1. 課程6: Mortgage Prepayment Basics

2. Prepayment Basics: A Mobile Population
The history of US has been of one migration, from overseas, east to west, north to south, etc
20% of US households will change their place of residence at least once in a given year (Census Bureau)
8.5% all homeowners will move in a normal year (Census Bureau)
About 8% of all mortgages outstanding are likely to be prepared in any given year due to changes in residence
Investors in diversified pool of mortgages can expect about 8% of their principal to be returned to them due to prepayments
Not all moves results in prepayment since some mortgages are assumable

3. Prepayment are very important to Mortgage Investing
Homeowner prepayments are the most important aspect of mortgage or mortgage passthrough investing
Changes in prepayment rates are the most important risk facing mortgage securities investors.
Fortunately, the basic forces driving prepayments are easy to understand
Prepayments are driven by:
career changes
lifestyle changes
changes in interest rates
Does this mean prepayments can be easily forecast?

4. The “Four Faces” of Prepayments
No-Choice Prepayments
Some prepayments will occur regardless of interest rate levels
new job, mandatory job transfer, growing family, death, divorce, natural disasters etc.
no choice prepayments act as the base upon which other types of prepayments build. See figure 3A
Better-Home Prepayment
households change homes to suit lifecycle stage
key consideration is affordability
affordability is a function of interest rate levels and house price
See figure 3B

5. The “Four Faces” of Prepayments
Better Rate Prepayments (see figure 3C)
when mortgage rates drop most people refinancing their mortgages
these financially driven prepayments are the most powerful face of prepayment
as illustrated in the figures financially driven prepayments quickly dominate
traditionally refinancing did not occur until current rates were 1.5% to 2.0% below homeowners existing mortgage rate
in the early 1990 homeowners became prepayment conscious
refinance now can occur at lower spreads

6. No-Telling Prepayments
No-Telling Prepayments (See Figure 3D)
while many households refinance when rates drop there are many who do not -- Why?
brain dead/procrastinators
does not make economic sense
job loss
deteriorating credit rating
decline in home value
gamblers waiting for further rate declines
no-telling prepayment effectively puts a cap on the level that prepayment will actually reach

7. A B D C FIGURE 3 CPR “No Choice” Prepayments “Better Home” Prepayments
Floor
-3%
-2%
-1% 0%
+1%
+2%
-3%
-2%
-1% 0%
+1%
+2%
Interest rate spread
Interest rate spread
CPR
CPR
“No Telling” Prepayments
“Better Rate” Prepayments D C
Ceiling
-3%
-2%
-1% 0%
+1%
+2%
-3%
-2%
-1% 0%
+1%
+2%
Interest rate spread
Interest rate spread

8. Travelling on the Prepayment Curve
The prepayment curve shown in Figure 4 is the sum of the four faces of prepayments
It shows how borrower prepayment behavior changes depending on how far existing mortgage rate is above or below current mortgage rates
The dominant feature on the curve is the refinancing area between E and F, where better rate prepayments raise prepayment speed
No-telling prepayments (or the lack thereof) impose a ceiling on the level that prepayments reach above point F
Better homes prepayments are the important feature between A and E when rates are not conducive to refinancing
Underlying everything else, no choice prepayment act as floor

9. The Prepayment Curve FIGURE 4 CPR Upper Cusp Lower Cusp Rate
A-E Better homes prepayment
dominates
E-F Better rate prepayment
dominant feature of curve
F-G No telling prepayment
which acts as ceiling
60%
50% G F
40%
Upper
Cusp
30% E
20% D
Lower
Cusp C B
10% A 0%
-3%
-2%
-1% 0%
+1%
+2%
+3%
Rate

10. Travelling on the Prepayment Curve
Identifying where the mortgage security lies on prepayment curve is important for two reasons:
it tells us what level of prepayment we should expect if rates stay where they are
more importantly it tells us about our relative exposure to prepayment changes when interest rates change
The rates on the mortgage underlying the security does not change when interest rate change
However, the difference between the existing homeowner rates and new mortgage rate does change
It is the difference in the two rates that triggers prepayments

11. Measuring Prepayment Speeds
There are four methods of measuring prepayment speeds
Prepayment based on FHA experience
Constant Prepayment Rates (CPR)
Single Monthly Mortality (SMM)
PSA Standard Prepayment Benchmark

12. FHA Prepayment Method
This prepayment method is based on data collected by FHA tracking mortgage prepayments based on seasoning
As figure 1B shows very few mortgages prepay in first year
An increasing number prepay in the second year and still more prepay in the third year
From third to 20th year prepayment is remarkable stable
After 20th year it rises slightly every year until maturity
Across the nation more than 6% but fewer than 8% of FHA/VA loans prepay during this stable period
FHA mortality tables are not good predictors of other loan types because FHA/VA loans are assumable

