Transcript Chapter 11
Mortgage PassThrough Securities
Fabozzi—Chapter 11
Introduction – pg 244
What is a mortgage pass-through security?
• A security comprised of a pool (portfolio) of residential
mortgages.
• All monthly interest and principal payments made by
homeowners are passed through to the security holders
(less fees).
Not all of the mortgages in the pool have the same
maturity or interest rate. So pass-throughs use:
• Weighted-Average Coupon Rate (WAC).
• Weighted-Average Maturity (WAM).
• WAC and WAM weight the coupon or maturity by
outstanding amount of mortgage.
Diagram Of A Pass-Through
Each Homeowner Pays:
-Interest
-Scheduled principal
-Prepayments
Pooled Monthly
Cash Flow:
-Pooled Interest
-Pooled Principal
-Pooled Prepays
Pass-through
coupon paid to
investors
Agency Pass-Throughs
Pass-throughs guaranteed by government-sponsored
agencies. There are three types:
1. Ginnie Mae (Government National Mortgage Association): Backed
by full faith and credit of US Government.
2. Freddie Mac (Federal Home Loan Mortgage Corporation): Not
guaranteed by US Government. But most consider it very low risk.
3. Fannie Mae (Federal National Mortgage Association): Not
guaranteed by US Government, but considered low risk.
Types of guarantees:
•
•
Fully modified pass-throughs: guarantee timely payment of interest
and principal even if mortgager fails to pay.
Modified pass-throughs: both interest and principal and interest are
guaranteed, but only interest is guaranteed to be timely. Principal
payment occurs when collected, but no later than a specified date.
Nonagency Pass-Throughs*
Issued by commercial banks, thrifts, and private conduits:
• They have no guarantees by the U.S. Government.
• Success of this market has been driven by credit enhancements.
External Credit Enhancements: Third-party guarantees
losses up to specific level (usually 10% loss). (See Page 247)
• Bond insurance – Guarantees interest and principal when due.
• Pool insurance** – Covers losses from defaults and foreclosures.
Internal Credit Enhancements:
• Reserve funds – cash reserve acct for payment of interest and principal.
• Excess Spread Accounts*** – gradually increase as pass through seasons
• Overcollateralization – Principal amount of mortgages paying into pool
exceeds principal amount issued by pool.
• Senior/Subordinate structure – by far most common enhancement.
• See next slide for example on Senior/Subordinate structure
Senior/Subordinate Structure
Securities sold against the pool of mortgages are classified
according senior/subordinate credit:
• Subordinate class absorbs first losses on underlying mortgages.
Example: $100 million security is divided into two classes:
•
•
•
•
$90 million senior class and $10 million subordinate class.
The subordinate class will absorb all losses up to $10 million.
Senior class experiences no losses until losses exceed $10 million.
Obviously subordinate bondholders will require a much higher yield
than senior bondholders.
Valuing a Mortgage PassThrough
To value a pass-through it’s necessary to project its cash
flow. This can be difficult:
• Interest payment – easy
• Scheduled principal payment – easy
• Prepayment – difficult
To value a pass-through assumptions must be made about
the prepayment rate in the underlying mortgage pool:
• The prepayment rate assumed is called the prepayment speed or speed.
• The yield calculated based on the projected cash flow is called a cash
flow yield.
How To Estimate Cash Flow
*In the early days the market used a naïve approach:
• Assumed no prepayments during the first 12 years.
• After 12 years, all mortgages were assumed to prepay.
*This was replaced by FHA Prepayment Experience:
• Prepayment rates were derived from historical data from the FHA
(Federal Housing Administration).
• FHA experience is not necessarily accurate for all mortgage pools.
• This is no longer used.
Another benchmark for prepayment is called the Conditional
Prepayment Rate (CPR):
• CPR is proportion of the remaining principal in pool that will be
repaid for the remaining term of the mortgage.
• CPR is an annual rate based on the characteristics of the mortgage
pool and future expected economic environment.
