FI - 4 slide 6 Fixed Income 4 Mortgage loans Pass-through securities Prepayments Agencies MBS CMO ABS

7. http://www.tfii.org FI - 4 slide 7 Mortgage Loans Mortgage is a loan secured by a specified real estate property. Conventional mortgage - credit of the borrower and collateral. Mortgage insurance - FHA, VA, FmHA guaranteed by US government, there are some private insurers as well.

8. http://www.tfii.org FI - 4 slide 8 Mortgage Market Mortgage originator - thrifts, banks origination fee (in points = %) PTI = payment to income ratio (include tax) LTV = loan to value ratio later on mortgages are securitized.

9. http://www.tfii.org FI - 4 slide 9 Mortgage Services Collecting payments, maintaining records Servicing fee - % of outstanding plus some other benefits. Mortgage insurer required when LTV>80%. Credit life - voluntary life insurance.

10. http://www.tfii.org FI - 4 slide 10 Fixed Rate Mortgage A series of equal payments with PV=loan. Example: 100,000 for 20 years with 6% and equal monthly payments.

11. http://www.tfii.org FI - 4 slide 11 Adjustable-Rate Mortgage (ARM) The contract rate is reset periodically, based on a short term interest rate. Adjustment from one month to several years. Spread is fixed, some have caps or floors. Market based rates. Rates based on cost of funds for thrifts. Initially low rate is often offered = teaser rate.

12. http://www.tfii.org FI - 4 slide 12 Balloon Mortgage One payment at the end. Sometimes they have renegotiation points.

13. http://www.tfii.org FI - 4 slide 13 Two-Step Mortgages A loan carries a fixed rate for some period (usually 7 years) and then reset rates. For example: 250 basis points plus average of 10-years Treasuries.

14. http://www.tfii.org FI - 4 slide 14 Risk in Mortgages Default risk Liquidity risk Interest rate risk Prepayment risk

15. http://www.tfii.org FI - 4 slide 15 Risk in Mortgages Default risk is highly affected by LTV. LTV>80% in 40% of loans LTV>90% in 15% of loans different state laws give different rights to lenders.

16. http://www.tfii.org FI - 4 slide 16 Prepayment Risk in Mortgages Sale of home Better interest rates Irrational factors

17. http://www.tfii.org FI - 4 slide 17 Mortgage Pass-Through Securities A group of mortgages form a pool which is securitized. Payments are pooled, service fee deducted and the rest divided. WAC = weighted average coupon rate WAM = weighted average maturity

18. http://www.tfii.org FI - 4 slide 18 Mortgage Pass-Through Securities Ginnie Mae = Government National Mortgage Association, MBS - guaranteed by GNMA. Freddie Mac = Federal Home Loan Mortgage Corporation, PC = participation certificate. Fannie Mae = Federal National Mortgage Association, MBS.

19. http://www.tfii.org FI - 4 slide 19 Role of Agencies guarantee timely payments 1. Coupon only 2. Both coupon and principal Ginnie Mae is guaranteed by the US government. Securities guaranteed by Ginnie Mae are called MBS = Mortgage Backed Securities.

20. http://www.tfii.org FI - 4 slide 20 Non-Agency Pass-Through Credit enhancement to AA or AAA. Overcollateralization Senior/subordinated structure shifting interest structure months% of prepayment to senior 1-6070 61-7260 73-8440 85-9620 97-10812

21. http://www.tfii.org FI - 4 slide 21 Prepayments Prepayment speed, conditional prepayment rate CPR (prepayment rate assumed for a pool). Single-Monthly mortality rate SMM. SMM = 1 - (1-CPR) 1/12

22. http://www.tfii.org FI - 4 slide 22 Example of prepayments Example: let CPR=6%, then SMM = 1-(1-0.06) 1/12 = 0.005143. An SMM of 0.5143% means that approximately 0.5% of the mortgage balance will be prepaid this month.

23. http://www.tfii.org FI - 4 slide 23 Example of prepayments If the balance at the beginning of a month is $290M, SMM = 0.5143% and the scheduled principal payment is $3M, then the estimated repayment for this month is 0.005143 (290,000,000-3,000,000)=$1,476,041

24. http://www.tfii.org FI - 4 slide 24 Prepayments A general model should be based on a dynamic transition matrix, very similar to credit migration. But note the difference of a pool of not completely rational customers and a single firm.

25. http://www.tfii.org FI - 4 slide 25 Prepayments Prevailing mortgage rate relative to original. Path of mortgage rates. Level of mortgage rates. Seasonal factors (home buying is high in spring summer and low in fall, winter). General economic activity.

26. http://www.tfii.org FI - 4 slide 26 Bond Equivalent Yield Bond equivalent yield = 2[ (1+y M ) 6 - 1] Yield is based on prepayment assumptions and must be checked! PSA benchmark = Public Securities Association. Assumes low prepayment rates for new mortgages, and higher rates for seasoned loans.

