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FRM Exam Part I · Mortgages and Mortgage-Backed Securities

Collateralized Mortgage Obligations and Tranching Explained

Updated 11 October 2026 · Fact-checked

A collateralized mortgage obligation (CMO) splits the cash flows of a mortgage pool into tranches with different priorities for principal. Sequential-pay, PAC and support tranches redistribute prepayment risk. IO and PO strips split interest from principal. To solve questions, trace who receives principal and who absorbs prepayment changes.

Understand Collateralized Mortgage Obligations and Tranching

A mortgage pass-through passes every borrower payment to investors pro rata. Its main risk is prepayment. When rates fall, borrowers refinance and principal returns early. When rates rise, prepayments slow and the security lasts longer. A CMO does not remove this risk. It redistributes it among tranches built from the same collateral.

In a sequential-pay CMO, all tranches receive interest on their outstanding balance, but principal goes to Tranche A first, then B, then C. Tranche A has the shortest average life and the least extension risk. The last tranche has the longest life and absorbs most of the uncertainty. Total prepayment risk in the pool is unchanged. It is just reallocated by maturity.

A PAC (planned amortization class) tranche has a schedule of principal payments that is protected as long as prepayment speeds stay within a band (the PAC collar, defined by lower and upper PSA speeds). The support tranche (also called companion tranche) absorbs the surplus when prepayments are fast and the shortfall when they are slow. So the PAC has low contraction and extension risk, and the support tranche has high risk and usually a higher yield. Fast prepayments can exhaust the support tranche. Once it is paid off, the PAC is exposed to contraction risk. Separately, very slow prepayments (below the lower collar) can cause the PAC to extend.

Contraction risk is the risk that prepayments speed up, shortening the life and forcing reinvestment at lower rates. Extension risk is the risk that prepayments slow, lengthening the life while rates are high. Together, these two risks are the source of the negative convexity of MBS.

A stripped MBS splits the pool into an IO (interest-only) and a PO (principal-only) class. The PO buys at a discount and gets the full face value over time, so faster prepayment raises its return and its price. The IO has no principal, so faster prepayment cuts its interest stream and its price. When rates fall and prepayments rise, PO prices rise and IO prices generally fall. When rates rise, prepayments slow, and IO prices can rise because the interest stream lasts longer. IO effective duration is often negative when prepayment effects dominate, and PO effective duration is large and positive. Credit risk matters little for agency collateral, because the agency guarantees timely payment. In non-agency deals, credit risk is allocated by subordination, with losses hitting junior tranches first.

Key formulas to remember

Principal priority in sequential-pay
Principal to Tranche A until paid off, then B, then C
Interest is paid on each tranche's outstanding balance every period. Cash flows of tranches sum to the collateral cash flows.
Conservation of cash flow
Σ tranche cash flows = collateral cash flows
Tranching redistributes risk. It does not create or destroy it.
Tranche interest
Interest = Coupon rate × Outstanding balance × (1 ÷ 12) for monthly pay
Use beginning-of-period balance. Ignore servicing fees unless given.
PAC protection
PAC schedule holds if prepayment speed stays between the lower and upper PSA bounds
Outside the collar, or after the support tranche is exhausted, the PAC schedule can fail.
Prepayment effect on strips
Faster prepayment: PO value ↑, IO value ↓. Slower prepayment: PO value ↓, IO value ↑
IO effective duration is often negative when prepayment effects dominate. PO effective duration is large and positive.

How to solve Collateralized Mortgage Obligations and Tranching questions

Use this approach for any CMO or strip question. Identify the structure, then decide who gets principal under the scenario given.

  1. 1Identify the tranche types in the deal: sequential, PAC, support, IO, PO.
  2. 2Note the collateral and the scenario: rates falling (faster prepayment) or rising (slower prepayment).
  3. 3List the priority of principal: which tranche gets paid first, and which is protected by a schedule.
  4. 4Compute interest for each tranche as coupon × outstanding balance ÷ 12 (or per period given).
  5. 5Allocate principal according to priority, reducing balances before the next period.
  6. 6Check that tranche cash flows sum to the collateral cash flows.
  7. 7State the effect on average life, contraction or extension risk, and price direction.
  8. 8Match the result to the option, checking whether the question asks about PAC, support or strips.

Quickest way: Who absorbs the shock?

When to use it: Use this for conceptual questions about which tranche gains or loses when prepayment speed changes.

