Mortgage pass-throughs and CMOs

How does a pass-through pay investors?

A mortgage pass-through security is created when lenders pool mortgages and sell securities backed by the pool. Each month the pool’s principal, interest and prepayments are passed through to the holders. Part of the interest pays the costs of the structure: the servicer collects payments, keeps records and starts foreclosure when needed, and a guarantor may charge a fee. These fees come out of the mortgage rate.

So investors do not earn the rate borrowers pay. They earn the pass-through rate , and the pool’s rate is measured as a weighted average.

$$\text{WAC} = \frac{\sum_i B_i \, r_i}{\sum_i B_i}$$

$$\text{WAM} = \frac{\sum_i B_i \, m_i}{\sum_i B_i}$$

$$\text{Pass-through rate} = \text{WAC} - \text{Fees}$$

The weighted average coupon (WAC) is the average mortgage rate in the pool, weighted by balance. The weighted average maturity (WAM) is the average remaining term in months, also weighted by balance. Large loans count for more than small ones, so a simple average is wrong.

The pool arithmetic can be asked from several sides: the WAC from the loans, the missing loan’s rate, or the pass-through rate from the WAC and fees.

Residential MBSbonds backed by home loans

• Mortgage pass-through security Memorize investors share the pool pro rata
  • Cash flows interest + scheduled principal + prepayments, after fees
  • Prepayment risk passed straight through, all of it
• Collateralized mortgage obligation (CMO) Memorize pass-throughs or loan pools re-cut into tranches
  • Redistributes prepayment risk does not remove it

Go deeper Why the pass-through rate is below the WAC

The gap pays for work and protection. The servicer collects payments, forwards proceeds, sends notices, keeps the balance records, supplies tax information and starts foreclosure when a borrower defaults. A guarantor of timely payment charges a fee. Both fees are set as a slice of the mortgage rate, which is why the investor’s rate is the WAC less that slice.

What is a CMO, and how does it reshape prepayment risk?

A collateralized mortgage obligation (CMO) takes mortgage pass-throughs, or several pools of loans, and re-cuts their cash flows into tranches. The senior-most tranches carry less prepayment and default risk. A CMO does not make prepayments disappear. It decides who feels them.

CMO structuresways to cut the same cash flows

• Time tranching Memorize the order of principal
  • Sequential-pay Use it principal to A, then B, then C
  • PAC and support Memorize PAC follows a schedule inside a prepayment band; support absorbs the surprise
  • Z-tranche (accrual) Use it no cash until a set date; interest is added to principal
  • Residual Use it whatever is left after every other tranche is paid
• Splitting the cash flows Memorize by type of payment
  • Principal-only (PO) Memorize principal only; value rises when prepayments speed up
  • Interest-only (IO) Memorize interest only, no par; value falls when prepayments speed up
  • Floater and inverse floater Use it coupon follows, or opposes, a reference rate; caps and floors

Sequential-pay and time-tranched structures

Lesson 1 introduced the sequential-pay tranche : principal goes to A until it is retired, then to B, then to C. Others receive interest only until their turn.

$$B_1 = B_0 - (\text{Scheduled} + \text{Prepaid})$$

PAC and support tranches

A planned amortization class (PAC) tranche makes scheduled, fixed principal payments over a set period, as long as prepayments stay between a minimum and a maximum speed. That gives it predictable cash flows. The support tranche (also called a companion tranche) takes everything the PAC does not: when prepayments run faster or slower than the band allows, the support tranche’s life shrinks or stretches. Inside the band, the support tranche absorbs all the prepayment risk.

Z-tranches and residual tranches

A Z-tranche (accrual or accretion bond) pays nothing at first. Each period its stated coupon is added to its principal, until a set date when principal and interest start to be paid. It is typically the last tranche. It helps the other tranches, because the interest it does not pay is free to pay them principal. Its holders have no reinvestment risk while it accrues. Its average life is usually over 20 years, so it is risky and hard to value.

A residual tranche collects whatever cash flow remains after every other tranche is paid. It suits investors who can accept and hedge the risk, such as hedge funds and long-term institutions. Banks usually avoid it because of capital requirements.

Splitting interest and principal

A principal-only (PO) security receives only principal. Its holder gets par, so a faster return of principal raises its value: when rates fall and prepayments rise, a PO gains. An interest-only (IO) security receives only interest and has no par value. When prepayments rise, the balance on which interest is paid shrinks, and the IO loses value. IOs can hedge interest rate risk in a portfolio.

Exam tip PO = principal back sooner = good. IO = interest stream cut short = bad. They are mirrors.

Floaters and inverse floaters

In the last group, floating-rate and inverse floater tranches have coupons linked to a reference rate, often with a cap and a floor. A floater’s coupon moves with the reference rate. An inverse floater’s coupon moves the opposite way, and it is used to hedge rate risk.

Which investor fits which tranche?

Investor need	Likely tranche
Cash needed in 2 to 3 years	Short sequential tranche or PAC
Insurer with liabilities in 10 to 15 years	Longer tranche
Seeks higher return and can hedge the risk	Support, Z or residual

Go deeper Why Z-tranches help the earlier tranches

While the Z-tranche accrues, its interest is not paid out. That cash is redirected to pay principal to the earlier tranches, which retires them faster and shortens their lives. The Z-tranche pays for this by waiting: it accrues at its coupon and ends up with a larger balance and a long average life.

Go deeper Inverse floaters as a leveraged bet on falling rates

An inverse floater’s coupon rises when the reference rate falls. In some structures the coupon moves by a multiple of the change in the reference rate, which makes the position behave like a leveraged bet on falling rates. Falling rates also tend to bring faster prepayments, so the structure’s prepayment risk matters to its value.