Business F723
Fixed Income Analysis
Week 7
Mortgage Backed Securities
2
Monthly Cash Flows
• Example p. 243, for a 100 PSA with a pass through rate of 7.5% a WAC of 8.125% and WAM of 357 months
• The calculations for this table are a bit involved, because the monthly payments on the mortgage pool decrease as prepayments are made on some of those mortgages
3
Monthly Payments
• Calculating the scheduled monthly payment requires keeping track of the total amount of accumulated prepayments as a fraction of the initial principal
• Exact formula for this calculation is not given in this textbook
4
Principal
• The scheduled principal is the difference between the monthly payment and the interest on the outstanding principal
• Prepayment estimates = SMM multiplied by (the outstanding principal less the scheduled principal payment)
• Outstanding balance = previous balance less scheduled principal and prepayment
5
Actual Cash Flows
• The cash flows forecast in the previous table are just predictions
• If the estimate of 100 PSA is reasonable, the cash flows will still be different from what was predicted
note: most of the PSA benchmark is based on experience, but the linear slope for the first 30 months is just an assumption
6
Prepayment Rate
• The actual rate of prepayments can vary over time for several different reasons– Prevailing mortgage rates; spread, path
(refinancing burnout), and level– Characteristics of the loans– Seasonal factors (low housing turnover in
winter months)– General economic activity
7
Prepayment Models
• To account for the changing factors over the life of MBS, some have built models to predict prepayment behaviour– From Goldman, Sachs: monthly prepayment =
(refinancing incentive)x(seasoning multiplier) x(month multiplier)x(burnout multiplier)
• Typically not publicly reported
8
Non-Agency Pass-throughs
• Since these mortgages are not fully insured, we need to adjust for potential defaults
• Public Securities Association has also defined a benchmark for the default rate
• Standard Default Assumption (SDA)• ## SDA is the relative rate of defaults
expected compared to the average (100 SDA)
9
Standard Default Assumption
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0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
0.70%
0 20 40 60 80 100 120 140 160 180 200
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10
Cash Flow Yield
• Similar to IRR, the discount rate that sets the present value of the forecast cash flows equal to the price
• Market convention converts the monthly yield into a bond equivalent basis
112yield equivalent bond 6 my
11
Limitations of Cash Flow Yield
• Can not be used for future value calculation due to reinvestment risk
• Assumes security is held to maturity (price risk)
• Prepayment rates and default/delinquency rates must be equal to what was predicted
12
Yield Spread
• The main difference between treasury bonds and agency (fully modified) MBS is the prepayment risk
• What level of spread would compensate for the added risk?
• Option pricing models have been used to determine the appropriate spread
13
Average Life
• To which maturity treasury bond should we compare the MBS?
• Could use Macaulay duration, but main measure in use is average life
monthsin time
principal total
at time received principal12life average
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14
Average Life vs. PSA
• The average life will be different with different prepayment assumptions
• As prepayments increase, average life will decrease
PSA speed 50 100 165 300 500 700Average Life 15.11 11.66 8.76 5.63 3.68 2.78
Average Life of 357 month example
15
Negative Convexity
• Prepayments are similar to call provisions with no call premium
• Not all mortgages will prepay since there is a cost to the borrower to refinance
• Price increases will be limited due to the increased likelihood of prepayments as the interest rate declines
16
Contraction Risk
• If interest rates decrease, the amount of prepayments will increase
• As prepayments increase, the principal will have to be reinvested at lower rates
• Average life, and Macaulay’s duration will decrease… this is called contraction risk
17
Extension Risk
• If interest rates rise, prepayments will decline
• Expected cash flows will be unavailable for reinvestment at new, higher rates
• Average life, and Macaulay’s duration will increase… this is called extension risk
18
Asset/Liability Management
• Depository institutions are more concerned with extension risk
• Pension funds and others with very long investment horizons are more concerned with contraction risk
• Synthetic securities can be built to transfer some of these risks
19
Prepayments and Return
• Prepayments can enhance the return compared to the cash flow yield, if the MBS trades at a discount
• A prepayment causes the realized capital gain to occur earlier
• If the MBS trades at a discount, its coupon rate is lower than required, so prepayments allow beneficial reinvestment
20
CMOs
• Collateralized Mortgage Obligations are a variant of MBSs
• Called a pay-through structure rather than a pass-through structure because there are different classes of owners receiving different cash flows, but having the same level of seniority
• Different classes are called tranches
21
Sequential Pay Tranches
• Principal payments are directed at each tranche in turn until that tranche is paid off
• principal pay-down window is the time period in which that tranche is receiving payments towards the principal
• Tranche B in example on p. 261 has a principal pay-down window from month 81-100
22
Accrual Bonds
• A class of tranche that receives no interest or principal until the other tranches have been fully paid off
• The interest payments that this tranche would have received are treated as principal prepayments for the other tranches
23
Floating Rate Tranches
• A floating rate tranche can be created by splitting a tranche into a floating rate tranche and an inverse floating rate tranche
• The total interest paid to the two tranches will be the same as the interest paid to the original tranche
• coupon leverage will be created if the two tranches are not of the same size
24
Planned Amortization Class
• A PAC tranche is protected from prepayment risk because it gets principal payments at a fixed rate
• This is accomplished by issuing support bond tranches
• The PAC gets principal payments according to the schedule, anything left over goes to the support bond tranche
25
PAC Collars
• If the support bond tranche is paid off, the PAC tranche will lose its protection
• The range of prepayment speeds that can be handled is called the collar
• The size of the collar can change over time based on the actual speed of prepayments
26
Targeted Amortization Class
• A TAC bond tranche is protected against contraction risk, but not extension risk
• Prepayments in excess of a certain rate are borne by the support bonds, but slower than expected prepayments are shared equally
• A reverse TAC bond protects vs. extension risk, but not contraction risk
27
VADM
• Very Accurately Determined Maturity bonds are created much like PACs except that there is also an accrual bond tranche
• The accrued interest for the accrual bond tranche can be used to satisfy the scheduled principal payments if the prepayment speed is slower than expected
28
Support Bonds
• These bonds are the tranches that take extra prepayment risk to allow the PAC, TAC, or VADM to reduce that risk
• As such these bonds are very risky and investors will demand a higher rate of return to buy these tranches
29
Credit Risk
• A CMO is a business entity
• If issued by an agency or fully modified, there is no credit risk
• If issued by a private conduit, the level of credit risk must be assessed– Private label CMO; assets are agency MBS– Whole loan CMO; assets are mortgages
Structural Credit Enhancement
• Senior/subordinated tranches
• Subordinated tranches absorb the first wave of defaults
• Given the example on p. 302 you can give the different tranches credit ratings from NR to B to AAA depending on how much protection they have
30
31
Stripped MBS
• Interest only or principal only tranches
• All interest collected is paid to one tranche, all principal payments, scheduled or prepayments is paid to the other tranche
• Interest only tranche hurt by prepayments
• Principal only tranche gets money quicker if prepayments increase
32
Notional Interest Only
• A tranche that is created by paying one or more tranches lower coupon payments than the WAC
• The excess interest is paid out to a tranche as a percent of a notional value– e.g. $100 m tranche receives 6%, WAC 7%– 1% of $100 m = 5% of $20 m– so a tranche can be created paying 5% on a
notional value of $20 m