13. Constant Prepayment Rate (CPR) Method
Assumes a constant percentage of the remaining principal in pool is prepaid each month for the remaining term of the mortgage
A 10% CPR means we can expect 10% of the remaining mortgage balance to be prepaid each and every future year
The CPR is based on the characteristics of the pool, current and expected future economic environment
Its advantage is simplicity and ease of application
It suffers from disadvantage that prepayments are treated as constant
Figure A1 illustrates the CPR

14. 6% CPR PREPAYMENTS 100% FHA PREPAYMENTS FIGURE A1 12% 6% 0% FIGURE 1B
YEARS
FIGURE 1B
100% FHA PREPAYMENTS
12% 6% 0%
YEARS

15. Single Mortality Rate (SMM) Method
The CPR is annual prepayment rate. The annual rate is converted into monthly prepayment rate called the single monthly mortality rate (SMM) as follows
SMM = 1 - (1 - CPR)1/ (1)
if the CPR is 6% the corresponding SMM is:
SMM = 1 - (1 -.06)1/12 = or .51%

16. Application of SMM to calculate prepayment
Prepayment for month t = SMM times beginning mortgage balance for month t minus scheduled principal for month t)
Mortgage has remaining balance of $50,525. With SMM of % and the schedule principal payment of $67, the prepayment for the month t is
= x ($50,523 - $67) = $260

17. PSA Standard Prepayment Method
Developed by Public Securities Association (PSA)
Benchmark is expressed as monthly series of annual CPR.
assumes that prepayment will be low for newly originated mortgages and will then speed up as the mortgage seasons
the PSA captures the advantages of both CPR and FHA methods
like the CPR, the PSA provides easy- to- calculate and easy- to- understand method
like the FHA, the PSA includes gradual increase in prepayment frequency

18. PSA Prepayment Curve.
The standard PSA prepayment curve, called 100% PSA is as follows:
it assumes 0.2% CPR for the first month.
the rate increases by 0.2% per month until the 30th month (top of the ramp) when it reaches a CPR of 6% per year .
it remains at 6% per year for the remaining stated maturity of the pool
if t £ 30, CPR = (6%)(t)/30,
if t > 30, CPR = 6%
where t is the number of months since mortgage origination.

19. PSA Prepayment Curve (Contd)
Slower or faster prepayment are then stated as percent of standard PSA, e.g. 50% PSA (slower), 150% PSA (faster)
The PSA is now the standard for quoting prepayment rate in the industry
Figure 2 illustrates the PSA method

20. PSA RAMP & SPEEDS FIGURE 2 CPR SPEED 18% 15% 12% RAMP 9% 200% PSA 6%3% 0%
RAMP
200% PSA
100% PSA
50% PSA
SEASONING (years)

21. Converting PSA to CPR and CPR to SMM
Converting PSA to CPR during PSA Ramp period
Monthly CPR = (PSA x .06 x n)/30
where n = mortgage loan age in months up 30
Example: mortgage age (n) = 5; PSA = 100%
Monthly CPR = (100% x.06 x 5)/30 = 1%
Converting CPR to SMM
SMM = 1 - ( )1/12 =
Thus 1% CPR = % SMM; or of the mortgage pool principal balance is expected to prepay in month 5

22. Converting PSA to CPR and CPR to SMM
Converting PSA to CPR after PSA Ramp period (months )
CPR = PSA x .06
Example: PSA = 100%
CPR = 100% x .06 = 6%
Converting CPR to SMM
SMM = 1 - (1 - CPR)1/12
SMM = 1 - ( )1/12 =
6% CPR = 0.51% SMM; 0.51 of the pool principal balance is expected to prepay each month until maturity (31 to 360 months)

23. More Application of PSA
If we assume 150% PSA (i. e. one and one-half times faster than standard PSA) the SMM for month 5, will be computed as follows:
for month 5: CPR = (150 x .06 x 5)/30 = 1.5%
SMM = 1 - ( )1/12 =
Note: it is the CPR that is a multiple not the SMM

24. Various Prepayment Issues to Consider
Assumable and Nonassumable mortgages
Wall Street projections and averages: most of the industry relies on the prepayment projections prepared by the major investment houses, available on-line as BLOOMBERG screens
Burnout: after a pool has stayed in refinancing range for some time prepayments decrease. This is call burnout
Seasoning: aging of mortgage loans and associated changes in prepayments
Path Dependence: future prepayment for a mortgage pool are dependent on that pool’s past prepayments, which in turn are dependent on the path interest rates have taken since pool’s origination (See figure 5 )

