Mortgage Pools, Pass-Throughs, Lecture

Mortgage Pools, Pass-Throughs, Lecture - Debt Instruments...

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Debt Instruments and Markets Professor Carpenter Mortgage Pools, Passthroughs, and CMOs 1 Mortgage Pools, Pass-Throughs, and CMOs market risk, idiosyncratic risk, path- dependence, burnout, OAS, negative convexity, negative duration, tranche, PAC, TAC, Z-Bond Concepts and Buzzwords Fixed-Rate Mortgages Prepayment Risks Valuation of Mortgage Pools (Pass-Throughs) CMOs Interest Rate Sensitivity Readings Veronesi, Chapter 12 Tuckman, Chapter 21
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Debt Instruments and Markets Professor Carpenter Mortgage Pools, Passthroughs, and CMOs 2 Basic Fixed Rate Mortgage With a basic fixed rate mortgage, the borrower is scheduled to make level monthly payments consisting of interest on the amount of the loan outstanding, at the pre- determined fixed mortgage rate, and principal payments which reduce the outstanding loan balance. The size of the monthly payment is set so that the original loan is paid off after a prespecified amount of time, typically 30 years. In other words, the fixed monthly payment makes the present value of the 30-year stream, discounted at the mortgage rate , equal to the principal amount of the loan. Monthly Payment By convention, the quoted mortgage rate is annualized with monthly compounding. Using the annuity formula from the yield lecture, we can get a closed form expression for the monthly payment: 12 + 12 r prin = pmt = pmt pmt = prin n =1 360 ( / ) / ( ( / ) ) ( ( / ) ) 1 12 1 1 12 1 1 12 360 360 + × + r r r r m n m m m m Example: If the original balance is $100,000 and the mortgage rate is 7.25%, then the monthly payment is $682.18.
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Debt Instruments and Markets Professor Carpenter Mortgage Pools, Passthroughs, and CMOs 3 Amortization Schedule for 30-Year, Monthly 7.25% Mortgage Month Beginning Principal Balance Monthly Payment Monthly Interest Scheduled Principal Repayment Ending Principal Balance 1 100,000.00 682.18 604.17 78.01 99,922 2 99,921.99 682.18 603.70 78.48 99,844 3 99,843.51 682.18 603.22 78.96 99,765 4 99.764.55 682.18 602.74 79.43 99,685 360 678.08 682.18 4.10 678.08 0 Note that on any month, the present value of the remaining stream of payments, discounted at the fixed mortgage rate equals the remaining principal balance. Semi-Annual Payment Formula We’ll assume semi-annual payments so we don’t have to rebuild our binomial tree. For a T-year fixed rate, level pay mortgage with semi-annual mortgage (coupon) rate c , the formulas become Example: For a 2-year, 5.5% mortgage with semi-annual payments and $100 principal, the semi-annual payment is $26.74. prin = pmt (1 + c /2) n = pmt c /2 n = 1 2 T (1 (1 + c /2) 2 T ) pmt = prin × c /2 1 (1 + c /2) 2 T
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Debt Instruments and Markets Professor Carpenter Mortgage Pools, Passthroughs, and CMOs 4 Amortization Schedule for 2-Year, 5.5% Semi-Annual Mortgage We can think of this as a single mortgage, a pool of identical mortgages, or a pass-through security that receives a fixed fraction of all cash flows that flow through the pool.
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  • Spring '15
  • Jennifer
  • Mortgage loan, fixed rate mortgage, collateralized mortgage obligation, Professor Carpenter, Passthroughs

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