1. Fall-01 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html FIBI Zvi Wiener 02-588-3049 mswiener@mscc.huji.ac.il Fixed Income Instruments 4

2. Zvi WienerFIFIBI - 4 slide 2 Fixed Income 4 Mortgage loans Pass-through securities Prepayments Agencies MBS CMO ABS

3. Zvi WienerFIFIBI - 4 slide 3 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.

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5. Zvi WienerFIFIBI - 4 slide 5 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.

6. Zvi WienerFIFIBI - 4 slide 6 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.

7. Zvi WienerFIFIBI - 4 slide 7 Fixed Rate Mortgage A series of equal payments with PV=loan. Example: 100,000 for 20 years with 6% and equal monthly payments.

8. Zvi WienerFIFIBI - 4 slide 8 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.

9. Zvi WienerFIFIBI - 4 slide 9 Balloon Mortgage One payment at the end. Sometimes they have renegotiation points.

10. Zvi WienerFIFIBI - 4 slide 10 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.

11. Zvi WienerFIFIBI - 4 slide 11 Risk in Mortgages Default risk Liquidity risk Interest rate risk Prepayment risk

12. Zvi WienerFIFIBI - 4 slide 12 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.

13. Zvi WienerFIFIBI - 4 slide 13 Prepayment Risk in Mortgages Sale of home Better interest rates Irrational factors

14. Zvi WienerFIFIBI - 4 slide 14 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

15. Zvi WienerFIFIBI - 4 slide 15 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.

16. Zvi WienerFIFIBI - 4 slide 16 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.

17. Zvi WienerFIFIBI - 4 slide 17 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

18. Zvi WienerFIFIBI - 4 slide 18 Prepayments Prepayment speed, conditional prepayment rate CPR (prepayment rate assumed for a pool). Single-Monthly mortality rate SMM. SMM = 1 - (1-CPR) 1/12

19. Zvi WienerFIFIBI - 4 slide 19 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.

20. Zvi WienerFIFIBI - 4 slide 20 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

21. Zvi WienerFIFIBI - 4 slide 21 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.

22. Zvi WienerFIFIBI - 4 slide 22 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.

23. Zvi WienerFIFIBI - 4 slide 23 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.

24. Zvi WienerFIFIBI - 4 slide 24 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.

25. Zvi WienerFIFIBI - 4 slide 25 100 PSA 030Age in months Annual CPR in % 0.2 6

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30. Zvi WienerFIFIBI - 4 slide 30 Effective Duration

31. Zvi WienerFIFIBI - 4 slide 31 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

32. Zvi WienerFIFIBI - 4 slide 32 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.

33. Zvi WienerFIFIBI - 4 slide 33 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.

34. Zvi WienerFIFIBI - 4 slide 34 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.

35. Zvi WienerFIFIBI - 4 slide 35 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.

36. Zvi WienerFIFIBI - 4 slide 36 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.

37. Zvi WienerFIFIBI - 4 slide 37 Other CMOs PAC = Planned Amortization Class, IO = interest only, PO = principal only, IO, PO strips.

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40. Zvi WienerFIFIBI - 4 slide 40 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)

41. Zvi WienerFIFIBI - 4 slide 41 Front office Middle office Back office Institutional investor (buyer) Market Maker (dealer)

42. Zvi WienerFIFIBI - 4 slide 42 Front Office Trade execution Investment decisions Contact with counterparties Real-time market monitoring

43. Zvi WienerFIFIBI - 4 slide 43 Middle Office Risk management Benchmark Valuation Economic forecasts Some investment decisions Internal grading, scoring Pricing of services Profitability of business lines

44. Zvi WienerFIFIBI - 4 slide 44 Back Office Trade settlement, clearing Margin management Accounting Administration Record maintenance Regulatory compliance Inventory reporting

45. Fall-01 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html FIBI Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Pfandbrief

46. Zvi WienerFIFIBI - 4 slide 46 Pfandbrief Bonds issued by German banks which are subject to special Pfandbrief legislation. There are two types of Pfandbriefe depending on the collateral. Oeffentliche Pfandbriefe are bonds fully collateralized by loans to public-sector entities, while Hypotheken-Pfandbriefe are fully collateralized by residential and commercial mortgages, with LTV<60%.

47. Zvi WienerFIFIBI - 4 slide 47 Pfandbrief Mortgage Banks - about 20% of the business volume of all banking groups. Only few Mortgage Banks are independent, most belong to a larger banking group. – residential mortgage loans – commercial mortgage loans – public sector lending refinancing through the issuing of Pfandbriefe

48. Zvi WienerFIFIBI - 4 slide 48 Public Sector Loans in Germany bn Euros2000% Mortgage banks25954.5 Public banks13528.4 Savings banks275.7 Commercial banks306.3 Cooperative banks7.51.6 Agencies163.4 Total476100

49. Zvi WienerFIFIBI - 4 slide 49 Commercial Loans in Germany bn Euros2000% Mortgage banks11050.4 Public banks35.516.3 Savings banks4018.2 Commercial banks167.3 Cooperative banks167.4 Others10.3 Total218100

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51. Zvi WienerFIFIBI - 4 slide 51 The Mortgage Loan Portfolio (12/00) 36% commercial property 64% residential property Total Volume: 342,726 million Euro Foreign loans 28,690 million Euro

52. Zvi WienerFIFIBI - 4 slide 52 Refinancing of the German Mortgage Banks Largest bond market in Europe Outstanding volume in 2000 - 1.1 trillion euro Gross sales 2000 - 216 billion euro Issuers private Mortgage Banks private ship Mortgage Banks public sector credit institutions

53. Zvi WienerFIFIBI - 4 slide 53 Jumbo Pfandbrief above 500 million euro Straight bond format Structured Pfandbriefe maturities 1-10 years are eligible collateral

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55. Zvi WienerFIFIBI - 4 slide 55 European “Pfandbrief”countries

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61. Zvi WienerFIFIBI - 4 slide 61 PEX

62. Fall-01 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html FIBI Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html DAC

63. Zvi WienerFIFIBI - 4 slide 63 Life Insurance yearly contribution 10,000 NIS yearly risk premium 2,000 NIS first year agent’s commission 3,000 NIS promised accumulation rate 8,000 NIS/yr After the first payment there is a problem of insufficient funds. 8,000 NIS are promised (with all profits) and only 5,000 NIS arrived.

64. Zvi WienerFIFIBI - 4 slide 64 10,000 NIS Risk 2,000 NIS Client’s 8,000 NIS Agent 3,000 NIS insufficient funds if the client leaves insufficient profits

65. Zvi WienerFIFIBI - 4 slide 65 Risk measurement The reason to enter this transaction is because of the expected future profits. Assume that the program is for 15 years and the probability of leaving such a program is . Fees are – 0.6% of the portfolio value each year – 15% real profit participation