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Chap13

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  • 1. Fundamentals of Investments 13 C h a p t e r Mortgage-Backed Securities second edition Valuation & Management Charles J. Corrado Bradford D. Jordan McGraw Hill / Irwin Slides by Yee-Tien (Ted) Fu
  • 2. Mortgage-Backed Securities
    • Our goal in this chapter is to examine the investment characteristics of mortgage pools.
    Goal
  • 3. A Brief History of Mortgage-Backed Securities
    • Traditionally, local banks wrote most home mortgages and then held the mortgages in their portfolios of interest-earning assets.
    • Then, when market interest rates climbed to near 20% in the early 1980s, bank customers flocked to withdraw funds from their savings deposits to invest in money market funds.
    • Today, an originator usually sells the mortgage to a mortgage repackager, who accumulates them into mortgage pools.
  • 4. A Brief History of Mortgage-Backed Securities
    • Financed by mortgage-backed bonds (also called mortgage pass-throughs ), each mortgage pool is set up as a trust fund. A servicing agent collects the mortgage payments and then passes the cash flows through to the bondholders.
    • The transformation from mortgages to mortgage-backed securities (MBSs) is called mortgage securitization .
  • 5. Work the Web
    • For more information on mortgage-backed securities, visit:
      • http://www. investinginbonds .com
  • 6. Fixed-Rate Mortgages
    • The size of the monthly payment is determined by the requirement that the present value of all monthly payments, based on the financing rate specified in the mortgage contract, be equal to the original loan amount.
    Fixed-rate mortgage Loan that specifies constant monthly payments at a fixed interest rate over the life of the mortgage.
  • 7. Fixed-Rate Mortgages
    • where r = annual mortgage financing rate
      • T = mortgage term in years
  • 8. Fixed-Rate Mortgages 13 - McGraw Hill / Irwin @2002 by the McGraw- Hill Companies Inc.All rights reserved.
  • 9. Fixed-Rate Mortgage Amortization
    • Each monthly mortgage payment has two separate components:
      • payment of interest on outstanding mortgage principal
      • pay-down, or amortization , of mortgage principal
    • The relative amounts of each component change throughout the life of the mortgage.
  • 10. Fixed-Rate Mortgage Amortization
    • Suppose a 30-year $100,000 mortgage loan is financed at a fixed interest rate of 8%.
    • Monthly payment =
    • In the first month,
      • Interest payment = $100,000  .08/12 = $666.67
      • Principal payment = $733.76 – $666.67 = $67.09
      • New principal = $100,000 – $67.09 = $99,932.91
    • In the second month,
      • Interest payment = $99,932.91  .08/12 = $666.22
      • Principal payment = $733.76 – $666.22 = $67.54
      • New principal = $99,932.91 – $67.54 = $99,865.37
  • 11. Fixed-Rate Mortgage Amortization
    • Mortgage amortization can be described by an amortization schedule , which states the scheduled principal payment, interest payment, and remaining principal owed in any month.
  • 12. Fixed-Rate Mortgage Amortization 13 -
  • 13. Fixed-Rate Mortgage Amortization 13 - McGraw Hill / Irwin
  • 14. Fixed-Rate Mortgage Prepayment & Refinancing
    • A mortgage borrower has the right to pay off all or part of the mortgage ahead of its amortization schedule. This is similar to the call feature of corporate bonds and is known as mortgage prepayment .
    • During periods of falling interest rates, mortgage refinancings are an important reason for mortgage prepayments.
    • Hence, mortgage investors face the risk of a reduced rate of return.
  • 15. Government National Mortgage Association
    • The Government National Mortgage Association (GNMA), or “Ginnie Mae,” is a government agency charged with the mission of promoting liquidity in the secondary market for home mortgages.
    • GNMA mortgage pools are based on mortgages issued under programs administered by the Federal Housing Administration (FHA), the Veteran’s Administration (VA), and the Farmer’s Home Administration (FmHA).
