1 Collateralized Mortgage Obligations. 2 Motivation for development of CMO structure MPTs are unattractive investment for institutional investors because

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 amo

ng different classes of bond holders• Note: In contrast MPTs represents horizontal slicing of cash flows

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A Tranching Example• Assume you lent $2 million to Olympus Properties at 8% interest which Olympus agreed t

o 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

8%

0%

7% Cost

1% profit

Olympus Bank Two8% Interest 7% Interest Profit

Year 1 $160,000 ($140,000) $20,000

Year 2 80,000 (70,000) 10,000

Total $240,000 ($210,000) $30,000

Year 1 Year 2

Figure 1 : Normal Collateralized Borrowing $30,000 profit

7%

Figure 2: Tranched Collateralized Borrowing $50,000 profit

8%

0%5% Cost 7% Cost

1% Profit3% Profit

Olympus Bank One Bank Two8% Interest 5% Interest 7% Interest Profit

Year 1 $160,000 ($50,000) ($70,000) $40,000

Year 2 80,000 (0) (70,000) 10,000

Total $240,000 ($50,000) ($140,000) $50,000

Year 1 Year 2

5%

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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

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Plain Vanilla CMOs: Structural Characte

ristics (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

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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

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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)

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Plain Vanilla: Sequential CMOs• Provides multiple class of securities• No pro rata distribution: investors have claim on distinct c

ash flow• Prepayment risk is borne sequentially not equally by inve

stor groups• CMOs are an excellent example of financial innovation th

at renders the market more “complete”• A market is said to be relatively complete when there is a wid

e variety of assets; enough that almost any eventuality can be either bet upon or protected against, with a portfolio of liquid assets

$

A B C

Expected PrepaymentsSequential CMO Structure

Annual Tranche Principal Payments

190% PSA, Principal Payments Only

0 5 10 30Years

$

Years

Fast PrepaymentsSequential CMO Structure



AB C

0 4 7 30

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.

$

Years

Slow PrepaymentsSequential CMO Structure



A B C

0 6 13 30

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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

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Calculating Bond Value and Residual

• What amount of overcollateralization is sufficient?• Worst Case Scenario : Pattern of prepayments and interi

m 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 coupo

ns

– the tranches have different coupons; and

– coupons of the tranches overlap those of the collateral

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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 t

o be guaranteed.• The “worse case” never really occurs. So the cash flows

are always more than adequate.

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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)(.007338) = $146,760

PV of $146,760 @ 10%, 360 = (146,760)(113.950) = $16,723,422.34

Total amount of CMO bonds should not exceed $16,723,422.34

A 15% 8.25% $2,208,513

B 20% 8.75% $3,344,198

C 35% 9.25% $5,853,198

Z 30% 10.00% $5,017,026

Total $16,723, 422

Residual = $20,000,000 - $16,723,422 = $3,276,578

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Use of the residual• The residual is retained by the issuer• Represents return to the issuer since the amount of overc

ollateralization 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.

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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.

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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 $605.46 . 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 $605.46 represents extra income to the issue or an addition to residual.

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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

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Pricing Issues• CMO security should have a high yield than a Treasury security o

f 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?

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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 outst

anding principal of the collateral• Cash flows extremely sensitive to prepayment• Fixed rate residuals are bearish

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Behavior of residuals.• Rate of return is greater in high interest rate enviro

nment --- 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.

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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

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New kind of CMO: Certainty in maturity

• Planned Amortization Class (PAC): – PAC receives fixed payments over a predetermined peri

od 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

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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?

$

Years

Expected PrepaymentsPAC/Companion Structure



PAC

CompanionNote: 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

$

Years

Fast PrepaymentsPAC/Companion Structure



PAC

Companion

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

$

Years

Slow PrepaymentsPAC/Companion Structure



PAC

Companion

Note: With slower prepayment there is much less principalin early years than anticipated. But more principal is available later. PAC has priority on receiving principal.Companion must defer its own amortization.

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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.

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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.

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How a reverse floater works• We can illustrate how an Reverse Floater works with FHLMC Series

128 CMO issued in January 1990. 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

– 42.4 - 4x LIBOR• The weighted average coupon = (64/80)(Floater coupon rate) +

(16/80)(Inverse floater coupon rate)

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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+0.65 = 10.65

– Inverse floater coupon rate = 42.4 - 4 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.

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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

Factors • A factor refers to amount of original face value of mortgage passthrough th

at is outstanding

– a factor of 0.62734 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 1.000 until your principal payment window starts, then the factor will drop with every payment until it reaches 0.000 at maturity.

• For MBS the factor starts at 1.00 and declines with every payment until it reaches 0.00 at maturity

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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 0.7325, 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 $92.4375 of par

– Thus, the purchase price to new investor is $677,104.69 ($1,000,000 x .7325 x 0.924375), ignoring accrued interest.

– See figure next page

39

Using Factors

DETERMINING PURCHASE PRICE

Tranche Face Amount: $1,000,000Factor: x 0.7325Outstanding Principal Amount: = $732,500Price: x 92 14/32Purchase Cost: = $677,104.69

Does not include accrued interest

FINDING FACE AMOUNT, GIVEN CASH

Available Cash: $1,000,000.00Price: 92 14/32Maximum Principal Purchase: = $1,081,812.04Factor: 0.7325Maximum Face Amount: = $1,476,876.50

Does not include accrued interest

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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 aw

aiting 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

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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

42

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.

Documents

1 Collateralized Mortgage Obligations. 2 Motivation for development of CMO structure MPTs are unattractive investment for institutional investors because