Understanding Mortgage Dollar Rolls

RMBS Trading Desk Strategy

Understanding Mortgage Dollar Rolls October 2, 2006

Sharad Chaudhary 212.583.8199 sharad.chaudhary@bankofamerica.com

RMBS Trading Desk Strategy

Ohmsatya Ravi 212.933.2006 ohmsatya.p.ravi@bankofamerica.com

Qumber Hassan 212.933.3308 qumber.hassan@bankofamerica.com

Sunil Yadav 212.847.6817 sunil.s.yadav@bankofamerica.com

Ankur Mehta 212.933.2950 ankur.mehta@bankofamerica.com

RMBS Trading Desk Modeling

ChunNip Lee 212.583.8040 chunnip.lee@bankofamerica.com

Marat Rvachev 212.847.6632 marat.rvachev@bankofamerica.com

Vipul Jain 212.933.3309 vipul.p.jain@bankofamerica.com

Dollar rolls serve as the primary channel for mortgage securities borrowing and lending in the MBS TBA market, and as such they play a critical role in providing liquidity to

the market. The borrowing rate associated with a dollar roll provides significant

information on technicals in the MBS market. A background in the conventions and

calculations associated with dollar rolls is thus critical to understanding relative value

in the MBS market. The primary goal of this primer is to provide this background.

Functionally speaking, dollar roll transactions are a form of securities lending and are closest in spirit to repurchase agreements (repos). In a typical repo, a lender agrees to

sell securities to a buyer in return for cash. At the termination of the transaction, the

securities are resold at a predetermined price plus an interest payment. A dollar roll is

analogous to a repurchase transaction except that the party borrowing the securities has

the flexibility of returning “substantially similar” securities, instead of the same ones.

In addition to providing financing opportunities for mortgage pass-through positions and enhancing liquidity in the TBA market, dollar rolls also serve other needs. Dollar

rolls are used to obtain collateral for CMO deals and TBA transactions, to avoid

operational issues associated with taking delivery of mortgage pools, to hedge specified

pool positions, and to express a view on prepayment speeds.

As financing transactions, dollar rolls can offer attractive borrowing rates and a considerable portion of this primer is devoted to explaining how to calculate the

implied financing rate associated with a particular dollar roll. The sensitivity of roll

pricing to different factors such as prepayment speeds and reinvestment rates is also

explored.

Historical data suggest that dollar rolls can offer financing advantages of as much as 15 bps to 100 bps versus 1-month LIBOR. This advantage should not be construed as a

“free lunch”, however, since it comes with risks attached. These risks include being

redelivered collateral with inferior prepayment characteristics relative to the original

securities that were delivered and prepayment risk. Credit risk and liquidity risk play a

relatively minor part in dollar rolls.

Our primer concludes with a “real life” example of how dollar rolls trade in practice. We review the history of roll levels on FNMA 6s and comment on the various factors

that led to the roll trading in a 2 to 15 tick range between 2003 and 2004.

This document is NOT a research report under U.S. law and is NOT a product of a fixed income research department. This document has been prepared for Qualified Institutional Buyers, sophisticated investors and market professionals only. To our U.K. clients: this communication has been produced by and for the primary benefit of a trading desk. As such, we do not hold out this piece of investment research (as defined by U.K. law) as being impartial in relation to the activities of this trading desk. Please see the important conflict disclosures that appear at the end of this report for information concerning the role of trading desk strategists.

RMBS Trading Desk Strategy

I. INTRODUCTION

As one of the most liquid fixed income sectors in the world, mortgage-backed securities

(MBS), particularly those backed by agency guarantees, constitute an active subsector of

global securities lending markets because of their high credit quality and liquidity. Securities

lending transactions in MBS are usually structured in one of two ways: as repurchase agreements (repos), or as dollar rolls. Repurchase agreements are securities lending transactions in which one party (the lender) agrees to sell securities to another party (the

borrower) in return for cash (or securities), with a simultaneous agreement to repurchase the

same securities at a specific price at a later date.1 At the termination of the transaction, the

securities are resold at the predetermined price plus an interest payment (calculated based on

a previously determined interest rate). A dollar roll is analogous to a repurchase transaction,

except that it provides the party borrowing the securities with additional flexibility of

returning “substantially similar” securities, instead of the same ones.2 In addition, unlike a

repo, the party borrowing the security owns the principal and interest payments generated

during the roll period.

The popularity of mortgage repos and dollar rolls can be gauged from the fact that parties to

these agreements span the entire range of institutional participants in the mortgage market:

broker-dealers, GSEs, banks, pension funds, hedge funds, insurance companies, mutual

funds and overseas investors. The needs and motivations of these participants vary from

transaction to transaction, depending upon whether they are acting as a borrower or lender of

securities (or sometimes even both). For example, a broker-dealer might borrow securities to

cover a short position, or simultaneously borrow and lend securities to earn a high rate on

the securities loaned versus the securities borrowed. To give a specific example relevant to

the mortgage sector, during times of heavy Agency CMO issuance activity the demand for

mortgage pools by broker-dealers can lead to very attractive financing rates for MBS holders

who choose to “roll” their securities to these dealers. The ability of MBS investors to “roll”

the pass-through securities they have in position lowers funding costs and can significantly

enhance returns on these positions versus other fixed-income alternatives.

