class #21; chap. 26. purpose: understand cash flows from securitization pool of fully amortizing...
TRANSCRIPT
Class #21; Chap. 26
Purpose: Understand cash flows from securitization
Pool of fully amortizing mortgages GNMA Bond1. Cash flows generated by the pool of mortgages 2. Cash flows to bond holders 3. Bond valuation4. Cash flows to bond holders with prepayment risk – interest only loan
pool (after prepayment risk)
Prepayment risk 1. PSA Model2. Option Adjusted Spread
Collateralized Mortgage Obligations (CMOs)1. Interest only loans2. Fully Amortizing loans with Prepayment risk (FYI)
2
GNMA BondCash Flows Generated by the mortgage pool
3
4
Loan pool SPV
12%Interest payments
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
5
PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT
mnmrmr
PMTPV)/1(
11
/
1
mnmr
PMT
mr
PMT
mr
PMTPV
)/1(...
)/1(/1 2
What is the present value?
mill100000,100000,1
What is the interest rate?
%12r
What is the number of compounding periods
per year?
12m
How many years?
30years
Payments from mortgage pool
1m 2m 3m 4m 5m 356m 357m 358m 359m 360m
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
6
n × m = 12 * 30 = 360r/m = .12/12 interest rate = 1% per monthPV = 1000 * $100,000 = $100,000,000PMT (Constant monthly payment to pay off the mortgage over its life )= ?
MPMTmrmr
PMTPVmn
100)12/12.1(
11
12/12.
1
)/1(
11
/
13012
60.612,028,1$21833.97
000,000,100
)12/12.1(1
112/12.
1
000,000,100
3012
PMT
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
GNMA BondPayment to the Bond Holders
7
8
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.
Loan pool SPV
12%Interest payments
0.44%Servicing Fee
11.56%Interest payments
0.06%Insurance Fee
11.5%Interest payments
Mortgage coupon rate 12.00%
Servicing Fee – 0.44%
GNMA Insurance Fee – 0.06%
GNMA Pass-Through Bond Coupon 11.50%
9
40.291,990$9804.100
000,000,100
)12/115.1(1
112/115.
1
000,000,100
3012
PMT
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
GNMA BondValuing a Pass-Through Bond
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11
World Bank has originated 1,000 fixed rate fully amortizing mortgages with an average size of $100,000, 30 years to maturity and 12% aggregate interest rate compounded monthly. World Bank sells the pool of mortgages to an SPV they created to facilitate the securitization. After 1 year the mortgage interest rate has dropped to 10% find the current value of the pass-through security. Assume no pre-payments default risk.
Step #1 find the new rate
New Rate = 0.1 – 0.0044 – 0.0006 = 0.095
Step #2 find the current value
PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT
1m 2m 3m 4m 5m 344m 345m 346m 347m 348m
How many years
990K 990K 990K 990K 990K 990K 990K 990K 990K 990K
1m 2m 3m 4m 5m
What are the payments?
12
mnmrmr
PMTPV)/1(
11
/
1
Step #1 find the new rate
New Rate = 0.1 – 0.0044 – 0.0006 = 0.095
2912)12/095.01(
11
12/095.0
140.291,990$PV
Step #2 find the current value
99.837,045,117PV
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.
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.
a)Find the aggregate semiannual payment to the GNMA bond holder
b)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.
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Pre-payment Risk
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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
15
Bond payments with & without Pre-payment
Affects of prepayment:1. Cause monthly cash flows from the pool to vary2. Cause payments from the pool to decrease as the MBS ages
16
17
Are interest rates high or low?
Bond payments with & without Pre-payment
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)
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How do you value the bond with prepayments?
Bond payments with & without Pre-payment
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Is it possible to know how many loans will be prepaid and when?
Bond payments with & without Pre-payment
No! so we guess a.k.a. build a model
Modeling Prepayments
(Assume all payments are made in arrears)
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1. Public Securities Association (PSA)
2. Option Adjusted Spread (OAS)
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1. In the first month the pool exists the pre-payment rate is .2%2. For the first 30 months of the pool’s life the pre-payment rate
increases by .2%3. Maximum pre-payment rate = 6%
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Months of existence Prepayment rate
1 .2 %
2 .4 %
3 .6 %
⁞ ⁞
29 5.8 %
30 6 %
31 6 %
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Do prepayments actually behave this way?
Actual Prepayments can deviate from PSA because:1. Mortgage rates may fall – mortgagees refinance2. Age of the mortgage pool3. Whether payments are fully amortized4. Assumability of mortgages in the pool5. Size of pool6. Conventional or nonconventional mortgage (FHA/VA)7. Geographic location8. Age and job status of mortgagee in the pool
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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
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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.
