Class #21; Chap. 26

Purpose: Understand cash flows from securitization

Pool of fully amortizing mortgages GNMA Bond
1.
2.
3.
4.

Prepayment risk
1.
2.

Cash flows generated by the pool of mortgages
Cash flows to bond holders
Bond valuation
Cash flows to bond holders with prepayment risk – interest only loan
pool (after prepayment risk)
PSA Model
Option Adjusted Spread
Collateralized Mortgage Obligations (CMOs)
1.
Interest only loans
2.
Fully Amortizing loans with Prepayment risk (FYI)
2
GNMA Bond
Cash Flows Generated
by the mortgage pool
3
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
Loan pool
SPV
12%
Interest payments
4
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
Payments from
mortgage pool
What is the
present value?
1,000100,000  100mill
What is the
interest rate?
r  12%
PMT
PMT
PMT
PMT
PMT
PMT
1m
2m
3m
4m
5m
356m
PV 
PMT
357m
PMT
358m
PMT
PMT
PMT


...

1  r / m (1  r / m) 2
(1  r / m) mn
PMT
359m
PMT
360m
How many
years?
years  30
What is the number
of compounding
periods per year?
m  12
PV  PMT 

1 
1
1

r / m  (1  r / m) mn 
5
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 )= ?
PV  PMT 


1 
1
1 
1
1


PMT

1




  100M
r / m  (1  r / m) mn 
.12 / 12  (1  .12 / 12)1230 
PMT 
100,000,000
100,000,000

 $1,028,612.60
97.21833

1 
1
1

.12 / 12  (1  .12 / 12)1230 
6
GNMA Bond
Payment to the Bond Holders
7
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 prepayments or defaults.
Loan pool
SPV
11.56%
12%
11.5%
Interest payments
Interest payments
0.44%
Servicing Fee
Interest payments
0.06%
Insurance Fee
Mortgage coupon rate
12.00%
Servicing Fee
– 0.44%
GNMA Insurance Fee
– 0.06%
GNMA Pass-Through Bond Coupon
11.50%
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.
PMT 
100,000,000
100,000,000

 $990,291.40
100.9804


1
1
1

.115/ 12  (1  .115/ 12)1230 
Use the payment rate less fees
9
GNMA Bond
Valuing a Pass-Through Bond
10
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
How many
years
Step #2 find the current value
What are the payments?
PMT
990K
PMT
990K
PMT
990K
PMT
990K
PMT
990K
PMT
990K
PMT
990K
PMT
990K
1m
2m
3m
4m
5m
344m
345m
346m
PMT
990K
347m
PMT
990K
348m
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
PV  PMT 

1 
1
1

r / m  (1  r / m) mn 
PV  $990,291.40


1
1
1

0.095/ 12  (1  0.095/ 12)1229 
PV  117,045,837.99
12
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.
13
Pre-payment Risk
14

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 vary
2. Cause payments from the pool to decrease as the MBS ages
16
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)
17
Bond payments with & without Pre-payment
How do you value the bond with
prepayments?
18
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
19
Modeling Prepayments
(Assume all payments are made in arrears)
20
1.
Public Securities Association (PSA)
2.
Option Adjusted Spread (OAS)
21
1.
2.
3.
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%
Months of existence
Prepayment rate
1
.2 %
2
.4 %
3
.6 %
⁞
⁞
29
5.8 %
30
6%
31
6%
22
Do prepayments actually behave this way?
23
Actual Prepayments can deviate from PSA because:
1.
Mortgage rates may fall – mortgagees refinance
2.
Age of the mortgage pool
3.
Whether payments are fully amortized
4.
Assumability of mortgages in the pool
5.
Size of pool
6.
Conventional or nonconventional mortgage (FHA/VA)
7.
Geographic location
8.
Age and job status of mortgagee in the pool
24




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
25
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.
26
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% PSA
Assume that all payments are made in arrears
27

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 optionBank owns the bond (they receive
coupon payments) . So, this is
positive value to the bank

Mortgage value:
Vmortgage  Vbond  Vperpay option
to 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.

GNMA Pass-through Value:
VGNMA  Vt bond  Vperpay option


Why is it a T-bond? What
assumption are we making?
Is the assumption realistic?
28
Collateralized Mortgage
Obligations (CMOs)
29

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
The trust issues passthrough securities
GNMA pass-throughs
Trust issues CMO
Class A
Class B
Class C
GNMA insurance
30

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
FI purchases
GNMA
pass-throughs
Mortgages
FI places pass-throughs
in trust off balance sheet
They receive
FHA/VA insurance
Bank places them in a
trust off balance sheet
The trust issues passthrough securities
GNMA pass-throughs
Trust issues CMO
Class A
Class B
Class C
GNMA insurance
31



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)
Principal
& Interest
REMICS
Real Estate Mortgage
Investment Conduit
Promised coupon (1.3% for example)
Class A
Class B
Pool of mortgages
or pass-throughs
Class C
32