Prepayments Using CPR
Since CPR is an annual rate, it has to be converted to a monthly
rate, called the single-monthly mortality rate (SMM):
Formula 11.1 SMM 1 (1 CPR)1/12
An SMM of x% means:
• Approximately x% of remaining mortgage balance at the beginning of
the month (less scheduled principal payment) will prepay that month:
Formula 11.2
Prepayment for month t SMM (beginning mortgage balance for month t
scheduled principal payment for month t )
One model that uses the CPR/SMM to estimate prepayment
CFs is the Public Securities Association Prepayment Model
(PSA Prepayment Model).
PSA Prepayment Model
Is a series of monthly annual prepayment rates:
• Assumes prepayments are low for new mortgages and will speed up as
the mortgages become seasoned*.
PSA Model for 30-year mortgages:
• CPR of 0.2% for first month increasing 0.2% each month for next 30
months (this is called seasoning).
• When CPR reaches 6%, assume 6% per year for remaining years.
• This is referred to as the 100 PSA Model (or 100% PSA Model).
Mathematically: (where t = # months since mtg originated)
t 30 : CPR 6% (t / 30)
t 30 : CPR 6%
Slower or faster speeds can be considered:
• 50 PSA means 0.5 CPR, 150 PSA means 1.5 CPR, etc.
100 PSA Model Graphically
7
Annual CPR %
6
Why does seasoning occur
for 30 months?
5
4
3
2
1
0
Mortgage Age (Months)
Few people prepay when first
purchasing a home.
However, the longer someone
lives in a home the more likely
someone may sell it (and thus
prepay).
Example of 100 PSA Model
100 PSA Model: page 251
• Month 5:
• CPR = 6% (5/30) = 1% or 0.01
• SMM = 1 – (1 – 0.01)1/12 = 0.000837
• Month 20:
• CPR = 6% (20/30) = 4% or 0.04
• SMM = 1 – (1 – 0.04)1/12 = 0.003396
• Month 31-360:
• CPR = 6% or 0.06
• SMM = 1 – (1 – 0.06)1/12 = 0.005143
Example of 165 PSA Model
165 PSA Model – Multiply CPR by 1.65: pg 251
• Month 5:
• CPR = 1.65 6 (5/30) = 1.65% or 0.0165
• SMM = 1 – (1 – 0.0165)1/12 = 0.001386
• Month 20:
• CPR = 1.65 6 (20/30) = 6.6% or 0.066
• SMM = 1 – (1 – 0.066)1/12 = 0.005674
• Month 31-360:
• CPR = 1.65 9.9% or 0.099
• SMM = 1 – (1 – 0.099)1/12 = 0.007828
Cautions Using PSA Model
Calling PSA Model a “model” may be a bit strong.
It is really more market convention:
• It is not based on rigorous statistical modeling of particular
pool of mortgages.
• Your text refers to it as the PSA Benchmark.
PSA Model is based on a study by PSA on FHA
prepayment experience.
Using CPR is useful, but it does have many
limitations*.
Factors Affecting Prepayments
and Prepayment Modeling
A prepayment model is a statistical model used to forecast
prepayments.
• Wall Street firms and research firms have developed different
prepayment models.
• Firms usually use different models for agency and nonagency passthroughs.
We will consider a prepayment model developed by Bear
Stearns, (once) a major dealer in the mortgage market:
• We will use this model to see if we can determine some factors that
affect prepayment.
The Bear Stearns Model
The Bear Stearns Model is an agency prepayment
model.
The model consists of three components:
• Housing turnover.
• Cash-out refinancing.
• Rate/term refinancing.
Housing Turnover
Refers to existing home sales (not newly constructed homes)
3 factors forecast prepayment due to housing turnover:
• Seasoning effect
• Housing price appreciation effect
• Seasonality effect
*Seasoning effect:
• B/S model suggests seasoning occurs much fast than PSA Model indicates
(prepayments reach 6% CPR in 15 months, not 30 months)
• Why? Refinancing waves. Age of loan < length of time owning home.
**Housing price appreciation effect:
• As house prices increase there is greater incentive for cash-out refinancing.