25. FIGURE 5 PATH DEPENDENCY 2 13% 12% 11% 10% 9% 8% 7% 6% 5% 8% 0 1 2 3 4
Interest Rate
Path A 8%
Interest Rate
Path B
YEARS

26. Factors Affecting Prepayment
Prevailing mortgage rate and market conditions
spread between contract rate and prevailing mortgage rate
path dependence
refinancing burnout
level of mortgage rates
housing turnover and affordability
Seasonal factors
home buying starts in spring and reaches its peak in summer
in fall and winter home buying declines

27. Factors affecting prepayment (contd).
Characteristics of the underlying mortgage Loans
contract rate
conventional versus FHA/VA
amount of seasoning
FRMs versus ARMs
pool factor
geographical location of underlying properties
General economic activity
general economic activity affects prepayment through its effects on housing turnover as growing economy increases personal income and opportunities for worker migration

28. What to remember about Prepayment Projections
The most important thing to remember about accurate long-term prepayment projections is that there aren’t any
prepayment projections remain inherently unreliable
Interest rates must be forecast
to reliably predict future prepayments, we must first reliably predict future interest rates
if you can consistently predict future interest rate movement bond futures is your calling not prepayment projections
Interest rates and prepayments change continually

29. Pricing of MPT’s Estimate the necessary cash flow
Discount the estimated cash flow at an appropriate interest rate.
Problem:
cash flows of MPTs are not known with certainty.
appropriate discount rate is difficult to determine

30. Basic Principles of valuation of MBS
Current Coupon
Treasury Yield
Curve
Discount at
Treasury Rates
Pertinent to Each
Cash Flow Plus
Spread
Market Price
Treasury
Interest Rate
Scenarios
Projected
Cash Flows
Non-Treasury Indices
Generated from
Treasury Scenarios
Prepayment
Model

31. Constructing MBS Cash Flows
Project monthly Payment
MPt = MB t-1 [{i(1 + i)n-t+1}/{(1 + i)n-t+1 - 1}]
MPt = projected monthly mortgage payment for month t
MB t-1 = projected mortgage balance at the end of month t-1
n = original number of months of mortgage
i = simple monthly interest rate(annual rate/12)

32. MPT Cash flow (Contd).
Project Monthly Mortgage Interest, servicing and guarantee
I t = MB t-1 . i
NIt = MB t-1 (i - s - g)
St = MB t-1 s
Gt = MB t-1 g
It = projected monthly interest for month t.
NIt = projected interest net of servicing and guarantee fee
St = projected servicing fee for month t
Gt = projected guarantee fee for month t
s = servicing fee rate

33. MPT Cash flow (Contd).
Projected Monthly Scheduled Principal and Prepayment
SPt= MPt - It
PRt = SMMt(MB t-1 - SPt)
PRt = monthly principal prepayment for month t
SPt = monthly scheduled principal payment for month t
SMMt = assumed single monthly mortality rate for month t

34. MPT Cash flow (Contd) Investor's Cash Flow CFt = NIt + SPt + PRt
CFt = projected cash flow to investor for month t
NIt = interest net of servicing and guarantee fees

35. Illustration Original mortgage balance = $100,000 Mortgage rate = 9.5%
Servicing fee and guaranteed fee = 0.5%
360 months to maturity
Coupon rate = 9%.
Prepayment at 100% PSA
Note: The interest rate on passthrough is always less than that paid on the mortgage, usually by the amount of servicing and guarantee fee (.5% in the above case)

36. Short Cut Approach to Calculate Cash Flows
bt = (1 - SMMt(1 - SMMt-1) ... (1 - SMM2)(1 - SMM1)
MPt = b t-1 MP*
SPt = b t-1 P t*
bt = the projected mortgage balance in month t per $1
of the principal given projected prepayments through
month t (POOL FACTOR akin to earnings announcement)
MP* = monthly mortgage payment on the original principal
assuming no prepayments.
MPt = projected monthly mortgage payment in month t
SPt = projected schedule principal payment
P t* = scheduled principal payments on the original
balance assuming no prepayment.

