class #21; chap. 26. purpose: understand cash flows from securitization pool of fully amortizing...

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)

GNMA BondCash Flows Generated by the mortgage pool

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

PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT

mnmrmr

PMTPV)/1(

)/1(...

)/1(/1 2

What is the present value?

mill100000,100000,1

What is the interest rate?

What is the number of compounding periods

per year?

How many years?

30years

Payments from mortgage pool

1m 2m 3m 4m 5m 356m 357m 358m 359m 360m

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(

12/12.

60.612,028,1$21833.97

000,000,100

)12/12.1(1

112/12.

000,000,100

GNMA BondPayment to the Bond Holders

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%

40.291,990$9804.100

000,000,100

)12/115.1(1

112/115.

000,000,100

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

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?

mnmrmr

PMTPV)/1(

Step #1 find the new rate

New Rate = 0.1 – 0.0044 – 0.0006 = 0.095

2912)12/095.01(

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.

Pre-payment Risk

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

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

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)

How do you value the bond with prepayments?

Is it possible to know how many loans will be prepaid and when?

No! so we guess a.k.a. build a model

Modeling Prepayments

(Assume all payments are made in arrears)

1. Public Securities Association (PSA)

2. Option Adjusted Spread (OAS)

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%

Months of existence Prepayment rate

1 .2 %

2 .4 %

3 .6 %

⁞ ⁞

29 5.8 %

30 6 %

31 6 %

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

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

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.

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

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:

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)

GNMA pass-throughs

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

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)

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)

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)

Pool of mortgagesor pass-throughs

Principal

& Interest

REMICSReal Estate Mortgage Investment Conduit

Class A

Class B

Class C

Promised coupon (1.3% for example)

Principal Payment

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

ExampleCMO with Fully Amortizing Mortgages

(No Pre-payment risk)

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

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 #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

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

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

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.

Month Payment Interest Principal Pre-payment Remaining Principal

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

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

(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

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

4,880,391.39 3,488,134.40 1,392,256.99 3,986,439.31 991,231,131.96

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

Step #2 Coupon Payments

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

Step #3 Principal Payments

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

Total Payment

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)

Appendix

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 …

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

Principal

Equity

Tranches Pool of Credit

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

Equity

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

Equity

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

Equity

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.

0% - 3%

3% - 7%

7% - 10%

10% - 15%

15% - 30%

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( 3% defaults AND 0.02% does not default) × 0%

0% - 3%

3% - 7%

7% - 10%

10% - 15%

15% - 30%

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

0% - 3%

3% - 7%

7% - 10%

10% - 15%

15% - 30%

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%

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

class #21; chap. 26. purpose: understand cash flows from securitization pool of fully amortizing...

pool of mortgages

mortgage pool

securitization pool

monthly payments

payments world bank

loan pool spv

amortizing mortgages

fixed rate

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