1. Loan Securitization Cash 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 – interest only loan pool (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 Bond Cash 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
Loan pool
SPV
12%
Interest payments

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
1m m m m m m m m m m
What is the present value?
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. Payment to the Bond Holders
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.
Loan pool
SPV
12%
Interest payments
11.56%
Interest payments
11.5%
Interest payments
0.06%
Insurance Fee
0.44%
Servicing Fee
Mortgage coupon rate
12.00%
Servicing Fee
– 0.44%
GNMA Insurance Fee
– 0.06%
GNMA Pass-Through Bond Coupon
11.50%

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. Valuing a Pass-Through Bond
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 – – = 0.095
Step #2 find the current value
How many years
What are the payments?
990K
1m m m m m
PMT
1m m m m m
344m m m m m

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 – – = 0.095
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 the GNMA 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
Bond payments with & without Pre-payment
Affects of prepayment:
Cause monthly cash flows from the pool to vary
Cause payments from the pool to decrease as the MBS ages

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. (Assume all payments are made in arrears)
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%
Months of existence
Prepayment rate 1
.2 % 2
.4 % 3
.6 % ⁞ 29
5.8 % 30
6 % 31

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 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
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:
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.
Why is it a T-bond? What assumption are we making?
Is the assumption realistic? 28

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. (scheduled or pre-payments)
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)
Pool of mortgages
or pass-throughs
Principal
& Interest
REMICS
Real Estate Mortgage Investment Conduit
Promised coupon (1.3% for example)
Class B
Promised coupon (1% for example)
Class C

33. CMO Cash Flows The REMIC exists until all principal has been repaid
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)
Pool of mortgages
or pass-throughs
Principal
& Interest
REMICS
Real Estate Mortgage Investment Conduit
Promised coupon (1.3% for example)
Class B
Principal Payment
(scheduled or pre-payments)
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. Example CMO with Fully Amortizing Mortgages (No Pre-payment risk)
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.
Bonds
Principal
Coupon
Class A
100M
6% p.a.
Class B
300M
4.5% p.a.
Class C
600M
3.75% p.a.
The interest payments to bond holders will not always equal the interest received from the pool some interest may be taken in frees some may be held to cover future interest payments
$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, ,395,037.34
2,785,209.08
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
From the annuity formula:
Monthly payment = 4,890,171.74
$4,890, $3,500,000.00
The interest payments to bond holders will not always equal the interest received from the pool some interest may be taken in frees some may be held to cover future interest payments
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
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:
Class A will receive the full principal payment as long as it still has principal outstanding
Class C:

39. 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
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, $1,399, =1,885,993.92
Class B: $1,125, = $1,125,000
Class C: $1,875, = $1,875,000

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

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.
Bonds
Principal
Coupon
Class A
100M
6% p.a.
Class B
300M
4.5% p.a.
Class C
600M
3.75% p.a.
The interest payments to bond holders will not always equal the interest received from the pool some interest may be taken in frees some may be held to cover future interest payments

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
Month
Payment
Interest
Principal
Pre-payment
Remaining Principal 1 2 3
4,890,171.74
3,500,000
1,390,171.74
2,000,000
996,609,828.26
(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
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, – 3,500,000 =
1,390,171.74

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)
Step #1 Build the payment schedule
(0.004)(996,609,828.26) =
3,986,439.31
Month
Payment
Interest
Principal
Pre-payment
Remaining Principal 1 2 3
4,890,171.74
3,500,000
1,390,171.74
2,000,000
996,609,828.26
4,880,391.39
3,488,134.40
1,392,256.99
3,986,439.31
991,231,131.96
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) =
3,488,134.40
4,880, – 3,488, =
1,392,256.99
996,609,828.26
– 1,392,256.99
– 3,986,439.31
991,231,131.96

