How does an amortizing swap match a mortgage portfolio's declining notional?

Question

AcadiFi · Accepted Answer

An amortizing swap has a declining notional schedule that matches a reference amortization — typically designed to track a bond, loan, or mortgage pool whose principal pays down over time.

Structure for your hedge: $200M fixed-rate mortgage pool with 30-year amortization financed by 3M SOFR debt. You enter a 10-year amortizing swap to pay fixed and receive SOFR, with notional declining per the weighted average mortgage amortization schedule.

Cash flow illustration (simplified, annual):

- Year 1: notional $200M.
- Year 2: notional $195M (after principal paydowns).
- Year 5: notional $175M.
- Year 10: notional $140M.

Each period, the swap pays = (Fixed_Rate − SOFR) × Notional_t × Day_Count. As notional shrinks, so do the cash flows — matching the shrinking interest rate exposure on your mortgages.

```mermaid
flowchart LR
    A[$200M Notional] --> B[Year 2: $195M]
    B --> C[Year 5: $175M]
    C --> D[Year 10: $140M]
```

Pricing: discount each scheduled cash flow separately. Because near-end cash flows weigh less (smaller notional), the par fixed rate on an amortizing swap typically differs from a vanilla swap of equal final maturity — often closer to the mid-tenor yield.

Prepayment risk: if mortgages prepay faster than scheduled, your hedge over-hedges. Counterparties sometimes offer prepay-linked swaps but these carry significant spread for the embedded prepayment option.

On the exam, remember: amortizing swap fixed rate is a weighted average of the underlying forward zero rates, weighted by notional × DF.

How does an amortizing swap match a mortgage portfolio's declining notional?

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