  • 16. Government National Mortgage Association
    • Mortgages in GNMA pools are said to be fully modified because GNMA guarantees bondholders full and timely payment of both principal and interest.
    • Note that although investors in GNMA pass-throughs do not face default risk, they still face prepayment risk.
      • Prepayments are passed through to bondholders.
      • If a default occurs, GNMA fully “prepays” the bondholders.
  • 17. GNMA Clones
    • Besides GNMA, there are two other significant mortgage repackaging sponsors:
    • Federal Home Loan Mortgage Corporation (FHLMC), or “Freddie Mac,” and
    • Federal National Mortgage Association (FNMA), or “Fannie Mae.”
    • Both are government-sponsored enterprises (GSEs) and trade on the New York Stock Exchange.
  • 18. GNMA Clones
    • Like GNMA, both FHLMC and FNMA operate with qualified underwriters who accumulate mortgages into pools financed by an issue of bonds.
    • However, since FHLMC and FNMA are only GSEs, their fully modified pass-throughs do not carry the same default protection as GNMA fully modified pass-throughs.
  • 19. Work the Web
    • Visit the GNMA website at:
      • http://www. ginniemae . gov
    • Check out the FNMA and FHLMC websites at:
      • http://www. fanniemae .com
      • http://www. freddiemac .com
  • 20. PSA Mortgage Prepayment Model
    • Mortgage prepayments are typically described by stating a prepayment rate , which is the probability that a mortgage will be prepaid in a given year.
    • Conventional industry practice states prepayment rates using a model specified by the Public Securities Association (PSA).
      • Prepayment rates are stated as a percentage of a PSA benchmark.
  • 21. PSA Mortgage Prepayment Model
    • In the PSA model, the rates are conditional on the age of the mortgages in the pool. They are conditional prepayment rates (CPRs) .
    • For seasoned ( > 30 months old) mortgages , the CPR is a constant (6% annually for 100% of the PSA benchmark (100 PSA)).
    • For unseasoned (< 30 months old) mortgages , the CPR rises steadily in each month until it reaches an annual rate of 6% (for 100 PSA) in month 30.
  • 22. PSA Mortgage Prepayment Model
  • 23. PSA Mortgage Prepayment Model
    • By convention, the probability of prepayment in a given month is stated as a single monthly mortality (SMM) .
    SMM = 1 – (1 – CPR ) 1/12
  • 24. PSA Mortgage Prepayment Model
    • The average life of a mortgage in a pool is the average time for a single mortgage in the pool to be paid off, either by prepayment or by making scheduled payments until maturity.
    • For a pool of 30-year mortgages,
    Prepayment Schedule Average Mortgage Life (years) 50 PSA 20.40 100 PSA 14.68 200 PSA 8.87 400 PSA 4.88
  • 25. Work the Web
    • Visit the Public Securities Association at:
      • http://www. psa .com
  • 26. Cash Flow Analysis GNMA Fully Modified Mortgage Pools
    • Each month, GNMA mortgage-backed bond investors receive pro rata shares of cash flows derived from fully modified mortgage pools.
    • Each monthly cash flow has three components (less the servicing and guarantee fees):
      • Payment of interest on outstanding mortgage principal.
      • Scheduled amortization of mortgage principal.
      • Mortgage principal prepayments.
  • 27. Cash Flow Analysis GNMA Fully Modified Mortgage Pools 13 - McGraw Hill / Irwin
  • 28. Macaulay Durations for GNMA Mortgage-Backed Bonds
    • The interest rate risk for a bond is often measured by Macaulay duration, which assumes a fixed schedule of cash flow payments.
    • However, the schedule of cash flow payments for mortgage-backed bonds is not fixed.
      • With falling interest rates, prepayments speed up, and vice versa.
  • 29. Macaulay Durations for GNMA Mortgage-Backed Bonds
    • Historical experience indicates that interest rates significantly affect prepayment rates, and that Macaulay duration is a very conservative measure of interest rate risk.