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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.
a)Calculate the payment to bond holders, GNMA and the SPV at the end of month 2 assuming 100% PSAAssume that all payments are made in arrears
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The mortgagee can view the mortgage as the combination of a bond and an option to prepay early
◦ Bond: Every month the bank collects a payment of principal and interest much like a coupon on a bond
◦ Option: At any point in time the mortgagee can prepay the mortgage so the bank has sold a prepayment option
Mortgage value:
GNMA Pass-through Value:
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optionperpaybondbankto
mortgage VVV
optionperpaybondtGNMA VVV
Why is it a T-bond? What assumption are we making?
Is the assumption realistic?
Bank owns the bond (they receive coupon payments) . So, this is positive value to the bank
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.
Collateralized Mortgage Obligations (CMOs)
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GNMA pass-throughs
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Mortgages origination/purchase
They receive FHA/VA insurance
Bank places them in a trust off balance sheet
The trust issues pass-through securities
GNMA insurance
FI purchases GNMA pass-throughs
FI places pass-throughs in trust off balance sheet
Trust issues CMO
Class A
Class B
Class C
CMO is another way of repackaging the cash flows from a pool of mortgages to make securities more attractive to specific investors
GNMA pass-throughs
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Mortgages origination/purchase
They receive FHA/VA insurance
Bank places them in a trust off balance sheet
The trust issues pass-through securities
GNMA insurance
FI purchases GNMA pass-throughs
FI places pass-throughs in trust off balance sheet
Trust issues CMO
Class A
Class B
Class C
CMO is another way of repackaging the cash flows from a pool of mortgages to make securities more attractive to specific investors
FI purchases Mortgages
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)
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Pool of mortgagesor pass-throughs
Principal
& Interest
REMICSReal Estate Mortgage Investment Conduit
Class A
Class B
Class C
Promised coupon (2% for example)
Promised coupon (1.3% for example)
Promised coupon (1% for example)
Principal Payment
(scheduled or pre-payments)
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)
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Pool of mortgagesor pass-throughs
Principal
& Interest
REMICSReal Estate Mortgage Investment Conduit
Class A
Class B
Class C
Promised coupon (2% for example)
Promised coupon (1.3% for example)
Promised coupon (1% for example)
Principal Payment
(scheduled or pre-payments)
Principal Payment
(scheduled or pre-payments)
Principal Payment
(scheduled or pre-payments)
The REMIC exists until all principal has been repaid
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)a)Calculate the monthly payment to bond holders at the end of month 3 with no prepaymentb)Calculate the payment to bond holders at the end of month 2 if $1,000,000 is prepaid at the end of each month
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ExampleCMO with Fully Amortizing Mortgages
(No Pre-payment risk)
35
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.
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Bonds Principal Coupon
Class A 100M 6% p.a.
Class B 300M 4.5% p.a.
Class C 600M 3.75% p.a.
$1,000M = 20,000×$50,000
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
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Month Interest Principal Remaining Principal
1 $3,500,000.00 $1,390,171.74 $998,609,828.26
2 $3,495,134.40 $1,395,037.34 $997,214,790.92
3 $3,490,251.77 $1,399,919.97 $995,814,870.96
4 $3,485,352.05 $1,404,819.69 $994,410,051.27
5 $3,480,435.18 $1,409,736.56 $993,000,314.71
6 $3,475,501.10 $1,414,670.64 $991,585,644.07
Step #1 Coupon PaymentsClass A: (0.06/12)($100M – 2,785,037.34) = $486,073.95Class B: (0.045/12)($300M) = $1,125,000 Class C: (0.0375/12)($600M) = $1,875,000
$3,486,073.95
Total principal paid over the first 2 months
1,390,171.74 +1,395,037.34
2,785,209.08
Interest = (0.042/12) ×(1,000,000,000)
From the annuity formula:
Monthly payment = 4,890,171.74
$4,890,171.74 - $3,500,000.00
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
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Month Interest Principal Remaining Principal
1 $3,500,000.00 $1,390,171.74 $998,609,828.26
2 $3,495,134.40 $1,395,037.34 $997,214,790.92
3 $3,490,251.77 $1,399,919.97 $995,814,870.96
4 $3,485,352.05 $1,404,819.69 $994,410,051.27
5 $3,480,435.18 $1,409,736.56 $993,000,314.71
6 $3,475,501.10 $1,414,670.64 $991,585,644.07
Step #2 Principal PaymentsClass A: $1,399,919.97Class B: 0Class C: 0
Class A will receive the full principal payment as long as it still has principal outstanding
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
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Month Interest Principal Remaining Principal
1 $3,500,000.00 $1,390,171.74 $998,609,828.26
2 $3,495,134.40 $1,395,037.34 $997,214,790.92
3 $3,490,251.77 $1,399,919.97 $995,814,870.96
4 $3,485,352.05 $1,404,819.69 $994,410,051.27
5 $3,480,435.18 $1,409,736.56 $993,000,314.71
6 $3,475,501.10 $1,414,670.64 $991,585,644.07
Step #3 sum principal and interest paymentsClass A: $486,073.95 + $1,399,919.97 =1,885,993.92 Class B: $1,125,000 + 0 = $1,125,000 Class C: $1,875,000 + 0 = $1,875,000
Example CMO with Fully Amortizing
Mortgages and pre-payment risk
40
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.