Seasonality effect:
• Home buying increases in spring and peaks in late summer (low in winter).
• Prepayments follow this pattern because home sales cause prepayments.
Cash-Out Refinancing
Cash-out refinancing occurs when house prices increase:
• Homeowners refinance not to get a better interest rate, but to get cash
from equity of their home.
• However, the rate of refinancing will depend not only on house prices,
but also on the interest rate of new mortgages.
Bear Stearns model compares the pool’s WAC with the
prevailing mortgage rates. The model suggests:
• *Prepayments exist for WAC/Prevailing mortgage rate > 0.60.
• Prepayments increase as WAC/Prevailing mortgage rate increases.
• **The greater the price appreciation for a given ratio the greater the
project prepayments.
Rate/Term Refinancing
Not all investors refinance to get cash out:
• Some refinance to get a lower interest rate or a shorter term
on their mortgage.
To capture this, the Bear Stearns model captures two
potentially important dynamics:
• Burnout effect – The fact that the lower interest rates go,
eventually the slower the rate of refinancing (eventually
everyone who can refinance has refinanced).
• Threshold-media effect – as mortgage rates drop to historic
levels, borrowers become more aware of these opportunities
due to advertisements and media (again, eventually every
who can refinance will, as rates decline).
Non-Agency CF Estimation
Non-agency CF estimation must consider all of the
attributes of agency CF estimation:
*However, one more issue must be considered:
• Default and delinquencies (i.e., late payments).
A benchmark for default rates has been introduced
by the PSA:
• Called the PSA Standard Default Assumption (SDA)
benchmark.
100 SDA (std default assumption)
From month 1-30:
• Default rate in month one is 0.02%
• Default rate increases 0.02% each month for 30 months (when
default rate is 0.60%).
From month 30-60:
• Default rate remains at 0.60%.
From month 61-120:
• Default rated declines linearly from 0.60% to 0.03%
From month 121 on:
• Default rate remains constant at 0.03.
Note, can also consider 200 SDA, 50 SDA, etc.
Annualized Default Rate (%)
100 SDA Graphically
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Mortgage Age (Months)
Cash Flow Yield
Once a projected CF and pass-through price is calculated, its
yield can also be calculated.
Recall from chapter 3 that the yield is the interest rate that
makes the PV of the expected CFs equal the asset’s price:
• A mortgage pass-through has a monthly yield which has to be annualized.
• Recall that market convention dictates using the bond equivalent yield
(i.e., multiplying the semiannual yield by 2).
• However, mortgage pass-throughs have monthly yields, so to make them
comparable to yields on semiannual yielding bonds we must:
Bond equivalent yield 2 [(1 yM )6 1]
semiannual
cash flow yield
Caution Using CF Yield
Remember that CF yield is based on prepayment
assumptions that may or may not be accurate.
Even if the assumptions are accurate, the CF yield
will be realized yield only if the following are true:
• Investor reinvests all CFs at the CF yield.
• Investor must hold the pass-through security until all the
mortgages have been paid off.
Prepayment Risks
Suppose an investor buys a 10% Ginnie Mae when mortgage rates are
10% and later mortgage rates decline to 6%.
Prepayments will increase. This creates two adverse consequences:
• First, the Ginnie Mae price will rise, but not as much as an option-free bond
would. That is the upside potential is truncated.
• Second, the cash flow must be reinvested at a lower rate
• Taken together these adverse effects are referred to as contraction risk.
Suppose mortgage rates increase from 10% to 15%:
• Ginnie Mae will decline in price almost as much as an option-free bond
(although not quite as much) because prepayments slow down.
• Investors wish prepayments would increase and be reinvested at a higher rate.
• Taken together these are known as extension risk.
Note: prepayments can sometimes enhance investor performance if
bonds were purchased at a discount (see pp. 268-269)
Secondary Market Quotes of
Mortgage Pass-Throughs
Pass-throughs are quoted in same manner as
Treasury securities:
• For example: 94-05 means 94 and 5/32 percent of face
value.