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.