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Bonds Principal Coupon
Class A 100M 6% p.a.
Class B 300M 4.5% p.a.
Class C 600M 3.75% p.a.
Month Payment Interest Principal Pre-payment Remaining Principal
1
2
3
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)
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Step #1 Build the payment schedule
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
(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
1,000,000,000
– 1,390,171.74
– 2,000,000
996,906,868.26
4,890,171.74 3,500,000 1,390,171.74 2,000,000 996,609,828.26
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)
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Step #1 Build the payment schedule
Month Payment Interest Principal Pre-payment Remaining Principal
1
2
3
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
(0.042/12)(996,609,828.26) =
3,488,134.404,880,391.39 – 3,488,134.40 =
1,392,256.99
(0.004)(996,609,828.26) =
3,986,439.31
996,609,828.26
– 1,392,256.99
– 3,986,439.31
991,231,131.96
4,880,391.39 3,488,134.40 1,392,256.99 3,986,439.31 991,231,131.96
4,890,171.74 3,500,000 1,390,171.74 2,000,000 996,609,828.26
Month Payment Interest Principal Pre-payment Remaining Principal
1
2
3
4,880,391.39 3,488,134.40 1,392,256.99 3,986,439.31 991,231,131.96
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)
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Step #1 Build the payment schedule
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
(0.042/12)(991,231,131.96) =
3,469,308.96
4,860,869.79 – 3,469,309.96 =
1,391,560.87
(0.006)(991,231,131.96) =
5,947,386.79
996,609,828.26
– 1,391,560.87
– 5,947,386.79
983,892,184.30
4,860,869.79 3,469,308.96 1,391,560.87 5,947,386.79 983,892,184.30
4,890,171.74 3,500,000 1,390,171.74 2,000,000 996,609,828.26
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)
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Step #2 Coupon Payments
Month Payment Interest Principal Pre-payment Remaining Principal
1 4,890,171.74 $3,500,000.00 1,390,171.7371 2,000,000.00 $996,609,828.26
2 4,880,391.39 $3,488,134.40 $1,392,256.99 3,986,439.31 $991,231,131.96
3 4,860,869.83 $3,469,308.96 $1,391,560.87 5,947,386.79 $983,892,184.30
Class A: (0.06/12)($100M – 8,768,868.04) = $456,155.66Class B: (0.045/12)($300M) = $1,125,000 Class C: (0.045/12)($435M) = $1,875,000
Repaid principal
1,000,000,000 – 991,231,131.96 = 8,768,868.04
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)
46
Step #3 Principal Payments
Month Payment Interest Principal Pre-payment Remaining Principal
1 4,890,171.74 $3,500,000.00 1,390,171.7371 2,000,000.00 $996,609,828.26
2 4,880,391.39 $3,488,134.40 $1,392,256.99 3,986,439.31 $991,231,131.96
3 4,860,869.83 $3,469,308.96 $1,391,560.87 5,947,386.79 $983,892,184.30
Class A: 7,338,947.66Class B: 0Class C: 0
Principal Payment
1,391,560.87 + 5,947,386.79 = 7,338,947.66
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)
47
Total Payment
Month Payment Interest Principal Pre-payment Remaining Principal
1 4,890,171.74 $3,500,000.00 1,390,171.7371 2,000,000.00 $996,609,828.26
2 4,880,391.39 $3,488,134.40 $1,392,256.99 3,986,439.31 $991,231,131.96
3 4,860,869.83 $3,469,308.96 $1,391,560.87 5,947,386.79 $983,892,184.30
Class A: $456,155.66 + $7,338,947.66 = $7,795,103.32Class B: $1,125,000 Class C: $1,875,000
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
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 …
51
Collateralized Debt Obligations (CDO):◦ These are securities backed by a pool of bonds loans or other
assets. CDOs do not specialize in one type of debt but they are usually non-mortgage loans or bonds
Residential Mortgage backed security (RMBS):◦ These securities are backed by a pool of residential mortgages.◦ The cash flows from the pool are distributed to RMBS holders
depending on their priority
52
Principal
53
Equity
BB
BBB
A
AA
Tranches Pool of Credit
AAA
3%
0%
7%
10%
15%
30%
100%
Collect principal into on big pool
Question: What are these Tranches? Each tranche represents a claim on a fraction of the principal in the pool
For example, if you own a piece of the
equity tranche (bond), then you have a claim on the first 3% of debt in the pool to default
Principal
54
Equity
BB
BBB
A
AA
Tranches Pool of Credit
AAA
3%
0%
7%
10%
15%
30%
100%
Question: What does it mean to have a claim on the principal in the pool?
