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Explain the mechanics of agency MBS products such as interest-only securities (IOs), principal-only securities (POs) and collateralized mortgage obligations (CMOs).

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

The idea

Agency products reallocate pool cash flows. A strip splits a pool into an interest-only security (IO), which receives interest, and a principal-only security (PO), which receives principal. Together they replicate the pass-through. Pass-through price = IO price + PO price. A PO is bought at a discount, so faster prepayments raise its value and its price rises when rates fall. An IO loses cash flows when prepayments speed up, so its price can rise when rates rise, which is negative duration. A collateralized mortgage obligation divides the collateral into tranches. Sequential tranches receive principal in order, so the first has the shortest average life. PAC tranches are protected within a prepayment band by support tranches. Floaters and inverse floaters share the collateral coupon. The exam point is that prepayment risk is redistributed, not removed.

Formulas

IO price from the pass-through and PO

IO price = pass-through price − PO price

pass-through price
the price of the whole pool
PO price
the price of the principal-only strip

The strips together replicate the pass-through, so price changes also add up. When rates fall the PO gains and the IO usually loses.

A practice question

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

Mortgage rates fall sharply. What happens to the price of a principal-only (PO) strip, all else equal?

  1. It falls, because faster prepayments reduce the interest payments the PO receives.Why not: A PO receives no interest; loss of interest hurts the IO.
  2. It is unchanged, because total principal is fixed at the original balance.Why not: Ignores time value: earlier receipt of the same principal has a higher present value.
  3. It falls, because lower rates extend the PO's cash flows.Why not: Extension occurs when rates rise, not fall.
  4. It rises, because earlier repayment of principal raises its present value. - correct

A PO receives a fixed total of principal; prepayments speed the receipt, which raises the present value and the return on a discounted purchase.

A harder one

A pool is stripped into an IO and a PO. When rates fall 100 basis points, the pass-through price rises by 2.0 points while the PO price rises by 9.5 points. The change in the IO price is closest to:

  1. -7.5 points - correct
  2. +7.5 pointsWhy not: Sign error: takes the absolute difference and gives it a positive sign.
  3. +11.5 pointsWhy not: Adds the pass-through and PO changes instead of subtracting.
  4. +2.0 pointsWhy not: Assumes the IO moves with the pass-through.

IO + PO = pass-through, so the IO change = 2.0 - 9.5 = -7.5 points. The IO loses value as prepayments accelerate.

The hardest tier

A CMO tranche of USD 100 million is backed by collateral paying 6.50%. It is split into a USD 75 million floater paying the index plus 0.50% and a USD 25 million inverse floater paying K - 3 x index, so that total interest always equals the collateral interest regardless of the index. K is closest to:

  1. 26.0%Why not: Ignores the floater spread: 650 / 25.
  2. 24.5% - correct
  3. 25.5%Why not: Subtracts the 0.5% spread without scaling it by the 75/25 weighting.
  4. 27.5%Why not: Adds the floater spread cost instead of subtracting it: (650 + 37.5) / 25.

Total interest: 75 x (L + 0.5) + 25 x (K - 3L) = 37.5 + 25K, with L cancelling. Setting this equal to 6.5 x 100 = 650 gives K = 612.5 / 25 = 24.5%.

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