1. Collateralized Mortgage Obligations

2. Motivation for development of CMO structure
MPTs are unattractive investment for institutional investors because of extension and contraction risk arising from prepayment
Extension risk
Financial institutions: short term liabilities
Insurance companies: guaranteed investment contracts (GIC)
Contraction Risk
Pension funds and life companies: defined benefit plans and annuity policy
The CMOs solves these problems by creating short-term, medium term, and long-term security classes or tranches where principal is returned in each of these time frames.

3. Tranches Tranche is a French word meaning “slice”
Thus the creation of CMO involving the vertical slicing of cash flow from mortgages or MPTs pool into bond classes called tranches
CMOs redirect cash flows so as to mitigate the effects of prepayment.
CMOs do no eliminate prepayment risks.
They redistribute various forms of prepayment risks among different classes of bond holders
Note: In contrast MPTs represents horizontal slicing of cash flows

4. A Tranching Example
Assume you lent $2 million to Olympus Properties at 8% interest which Olympus agreed to pay in installments of $1 million in one year, and the other $1 million in two years. To fund the investment you borrow from Bank Two at 7% for two years using the Olympus Properties loan as collateral. The cash flow from the Olympus loan is used to repay Bank Two. As illustrated in Figure 1you make a profit of $30,000.
Suppose you can also borrow from Bank One at 5% but for a period no longer than one year. Since you need a two-year loan to fund the investment to Olympus Properties you can not use the Bank One loan without financial “engineering”. Enter split-up borrowing. You tranche (slice) the principal payments you will be receiving from Olympus in half as shown in Figure 2. The first million is used as collateral to borrow from Bank One at 5%, and use the second million to borrow from Bank Two at 7%.
The terms of Olympus borrowing are not exactly suited to any of the lenders.
Tranching allows you to split your borrowing and give Bank Two and Bank One exactly what each wants and increase your profits from $30,000 to $50,000
This the real idea behind CMOs

5. Figure 1 : Normal Collateralized Borrowing $30,000 profit8% 7%
7% Cost 0%
Year Year 2
Olympus Bank Two
8% Interest 7% Interest Profit
Year $160, ($140,000) $20,000
Year , (70,000) ,000
Total $240, ($210,000) $30,000

6. Figure 2: Tranched Collateralized Borrowing $50,000 profit8% 5%
7% Cost
5% Cost 0%
Year 2
Year 1
Olympus Bank One Bank Two
8% Interest % Interest % Interest Profit
Year $160, ($50,000) ($70,000) $40,000
Year , (0) (70,000) ,000
Total $240, ($50,000) ($140,000) $50,000

7. Plain Vanilla CMOs: Structural Characteristics
Collateral (MPTs) pledged to trustee
Four classes of bonds or Tranches
A,B,C and Z
A,B,C retired sequentially
Z class accrual bond
First three classes (A,B,C), with A representing the shortest maturity, receive periodic interest payments from the underlying collateral
Scheduled and unscheduled payment of principal are used to retire Class A first, then class B, then class C
Note the sequential nature of cash flow distribution

8. Plain Vanilla CMOs: Structural Characteristics (cont).
Once the first three tranches have been retired, the cash flow from the collateral is used to satisfy the obligation of the Z-bond (original principal, plus accrued interest).
The Z tranche is an accrual bond. The face amount of the Z bond accretes at its stated coupon.
The cash flows are normally paid to the bond holders on semiannual basis even though borrowers pay monthly
To compensate the CMO investor, the issuer assumes a reinvestment rate at which the cash flows are reinvested until the pay out period

9. Additional Features of CMOs
The number of the tranches is a compromise between splitting the cash flow into as many pieces as possible and sufficient tranche size to preserve liquidity in the secondary market
treated as debt not assets
sale of CMO does not permit the issuer to remove the issue off its books

10. Arbitrage Opportunities
The collective tranches are sold for a higher price than the total purchase price of the collateral (MPTs)
Much of CMOs are sold at lower interest rate associated with short term bond that more closely track the shape of the yield curve
MPTs are sold at specified yield on longer end of Treasury yield curve
Pricing along the yield curve maximizes the value of the mortgage if yield curve is positively sloped (short term rates lower than long term rates)

