Asset-Backed SecuritiesAsset-Backed Securities

ABS derive their cash flows from a pool of underlying assetsMBS = mortgage backed securitiesCARS = certificates for automobile receivablesCARDS = certificates for amortizing revolving

debtsHELS = home equity loan securities

Asset-Backed SecuritiesAsset-Backed Securities

The underlying assets generate cash flows of principal and interest which can be repackaged and sold to investors.

Fixed income assets

Principal

Interest

Asset-backed securities

Asset-Backed SecuritiesAsset-Backed Securities

In ABS, the underlying assets are collected into a pool.Pool assets are standardized.

The asset pool is placed in trust.Claims on the cash flows generated by the asset

pool are structured:Pass-through structuresMulti-class structures

Securities representing these claims are sold.

SecuritizationSecuritization

By pooling and repackaging cash flows, ABS issuers can convert illiquid fixed income assets into marketable bonds.

Requires trust structure to hold underlying assets, and

Credit enhancement to achieve investment grade bond ratingExternal: guaranteesInternal: over-collateralization.

IssuersIssuers

Mortgage related agenciesGinnie Mae (pass-thoughs)Freddie Mac (PCs)Fannie Mae (MBS)

Private label MBSCiti, GE, Prudential

Private label ABSGMAC and other auto companiesFinance companiesCredit card issuers

InvestorsInvestors

Insurance companiesPension fundsMutual fundsWealthy individuals

MBSMBS

Backed by mortgage loans.A mortgage loan is a loan secured by real estate

The “mortgage” is a security agreement that gives the lender the right to seize by foreclosure the property securing the loan if the borrower defaults

Mortgage loans are originated by banks and other financial firms.

Once originated, a mortgage loan may be held, sold to an investor for cash, or pooled and securitized.

Mortgage Loan TypesMortgage Loan Types

Fixed-rate, level pay (“plain vanilla”)Term of loan is fixed (30 years is common in US)Contract rate of interest is fixed for the life of the

loan.Payments (usually monthly) are constant for the

term of the loanThe payments fully amortize the loan.

FHA, conventional, conforming, nonconforming, jumbo

Mortgage Loan TypesMortgage Loan Types

Graduated payment loans (GPMs)Low initial payments and period of negative

amortizationGraduated equity loans (GEMs)

Fixed coupon with growing paymentsBalloonsAdjustable rate mortgages (ARMs)

Various index ratesCaps and collars

Mortgage Loan PaymentsMortgage Loan Payments

The payments on a plain vanilla mortgage are determined by

€

X =P0

i12

1− 1+ i12( )

−12T

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟

Initial principal

Contract rate of interest

Mortgage term in years

For ExampleFor Example

The monthly payments on a $187,000 loan written at 10% for 15 years is

€

X =$187,000.10

12

1− 1+.1012( )

−180

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ =$2,009.51

In Excel, you can use the financial function PMT(rate, nper, pv,fv,type)

Mortgage Loan PaymentsMortgage Loan Payments

Each payment consists of interest equal to i/12 times the amount of principal

owing at the time the payment is due, andscheduled principal repayment

Payments are calculated such that the interest due is paid first and then the remainder of the payment is used to reduce the principal owed.

A table listing the payments and how they are divided between interest and principal is called an amortization schedule.

Amortization ScheduleAmortization Schedule

For example, here are the first few lines of an amortization schedule for a 15-year, 10% fixed rate loan with an initial principal of $187,000

Balance Scheduled Balance Before Principal After

Payment Due date Payment Payment Interest Repayment Payment1 1/15/93 $187,000.00 $2,009.51 $1,558.33 $451.18 $186,548.822 2/15/93 $186,548.82 $2,009.51 $1,554.57 $454.94 $186,093.883 3/15/93 $186,093.88 $2,009.51 $1,550.78 $458.73 $185,635.154 4/15/93 $185,635.15 $2,009.51 $1,546.96 $462.55 $185,172.605 5/15/93 $185,172.60 $2,009.51 $1,543.11 $466.41 $184,706.206 6/15/93 $184,706.20 $2,009.51 $1,539.22 $470.29 $184,235.907 7/15/93 $184,235.90 $2,009.51 $1,535.30 $474.21 $183,761.698 8/15/93 $183,761.69 $2,009.51 $1,531.35 $478.16 $183,283.539 9/15/93 $183,283.53 $2,009.51 $1,527.36 $482.15 $182,801.38

Amortization ScheduleAmortization Schedule

A better way to visualize the amortization process is to look at a graph of the payments

$0.00

$500.00

$1,000.00

$1,500.00

$2,000.00

$2,500.00

1 23 45 67 89 111 133 155 177

PrincipalInterest

Amortization ScheduleAmortization Schedule

The principal balance remaining after any number of payments can be determined by constructing an amortization schedule or by employing the formula

Amortization ScheduleAmortization Schedule

The logic of this formula is that the principal balance remaining after s payments is always the present value of the remaining 12T-s payments discounted at the contract rate of interest