As our discussion and examples suggest, dollar roll transactions play an important role in

enhancing liquidity in the MBS market by facilitating market making and the creation of

structured securities. Unfortunately, it is not easy to quantify this liquidity because no

official statistics exist for the volume of dollar roll transactions since they take place “over-

the-counter.” In other words, dollar rolls are privately negotiated transactions between two

parties that take place through a trading desk or an electronic trading system. However, data

from TradeWeb and the Bond Market Association suggest that dollar rolls constitute

1 Securities lending has been defined as the “temporary exchange of securities, generally for cash or other securities of at least an equivalent value, with an obligation to redeliver a like quantity of the same securities on a future date.” An excellent introduction to this subject can be found in Securities Lending Transactions: Market Developments and Implications, Technical Committee of the International Organization of Securities Commissions (IOSCO), Bank of International Settlements (BIS) Committee on Payment and Settlement Systems (CPSS), July 1999. 2 “Substantially similar” is defined in the American Institute of Certified Public Accountants’ Statement of Position 90-3 as meaning that the original and returned security should be of the same agency/program, original maturity, and coupon and both should satisfy “Good Delivery” requirements. Some of the requirements associated with “Good Delivery” are spelled out in The TBA Market section.

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RMBS Trading Desk Strategy

anywhere from one-third to two-thirds of all “To Be Announced” (TBA) transactions.3

These numbers and information on Agency MBS trading volumes released by the Federal

Reserve Bank of New York lead us to an estimated daily volume of $20 billion in dollar roll

transactions in 2006. However, we should point out that a daily number is somewhat

misleading in this context since most roll activity takes place two to five days before TBA

settlement dates. Turning to the composition of participants in these transactions, based on

trading desk flows, we estimate that money managers and U.S. banks account for nearly

50% of dollar roll activity, with the other half attributable to the GSEs, mortgage servicers,

insurance companies and overseas investors.

The primary goal of this primer is to describe and discuss the conventions and

calculations associated with dollar roll transactions. Consequently, we begin by

sketching some of the key conventions associated with the MBS TBA market, which is

the market where these transactions take place. The next section explains some of the

basic aspects of dollar roll transactions and provides practical examples of how and

why these agreements are executed by market participants. From there, we delve into

the nuts and bolts of calculating the all-important financing rate associated with these

transactions. This is followed by a sensitivity analysis that demonstrates how this

financing rate depends upon prepayment assumptions and the reinvestment rate. The

sensitivity analysis provides a natural segue into a more detailed discussion of the risks

associated with the dollar roll—with redelivery and prepayment risks being the crucial

ones. The paper concludes with a review of recent trading activity in the rolls associated

with a specific coupon to provide readers with some “real-life” background for the

dollar roll market.

3 TradeWeb is a multi-dealer electronic auction system that links fixed-income securities dealers with buy-side institutions. Besides TBA-MBS, other products traded on the platform include US Treasuries, agencies and several other types of debt securities. The Bond Market Association is a private trade association that represents security firms and banks that underwrite, distribute, and trade debt securities. The Association’s membership includes all major dealers.

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II. THE TBA MARKET

As a preface to an explanation of the dollar roll market, it is useful to review some

features of the “To Be Announced” (TBA) market for mortgage pass-throughs that play

a particularly important role in dollar roll transactions. The TBA nomenclature captures

two important features of how this market operates:

The market is a forward delivery market with participants entering into forward contracts to buy or sell MBS on a monthly settlement schedule set by the Bond Market

Association. A settlement date is typically 30 days into the future but can be as much

as two to six months in the future. The current settlement month is known as the front month and the settlement months following the front month are typically known as back months. The actual numbers of pools and pool numbers are not known at the initiation of the forward contract but are “announced” on 48-hour day: two business

days before the agreed settlement date, prior to 3pm EST. Other general trade

parameters such as the agency type, price, coupon and par amount are known at the

time the trade is executed.

The pools delivered by the seller on the settlement date have to satisfy Good Delivery Guidelines. These are also established by the Bond Market Association and detail the specifics associated with confirming and settling MBS. For example, the guidelines

govern the maximum number of pools per lot and maximum allowable variance

between the face amount of the pools delivered and the agreed-upon face amount.

Current standards for Good Delivery include a maximum of three pools per lot and a

maximum variance of 0.01% per lot. In other words, for a $1 million lot, the sum of

current face amounts of the pools should be within 0.01% of $1 million, or between

$999,900 and $1,000,100.