11. Plain Vanilla: Sequential CMOs
Provides multiple class of securities
No pro rata distribution: investors have claim on distinct cash flow
Prepayment risk is borne sequentially not equally by investor groups
CMOs are an excellent example of financial innovation that renders the market more “complete”
A market is said to be relatively complete when there is a wide variety of assets; enough that almost any eventuality can be either bet upon or protected against, with a portfolio of liquid assets

12. $ Expected Prepayments A B C Sequential CMO Structure
Annual Tranche Principal Payments A B C 5 10 30
Years
190% PSA, Principal Payments Only

13. $ Fast Prepayments A B C Years Sequential CMO Structure
Annual Tranche Principal Payments
Note: (1) with faster prepayment (300%) tranche A is paid sooner
(2) The rules that govern how the principal is allocated among
tranches are fixed, but the prepayments are not. A B C 4 7
Years 30
300% PSA, Principal Payments Only

14. $ Slow Prepayments A C B Years Sequential CMO Structure
Annual Tranche Principal Payments A C B 6
Years 13 30
140% PSA, Principal Payments Only

15. Bonds outstanding and Residuals in CMOs
The amount of outstanding bonds must be small enough to assure that the cash inflows from the collateral will be sufficient to pay the bondholders
Solution: overcollateralization.
The difference between the bond payments required and the cash flows received is called the residual
This residual represents equity invested by the issuer of CMO

16. Calculating Bond Value and Residual
What amount of overcollateralization is sufficient?
Worst Case Scenario : Pattern of prepayments and interim reinvestment rates which will just barely meet bond payments
Calculating the amount can be very complex when:
the individual mortgages in the collateral have different coupons
the tranches have different coupons; and
coupons of the tranches overlap those of the collateral

17. The Present value method for calculating bond value and residual
For CMOs where the coupons on the mortgages are less than any of the coupons on the bonds
Bonds sell at a discount from par
Assume “zero prepayments” = worse case
Discount the cash flows from the collateral at the highest of the coupons on the CMO bonds
Resulting PV will be no less than the amount of bonds to be guaranteed.
The “worse case” never really occurs. So the cash flows are always more than adequate.

18. Illustration of Bond Value and Residual Calculation
Assumptions:
Collatral: $20,000,000 in mortgage principal, 8%, 360 months
CMO structure: four tranches; A (15%), B (20%), C (35%), Z (30%)
Coupon: A = 8.25%, B = 8.75%, C = 9.25%, Z = 10.00%
Debt service = (20,000,000)( ) = $146,760
PV of 10%, 360 = (146,760)( ) = $16,723,422.34
Total amount of CMO bonds should not exceed $16,723,422.34
A % % $2,208,513
B % % $3,344,198
C % % $5,853,198
Z % % $5,017,026
Total $16,723, 422
Residual = $20,000,000 - $16,723,422 = $3,276,578

19. Use of the residual The residual is retained by the issuer
Represents return to the issuer since the amount of overcollateralization is equivalent to equity investment.
For issuers who do not own mortgages, the residuals are the main inducement for undertaking the risk and expense of initiating the CMO.
shortfall from reinvestment of interim cash flow is paid from residual or overcollatralization.

20. Reinvestment of interim cash flows
Payment to CMO investors are made quarterly or semiannually.
However, the cash flows from the collateral are received monthly
CMO issuer reinvests cash flows to compensate investors
The cash flows are reinvested at extremely low rates to maximize the probability of realizing the promised outcome.
Currently, the rating agencies assume cash flows will be reinvested at the low rate of 5.5% the first year, 4% the second year, and 3% thereafter.

21. Reinvestment of cash flows
Assume CMO is 2 years old (3% reinvestment period is in effect)
The next scheduled payment is July 1st.
Current Treasury Bill rate is 7%
The $100 received in January is assumed to be reinvested at the 7% Treasury bill rate for 5 months.
However, $100 expected in February must be ASSUMED to be reinvested forward at only 3%.
$100 invested at 7% for 5 months, $100 for four months at 3%, etc. will accumulate to $ This is the maximum amount that can be assumed available for the July bond payment
Because rates are virtually certain to be greater than 3% actual amount available will greater than $605.46
The difference between actual amount available and the $ represents extra income to the issue or an addition to residual.

