Fixed Income Securities and their Derivatives
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Transcript of Fixed Income Securities and their Derivatives
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