1.Receive payments
Cash Flows
Principal & Interest
As a claimholder, you are entitled to a fraction of these
cash flows
Payment Waterfall: Interest & principal payments trickle down from the senior to junior tranches. The exact distribution is specific to the CDO and is defined in the contract.
2% of the pool defaults
Principal
55
Equity
BB
BBB
A
AA
Tranches Pool of Credit
AAA
3%
0%
7%
10%
15%
30%
100%
Question: What does it mean to have a claim on the principal in the pool?
2.Suffer losses from default
Default
Credits will default
As a claimholder, you suffer losses if the defaulted principal exhausts the “credit
enhancement” for your bond class
5% more of the pool defaults
At this point both the 0-3 and 3-7 tranches have
been wiped out – they no longer receive payments 15% more of the pool defaults
2% of the pool defaults
Principal
56
Equity
BB
BBB
A
AA
Tranches Pool of Credit
AAA
3%
0%
7%
10%
15%
30%
100%
Question: What does it mean to have a claim on the principal in the pool?
2.Suffer losses from default
Default
Credits will default
As a claimholder, you suffer losses if the defaulted principal exhausts the credit
enhancement
The AA tranche is receiving interest and principal payments on a fraction of the original principal
15% more of the pool defaults8% more of the pool defaults
30% of the principal in the pool must default before the AAA tranche gets hit. What are the chances?
Any asset can be priced by finding the expected value in the future and discounting back to today
To find the expected value we need to know the probability of experiencing a 1%, 2%, 3% …. Percent loss in the underlying pool
We can get this from the loss distribution, which needs to be estimated.
57
58
0% - 3%
3% - 7%
7% - 10%
10% - 15%
15% - 30%
Tranches Pool of Credit
Question: What is the value of the equity tranche
30% - 100%
P( 0% defaults AND 3% does not default) × 3%
+ P( 0.1% defaults AND 2.9% does not default) × 2.9%
+ P( 0.2% defaults AND 2.8% does not default) × 2.8%
+ P( 0.3% defaults AND 2.7% does not default) × 2.7%
+ P( 0.4% defaults AND 2.6% does not default) × 2.6%
+ P( 2.8% defaults AND 0.02% does not default) × 0.2%
+ P( 2.9% defaults AND 0.02% does not default) × 0.1%
+ P( 3% defaults AND 0.02% does not default) × 0%
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0% - 3%
3% - 7%
7% - 10%
10% - 15%
15% - 30%
Tranches Pool of Credit
Question: What is the value of the equity tranche
30% - 100%
Joint Loss Distribution
We can get the probability of each event by summing the area under the curve
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0% - 3%
3% - 7%
7% - 10%
10% - 15%
15% - 30%
Tranches Pool of Credit
Question: Is pool diversification (correlation) important
30% - 100%
Joint Loss Distribution
An increase in correlation will change the shape of the loss distribution. This increase the equity tranche value and decrease the AAA tranche value
YES!!!!!!!!!!!!
Higher Probability of experiencing losses
Is the AAA tranche more/less valuable
Typical Sub-prime Borrower and Loan Characteristics
◦ FICO credit score 650 and below
◦ Prior mortgage delinquencies are acceptable
◦Bankruptcy filing within the last 3 to 5 years are acceptable
◦ Foreclosure within the last 3 to 5 years are acceptable
◦Debt-to-Income (DTI) ratios of 40% or higher
◦ Loan-to-Value (LTV) ratios greater than 80%
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Off balance sheet vehicles – SPV/SIV
Pass-through Securities◦ Agencies: Freddie, Fannie, Ginnie
Benefits and Risks of Securitization
Cash flows from securitization
Pricing:◦ Prepayment Models◦ Option Adjusted Spread
Other Securitizations◦ CMO, CDO, RMBS
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