Settlement fails on TBA transactions turn out to play an important role in the economics of dollar rolls. In a TBA transaction, the seller does have the option to fail to

deliver the securities to the buyer. In this situation, the buyer does not have to pay the

seller until the securities are delivered. The price of the security, including the accrued

interest that is to be paid, does not change. In essence, then, the buyer is compensated

for the fail by reinvestment income on the money that was to be paid for the pools.

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RMBS Trading Desk Strategy

III. DOLLAR ROLLS The close tie between the dollar roll and TBA markets arises from the fact that the process of

trading rolls is indistinguishable from that of trading TBAs from the perspective of a pass-

through trading desk. To understand why this is the case, recall the definition of a dollar roll

again: these are essentially repurchase agreements in which the seller of securities is

obligated to repurchase securities that are substantially similar to, but not identical with, the

securities originally sold. It is useful to further unpack this definition a little and think of a

dollar roll as a combination of two simultaneous transactions: a buy and a sell order for a

mortgage pass-through security for two different settlement dates. By convention, the Seller of roll is the party who sells mortgage securities for a settlement month (the front month) and agrees to buy back “substantially similar” securities for a future settlement month (the

back month). On the other side of the transaction, the Buyer of roll is the party who buys securities for the front month and agrees to sell “substantially similar” securities for the back

month. The equivalence of the dollar roll and TBA markets becomes clear when we realize

that the roll buyer’s commitment to return securities in the second leg of the dollar roll can

be hedged by getting long TBAs for the future settlement month.

Pricing on a dollar roll transaction can be requested from a pass-through desk by specifying

the size of the MBS position to be rolled (based on original face amount), long/short,

agency, maturity, coupon, the month the position is expected to settle, and the future

settlement month that the position should be rolled to. The roll price (also known as the drop) is equal to the difference between the purchase and sale prices of the mortgage security on the two settlement dates and is expressed in ticks. For example, a trading desk

might tell a customer: I can offer you $500 million of the FNMA 6 Sep/Oct roll at 11+.

As an intuition building exercise, it is useful to review some concrete examples of roll

transactions.

Investor A is long FNMA 6s for October delivery. At some time prior to October settlement day, investor A decides it does not want to have a forward position on

FNMA 6s for October settle and rolls the position forward to November. The decision

to roll could be based on an attractive drop between the October and November prices,

or operational issues such as not being willing or able to take delivery of the security

in October. By selling the roll, Investor A remains invested in mortgages and can

potentially also lock in an attractive financing rate on the funds obtained during the

roll period.

Mechanically, Investor A sells FNMA 6s for October settlement and purchases FNMA

6s for November settlement. The only transfer that takes place on the October

settlement date is a cash transfer that reflects the difference between the price of

FNMA 6s that the investor agreed to pay when they purchased them and the front

month price of FNMA 6s when they rolled these bonds (both prices are for October

settlement).

Investor B holds a collection of FNMA 6 pools and decides to lend these pools to the pass-through trading desk of broker-dealer X for October delivery in return for

“substantially similar” FNMA 6s pools in November. Investor B is motivated to do

this transaction by the fact that it can obtain attractive financing rates over the

October-November roll period. Based on recent history, the comparative advantage of

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RMBS Trading Desk Strategy

financing rates obtained through dollar rolls can be anywhere from 15 bps to 100 bps

over 1-month LIBOR.

Mechanically, investor B sells FNMA 6s from its inventory to pass-through desk X for

October settle and buys FNMA 6s for November settle. The FNMA 6s held in Investor

B’s inventory are transferred from its inventory to the inventory of the pass-through

trading desk.

Investor B delivers FNMA 6s to pass-through desk X for October settle. At the same time, it enters into a forward commitment to purchase FNMA 6s for November settle.

Before November settlement, Investor B and desk X agree to roll the transaction to

December. Desk X sells the FNMA 6s for October settle to investor C while

simultaneously agreeing to buy FNMA 6s for November settle with investor D. On

being notified of Investor B’s intention to roll their 6s from November to December,

Desk X sells the November/December FNMA 6 roll to Desk Y.

This sequence of transactions demonstrates how the dollar roll market adds liquidity to

the pass-through market by providing an outlet for market making pass-through trading

desks to maintain a neutral position in pass-throughs or go long or short.

The Agency CMO trading desk of broker-dealer X can use the dollar roll market both for taking delivery of the collateral required for issuing a CMO and for hedging the

collateral that they have in inventory for soon-to-be-issued CMOs. Normally, CMO

deals are collateralized by current coupon pools, but these pools can be hard to find

because of the lag between current interest rates and the time when the corresponding

pass-through pools are actually created.4 A supply crunch in CMO deal collateral

impacts the roll market though increased demand for collateral in the front month. This

bids up prices for front-month settlement TBAs relative to back-month TBAs and

increases the drop in the roll market. In addition, CMO deals are frequently done using

“story collateral” i.e., collateral with desirable prepayment characteristics. In this case,

the roll may be bid up to induce the owners of the bonds of these desirable

characteristics to either deliver them in to TBA or to sell them outright.