    • In practice, effective duration is used to calculate predicted prices for mortgage-backed securities based on hypothetical interest rate and prepayment scenarios.
  • 30. Collateralized Mortgage Obligations
    • The three best-known types of CMOs are:
      • interest-only (IOs) and principal-only (POs) strips,
      • sequential CMOs, and
      • protected amortization class securities (PACs).
    Collateralized mortgage obligations (CMOs) Securities created by splitting mortgage pool cash flows according to specific allocation rules.
  • 31. Interest-Only and Principal-Only Strips
    • Interest-only strips (IOs) pay only the interest cash flows to investors, while principal-only strips (POs) pay only the principal cash flows to investors.
    • IO strips and PO strips behave quite differently in response to changes in prepayment rates and interest rates.
      • Faster prepayments imply lower IO strip values and higher PO strip values, and vice versa.
  • 32. Interest-Only and Principal-Only Strips 13 - McGraw Hill / Irwin
  • 33. Sequential CMOs
    • Sequential CMOs carve a mortgage pool into a number of tranches (slices).
      • For example, A, B, C, and Z-tranches.
    • Each tranche is entitled to a share of mortgage pool principal and interest on that share of principal.
    • However, cash flows are distributed sequentially, so as to create securities with a range of maturities.
  • 34. Sequential CMOs
    • Cash flows are passed through as follows:
      • All payments of principal will go to the topmost tranche (in alphabetical order), until all the principal in that tranche has been paid off.
      • All tranches receive proportionate interest payments. These are passed through immediately, except for the Z-tranche. Interest on Z-tranche principal is paid as cash to the topmost tranche in exchange for a transfer of an equal amount of principal, until all the principal in the topmost tranche has been fully paid off.
  • 35. Sequential CMOs 13 - McGraw Hill / Irwin
  • 36. Protected Amortization Class Bonds
    • Protected amortization class (PAC) bonds take priority for scheduled payments of principal. The residual cash flows are paid to PAC support (or companion) bonds .
    • PAC cash flows are predictable as long as prepayments remain within a specified band.
  • 37. Protected Amortization Class Bonds
    • Creating a PAC bond entails three steps.
      • Specify two PSA prepayment schedules that form the upper and lower prepayment bounds of the PAC bond. These bounds define a PAC collar .
      • Calculate principal-only (PO) cash flows for the two prepayment schedules specified in  .
      • On a priority basis, at any point in time, PAC bondholders receive payments of principal according to the PSA prepayment schedule with the lower PO cash flow as calculated in  .
  • 38. Protected Amortization Class Bonds 13 - McGraw Hill / Irwin
  • 39. Work the Web
    • Check out the CMO section at:
      • http://www. bondresources .com
  • 40. Yields for MBSs and CMOs
    • The yield to maturity for a mortgage-backed security conditional on an assumed prepayment pattern is called the cash flow yield .
    • Essentially, cash flow yield is the interest rate that equates the present value of all future cash flows on the mortgage pool to the current price of the pool, assuming a particular prepayment rate.
  • 41. Chapter Review
    • A Brief History of Mortgage-Backed Securities
    • Fixed-Rate Mortgages
      • Fixed-Rate Mortgage Amortization
      • Fixed-Rate Mortgage Prepayment and Refinancing
    • Government National Mortgage Association
      • GNMA Clones
    • Public Securities Association Mortgage Prepayment Model
  • 42. Chapter Review
    • Cash Flow Analysis of GNMA Fully Modified Mortgage Pools
      • Macaulay Durations for GNMA Mortgage-Backed Bonds
    • Collateralized Mortgage Obligations
      • Interest-Only and Principal-Only Mortgage Strips
      • Sequential Collateralized Mortgage Obligations
      • Protected Amortization Class Bonds
    • Yields for Mortgage-Backed Securities and Collateralized Mortgage Obligations

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