Fixed Income Securities and their Derivatives


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Fixed Income Securities and their Derivatives

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