This list of transactions does not exhaust all the possible uses dollar rolls can be put to. For

example, rolls can be used for hedging a specified pool position: when rolls are trading rich, the attractive characteristics of specified pools are worth less since the cost of hedging

specified pools with TBAs increases (or the carry advantage of specified pools is reduced).5

Finally, sophisticated investors can use the roll market to express a view on prepayment

rates on different coupons. As discussed later in this paper, it is sometimes beneficial to

maintain ownership of pass-throughs rather than roll them and vice versa, depending on the

prepayment rate realized in the front month of the roll, and whether the pass-through is a

discount or a premium security.

4 It typically takes four to eight weeks to close a mortgage. 5 Specified pool trades take place outside the TBA market and are executed by specifically identifying certain pools that an investor wishes to acquire. In general, investors “pay up” for these specified pools—for example, for the prepayment protection offered by a premium pool with a low average loan size or for the extension protection offered by slightly seasoned discount pools relative to TBA discount pools.

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RMBS Trading Desk Strategy

Comparing Mortgage Dollar Rolls and Repos

To round up our introductory review of dollar roll transactions, it is instructive to compare a

dollar roll to a mortgage repurchase transaction (also known as a repo):

All the cash flows generated during the roll period belong to the buyer of the dollar roll. Thus, for example, if a record date falls during the term of the roll, the principal and

interest for the front month are paid to the buyer of the dollar roll.6 In a repo

transaction, principal and interest go to the original owner.

Securities “substantially similar” to the original ones borrowed can be returned in a dollar roll. In a repo, the ownership of the security is not transferred and the same

security needs to be returned.

There is considerable flexibility in terms of setting the length of repo transaction, with typical maturities ranging from one to 30 days. The settlement dates for dollar rolls

typically match TBA settlement dates.

The collateral backing a repo transaction can consist of small collections of pools, agency CMOs and non-agency CMOs, while dollar rolls trade in the TBA market. The

perceived fungibility or interchangeability of mortgage pools plays a crucial role in

terms of being able to perform roll transactions.

The flexibility to deliver substantially similar collateral in a dollar roll makes dollar roll

transactions far more common than mortgage repos. In general, mortgage repos are

collateralized by structured securities or specified pools. From both an operational and a

financing advantage perspective, it usually makes more sense to roll pass-throughs than to

repo them.

6 The record date is the date for determining the registered owner of the next scheduled payment of principal and interest for the mortgage security. The record date for MBS is typically the last business day of the month.

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RMBS Trading Desk Strategy

III. PRICING DOLLAR ROLLS Dollar Roll Calculations

Let’s review the definition of a dollar roll once again: a dollar roll is a combination of two

simultaneous transactions: a buy and a sell order for a mortgage pass-through security for

two different settlement dates. Thus, a natural entry-point for thinking about the value of

dollar rolls is to analyze the economics of holding onto pass-through securities versus

“rolling” them. To this end, Figure 1 itemizes the cash flows associated with the two

alternatives. It would be more advantageous to roll securities versus holding them if the cash

flows in the “Financing” box of the figure added up to more than the cash flows in the

“Holding” box.

The forward repurchase price plays a crucial role in determining which of the two

alternatives presented in the figure is more advantageous. If this were a repo transaction, the

repurchase price would equal the initial sale price, plus an interest payment at a previously

determined interest rate (the repo rate). The repo rate is typically lower than prevailing short-

term rates since the repo transaction is a form of collateralized borrowing. Thus, the lender

of securities (the borrower of money) benefits because even though they are paying more to

repurchase their securities, they are (typically) able to invest the funds received from the

initial sale of securities at a higher rate than their borrowing rate (the repo rate).

A dollar roll introduces one crucial twist to the above situation. Since the principal and interest earned on the security over the roll period belong to the lender of cash (the roll

buyer), in an upwardly sloping yield curve environment, the forward price is usually

lower than the initial price to compensate the seller of the roll for losing one month of

positive carry on the position.7 Other than that, the situation is exactly analogous to the repo agreement discussed above. After taking the lost carry into account, the forward

price is set at a level that defines a financing rate for the transaction. The security owner

then compares this financing rate to their other alternatives to determine whether to

hold or “roll” their securities.

Figure 1. Cash Flows Associated with Rolling versus Holding Pass-throughs

Cash Flows of the Roll (Financing the Mortgage Securities) + Sale of Security at initial price (plus accrued interest) + Reinvestment income on sale proceeds – Repurchase of security at the forward price (plus accrued interest)

Cash Flows From Holding Mortgage Securities + Coupon Payment + Scheduled payment of principal + Prepaid principal + Reinvestment income on interest and principal received during roll period – Discount on interest and principal received after the roll period

Source: Banc of America Securities

7 The carry on a fixed income investment is usually defined as the interest income on the position less the cost of financing it. In case of dollar rolls, an investor needs to also consider the premium/discount received on pay-downs. Note also that the forward

price (back-month settlement price) need not be lower than the initial price (front-month settlement price) even when the yield

curve is upwardly sloping if prepayment speeds on premium coupons are very fast.