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)
996,609,828.26
– 1,391,560.87
– 5,947,386.79
983,892,184.30
Step #1 Build the payment schedule
(0.006)(991,231,131.96) =
5,947,386.79
Month
Payment
Interest
Principal
Pre-payment
Remaining Principal 1 2 3
4,890,171.74
3,500,000
1,390,171.74
2,000,000
996,609,828.26
4,880,391.39
3,488,134.40
1,392,256.99
3,986,439.31
991,231,131.96
4,860,869.79
3,469,308.96
1,391,560.87
5,947,386.79
983,892,184.30
0.4% of principal has been pre-paid this will reduce the monthly payments by 0.4% → ( )(4,880,391.39) = 4,860,869.79
(0.042/12)(991,231,131.96) =
3,469,308.96
4,860, – 3,469, =
1,391,560.87

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)
Month
Payment
Interest
Principal
Pre-payment
Remaining Principal 1
4,890,171.74
$3,500,000.00
1,390,
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
Repaid principal
1,000,000,000 – 991,231, = 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

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)
Month
Payment
Interest
Principal
Pre-payment
Remaining Principal 1
4,890,171.74
$3,500,000.00
1,390,
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
Principal Payment
1,391, ,947, = 7,338,947.66
Step #3 Principal Payments
Class A: 7,338,947.66
Class B:
Class C:

47. 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)
Month
Payment
Interest
Principal
Pre-payment
Remaining Principal 1
4,890,171.74
$3,500,000.00
1,390,
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, $7,338, = $7,795,103.32
Class B: $1,125,000
Class C: $1,875,000

48. Lecture Summary Fully Amortizing Mortgages Prepayment Risk
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)
Interest only pool with or without prepayment
Fully amortizing mortgage pool (FYI)
Fully amortizing mortgage pool with prepayment (FYI)

49. Appendix

50. Other Securitizations

51. 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 …

52. CDO & RMBS 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

53. Basic Idea
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
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
Collect principal into on big pool
30% AA
15% A
10%
BBB 7% BB 3%
Equity 0%

54. As a claimholder, you are entitled to a fraction of these cash flows
Basic Idea
Question: What does it mean to have a claim on the principal in the pool?
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 7% BB 3%
Equity 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.

55. Basic Idea
Question: What does it mean to have a claim on the principal in the pool?
Suffer losses from default
Pool of Credit
Principal
Tranches
As a claimholder, you suffer losses if the defaulted principal exhausts the “credit enhancement” for your bond class
100%
AAA
Default
Credits will default
30% AA
15% A
10%
BBB 7%
At this point both the 0-3 and 3-7 tranches have been wiped out – they no longer receive payments BB 3%
Equity 0%
2% of the pool defaults
15% more of the pool defaults
5% more of the pool defaults

56. Basic Idea
Question: What does it mean to have a claim on the principal in the pool?
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%
It depends how diversified the pool is. If there is a lot of diversification ie low correlation, then there is little chance that the AAA tranche will experience losses. If correlation is high then there is a good chance that the AAA tranche will experience losses
30% of the principal in the pool must default before the AAA tranche gets hit. What are the chances? AA
The AA tranche is receiving interest and principal payments on a fraction of the original principal
15% A
10%
BBB 7% BB 3%
Equity 0%
2% of the pool defaults
15% more of the pool defaults
8% more of the pool defaults

57. Pricing:
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.

58. Pricing: Question: What is the value of the equity tranche
Pool of Credit
Tranches
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%
30% - 100%
+ P( 0.4% defaults AND 2.6% does not default) × 2.6%
15% - 30%
10% - 15%
+ P( 2.8% defaults AND 0.02% does not default) × 0.2%
7% - 10%
+ P( 2.9% defaults AND 0.02% does not default) × 0.1%
3% - 7%
+ P( 3% defaults AND 0.02% does not default) × 0%
0% - 3%

59. Pricing: 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

60. Pricing: (Correlation)
Question: Is pool diversification (correlation) important
YES!!!!!!!!!!!!
Pool of Credit
Joint Loss Distribution
Tranches
Higher Probability of experiencing losses
30% - 100%
Is the AAA tranche more/less valuable
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

61. Sub-prime RMBS 101 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%

62. Sample Subprime RMBS

63. CDO of RMBS or RMBS2

64. Lecture Summary 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