22. Other Minor Provisions of CMOs
Nuisance call: CMO bonds redeemed when remaining principal is small fraction of initial face value
Calamity clause: monthly payment instead of normal semiannual when reinvestment rates are insufficient

23. Pricing Issues Should there be difference in yield?
CMO security should have a high yield than a Treasury security of the similar maturity
The different maturities of CMOs resembles that of tax-exempt serial bonds
Z bond attached to CMO’s is an innovation not present in tax-exempt bonds
Tax-exempt serial bonds will have more maturity certainty than CMOs
Should there be difference in yield?

24. Behavior of Fixed Rate Residuals
First residual cash flows come mainly from the excess interest (WAC - coupon tranche)
Residual cash flow largest in early years
The size of the residual is proportional to the outstanding principal of the collateral
Cash flows extremely sensitive to prepayment
Fixed rate residuals are bearish

25. Behavior of residuals.
Rate of return is greater in high interest rate environment --- why
Both amount and timing of cash flow affected by prepayment
Narrow price range between tranches is trade-off in price stability from Z tranche and residuals.

26. CMOs: Variations in Amortization
The sequential CMOs were profitable for investment bankers and issuers and popular with investors
The maturity provided by sequential CMOs does not have the same certainty as that provided by other bonds when actual prepayment rates do not match the assumed prepayment
This relative lack of certainty in maturity is undesirable to some investors
To provide for more cash flow certainty all principal payment in excess of what goes to a tranche is given to a designated tranche instead of sequential pay tranches

27. New kind of CMO: Certainty in maturity
Planned Amortization Class (PAC):
PAC receives fixed payments over a predetermined period of time and a range of prepayment scenarios
Payments in excess of PAC amortization schedule goes to support or companion tranche
Offers greatest degree of cash flow certainty
If prepayments speeds up the PAC still receives the planned principal payments, but companion tranche must bear the entire remaining prepayment. Thus companion tranche becomes a short term security

28. New Kind of CMOs: Certainty in maturity
Targeted Amortization Class (TACs)
the cash flow to investors are targeted to a specific prepayment speed or PSA, known as the pricing speed
if the speed of prepayment goes above this target any excess cash flow is used to pay off one or more tranches known as companion or support tranches
since these companion tranches are issued in tandem with the PACs or TACs they absorb any significant variation in prepayment. The PACs and TACs are in effect insulated.
the net effect is that everything being equal companion or support tranches should have higher yields. WHY?

29. $ Expected Prepayments Companion PAC Years PAC/Companion Structure
Annual Tranche Principal Payments
Note: Companion tranche receives payments
over the entire life of mortgage pool and has
significant long term, medium term and short
term components with prepayment as expected
Companion
PAC
Years
190% PSA, Principal Payments Only

30. $ Fast Prepayments Companion PAC Years PAC/Companion Structure
Annual Tranche Principal Payments
Note: With faster prepayment (300 PSA) the
CMO receives much higher principal payments
than expected in early years. The PAC still
receivesits planned principal payment.
Companion tranche must bear the entire
remaining prepayment increase
Companion
PAC
Years
300% PSA, Principal Payments Only

31. $ Slow Prepayments Companion PAC Years PAC/Companion Structure
Annual Tranche Principal Payments
Note: With slower prepayment there is much less principal
in early years than anticipated. But more principal is
available later. PAC has priority on receiving principal.
Companion must defer its own amortization.
Companion
PAC
Years
100% PSA, Principal Payments Only

32. CMO: Variations in coupon
Some investors want their return to float with market even if protected from prepayment fluctuations
Floater
Coupon adjusts periodically to a fixed spread over the index rate such as the LIBOR
Offers a variable payout as opposed to the constant payout of PACs or TACs
Reverse Floater
To allow variable payout on the floater a reciprocal security known as reverse floater is created
Coupon on reverse floater adjusts in opposite direction to its index.
The floater and the reverse floater share interest payments from a pool of fixed rate mortgages
If interest rates rise the coupon on the floater takes more of the interest and reverse floater take less and vice versa.