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RMBS Trading Desk Strategy

A worked example illuminates several of these issues. Recall that the roll price, which is referred to as the drop in market parlance, is equal to the difference between the purchase and sale prices of the mortgage security on the two settlement dates. An investor who owns

30-year FNMA 6s enters into a dollar roll transaction by selling $1 million of the

September/October 2004 roll on 30-year FNMA 6s. As of August 27th 2004, FNMA TBA 6s

for September settlement were trading at 103-14 and the drop for the September/October roll

was 11.8 ticks. Thus, the investor is committing to simultaneously selling $1 million FNMA

6s for September settlement at 103-14 and buying $1 million FNMA 6s for October

settlement at a price of 103-2.2.

In addition, we make the following assumptions:8

The 1-month reinvestment rate over the roll period for the investor is equal to 1.77%; TBA FNMA 6s have a WAC of 6.50% and a WAM of 356 months; The expected prepayment speed for this collateral in September is 28.2% CPR; The payment date for September principal and interest payments is October 25, 2004

(following FNMA’s stated delay of 54 days).

Based on these assumptions, cash flows from the roll transaction are shown in Figure 2. The

seller of the roll delivers $1,000,000 face value of FNMA 6s and receives $1,036,708.33 on

the front- month settlement date (September 15). The seller then reinvests these proceeds at

1.77% until October 14th (the back month settlement date) and obtains $1,038,186.51. To

facilitate the comparison to the buy-and-hold situation, we assume that what the seller buys

back is the amount left after a total principal pay-down of $28,131.44.9

Figure 2. Cash Flows from Rolling FNMA 6s

Date Transaction Cash Flow 15-Sep Sell $ 1,000,000 FNCL 6s @ 103-14 $1,034,375.00

Plus 14 days accrued interest (6% * 14/360 * 1,000,000) $2,333.33

$1,036,708.33

Reinvest proceeds @ 1.77%

29 actual days/360 * 1.77% * 1,036,708.33 $1,478.17

$1,038,186.51

14-Oct Purchase $ 971,868.55 FNCL 6s @ 103-2.2 -$1,001,692.77

Plus 13 days accrued interest (6% * 13/360 * 971,868.55) -$2,105.72

-$1,003,798.49

Net Proceeds from the Roll $34,388.02

Source: Banc of America Securities

Now, consider the situation in Figure 3 where the investor holds on to the $1 million FNMA

8 Readers with access to Bloomberg can verify the results obtained in Figures 2 through 4 by using the assumptions listed below and a roll calculator such as Bloomberg’s Roll Analysis function (FNCL 6 <Mtge> RA <Go>). 9 The total principal pay-down includes both the scheduled and unscheduled principal payments. The unscheduled principal payment assumes a prepayment rate of 28.2% CPR in September.

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RMBS Trading Desk Strategy

6s instead of rolling these bonds. In this case, they would own $971,868.55 face of FNMA

6s on October 14 because of principal pay-downs. Also, because the investor held the MBS

as of the September record date, they are entitled to the September principal and interest

payments on the pools. These payments will be received on the payment date of October 25.

Specifically, as Figure 3 shows, a total cash flow of $33,131.44 would be received on this

date consisting of an interest payment of $5,000 and a principal payment of $28,131.44. To

make the situation comparable to Figure 2, we need to discount these cash flows back to

October 14. The principal and interest payments received on October 25 are worth

$33,113.53 on October 14 when discounted at an annualized reinvestment rate of 1.77%.

Figure 3. Cash Flows from Holding FNMA 6s

Date Transaction Cash Flow 25-Oct Receive Principal and Interest on FNMA 6s

Receive Interest (6% * 30/360 * 1,000,000) $5,000.00

Receive Principal:

Scheduled Principal $927.14

Prepaid Principal (@28.2% CPR) $27,204.30

$33,131.44

Net Proceeds from Holding FNMA 6s (as of Oct 14) $33,113.53 Present value of Principal and Interest Cash Flow Rcvd on Oct 25

33,131.44/(1 + (1.77% * 11/360))

Cash Value of Rolling vs Holding FNMA 6s $1,274.48

Source: Banc of America Securities

Thus, the owner of the 6s earns an additional $1,274.48 ($34,388.02 – $33,113.53) during

the roll period by rolling their securities instead of holding onto them. In this specific

example then, it is more advantageous to roll.