  1. Fast prepayments (rates down): contraction risk. PO up, IO down, support tranche shortens sharply, PAC stays on schedule inside the collar.
  2. Slow prepayments (rates up): extension risk. PO down, IO up, support tranche lengthens sharply.
  3. The support tranche's average life is the most variable of all the tranches. It shortens sharply under fast prepayment and extends sharply under slow prepayment.
  4. Ranking of prepayment risk, lowest to highest: PAC, then sequential first tranche to last, then support.
  5. Rule: protection for one tranche means more risk for another, since total risk is conserved.

Common mistakes in Collateralized Mortgage Obligations and Tranching

  • Saying CMOs eliminate prepayment risk

    Tranching sounds like risk reduction.

    Fix: Remember that total risk is conserved. CMOs reallocate it, so the support tranche carries what the PAC avoids.

  • Thinking the PAC is protected at any prepayment speed

    Students forget the collar.

    Fix: PAC protection holds only within the PSA band and while the support tranche remains outstanding.

  • Mixing up IO and PO price reactions

    Both are tied to the same pool, so they seem to move together.

    Fix: Fast prepayment hurts IO (less interest) and helps PO (cash sooner). They move in opposite directions.

  • Paying principal to all sequential tranches at once

    Pass-through logic is carried over.

    Fix: Principal goes only to the first outstanding tranche. Interest goes to all, on their balances.

  • Confusing contraction risk with extension risk

    Both words describe changes in average life.

    Fix: Contraction means shortening (rates fall, fast prepayment). Extension means lengthening (rates rise, slow prepayment).

Worked examples

Example 1

A sequential-pay CMO has Tranche A of ₹60 crore and Tranche B of ₹40 crore, each with a 6% annual coupon. In month 1 the collateral pays ₹2 crore of principal. Compute the month-1 interest to Tranche B and the principal paid to Tranche B.

Show the solution
  1. Tranche B's balance is ₹40 crore at the start of month 1.
  2. Interest = 6% × ₹40 crore ÷ 12 = ₹0.2 crore.
  3. Principal goes first to Tranche A, which is still outstanding, so Tranche B receives ₹0 principal.

Answer: Tranche B receives ₹0.2 crore of interest and no principal in month 1.

Example 2

Interest rates fall sharply and prepayments stay high until the support tranche is fully paid off. After that, prepayments remain high. Which statement about the PAC tranche is most accurate? A) The PAC schedule is guaranteed; B) The PAC faces contraction risk; C) The PAC faces extension risk only; D) The IO strip rises in value.

Show the solution
  1. Fast prepayments mean rates fell, so contraction is the concern.
  2. The support tranche has been exhausted, so it can no longer absorb the surplus principal.
  3. With no support tranche left, the excess principal flows to the PAC. The PAC receives principal faster than planned, so its average life shortens.
  4. D is wrong because faster prepayment reduces IO interest. A is wrong because with the support tranche gone the PAC schedule is no longer protected. C is wrong because the risk is contraction, not extension.

Answer: B: The PAC faces contraction risk, because once the support tranche is gone, surplus principal goes to the PAC and shortens its average life.

Exam tips

  • Questions are mostly conceptual: identify the direction of price or average-life change under fast or slow prepayment.
  • Remember that the support tranche absorbs risk first and the PAC only has protection within the collar.
  • For IO and PO strips, anchor on this: PO is like a discount zero-coupon, so faster prepayment helps it.
  • In numerical questions, update tranche balances each period and compute interest on the beginning balance.

Practice questions from Mortgages and Mortgage-Backed Securities

Collateralized Mortgage Obligations and Tranching in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Collateralized Mortgage Obligations and Tranching: frequently asked questions

What is the difference between a PAC and a support tranche?

A PAC has a planned principal schedule that is protected within a prepayment band. The support tranche absorbs surplus or shortfall principal to keep the PAC on schedule. As a result, the support tranche has much greater prepayment risk and usually a higher yield.

What is the difference between IO and PO strips?

An IO strip receives only the interest payments from the mortgage pool. A PO strip receives only the principal. Faster prepayments reduce IO value and raise PO value.

What is extension risk versus contraction risk in a CMO?

Extension risk is slower prepayment that lengthens the security's life when rates rise. Contraction risk is faster prepayment that shortens it when rates fall. PACs reduce both, while support tranches take on more of both.

Does tranching reduce the total risk of the mortgage pool?

No. Tranching redistributes prepayment and credit risk among investors according to priority. The sum of tranche cash flows equals the collateral cash flows.