Amortization ScheduleAmortization Schedule

Graphically

Principal Balance Outstanding

($50,000.00)

$0.00

$50,000.00

$100,000.00

$150,000.00

$200,000.00

1 16 31 46 61 76 91 106 121 136 151 166

Balance Remaining

Mortgage ServicingMortgage Servicing

ServicingCollection and forwarding of paymentsAdministration of escrow accounts

Servicing feesTypically 50 basis points

Right to service loan is sold by owner of mortgage loan

Mortgage ServicingMortgage Servicing

For exampleScheduled Balance

Servicing Principal AfterPayment Payment Fee Interest Repayment Payment

1 $2,009.51 $77.92 $1,480.42 $451.18 $186,548.822 $2,009.51 $77.73 $1,476.84 $454.94 $186,093.883 $2,009.51 $77.54 $1,473.24 $458.73 $185,635.154 $2,009.51 $77.35 $1,469.61 $462.55 $185,172.605 $2,009.51 $77.16 $1,465.95 $466.41 $184,706.206 $2,009.51 $76.96 $1,462.26 $470.29 $184,235.90

171 $2,009.51 $8.00 $152.03 $1,849.48 $17,354.50172 $2,009.51 $7.23 $137.39 $1,864.89 $15,489.61173 $2,009.51 $6.45 $122.63 $1,880.43 $13,609.18174 $2,009.51 $5.67 $107.74 $1,896.10 $11,713.08175 $2,009.51 $4.88 $92.73 $1,911.90 $9,801.17176 $2,009.51 $4.08 $77.59 $1,927.84 $7,873.34177 $2,009.51 $3.28 $62.33 $1,943.90 $5,929.44178 $2,009.51 $2.47 $46.94 $1,960.10 $3,969.34179 $2,009.51 $1.65 $31.42 $1,976.43 $1,992.90180 $2,009.51 $0.83 $15.78 $1,992.90 ($0.00)

This servicing annuity is worth about $5,450 at a

9.5% discount rate

PrepaymentsPrepayments

Payments made by borrowers in excess of their scheduled loan payments.Entire (as when the house is sold or refinanced)Partial (accelerated principal repayment)

Most prepayments are optional to the borrowerput option

Borrower incentives when ratesRiseFall

For ExampleFor Example

Consider a mortgage that’s been outstanding for two years and rates have fallen 2%

Original loan amount: $187,000.00Term (yrs): 15Contract rate of interest: 10.00%Monthly payment $2,009.51Balance after 24 payments $175,067.73New rate 8.00%Value of balance remaining $194,517.70Benefit of refinancing $19,449.97New montly payment $1,808.58

PrepaymentsPrepayments

To the extent that prepayments cannot be perfectly predicted, they create uncertainty about the term of mortgage loans.

This uncertainty is a disadvantage from the standpoint of an investor.

What’s worse: Prepayments are more likely when rates fall and less likely when they rise, so prepayment risk is positively correlated with interest rate risk

Pass-throughsPass-throughs

The simplest type of MBSSimilar mortgages are pooled andPrincipal and interest payments are passed through

to investors (pro rata)Less servicing and insurance (credit enhancement)

fees

Pass-through cash flows are uncertain because prepayments of mortgages within the pool are uncertain.

Prepayment modelsPrepayment models

To price a pass-through bond, an estimate of prepayments is needed.Prepayments will affect the duration of the bonds

(Can you see how?)

There are several “models” for estimating prepayments

However, none of these models is designed to describe borrower response to changes in interest rates.

CPRCPR

The constant prepayment rate model assumes a constant percentage of the outstanding principal will prepay each month.

CPR is an annual rate that can be translated to a single monthly mortality rate (SMM) as

€

SMM=1−1−CPR( )112

An SMM of z% means that z% of the principal remaining in the pool after all scheduled payments have been made will prepay during the month

CPRCPR

For example, a CPR of 6%Translates to an SMM of .514%So if you owned a pass-through with a

beginning of the month balance of $181,824.99 and $494.30 of scheduled principal payments, then prepayments would be predicted at

€

.00514$181,824.99−$494.30( )=$932.58

PSAPSA

The Public Securities Association standard specifies that the CPR is .2% during the first month of a pool,

Increases by .2% per month until the 30th month

Levels off at 6% for the remainder.Prepayment speeds are quoted as % of PSA

Slow: less than 100% PSAFast: greater than 100% of PSA

FHA ExperienceFHA Experience

HUD publishes data on FHA insured mortgages that can be used to extrapolate prepayment speeds.

Patterns can be discerned for different types of pools.

The pattern for a given pool type can then be used to estimate a prepayment speed for other pools of that type.

Example with 165% PSAExample with 165% PSA

$0.00

$500.00

$1,000.00

$1,500.00

$2,000.00

$2,500.00

$3,000.00

$3,500.00

$4,000.00

1 21 41 61 81 101 121 141 161

Effect of Changing PSAEffect of Changing PSA

Impact on durationExcel spreadsheet