Calculating the Implied Financing Rate of a Roll

The drop of a dollar roll along with the principal and interest cash flows received over the

roll period together imply a certain financing rate for the seller of the roll. Figure 4 shows

how to calculate this rate. The logic of the calculation goes as follows: the situation in Figure

2 is preferable to Figure 3 because the financing rate being offered to the seller of the roll is

less than the prevailing reinvestment rate. For a given drop, the advantage in Figure 2

decreases as the reinvestment rate goes down and the “breakeven” point occurs when it is

equal to the implied financing rate. At this point, the drop simply reflects the lost carry at

prevailing reinvestment rates. Thus, to find the implied financing rate, we need to solve for

the reinvestment rate in Figure 2, which equates the cash flows in this situation to Figure 3.

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RMBS Trading Desk Strategy

Figure 4. Calculating the Implied Financing Rate for Rolling FNMA 6s

Date Transaction Cash Flow 15-Sep Sell $ 1,000,000 FNCL 6s @ 103-14 $1,034,375.00

Plus 14 days accrued interest (6% * 14/360 * 1,000,000) $2,333.33

$1,036,708.33

r = implied financing rate Reinvest proceeds @ r%

29 actual days/360 * r% * 1,036,708.33 $1,036,708.33 * 29/360 * r%

$1,036,708.33 * (1 + 29/360 * r%)

14-Oct Purchase $ 971,868.55 FNCL 6s @ 103-2.2 $1,001,692.77

Plus 13 days accrued interest (6% * 13/360 * 971,868.55) $2,105.72

$1,003,798.49

Present value of Principal and Interest Cash Flow Rcvd on Oct 25 $33,113.53

$1,036,912.02

To calculate the implied financing rate, solve for r in the equation: $1,036,708.33 * (1 + 29/360 * r%) = $1,036,912.02

r = 0.24% Source: Banc of America Securities

Calculating the Breakeven Drop of a Roll

The breakeven drop is the difference between the front and back month TBA settlement prices such that the implied financing rate is equal to prevailing short-term reinvestment

rates. We typically take the short-term rate to be 1-month LIBOR. Figure 5 lists the

computations involved in calculating the breakeven drop for the roll on FNMA 6s. The

figure shows that the breakeven drop is equal to 7.6 ticks, which is 4.2 ticks less than the roll

price of 11.8 ticks. Thus, the investor earns 4.2 ticks of additional carry by rolling their

mortgage pools instead of simply holding onto them. The net advantage of rolling versus

holding tends to zero as the difference between the quoted drop and the breakeven drop

decreases.

Figure 5. Calculating the Breakeven Drop for Rolling FNMA 6s

Date Transaction Cash Flow 15-Sep Sell $ 1,000,000 FNCL 6s @ 103-14 $1,034,375.00

Plus 14 days accrued interest (6% * 14/360 * 1,000,000) $2,333.33

$1,036,708.33

Reinvest proceeds @ 1.77%

29 actual days/360 * 1.77% * 1,036,708.33 $1,478.17

$1,038,186.51

14-Oct X = breakeven drop Purchase $ 971,868.55 FNCL 6s @ 103-14 – X $971,868.55 * (103-14 – X)%

Plus 13 days accrued interest (6% * 13/360 * 971,868.55) $2,105.72

$2,105.72 + $971,868.55 * (103-14 – X)%

Present value of Principal and Interest Cash Flow Rcvd on Oct 25 $33,113.53

$35,219.25 + $971,868.55 * (103-14 – X)%

To calculate the breakeven drop, solve for X in the equation: $1,038,186.51 = $35,219.25 + $971,868.55 * (103-14 – X)%

X = 7.6 ticks

Source: Banc of America Securities

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RMBS Trading Desk Strategy

Roll “Specialness”

We say a roll is special, when the roll price (drop) is higher than the breakeven drop. This is same as saying that the implied financing rate is less than alternative money market rates. As

mentioned before, “special” rolls are created in times of heavy refinancing and CMO

production activity, and can contribute significantly to the carry on a mortgage position.

Dollar rolls trading special can have a significant impact on pay-ups for specified pools and

on the attractiveness of the coupon with the special roll versus other coupons in the coupon

stack. The attractiveness of “specified” characteristics decreases as the “specialness” of the

roll increases because the carry advantage of TBAs from special rolls reduces the value of

specified pool characteristics. The same logic applies to the relative attractiveness of

different coupons across the coupon stack – in general, TBA pass-through coupons with rich

rolls tend to trade at rich price levels relative to other coupons because of their carry

advantage in the roll market.

Roll “Trading-at-Fail”

When the implied financing rate is zero, the roll is said to be trading at fail. Why would

someone offer to lend money at a 0% interest rate? This can occur when a mortgage trading

desk or some investors are short a coupon and cannot find the collateral necessary for

satisfying TBA delivery requirements or if the CMO desk urgently needs mortgage

collateral to complete a planned issuance.