37. Illustration of short cut approach
Assuming a CPR of 6%, for month 210
MP210 = b209 MP*
Mortgage Constant at 9.5%, 360 months =
MP* = $100,000x = $840.85
Since SMM is for each month after the 30th, 1- (1-CPR)1/2
b209 = ( )( )...( ) = ( )209 =
MP210 = (.34039)(840.85) = $286.
This is the projected monthly payment in month 210

38. Illustration (contd).
The projected scheduled principal payment in month 210 is:
SP210 = b209 P*210
Scheduled principal payment in month 210 assuming no
prepayment is $255.62
The projected scheduled principal payment assuming prepayment for
month 210 is then:
SP210 = (.34039)($255.62) = $87

39. Additional Pricing Concepts
Weighted Average Coupon (WAC)
average of underlying mortgage rate weighted by dollar balance of each mortgage as of date of issue
Stated Maturity Date of Pool
longest maturity date for any mortgage in the pool assuming zero prepayment
Weighted Average Maturity (WAM)
remaining term of underlying mortgages weighted by principal balance
Weighted Average Life (WAL)
average number of years until investors principal is returned weighted by each principal balance
Pool Factor
outstanding balance divided by beginning balance

40. Price/Yield Relationship for Option-Free Bond

41. Price/Yield Relationship for Callable Bonds
Noncallable bond
a-a’ b
Callable bond a
a-b y*
Yield

42. Relationship between Prepayment and Premium, Discount and Par Mortgages
High coupon MPT at a premium
loses if prepayment is faster
gains if realized prepayment is slower
Low coupon MPT at a discount
gains if prepayment is faster
loses if prepayment is slower
At par MPT
unaffected

43. Logic of Option Adjusted Spread
Option Adjusted Spread analysis attempts to include the cost of prepayment option ( and other factor, delays) when calculating the spread the passthrough security offers above the Treasury yield curve.
The first step in calculating OAS is running a Monte Carlo simulation of numerous possible future interest rate paths
Next future monthly cash flows are calculated based upon prepayment model for each interest rate path
An average yield above Treasury yield is then calculated for each path
The OAS for a security is the average of individual spreads calculated for each future interest rate paths

44. Meaning of OAS
Often put forward as one method of identifying overpriced and underpriced mortgage backed securities
Typically, OAS on securities with similar duration are compared.
However that such comparison does not tell the investor which security to buy.
Suppose the OAS > 0:
a risk neutral investor who does not demand compensation for variability in cash flows (prepayment) will find such an investment attractive.
for a risk averse investor this positive OAS will not provide enough information to determine whether or not the extra yield is enough to cover the investors desired risk premium

45. An Equivalent way to view the ambiguity of OAS
An equivalent way to view this ambiguity
two MBS have same expected cash flows but the variability of the second security is greater.
risk averse investors will bid a lower price for the second mortgage related security
the result is that the second MBS will have a higher OAS
however, the meaning is clearly not that the second security is better one
BOTTOM LINE
Establishing that the expected return on a risky security is greater than the Treasury rate, or even greater than the expected return of some security with comparable risk, does not imply that it is good buy, unless you happen to be risk neutral. OAS provides such risk neutral information.

46. Cash Flow Yield Semiannual yield (IRR) = (1 + ym)6 - 1
Bond Equivalent Yield (BEY)
BEY = 2[(1 + ym)6 - 1], ym= monthly yield or IRR
To convert the bond equivalent yield to a monthly yield
ym = [1 + (0.5)(BEY)]1/6 - 1
Suppose an investor requires a BEY of 8.13%, then the corresponding monthly interest rate is
ym = [1 + (0.5)(.08130]1/ =
The projected cash flow can then be discounted at ym = %
Price is simply the present value of the projected cash flow

47. Market Making Substantial trading activity
daily average primary dealer transaction is $12.4 billion
Treasury is around $137 billion
Several factors foster trading in secondary market
Large capital committed by investment banking firms and commercial banks to make market
Institutional investors more willing to trade in passthroughs due improved liquidity
Improved Liquidity: narrow bid-ask spread
3 cents to 12.5 cents
risk of market making and competition
turnover ratio (ratio of dollar volume to amount of issue outstanding) = 3.57

48. Trading Mechanics Quotation (same as treasury) 94 5/32 = $94.15
MPT identification (pool prefix)
TBA trade: trading may occur while pool is still not specified
Many Issues of same coupon (different pools)
Prepayment characteristics (generic MPT)
Moral Hazard Problem: some sellers may deliver poor paying pool
Under and Overdelivery (2.5% tolerance per million dollar traded)
$975,000 or $1,025,000 for MPT of $1,000,000

49. Use of Dollar Rolls in MBS Trading
Repos (repurchase agreements
dealer use security to borrow from client (counterparty)
dealer pays loan + interest at end of period
identical collateral is returned by counterparty
vehicle for covering short position
Reverse Repo
Client borrows from dealer
Dollar Roll Transaction
sustantially the same security is returned by borrower
help market for MBS to operate smoothly