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Loan Securitization Cash Flows and Valuation

Loan Securitization Cash Flows and Valuation. Class #21; Chap. 26. Lecture Outline. Purpose: Understand cash flows from securitization Pool of fully amortizing mortgages GNMA Bond Cash flows generated by the pool of mortgages Cash flows to bond holders Bond valuation

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Loan Securitization Cash Flows and Valuation

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  1. Loan SecuritizationCash Flows and Valuation Class #21; Chap. 26

  2. Lecture Outline • Purpose: Understand cash flows from securitization • Pool of fully amortizing mortgages GNMA Bond • Cash flows generated by the pool of mortgages • Cash flows to bond holders • Bond valuation • Cash flows to bond holders with prepayment risk (after prepayment risk) • Prepayment risk • PSA Model • Option Adjusted Spread • Collateralized Mortgage Obligations (CMOs) • Interest only loans • Fully Amortizing loans with Prepayment risk (FYI)

  3. GNMA BondCash Flows Generated by the mortgage pool

  4. Example – Securitization Cash Flows World Bank has originated 1,000 fixed rate fully amortizing mortgages with an average size of $100,000, 30 years to maturity and 12% aggregate interest rate compounded monthly. World Bank sells the pool of mortgages to an SPV they created to facilitate the securitization. Calculate the monthly payment generated by the mortgage pool. Assume no pre-payment or default risk SPV 12% Interest payments Loan pool

  5. Example – Present Value of CF World Bank has originated 1,000 fixed rate fully amortizing mortgages with an average size of $100,000, 30 years to maturity and 12% aggregate interest rate compounded monthly. World Bank sells the pool of mortgages to an SPV they created to facilitate the securitization. Calculate the monthly payment generated by the mortgage pool. Assume no pre-payment or default risk PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT Payments from mortgage pool What is the present value? 1m 2m 3m 4m 5m 356m 357m 358m 359m 360m How many years? What is the interest rate? What is the number of compounding periods per year?

  6. Example – Find Constant Payment World Bank has originated 1,000 fixed rate fully amortizing mortgages with an average size of $100,000, 30 years to maturity and 12% aggregate interest rate compounded monthly. World Bank sells the pool of mortgages to an SPV they created to facilitate the securitization. Calculate the monthly payment generated by the mortgage pool. Assume no pre-payment or default risk n × m = 12 * 30 = 360 r/m = .12/12 interest rate = 1% per month PV = 1000 * $100,000 = $100,000,000 PMT (Constant monthly payment to pay off the mortgage over its life )= ?

  7. GNMA Bond Payment to the Bond Holders

  8. Example –Setup with Fees World Bank has originated 1,000 fixed rate fully amortizing mortgages with an average size of $100,000, 30 years to maturity and 12% aggregate interest rate compounded monthly. World Bank sells the pool of mortgages to an SPV they created to facilitate the securitization. Calculate the monthly payments to bond holders if the SPV collects a 44bp servicing fee and pays a 6bp GNMA insurance fee. Assume no pre-payments or defaults. SPV Loan pool 12% Interest payments 11.56% Interest payments 11.5% Interest payments 0.06% Insurance Fee 0.44% Servicing Fee

  9. Example – Payments w/ Fees World Bank has originated 1,000 fixed rate fully amortizing mortgages with an average size of $100,000, 30 years to maturity and 12% aggregate interest rate compounded monthly. World Bank sells the pool of mortgages to an SPV they created to facilitate the securitization. Calculate the monthly payments to bond holders if the SPV collects a 44bp servicing fee and pays a 6bp GNMA insurance fee. Assume no pre-payments or defaults. Use the payment rate less fees

  10. GNMA Bond Valuing a Pass-Through Bond

  11. Example – Value the Pass-through World Bank has originated 1,000 fixed rate fully amortizing mortgages with an average size of $100,000, 30 years to maturity and 12% aggregate interest rate compounded monthly. World Bank sells the pool of mortgages to an SPV they created to facilitate the securitization. After 1 year the mortgage interest rate has dropped to 10% find the current value of the pass-through security.Assume no pre-payments default risk. Step #1 find the new rate New Rate = 0.1 – 0.0044 – 0.0006 = 0.095 Step #2 find the current value How many years What are the payments? 990K PMT 990K PMT 990K PMT PMT 990K 990K PMT 990K PMT PMT 990K PMT 990K 990K PMT 990K PMT 1m 2m 3m 4m 5m 1m 2m 3m 4m 5m 344m 345m 346m 347m 348m