If a trading desk fails to meet TBA delivery requirements, the TBA buyer effectively

finances their purchase at a 0% financing rate. As we pointed out in the TBA section of the

paper, this is because the TBA buyer does not have to pay for the purchase until the

mortgage pools are delivered. Theoretically, the maximum value for a dollar roll drop should

not exceed the cost of failing to deliver the underlying security for the roll period. However,

strong demand for collateral from CMO desks or stringent requirements for failing to meet

TBA delivery requirements occasionally lead to rolls trading through fail levels close to

TBA settlement dates.

An interesting point about dollar rolls trading through the fail levels should be noted here.

There will be some scenarios in which the collateral that is likely to be delivered for back-

month TBAs will be substantially worse than the collateral delivered for the front-month.

This usually occurs when new production in a coupon changes the characteristics of TBA

delivered collateral by so much that an investor is better off by not rolling their bonds even

when the roll is trading through fail levels. It is worth pointing out that standard roll

calculations assume that the collateral delivered for back-month is same as the collateral

delivered for front month plus one month of additional aging.

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RMBS Trading Desk Strategy

IV. SENSITIVITY ANALYSIS OF DOLLAR ROLLS

Our analysis in the previous section can be distilled into a few simple observations. First, the

value of a dollar roll is the difference between the actual drop and the breakeven drop on the

underlying security. Whenever the actual roll price is greater than the breakeven drop, or

conversely, whenever the available reinvestment rate exceeds the implied financing rate,

rolling a security may be preferable to holding it.10 The calculations presented in Figures 2 through 5 should also make it clear that in addition to the actual drop, the value of the roll

also depends upon the prevailing reinvestment rate and the prepayment speed over the front

month of the roll. In what follows, we explore how the implied financing rate for a roll

transaction changes as a function of the roll price and prepayment speeds. We also explore

the relationship between the breakeven drop, prepayment speeds and the reinvestment rate.

Sensitivity Analysis of the Implied Financing Rate and the Breakeven Drop

Figure 6 shows the implied financing rate for the roll transaction we have been discussing

above as a function of the roll price and prepayment speeds. Moving along a row of the

figure gives us a feeling for how the breakeven financing rate changes as a function of the

drop assuming a fixed prepayment speed. Similarly, moving along a column tells us how the

breakeven rate changes as a function of prepayment speeds assuming a fixed drop.

Not surprisingly in light of our analysis, for a given prepayment rate, the breakeven

financing rate increases as the drop decreases and vice-versa. For a fixed drop, the figure

also shows that the implied financing rate decreases as prepayment speeds increase. The

crucial point here is that the 6s are a premium security and as such faster prepayment speeds

decrease the value of the captured carry for the buyer of the roll. By keeping the drop fixed,

they are lending money to the seller of the roll at more attractive rates.

Figure 6. Breakeven Finance Rate Sensitivity on FNMA 6s

CPR (%) -14.8 -13.8 -12.8 -11.8 -10.8 -9.8 -8.8 Range 13.2 -0.23 0.14 0.51 0.88 1.25 1.62 1.99 2.22

18.2 -0.42 -0.05 0.32 0.69 1.05 1.42 1.79 2.21

23.2 -0.62 -0.25 0.12 0.48 0.85 1.21 1.58 2.20

28.2 -0.83 -0.47 -0.10 0.26 0.63 0.99 1.35 2.18

33.2 -1.06 -0.69 -0.33 0.03 0.39 0.75 1.11 2.17

38.2 -1.30 -0.94 -0.58 -0.22 0.14 0.50 0.86 2.16

43.2 -1.56 -1.20 -0.85 -0.49 -0.13 0.22 0.58 2.14

Range 1.33 1.34 1.36 1.37 1.38 1.40 1.41

Drop (32nds)

Source: Banc of America Securities

Conversely, as shown in Figure 7, the breakeven drop decreases as prepayment speeds and

reinvestment rates increase. As before, faster prepayment speeds on premium securities

render them more unattractive for holding. This increases the value of a roll at a given

reinvestment rate by lowering the breakeven drop.

10 The point is that there are some risks associated with dollar rolls. These risks are detailed in the next section.

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RMBS Trading Desk Strategy

Figure 7. Breakeven Drop Sensitivity on FNMA 6s

CPR (%) 0.27% 0.77% 1.27% 1.77% 2.27% 2.77% 3.27% Range 13.2 13.3 12.0 10.6 9.2 7.9 6.5 5.2 -8.2

18.2 12.8 11.5 10.1 8.7 7.4 6.0 4.6 -8.2

23.2 12.3 10.9 9.6 8.2 6.8 5.4 4.0 -8.3

28.2 11.8 10.4 9.0 7.6 6.2 4.8 3.4 -8.3

33.2 11.2 9.8 8.4 7.0 5.6 4.2 2.8 -8.4

38.2 10.5 9.1 7.7 6.3 4.9 3.5 2.0 -8.5

43.2 9.8 8.4 7.0 5.6 4.1 2.7 1.3 -8.6

Range 3.5 3.6 3.6 3.7 3.8 3.8 3.9

Reinvestment Rate

Source: Banc of America Securities

How do these results change when we look at discount securities? In this situation, an

increase in the prepayment rate at a given roll price increases the implied financing rate. In addition, the breakeven drop increases with an increase in prepayment speeds. The point is that faster prepayment speeds on discounts render them more attractive for holding and this

decreases the value of a roll at a given drop. This is in contrast with the roll example on

premium 6s discussed above – there a rise in prepayment speeds at a given drop decreased

implied financing rates. However, the relationship between the drop and the implied

financing rate remains unchanged – the implied financing rate decreases with an increase in

the drop for both premium and discount pass-throughs.