33. Shifting Risks and Returns from floaters to inverse floaters
Tranching makes it possible to reduce interest rate risk for some investors by converting fixed rate mortgages to floating rates
Since the interest payment characteristics on underlying mortgages have not changed this risk reduction is accomplished by creating another tranche to which the risk is shifted
The sifting of risk from the floater doubles up the interest rate risk in the inverse floater with radical yield and price response
If interest rate fall the inverse floater investor receives the double benefit of a higher-rate security in a lower-rate environment.
If rates rise the inverse floater investor pays a double penalty for a lower-rate security in a higher interest rate environment.

34. How a reverse floater works
We can illustrate how an Reverse Floater works with FHLMC Series 128 CMO issued in January The coupon on the underlying collateral was 9% and the principal amount at time of issuance was $1 billion. As part of the CMO structure there was a floating rate class of $64 m. and a reverse floater with $16 m. in principal. Thus the floater and reverse floater represent $80 m. of the $1 billion CMO structure.
The coupon for the floating class is:
LIBOR +0.65
For the inverse class the coupon rate is
x LIBOR
The weighted average coupon = (64/80)(Floater coupon rate) + (16/80)(Inverse floater coupon rate)

35. Reverse floater illustration: cont.
The weighted average coupon rate is 9% regardless of level of LIBOR
For example assume LIBOR is 10%
Floater coupon rate = = 10.65
Inverse floater coupon rate = x 10 = 2.4
The weighted average coupon rate is:
(64/80)(10.5) + (16/80)(2.4) = 9
Thus the coupon on collateral can support aggregate interest payments that must made to these two classes.
However restriction must be placed on coupon rate for the reverse floater to prevent negative rate for that class. This is done true a floor cap.
In this deal the floor was zero.
This floor places a restriction on maximum coupon to be paid to floater.

36. Reverse floaters: cont.
In this case the maximum coupon for the floater is 11.25%.
.8x = 9 , x = 11.25%
To calculate this coupon substitute zero for the coupon rate for inverse floater in the formula for the weighted average coupon rate and then set the formula equal to 9 , i.e (64/80).x + (16/80)(0) = 9.
The presence of a reverse floater allows for the payment of higher coupon to the floater class than in the absence of reverse floater.
The multiple by which the coupon on reverse floater can change is called the coupon leverage
The larger the coupon leverage the more the reverse floater coupon will change for a given change in LIBOR.

37. Some Operational and Institutional Details in Connection with Mortgage Passthroughs
Operational details are the invisible part of the securities market such CMOs, MPTs etc
Yet these rules and conventions are the glue that hold the market
Operational details:
Lags
Factors
Settlement
Calculating Settlement Cash
Forward delivery
Delivery and remittance

38. Lag Days or Delays Lag Days or delays:
period elapsed between the receipt of mortgage payments by servicer, who passes it to security issuer who them makes payment to investors
There are three ways of describing lags
as an example consider a Fannie MBS that pays march interest on 25th April
Accrual method: considers time when homeowners interest begins accruing (March 1st) and when the MBS payment is made (April 25th). The convention is to assume each month has 30 days. This gives a lag of 55 days ( )

39. Lag Days or Delays
Current method: recognizes that interest is not lagged while it is still accruing, much like Treasury or corporate bond paying semi-annual interest.
With this method of describing lags month of March is ignored and the lag is 25 days
Mathematical, or true yield method: considers the difference between when payment would be made on mortgage loan and when it will be made on the CMO or MPT
April 25 is 24 days after April 1st (when payment is due from borrower), so we have 24-day lag
This method is currently used to calculate the effect of lags on security’s yield