  12. Example – Value the Pass-through World Bank has originated 1,000 fixed rate fully amortizing mortgages with an average size of $100,000, 30 years to maturity and 12% aggregate interest rate compounded monthly. World Bank sells the pool of mortgages to an SPV they created to facilitate the securitization. After 1 year the mortgage interest rate has dropped to 10% find the current value of the pass-through security.Assume no pre-payments default risk. Step #1 find the new rate New Rate = 0.1 – 0.0044 – 0.0006 = 0.095 Step #2 find the current value

  13. JP Morgan bundles 700 mortgages into a pool and sells them to an SPV they have created. Each mortgage has a principal value of $250,000. The aggregate interest coupon from the pool is 7% paid semiannually and all loans have a maturity of 12 years. The SPV charges a 70bp servicing fee and GNMA insurance premium is 10bp. • Find the aggregate semiannual payment to GNMA, the SPV, and bond holder • After 2 years have passed, a similar pool of credit can be packaged to yield a 9% aggregate coupon. Find the current value of the GNMA securitization to bond holders.

  14. Pre-payment Risk

  15. Securitization & Prepayment • Why are loans prepaid? • Refinancing • If rates fall, homeowners may choose to prepay their existing mortgage and get another at a lower rate • Housing turnover • The propensity of homeowners to move • If homeowners sell their house, they will payoff their mortgage

  16. Affects of Prepayment on Bond CFs Affects of prepayment: • Cause monthly cash flows from the pool to vary • Cause payments from the pool to decrease as the MBS ages Bond payments with & without Pre-payment

  17. Prepayment Reinvestment Risk Bond payments with & without Pre-payment Are interest rates high or low? • Bond holders receive larger cash flows in times when interest rates are low. • They will most likely have to reinvest at a lower rate • Suffer loss on interest earned (reinvestment risk)

  18. Prepayment Reinvestment Risk Bond payments with & without Pre-payment How do you value the bond with prepayments?

  19. Prepayment Reinvestment Risk Bond payments with & without Pre-payment Is it possible to know how many loans will be prepaid and when? No! so we guess a.k.a. build a model

  20. Modeling Prepayments (Assume all payments are made in arrears)

  21. Models of Prepayment • Public Securities Association (PSA) • Option Adjusted Spread (OAS)

  22. PSA Model • In the first month the pool exists the pre-payment rate is .2% • For the first 30 months of the pool’s life the pre-payment rate increases by .2% • Maximum pre-payment rate = 6%

  23. PSA Model Do prepayments actually behave this way?

  24. Problems with PSA Actual Prepayments can deviate from PSA because: • Mortgage rates may fall – mortgagees refinance • Age of the mortgage pool • Whether payments are fully amortized • Assumability of mortgages in the pool • Size of pool • Conventional or nonconventional mortgage (FHA/VA) • Geographic location • Age and job status of mortgagee in the pool

  25. Adjustment to PSA • A common adjustment is to assume some fixed deviation • FIs that assume prepayments exactly follow PSA say that the pool is 100% PSA • Pools can assume a 75% prepayment scheme • Pools can assume a 125% prepayment scheme

  26. Loews Investments purchases a pool of 700 mortgages with a total of $4,500,000 in mortgage principal find the total principal remaining in the pool at the end of month 3 using 200% PSA.

  27. Goldman Sachs purchases a pool of 500 30-year interest only mortgages with average principal of $250,000 each. Each mortgage has an annual interest rate of 5%. Goldman securitizes the mortgage pool by selling it to an SPV who collects a 50bps servicing fee. The SPV pays GNMA a 10bps insurance fee. • Calculate the payment to bond holders, GNMA and the SPV at the end of month 2 assuming 100% PSA Assume that all payments are made in arrears

  28. Option Model – Intuition • The mortgagee can view the mortgage as the combination of a bond and an option to prepay early • Option: At any point in time the mortgagee can prepay the mortgage • Bond: If they do not prepay, they have to continue making interest and principal payments – like a bond • Mortgage value: • GNMA Pass-through Value: Bank owns the bond (they receive coupon payments) . So, this is positive value to the bank • Why is it a T-bond? What assumption are we making? • Is the assumption realistic? 28 Because the mortgagee has the option to prepay, the bank may not receive all the interest income. This reduces the value of the bond (mortgage) relative to one without the option to prepay. That is, the bank has sold off some of the bond value in the form a pre-payment option.