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RMBS Trading Desk Strategy

V. RISKS ASSOCIATED WITH DOLLAR ROLLS

The dollar roll market has historically offered as much as 15 bps to 100 bps of a financing

advantage versus the 1-month LIBOR rate. However, as Chicago economists have taught us

over the past several decades, there is no such thing as a “free lunch” in financial markets, or

at least the cafeteria that offers one is not open for any length of time. We can categorize

some of the risks assumed by the seller of a dollar roll transaction as follows.

Redelivery Risk. While the mortgage pass-through pools returned in a dollar roll transaction will have to meet good delivery requirements, these requirements do not say anything about

the risk characteristics of these pools. In particular, these pools can and frequently do have

less desirable prepayment characteristics than the originally delivered pools – the seller

receives faster prepaying pools for rolls on premium passthroughs and slower prepaying

pools on discounts. This type of adverse selection, therefore, makes dollar rolls an unattractive financing option for the holders of vintage and specified pools unless the

characteristics of the pools to be returned are agreed on beforehand or the roll is rich enough

to compensate for the value of the collateral characteristics lost in the transaction.

Prepayment Risk. At the time of entering into the roll transaction, neither party to the transaction knows what the actual prepayment speed during the front month of the roll is

going to be. The value of rolling versus holding a premium security is increased by a faster

prepayment speeds and reduced by a slower prepayment speeds in the front month of the roll

(see the discussion accompanying Figures 6 and 7). For a discount security, the relationship

between the roll’s value and realized prepayment speeds is opposite.

Credit Risk. The risk of one of the parties to a dollar roll defaulting during the roll period is called credit risk. The risk is mitigated to a large extent by the fact that either party could sell

or buy the security in the market in case of a default. However, the risk of adverse market

movements during this period could make this transaction a little painful. The lack of a

haircut in a dollar roll further aggravates the credit risk problem.

Liquidity Risk. The inability of a one party to deliver securities to the other on the settlement date is defined as liquidity risk. This may arise in case of a market disruption such

as a squeeze. This is different from credit risk since the delinquent party will typically be

able to settle the transaction at a later date.

Our catalog of risks thus suggests that some due diligence is required before we can

conclude a particular dollar roll will “enhance” the carry on an MBS position. In particular,

the redelivery risk by itself suggests that roll prices should trade somewhat above carry. The

expected prepayment characteristics of the redelivered pool need to be considered in

conducting the analysis of whether it is better to hold or roll.

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RMBS Trading Desk Strategy

VI. A BRIEF HISTORY OF THE FNMA 6s ROLL

We conclude the primer by taking a look at how rolls actually trade in practice. Figure 8

illustrates roll prices on 30-year FNMA 6s from the beginning of 2003 to October, 2004.

The convention we use for the rolls associated with these prices is most easily understood by

looking at a specific month. In particular, suppose we look at roll values in the month of

August. Starting from the first day of the month, these values denote levels for the

August/September roll up until the pool notification day for August settlement, and refer to

levels for the September/October roll from the next day onward.

Turning our attention back to Figure 8, notice the dramatic changes in roll levels over the

observation period: the roll traded between a range of 2 to 15 ticks over the period in

question, reaching its lowest point in mid-June 2003 and its highest point in mid-May 2004.

What is behind these changes in roll prices? The figure clearly shows that there is a strong

correlation between interest rates as represented by the MBS current coupon rates and the

FNMA 6s roll. On average, roll prices were higher when interest rates were high and lower

when interest rates were low.11 Over the first half of 2003, the 6s roll gradually declined and

reached its lowest point of two ticks in mid-June (this reflects roll prices for the July/August

roll). This decrease on the premium 6s was largely due to the increase in refinancing activity

that resulted from rates decreasing, culminating in multi-year lows in mortgage rates in June

2003. At this juncture, 30-year 6s were prepaying at 60%–80% CPR. With the expectation

of suffering substantial losses from prepayment of principal on a premium security at par,

roll buyers were willing to pay very little to own 6s collateral from one settlement date to the

next settlement date. Notice how the 6s roll reached another local minimum in early March

of 2004 as interest rates rallied and renewed concerns of heightened prepayment rates.