1. Business F723 Fixed Income Analysis Week 7 Mortgage Backed Securities

2. 2 Monthly Cash Flows Example p. 243, for a 100 PSA with a pass through rate of 7.5% a WAC of 8.125% and WAM of 357 months The calculations for this table are a bit involved, because the monthly payments on the mortgage pool decrease as prepayments are made on some of those mortgages

3. 3 Monthly Payments Calculating the scheduled monthly payment requires keeping track of the total amount of accumulated prepayments as a fraction of the initial principal Exact formula for this calculation is not given in this textbook

4. 4 Principal The scheduled principal is the difference between the monthly payment and the interest on the outstanding principal Prepayment estimates = SMM multiplied by (the outstanding principal less the scheduled principal payment) Outstanding balance = previous balance less scheduled principal and prepayment

5. 5 Actual Cash Flows The cash flows forecast in the previous table are just predictions If the estimate of 100 PSA is reasonable, the cash flows will still be different from what was predicted note: most of the PSA benchmark is based on experience, but the linear slope for the first 30 months is just an assumption

6. 6 Prepayment Rate The actual rate of prepayments can vary over time for several different reasons –Prevailing mortgage rates; spread, path (refinancing burnout), and level –Characteristics of the loans –Seasonal factors (low housing turnover in winter months) –General economic activity

7. 7 Prepayment Models To account for the changing factors over the life of MBS, some have built models to predict prepayment behaviour –From Goldman, Sachs: monthly prepayment = (refinancing incentive)x(seasoning multiplier) x(month multiplier)x(burnout multiplier) Typically not publicly reported

8. 8 Non-Agency Pass-throughs Since these mortgages are not fully insured, we need to adjust for potential defaults Public Securities Association has also defined a benchmark for the default rate Standard Default Assumption (SDA) ## SDA is the relative rate of defaults expected compared to the average (100 SDA)

9. 9 Standard Default Assumption

10. 10 Cash Flow Yield Similar to IRR, the discount rate that sets the present value of the forecast cash flows equal to the price Market convention converts the monthly yield into a bond equivalent basis

11. 11 Limitations of Cash Flow Yield Can not be used for future value calculation due to reinvestment risk Assumes security is held to maturity (price risk) Prepayment rates and default/delinquency rates must be equal to what was predicted

12. 12 Yield Spread The main difference between treasury bonds and agency (fully modified) MBS is the prepayment risk What level of spread would compensate for the added risk? Option pricing models have been used to determine the appropriate spread

13. 13 Average Life To which maturity treasury bond should we compare the MBS? Could use Macaulay duration, but main measure in use is average life

14. 14 Average Life vs. PSA The average life will be different with different prepayment assumptions As prepayments increase, average life will decrease

15. 15 Negative Convexity Prepayments are similar to call provisions with no call premium Not all mortgages will prepay since there is a cost to the borrower to refinance Price increases will be limited due to the increased likelihood of prepayments as the interest rate declines

16. 16 Contraction Risk If interest rates decrease, the amount of prepayments will increase As prepayments increase, the principal will have to be reinvested at lower rates Average life, and Macaulay’s duration will decrease… this is called contraction risk

17. 17 Extension Risk If interest rates rise, prepayments will decline Expected cash flows will be unavailable for reinvestment at new, higher rates Average life, and Macaulay’s duration will increase… this is called extension risk

18. 18 Asset/Liability Management Depository institutions are more concerned with extension risk Pension funds and others with very long investment horizons are more concerned with contraction risk Synthetic securities can be built to transfer some of these risks

19. 19 Prepayments and Return Prepayments can enhance the return compared to the cash flow yield, if the MBS trades at a discount A prepayment causes the realized capital gain to occur earlier If the MBS trades at a discount, its coupon rate is lower than required, so prepayments allow beneficial reinvestment

20. 20 CMOs Collateralized Mortgage Obligations are a variant of MBSs Called a pay-through structure rather than a pass-through structure because there are different classes of owners receiving different cash flows, but having the same level of seniority Different classes are called tranches

21. 21 Sequential Pay Tranches Principal payments are directed at each tranche in turn until that tranche is paid off principal pay-down window is the time period in which that tranche is receiving payments towards the principal Tranche B in example on p. 261 has a principal pay-down window from month 81-100

22. 22 Accrual Bonds A class of tranche that receives no interest or principal until the other tranches have been fully paid off The interest payments that this tranche would have received are treated as principal prepayments for the other tranches

23. 23 Floating Rate Tranches A floating rate tranche can be created by splitting a tranche into a floating rate tranche and an inverse floating rate tranche The total interest paid to the two tranches will be the same as the interest paid to the original tranche coupon leverage will be created if the two tranches are not of the same size

24. 24 Planned Amortization Class A PAC tranche is protected from prepayment risk because it gets principal payments at a fixed rate This is accomplished by issuing support bond tranches The PAC gets principal payments according to the schedule, anything left over goes to the support bond tranche

25. 25 PAC Collars If the support bond tranche is paid off, the PAC tranche will lose its protection The range of prepayment speeds that can be handled is called the collar The size of the collar can change over time based on the actual speed of prepayments

26. 26 Targeted Amortization Class A TAC bond tranche is protected against contraction risk, but not extension risk Prepayments in excess of a certain rate are borne by the support bonds, but slower than expected prepayments are shared equally A reverse TAC bond protects vs. extension risk, but not contraction risk

27. 27 VADM Very Accurately Determined Maturity bonds are created much like PACs except that there is also an accrual bond tranche The accrued interest for the accrual bond tranche can be used to satisfy the scheduled principal payments if the prepayment speed is slower than expected

28. 28 Support Bonds These bonds are the tranches that take extra prepayment risk to allow the PAC, TAC, or VADM to reduce that risk As such these bonds are very risky and investors will demand a higher rate of return to buy these tranches

29. 29 Credit Risk A CMO is a business entity If issued by an agency or fully modified, there is no credit risk If issued by a private conduit, the level of credit risk must be assessed –Private label CMO; assets are agency MBS –Whole loan CMO; assets are mortgages

30. Structural Credit Enhancement Senior/subordinated tranches Subordinated tranches absorb the first wave of defaults Given the example on p. 302 you can give the different tranches credit ratings from NR to B to AAA depending on how much protection they have 30

31. 31 Stripped MBS Interest only or principal only tranches All interest collected is paid to one tranche, all principal payments, scheduled or prepayments is paid to the other tranche Interest only tranche hurt by prepayments Principal only tranche gets money quicker if prepayments increase

32. 32 Notional Interest Only A tranche that is created by paying one or more tranches lower coupon payments than the WAC The excess interest is paid out to a tranche as a percent of a notional value –e.g. $100 m tranche receives 6%, WAC 7% –1% of $100 m = 5% of $20 m –so a tranche can be created paying 5% on a notional value of $20 m