  29. Collateralized Mortgage Obligations (CMOs)

  30. Creating a CMO • CMO is another way of repackaging the cash flows from a pool of mortgages to make securities more attractive to specific investors Mortgages origination/purchase FI purchases GNMA pass-throughs FI places pass-throughs in trust off balance sheet They receive FHA/VA insurance Bank places them in a trust off balance sheet GNMA pass-throughs Trust issues CMO Class A Class B Class C The trust issues pass-through securities GNMA insurance

  31. Creating a CMO • CMO is another way of repackaging the cash flows from a pool of mortgages to make securities more attractive to specific investors Mortgages origination/purchase FI purchases GNMA pass-throughs FI purchases Mortgages FI places pass-throughs in trust off balance sheet They receive FHA/VA insurance Bank places them in a trust off balance sheet GNMA pass-throughs Trust issues CMO Class A Class B Class C The trust issues pass-through securities GNMA insurance

  32. CMO Cash Flows • CMO bond are backed by a pool of pass-throughs / Mortgages • Each CMO bond (tranche) has a guaranteed coupon • Each bond has different cash flow rights regarding principal payments (scheduled or pre-paid) Principal Payment (scheduled or pre-payments) Class A Promised coupon (2% for example) Principal & Interest REMICS Real Estate Mortgage Investment Conduit Promised coupon (1.3% for example) Class B Pool of mortgages or pass-throughs Promised coupon (1% for example) Class C

  33. CMO Cash Flows • CMO bond are backed by a pool of pass-throughs / Mortgages • Each CMO bond (tranche) has a guaranteed coupon • Each bond has different cash flow rights regarding principal payments (scheduled or pre-paid) Principal Payment (scheduled or pre-payments) Class A The REMIC exists until all principal has been repaid Promised coupon (2% for example) Principal Payment (scheduled or pre-payments) Principal Payment (scheduled or pre-payments) Principal & Interest REMICS Real Estate Mortgage Investment Conduit Promised coupon (1.3% for example) Class B Pool of mortgages or pass-throughs Promised coupon (1% for example) Class C

  34. Apex Capital Inc. has purchased $7,000,000 of face value in interest only mortgages. They allocate $1,500,000, 2,500,000 of principal to the Class A and B bonds respectively leaving $3,000,000 for the Class C bond. The Class A, B and C bonds pay a monthly coupon of 7% pa., 7.5% pa. and 4% pa. respectively. (Assume interest is paid in arrears) • Calculate the monthly payment to bond holders at the end of month 3 with no prepayment • Calculate the payment to bond holders at the end of month 2 if $1,000,000 is prepaid at the end of each month

  35. FYI Example CMO with Fully Amortizing Mortgages (No Pre-payment risk)

  36. Example: no pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. $1,000M = 20,000×$50,000

  37. Example: no pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. • Given the following schedule of interest and principal payments, calculate the payment to bond holders at the end of month 3 Interest = (0.042/12) ×(1,000,000,000) Total principal paid over the first 2 months 1,390,171.74 +1,395,037.34 2,785,209.08 Step #1 Coupon Payments Class A: (0.06/12)($100M – 2,785,037.34) = $486,073.95 Class B: (0.045/12)($300M) = $1,125,000 Class C: (0.0375/12)($600M) = $1,875,000 $3,486,073.95

  38. Example: no pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. • Given the following schedule of interest and principal payments, calculate the payment to bond holders at the end of month 3 Step #2 Principal Payments Class A: $1,399,919.97 Class B: 0 Class C: 0 Class A will receive the full principal payment as long as it still has principal outstanding

  39. FYI Example CMO with Fully Amortizing Mortgages and pre-payment risk

  40. Example: no pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon.

  41. Example: with pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. • Suppose the monthly amortization payment at origination is 4,890,171.74, find the payment to bond hold holders of each class at the end of month 3. Assume 100% PSA and all principal payments (scheduled and pre-payments occur a the end of the month) Step #1 Build the payment schedule 996,609,828.26 4,890,171.74 3,500,000 1,390,171.74 2,000,000 1,000,000,000 – 1,390,171.74 – 2,000,000 996,906,868.26 (0.042/12)(1,000,000,000) = 3,500,000 4,890,171.74 – 3,500,000 = 1,390,171.74 (0.002)(1,000,000,000) = 2,000,000 All principal payments (including prepayments) are maid at the end of the month so the interest payment after month 1 is based on the total size of the pool

