Outline a dollar roll transaction and the way it is valued.

FRM® Part I · Financial Markets and Products · Mortgages and Mortgage-Backed Securities · FRM1.FM.18.g

The idea

A dollar roll is a pair of TBA trades. The seller sells a given agency and coupon for this month's settlement and buys the same type back for next month's settlement at a lower price. The price difference is the drop. The seller gives up the coupon and principal paydown for the month and receives the drop plus income from investing the proceeds. Viewed as a collateralized loan, the roll has an implied financing rate, ignoring paydowns. Implied rate = (monthly coupon accrual − drop) ÷ price × 12. If that rate is below the repo rate, the roll is special and is cheaper financing than repo. Value = drop + reinvestment income − forgone coupon, per 100 of price. The pools returned are only substantially similar, so a specified pool's pay-up is lost. The exam point is to compare the implied rate with repo.

Formulas

Implied financing rate of a dollar roll

implied rate = (coupon accrual − drop) ÷ price × 12

coupon accrual: one month's coupon per 100, the annual coupon ÷ 12
drop: front-month price minus next-month price, per 100
price: the front-month sale price, per 100

Paydowns ignored. If it is below the repo rate the roll is special and is the cheaper financing.

Value of rolling rather than holding, per 100

roll value = drop + reinvestment income − forgone coupon

drop: the price difference between the two settlement months
reinvestment income: interest earned on the sale proceeds for the month
forgone coupon: the month's coupon given up by selling

Paydowns ignored. A specified pool's pay-up is lost because only a substantially similar pool comes back.

A practice question

From the question bank, with the reason each wrong option is wrong.

A dollar roll is best described as:

Selling a TBA for this month's settlement and buying the same one back for next month's. - correct
Buying and selling the same specific pool twice on one and the same settlement date.Why not: A roll involves two different settlement months and generic TBAs.
Exchanging dollar-denominated MBS for a currency forward.Why not: A dollar roll has no currency component.
Selling a pass-through and buying a Treasury note for the same settlement.Why not: Both legs of a roll are the same agency and coupon of MBS.

A dollar roll pairs a sale for the current settlement month with a purchase for the next, usually at a lower price. It works as secured financing for the seller.

A harder one

A 4.00% coupon TBA is sold for the front month at 100-00 and bought back for the next month at 99-27, so the drop is 5/32. Assume one month is 1/12 of a year and ignore paydowns. The implied financing rate of the roll is closest to:

1.88%Why not: Uses the drop alone: 0.15625 / 100 x 12, forgetting the coupon given up.
5.88%Why not: Adds the drop to the forgone coupon instead of subtracting it.
4.00%Why not: Takes the coupon rate and ignores the drop.
2.13% - correct

Monthly coupon per 100 = 4.00 / 12 = 0.3333. Drop = 5/32 = 0.15625. Implied rate = (0.3333 - 0.15625) / 100 x 12 = 2.125%.

The hardest tier

A holder of USD 25 million face of 4.50% coupon TBAs sells the front month at 101-00 and buys back the next month at 100-23, a drop of 9/32. Proceeds are reinvested at 4.00% per year for one month (1/12 of a year). Ignoring paydowns, the net gain of rolling relative to holding, including the coupon forgone by selling the front month, is closest to:

USD 154,479Why not: Leaves out the coupon given up, counting only the drop and reinvestment income.
USD 70,313Why not: Counts only the drop: 0.28125 / 100 x 25 million.
USD 60,729 - correct
USD -23,438Why not: Subtracts the forgone coupon from the drop but ignores the reinvestment income.

Per 100: drop 0.28125 + reinvestment 101 x 0.04 / 12 = 0.33667 - forgone coupon 4.5 / 12 = 0.375 gives 0.24292. On 25 million face: 0.0024292 x 25,000,000 = 60,729.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

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