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
Principal Payment
(scheduled or pre-payments)
Principal
& Interest
REMICS
Promised coupon (1.3% for example)
Real Estate Mortgage
Investment Conduit
Class B
Pool of mortgages
or pass-throughs
Class C
Principal Payment
(scheduled or pre-payments)
33
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)
b)
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
34
Example
CMO 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.
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
36
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)
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
Total principal paid over
the first 2 months
1,390,171.74
+1,395,037.34
2,785,209.08
From the annuity formula:
Step #1 Coupon Payments
Monthly payment = 4,890,171.74
$4,890,171.74 - $3,500,000.00
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
37
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
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 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
38
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
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 payments
Class 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
39
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.
Bonds
Principal
Coupon
Class A
100M
6% p.a.
Class B
300M
4.5% p.a.
Class C
600M
3.75% p.a.
41
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
Month
1
Payment
4,890,171.74
Interest
3,500,000
Principal
Pre-payment
1,390,171.74
2,000,000
Remaining Principal
996,609,828.26
2
3
(0.042/12)(1,000,000,000) =
3,500,000
(0.002)(1,000,000,000) =
2,000,000
4,890,171.74 – 3,500,000 =
1,390,171.74
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
1,000,000,000
– 1,390,171.74
– 2,000,000
996,906,868.26
42
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
Month
Payment
Interest
(0.004)(996,609,828.26) =
3,986,439.31
Principal
Pre-payment
Remaining Principal
1
4,890,171.74
3,500,000
1,390,171.74
2,000,000
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
(0.042/12)(996,609,828.26) =
3,488,134.40
4,880,391.39 – 3,488,134.40 =
1,392,256.99
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
996,609,828.26
– 1,392,256.99
– 3,986,439.31
991,231,131.96
43
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
Step #1 Build the payment schedule
Month
Payment
Interest
(0.006)(991,231,131.96) =
5,947,386.79
Principal
Pre-payment
– 1,391,560.87
– 5,947,386.79
983,892,184.30
Remaining Principal
1
4,890,171.74
3,500,000
1,390,171.74
2,000,000
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
4,860,869.79
3,469,308.96
1,391,560.87
5,947,386.79
983,892,184.30
(0.042/12)(991,231,131.96) =
3,469,308.96
4,860,869.79 – 3,469,309.96 =
1,391,560.87
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
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)
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
Step #2 Coupon Payments
Repaid principal
1,000,000,000 – 991,231,131.96 = 8,768,868.04
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
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)
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
Step #3 Principal Payments
Class A: 7,338,947.66
Class B:
0
Class C:
0
Principal Payment
1,391,560.87 + 5,947,386.79 = 7,338,947.66
46
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)
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
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
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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
Each tranche represents a claim on a
fraction of the principal in the pool
Question: What are these Tranches?
Pool of Credit
Principal
Tranches
100%
AAA
Collect principal
into on big pool
30%
AA
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
15%
A
10%
BBB
BB
Equity
7%
3%
0%
53
Question: What does it mean to have a claim on the principal in the pool?
1. Receive payments
Pool of Credit
Principal
Tranches
100%
AAA
Cash Flows
Principal & Interest
30%
AA
As a claimholder,
you are entitled to
a fraction of these
cash flows
15%
A
10%
BBB
BB
Equity
7%
3%
0%
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.
54
Question: What does it mean to have a claim on the principal in the pool?
2. Suffer losses from default
Pool of Credit
Principal
As a claimholder, you
suffer losses if the
defaulted principal
exhausts the “credit
enhancement” for your
bond class
Tranches
100%
AAA
Default
Credits will default
30%
AA
15%
A
10%
BBB
ofof
the
pool
defaults
15%2%
5%
more
more
ofthe
the
pool
pool
defaults
defaults
At this point both the 0-3
and 3-7 tranches have
been wiped out – they no
longer receive payments
BB
Equity
7%
3%
0%
55
Question: What does it mean to have a claim on the principal in the pool?
2. Suffer losses from default
Pool of Credit
Principal
Tranches
As a claimholder, you
suffer losses if the
defaulted principal
exhausts the credit
enhancement
100%
AAA
Default
Credits will default
30%
AA
15%
The AA tranche is receiving interest and principal
payments on a fraction of the original principal
30% of the principal in the pool must default before
the AAA tranche gets hit. What are the chances?
A
10%
BBB
BB
Equity
7%
3%
0%
ofof
the
pool
defaults
15%2%
8%
more
more
ofthe
the
pool
pool
defaults
defaults
56

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
Question: What is the value of the equity tranche
Pool of Credit
P( 0% defaults AND 3% does not default) × 3%
Tranches
+ 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%
30% - 100%
15% - 30%
10% - 15%
+ 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%
7% - 10%
3% - 7%
0% - 3%
58
Question: What is the value of the equity tranche
Pool of Credit
Joint Loss Distribution
Tranches
30% - 100%
15% - 30%
10% - 15%
7% - 10%
3% - 7%
0% - 3%
We can get the probability of each event by
summing the area under the curve
59
Question: Is pool diversification (correlation) important YES!!!!!!!!!!!!
Pool of Credit
Joint Loss Distribution
Tranches
Higher Probability of
experiencing losses
Is the AAA tranche
more/less valuable
30% - 100%
15% - 30%
10% - 15%
7% - 10%
3% - 7%
0% - 3%
An increase in correlation will change the shape of the loss distribution.
This increase the equity tranche value and decrease the AAA tranche value
60

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%
61
62
63

Off balance sheet vehicles – SPV/SIV

Pass-through Securities

Benefits and Risks of Securitization

Cash flows from securitization

Pricing:

Other Securitizations
◦ Agencies: Freddie, Fannie, Ginnie
◦ Prepayment Models
◦ Option Adjusted Spread
◦ CMO, CDO, RMBS
64