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Fixed Income Securities  and their Derivatives
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Fixed Income Securities and their Derivatives


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  • 1. Fixed Income Securities and their Derivatives
  • 2. Asset-Backed Securities
  • 3. Asset-Backed Securities
      • ABS derive their cash flows from a pool of underlying assets
        • MBS = mortgage backed securities
        • CARS = certificates for automobile receivables
        • CARDS = certificates for amortizing revolving debts
        • HELS = home equity loan securities
  • 4. Asset-Backed Securities
      • The underlying assets generate cash flows of principal and interest which can be repackaged and sold to investors.
    Fixed income assets Principal Interest Asset-backed securities
  • 5. Asset-Backed Securities
      • In ABS, the underlying assets are collected into a pool .
        • Pool assets are standardized .
      • The asset pool is placed in trust.
      • Claims on the cash flows generated by the asset pool are structured:
        • Pass-through structures
        • Multi-class structures
      • Securities representing these claims are sold.
  • 6. Securitization
      • By pooling and repackaging cash flows, ABS issuers can convert illiquid fixed income assets into marketable bonds.
      • Requires trust structure to hold underlying assets, and
      • Credit enhancement to achieve investment grade bond rating
        • External: guarantees
        • Internal: over-collateralization.
  • 7. Issuers
      • Mortgage related agencies
        • Ginnie Mae (pass-thoughs)
        • Freddie Mac (PCs)
        • Fannie Mae (MBS)
      • Private label MBS
        • Citi, GE, Prudential
      • Private label ABS
        • GMAC and other auto companies
        • Finance companies
        • Credit card issuers
  • 8. Investors
      • Insurance companies
      • Pension funds
      • Mutual funds
      • Wealthy individuals
  • 9. MBS
      • Backed by mortgage loans.
      • A mortgage loan is a loan secured by real estate
        • The “mortgage” is a security agreement that gives the lender the right to seize by foreclosure the property securing the loan if the borrower defaults
      • Mortgage loans are originated by banks and other financial firms.
      • Once originated, a mortgage loan may be held, sold to an investor for cash, or pooled and securitized.
  • 10. Mortgage Loan Types
      • Fixed-rate, level pay (“plain vanilla”)
        • Term of loan is fixed (30 years is common in US)
        • Contract rate of interest is fixed for the life of the loan.
        • Payments (usually monthly) are constant for the term of the loan
        • The payments fully amortize the loan.
      • FHA, conventional, conforming, nonconforming, jumbo
  • 11. Mortgage Loan Types
      • Graduated payment loans (GPMs)
        • Low initial payments and period of negative amortization
      • Graduated equity loans (GEMs)
        • Fixed coupon with growing payments
      • Balloons
      • Adjustable rate mortgages (ARMs)
        • Various index rates
        • Caps and collars
  • 12. Mortgage Loan Payments
      • The payments on a plain vanilla mortgage are determined by
    Initial principal Contract rate of interest Mortgage term in years
  • 13. For Example
      • The monthly payments on a $187,000 loan written at 10% for 15 years is
    In Excel, you can use the financial function PMT(rate, nper, pv,fv,type)
  • 14. Mortgage Loan Payments
      • Each payment consists of
        • interest equal to i /12 times the amount of principal owing at the time the payment is due, and
        • scheduled principal repayment
      • Payments are calculated such that the interest due is paid first and then the remainder of the payment is used to reduce the principal owed.
      • A table listing the payments and how they are divided between interest and principal is called an amortization schedule.
  • 15. Amortization Schedule
      • For example, here are the first few lines of an amortization schedule for a 15-year, 10% fixed rate loan with an initial principal of $187,000
  • 16. Amortization Schedule
      • A better way to visualize the amortization process is to look at a graph of the payments
  • 17. Amortization Schedule
      • The principal balance remaining after any number of payments can be determined by constructing an amortization schedule or by employing the formula
  • 18. Amortization Schedule
      • The logic of this formula is that the principal balance remaining after s payments is always the present value of the remaining 12T-s payments discounted at the contract rate of interest
  • 19. Amortization Schedule
      • Graphically
  • 20. Mortgage Servicing
      • Servicing
        • Collection and forwarding of payments
        • Administration of escrow accounts
      • Servicing fees
        • Typically 50 basis points
      • Right to service loan is sold by owner of mortgage loan
  • 21. Mortgage Servicing
      • For example
    This servicing annuity is worth about $5,450 at a 9.5% discount rate
  • 22. Prepayments
      • Payments made by borrowers in excess of their scheduled loan payments.
        • Entire (as when the house is sold or refinanced)
        • Partial (accelerated principal repayment)
      • Most prepayments are optional to the borrower
        • put option
      • Borrower incentives when rates
        • Rise
        • Fall
  • 23. For Example
      • Consider a mortgage that’s been outstanding for two years and rates have fallen 2%
  • 24. Prepayments
      • To the extent that prepayments cannot be perfectly predicted, they create uncertainty about the term of mortgage loans.
      • This uncertainty is a disadvantage from the standpoint of an investor.
      • What’s worse: Prepayments are more likely when rates fall and less likely when they rise, so prepayment risk is positively correlated with interest rate risk
  • 25. Pass-throughs
      • The simplest type of MBS
        • Similar mortgages are pooled and
        • Principal and interest payments are passed through to investors (pro rata)
        • Less servicing and insurance (credit enhancement) fees
      • Pass-through cash flows are uncertain because prepayments of mortgages within the pool are uncertain.
  • 26. Prepayment models
      • To price a pass-through bond, an estimate of prepayments is needed.
        • Prepayments will affect the duration of the bonds (Can you see how?)
      • There are several “models” for estimating prepayments
      • However, none of these models is designed to describe borrower response to changes in interest rates.
  • 27. CPR
      • The constant prepayment rate model assumes a constant percentage of the outstanding principal will prepay each month.
      • CPR is an annual rate that can be translated to a single monthly mortality rate (SMM) as
    An SMM of z% means that z% of the principal remaining in the pool after all scheduled payments have been made will prepay during the month
  • 28. CPR
      • For example, a CPR of 6%
      • Translates to an SMM of .514%
      • So if you owned a pass-through with a beginning of the month balance of $181,824.99 and $494.30 of scheduled principal payments, then prepayments would be predicted at
  • 29. PSA
      • The Public Securities Association standard specifies that the CPR is .2% during the first month of a pool,
      • Increases by .2% per month until the 30th month
      • Levels off at 6% for the remainder.
      • Prepayment speeds are quoted as % of PSA
        • Slow: less than 100% PSA
        • Fast: greater than 100% of PSA
  • 30. FHA Experience
      • HUD publishes data on FHA insured mortgages that can be used to extrapolate prepayment speeds.
      • Patterns can be discerned for different types of pools.
      • The pattern for a given pool type can then be used to estimate a prepayment speed for other pools of that type.
  • 31. Example with 165% PSA
  • 32. Effect of Changing PSA
      • Impact on duration
      • Excel spreadsheet
  • 33. Next:
  • 34. Pricing and Multiclass Structures