27. http://www.tfii.org FI - 4 slide 27 PSA prepayment benchmark The Public Securities Association benchmark is expressed as monthly series of annual prepayment rates. Low prepayment rates of new loans and higher for old ones. Assumes CPR increasing 0.2% to 6% with life of a loan. Actual rate is expressed as % of PSA.

28. http://www.tfii.org FI - 4 slide 28 100 PSA 030Age in months Annual CPR in % 0.2 6

29. http://www.tfii.org FI - 4 slide 29 PSA standard default assumptions 0 30 60 120Age in months Annual default rate (SDA) in % 0.3 0.6 Month 1 - 0.02% increases by 0.02% till 30m stable at 0.6% 30-60m declines by 0.01% 61-120m remains at 0.03% after 120m 0.02

30. http://www.tfii.org FI - 4 slide 30 Special Properties Negative convexity - if interest rates go up the price of a pass through security will decline more than a government bond due to lower prepayment rate.

31. http://www.tfii.org FI - 4 slide 31 CMO and stripped MBS (ch. 12) Collateralized Mortgage Obligations - are bond classes created by redirecting the cash flows of mortgage related products so as to mitigate prepayment risk. CMO is backed by a pool of pass-throughs, whole loans, or strips, structured in order to serve different types of clients. The bond classes are called tranches.

32. http://www.tfii.org FI - 4 slide 32 CMO Example Since 1983 - sequential-pay CMO. Each class is retired sequentially. Example: collateral is a pass-through with par of $400M pass-through coupon rate 7.5% WAC weighted average coupon 8.125% WAM weighted average maturity 357 mo.

33. http://www.tfii.org FI - 4 slide 33 CMO Example 4 tranches A,B,C,D divide the whole nominal, coupons will be distributed proportionally, but principals first go to A, until repaid, then to B, etc. Another example is an accrual CMO when one of the tranches does not get receive current interest. It is accrued and added to the principal.

34. http://www.tfii.org FI - 4 slide 34 CMO Example Some tranches are floaters, others inverse floaters. Floater: Variable Rate + spread Inverse Floater: Spread - Variable Rate Often LIBOR is used as variable rate.

35. http://www.tfii.org FI - 4 slide 35 Other CMOs PAC = Planned Amortization Class, IO = interest only, PO = principal only, IO, PO strips.

36. http://www.tfii.org FI - 4 slide 36 ABS Asset-Backed Securities (13) Collateral, credit enhancement, Payment structure (priorities), legal structure (SPV=special purpose vehicle) Auto loan backed securities Credit Card backed securities Home Equity loans (second lien)

37. http://www.tfii.org FI - 4 slide 37 Bonds with Embedded Options (14) Traditional yield analysis compares yields of bonds with yield of on-the-run similar Treasuries. The static spread is a measure of the spread that should be added to the zero curve (Treasuries) to get the market value of a bond.

38. http://www.tfii.org FI - 4 slide 38 Active Bond Portfolio Management (17) Basic steps of investment management Active versus passive strategies Market consensus Different types of active strategies Bullet, barbell and ladder strategies Limitations of duration and convexity How to use leveraging and repo market

39. http://www.tfii.org FI - 4 slide 39 Investment Management Setting goals, idea of ALM or benchmark GAAP, FAS 133, AIMR - reporting standards passive or active strategy - views, not transactions available indexes mixed strategies

40. http://www.tfii.org FI - 4 slide 40 Major risk factors level of interest rates shape of the yield curve changes in spreads changes in OAS performance of a specific sector/asset currency/linkage

41. http://www.tfii.org FI - 4 slide 41 Parallel shift T r Current TS Downward move upward move

42. http://www.tfii.org FI - 4 slide 42 Twist T rr steepening flattening

43. http://www.tfii.org FI - 4 slide 43 Butterfly T rr

44. http://www.tfii.org FI - 4 slide 44 Yield curve strategies Bullet strategy: Maturities of securities are concentrated at some point on the yield curve. Barbel strategy: Maturities of securities are concentrated at two extreme maturities. Ladder strategy: Maturities of securities are distributed uniformly on the yield curve.

45. http://www.tfii.org FI - 4 slide 45 Example bondcouponmaturityyielddurationconvex. A8.5%58.54.00519.81 B9.5%209.58.882124.17 C9.25%109.256.43455.45 Bullet portfolio: 100% bond C Barbell portfolio: 50.2% bond A, 49.8% bond B

46. http://www.tfii.org FI - 4 slide 46 Dollar duration of barbell portfolio = 0.502*4.005 + 0.498*8.882 = 6.434 it has the same duration as bullet portfolio. Dollar convexity of barbell portfolio = 0.502*19.81 + 0.498*124.17 = 71.78 the convexity here is higher! Is this an arbitrage?

47. http://www.tfii.org FI - 4 slide 47 The yield of the bullet portfolio is 9.25% The yield of the barbell portfolio is 8.998% This is the cost of convexity!