40. Lag Days and Yields
Lag days always work to reduce yield, because investors lose the use of their money which consists of interest, principal, or both.
The degree to which yield is reduced depends on number of lag days, the payment frequency and timing of principal payments
Table 1 illustrates the interplay between payment lags and the timing of principal payments.
The effect of lag days on yield depends on the relative importance of interest and principal payments
As shown in Table 1 with short term security (1 year) where virtually all cash received is principal a 14-lag causes a -0.63% reduction in yield more than offsetting the .17% gain in yield due to monthly payment

41. Monthly Pay, 9% Amortizing Mortgage, bought at PAR
Table 1: The Shifting Importance of Lag Days
Monthly Pay, 9% Amortizing Mortgage, bought at PAR
Security Type Short Term Medium Term Long Term
Amortization 1 YEAR 10 YEAR 30-YEAR
14 LAG DAYS
Monthly pay Yield Benefit 0.17% 0.17% 0.17%
Lag Days Yield Cost % % %
Net Yield Change % 0.09% 0.13%
Bond Equivalent Yield 8.54% 9.09% 9.13%
24 LAG DAYS
Monthly pay Yield Benefit 0.17% 0.17% 0.17%
Lag Days Yield Cost % % %
Net Yield Change % 0.03% 0.10%
Bond Equivalent Yield 8.13% 9.03% 9.10%
44 LAG DAYS
Lag Days Yield Cost % % %
Net Yield Change % % 0.06%
Bond Equivalent Yield 7.43% 8.91% 9.03%

42. Effect of Lag days
With 44-day lag as in Freddie Mac PC the effect is devastating leading to a -1.74% loss in effective yield on 1-year security. So BEY = 7.43% on 9% security bought at par
With 30-year security the 44-day lag leads to only a -0.12% reduction in yield
the reason for the dramatic difference is that with 30-year security most of cash paid to investor is interest, especially in early years
0.17% pickup in yield due to monthly payment more than offsets the 0.12 lag-day reduction in yield.
For the 14-day lag and long term investment, the investor is earning a 9.13% BEY on a 9.00% security purchased at par

43. Factors
A factor refers to amount of original face value of mortgage passthrough that is outstanding
a factor of for a $1 million MBS or CMO means $627,340 of the original face value is outstanding
With ordinary bonds factors are irrelevant
either all the bond is outstanding, it has been called, or it has matured, there is no in-between
If you own a particular tranche in a CMO the factor stays at until your principal payment window starts, then the factor will drop with every payment until it reaches at maturity.
For MBS the factor starts at 1.00 and declines with every payment until it reaches 0.00 at maturity

44. Using Factors (1) PURCHASE PRICE
One way to use factors is in determining purchases price.
Suppose we want to buy a tranche with original $1 million face amount that has began receiving principal payments.
The factor is currently , thus $732,500 of principal is still outstanding and $267,500 has already been paid to previous owners
The price of the tranche is 92 14/32, or $ of par
Thus, the purchase price to new investor is $677, ($1,000,000 x x ), ignoring accrued interest.
See figure next page

45. Using Factors FINDING FACE AMOUNT, DETERMINING PURCHASE PRICE
GIVEN CASH
Available Cash:
$1,000,000.00
Price:
¸ /32
Maximum Principal Purchase:
= $1,081,812.04
Factor: ¸
Maximum Face Amount:
= $1,476,876.50
Does not include accrued interest
DETERMINING PURCHASE PRICE
Tranche Face Amount:
$1,000,000
Factor: x
Outstanding Principal Amount:
= $732,500
Price:
x /32
Purchase Cost:
= $677,104.69
Does not include accrued interest

46. Using Factors (2) MAXIMUM AMOUNT TO PURCHASE:
In practice investors start with amount of money they want to invest and then determine the maximum face amount of tranche they can buy.
Figure - also shows how to calculate this maximum amount for given cash available.
Factors can also tell us how much we are going to be paid
Using the beginning and ending factors for the month we can determine what the precise principal and interest payments will be.
(3) EXCITEMENT OF FACTOR REPORTS
The excitement that factors generate is similar to that of stock market awaiting corporate earnings reports, or economic report in case of bond market.
This is because factors are the raw data from which prepayments speeds are calculated

47. Settlements Settlement practices for CMO
In general CMO settlement practices vary depending on whether the CMO is new or seasoned
Settlement of Seasoned Issues
Seasoned CMOs settle according to standard corporate bond settlement practices: As of 1995 this is three business days after purchase.
Agency passthroughs settlement
these settle on only one day of the month, with particular settlement date varying by issuer

48. Settlements New Issues: Forward Delivery
New CMO issues usually settle on the last or second to last day of the month in a month after the purchase month.
The settlement month could be one, two or three months later
Delay in settlement allows issuer to group all mortgage securities that will collateralize the CMO
The sale is generally “when”, as, and if issued” basis. This means a CMO may not be created at all.

