Transcript Com 4FJ3 - McMaster University

Business F723
Fixed Income Analysis
Week 7
Mortgage Backed Securities
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
2
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
3
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
4
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
5
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
6
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
7
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)
8
Standard Default Assumption
0.70%
Annualized Defalut Rate
0.60%
0.50%
0.40%
0.30%
0.20%
0.10%
0.00%
0
20
40
60
80
100
120
140
160
180
200
Months
9
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


bond equivalent yield  2  1  ym   1
6
10
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
11
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
12
Average Life
• To which maturity treasury bond should we
compare the MBS?
• Could use Macaulay duration, but main
measure in use is average life
t  principalreceivedat timet
averagelife  12 
totalprincipal
t 1
t  timein months
n
13
Average Life vs. PSA
• The average life will be different with
different prepayment assumptions
• As prepayments increase, average life will
decrease
PSA speed
Average Life
Average Life of 357 month example
50
100
165
300
15.11
11.66
8.76
5.63
500
3.68
700
2.78
14
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
15
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
16
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
17
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
18
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
19
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
20
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
21
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
22
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
23
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
24
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
25
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
26
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
27
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
28
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
29
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
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
31
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
32