Mortgage Pass-Through 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 Pass-Through

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 1/121 (1 )SMM CPR

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)30 : 6% ( / 30)

30 : 6%

t CPR t

t CPR

Slower or faster speeds can be considered:• 50 PSA means 0.5 CPR, 150 PSA means 1.5 CPR, etc.

100 PSA Model Graphically

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5

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Mortgage Age (Months)

Ann

ual C

PR %

Why does seasoning occur for 30 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 pass-throughs.

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.

100 SDA Graphically

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0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mortgage Age (Months)

Ann

ualiz

ed D

efau

lt R

ate

(%)

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:

6 2 [(1 ) 1]MBond equivalent yield y

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.