49. Pricing Implications of new issue delivery delay
New issue delivery delay has pricing implications for CMO buyer
The seller collects interest for two months at the long-term rate, while financing it at short term rate
The seller having already sold the security is not exposed to price risk
The seller arbitrages, earning a risk-free rate of return equal to the difference between the long and short term rates
The forward buyer gives up this profit but is exposed to price risk for two months
Therefore securities for forward delivery trade at lower prices than otherwise identical securities for current delivery
The further out the delivery the lower the price
If forward delivery prices were the same as current delivery prices, then every one will be a seller and no one will want to be buyers

50. Calculating Settlement Cash
Earlier we calculated the price paid by the buyer of CMO or MBS that did not include accrued interest.
The other part of price paid by buyer is accrued interest.
CMO and passthrough interest is paid on a 30/360 basis
Accrued interest is due from first of settlement month through the date of settlement
if we settled on 20th of the month, we pay 19 days of accrued interest
The principal that we pay accrued interest on is the same as the principal that we purchased, which is equal to the principal amount as of the beginning of the settlement month

51. Illustration
Suppose we purchase $1 million face value Fannie Mae tranche with 7.5% coupon at a price of 98 20/32 on Friday April 15th. Settlement is 3 business days later on Wednesday April 20th.
Principal we pay is based on factor released on Monday April 11, ( ) which represents principal outstanding after April 1 homeowner payments
Principal purchased = ( x$1,000,000) = $743,678.92
Purchase price = (743,678.92x = $733,452.43
Accrued interest to pay = {(.075/360)x743,678.92} = $
This is the first 19 days of 7.5% interest on $743,678.92
Total cash paid at settlement on April 20 = $736, ($733, $ )

52. Payments to holder of record
As holder of record on April 30th, the investor is entitled to his share of homeowners May 1st payments: (1) interest for April, (2) April’s prepayment, and (3) May 1st scheduled principal payments
Interest (one month) = (.075/12)($743,678.92) = $4,647.99
Principal = (April factor , minus May factor, ) x$1,000,000 = x $1,000,000 = $7,854.85
Total payment received on May 25th = $12, ($ $7,854.85) = $12,502.84)
The amount of 12, is known as soon as the May factors are released on May 11th.
Note: although we paid for and took delivery of CMO tranche by April 20th, we do not receive the April 25th payment, because that is lagged payment going to the holder of record as of end of March.

53. Blackout Settlement Period
Typically the exact principal for securities settling prior to the date when factors are released (11th April in our previous example ) is not known
The principal balance is based on previous month factor. So we do not know the correct amount of principal when we settle
The period when we have to pay for securities but do not yet know the exact principal is call black out period
First settlement is canceled and new settlement documents with and cash amount are prepared when correct factor is released
The buyer gets principal overpayment back from seller
The first settlement is known as “settling with money difference”

54. Delivery and Remittance
CMOs and other passthroughs exist in purely electronic world: the securities are book entries only
Freddie Mac and Fannie Mae do not offer physical certificates
Ginnie Mae CMO certificates are available at a steep price of $25,000 per certificate
Fannie Mae and Freddie Mac’s securities backed by conventional are delivered through Federal Reserve Bank wire system
Ginnie Mae securities are delivered through Participant’s Trust Company, PTC
Remittance of principal and interest are made in lump sum by wire to a nominee ,usually a broker, who has account with the Fed Reserve Bank
Based on factor and ownership information the nominee operations department divides the remittance into principal and interest for each investor or beneficial owner