  42. Example: with pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. • Suppose the monthly amortization payment at origination is 4,890,171.74, find the payment to bond hold holders of each class at the end of month 3. Assume 100% PSA and all principal payments (scheduled and pre-payments occur a the end of the month) Step #1 Build the payment schedule 996,609,828.26 4,890,171.74 3,500,000 1,390,171.74 2,000,000 991,231,131.96 4,880,391.39 3,488,134.40 1,392,256.99 3,986,439.31 996,609,828.26 – 1,392,256.99 – 3,986,439.31 991,231,131.96 (0.042/12)(996,609,828.26) = 3,488,134.40 4,880,391.39 – 3,488,134.40 = 1,392,256.99 (0.004)(996,609,828.26) = 3,986,439.31 0.2% of principal has been pre-paid this will reduce the monthly payments by 0.2% → (1 – 0.002)(4,890,171.74) = 4,880,391.39

  43. Example: with pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. • Suppose the monthly amortization payment at origination is 4,890,171.74, find the payment to bond hold holders of each class at the end of month 3. Assume 100% PSA and all principal payments (scheduled and pre-payments occur a the end of the month) 996,609,828.26 – 1,391,560.87 – 5,947,386.79 983,892,184.30 Step #1 Build the payment schedule 996,609,828.26 4,890,171.74 3,500,000 1,390,171.74 2,000,000 4,880,391.39 3,488,134.40 1,392,256.99 3,986,439.31 991,231,131.96 (0.042/12)(991,231,131.96) = 3,469,308.96 4,860,869.79 – 3,469,309.96 = 1,391,560.87 983,892,184.30 4,860,869.79 3,469,308.96 1,391,560.87 5,947,386.79 (0.006)(991,231,131.96) = 5,947,386.79 0.4% of principal has been pre-paid this will reduce the monthly payments by 0.4% → (1-0.004)(4,880,391.39) = 4,860,869.79

  44. Example: with pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. • Suppose the monthly amortization payment at origination is 4,890,171.74, find the payment to bond hold holders of each class at the end of month 3. Assume 100% PSA and all principal payments (scheduled and pre-payments occur a the end of the month) Repaid principal 1,000,000,000 – 991,231,131.96 = 8,768,868.04 Step #2 Coupon Payments Class A: (0.06/12)($100M – 8,768,868.04) = $456,155.66 Class B: (0.045/12)($300M) = $1,125,000 Class C: (0.045/12)($435M) = $1,875,000

  45. Example: with pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. • Suppose the monthly amortization payment at origination is 4,890,171.74, find the payment to bond hold holders of each class at the end of month 3. Assume 100% PSA and all principal payments (scheduled and pre-payments occur a the end of the month) Principal Payment 1,391,560.87 + 5,947,386.79 = 7,338,947.66 Step #3 Principal Payments Class A: 7,338,947.66 Class B: 0 Class C: 0

  46. Example: with pre-payment Freddie Mac purchased 20,000 conventional 30-year fixed rate mortgages with an average principal of 50,000 per mortgages. They use the mortgages to create CMO with the following bonds (tranches). The mortgage pool pays a 4.2% aggregate mortgage coupon. • Suppose the monthly amortization payment at origination is 4,890,171.74, find the payment to bond hold holders of each class at the end of month 3. Assume 100% PSA and all principal payments (scheduled and pre-payments occur a the end of the month) Total Payment Class A: $456,155.66 + $7,338,947.66 = $7,795,103.32 Class B: $1,125,000 Class C: $1,875,000

  47. Lecture Summary Fully Amortizing Mortgages • How to calculate payments from a pool of mortgages • How to calculate payments to bond holders • How to calculate the value of a pass-through • How to calculate payments with prepayment risk (PSA) Prepayment Risk • PSA Model • Option Adjusted Spread (Intuition) Collateralized Mortgage Obligations (CMO) • How to calculate payments to bond holders • Interest only pool with or without prepayment • Fully amortizing mortgage pool (FYI) • Fully amortizing mortgage pool with prepayment (FYI)

  48. Appendix

  49. Other Securitizations

  50. Other Securitizations • CMO • Sequential payment; Planned Amortization Class; Target Amortization Class; Companion Tranche; Z-Tranche • Mortgage-Backed Bond • Bond that is secured by mortgages (collateral) • Principal only pass-through strip • CMO class that receives only the principal payments • Interest only • CMO class that receives only the interest payments • Structured Credit • Instruments that are based on a pool of credit such as CDOs, RMBS …

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