What is a constant maturity swap (CMS) and how does it differ from a standard interest rate swap?

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AcadiFi · Accepted Answer

A constant maturity swap (CMS) is an interest rate swap where one leg pays a rate that resets periodically to a **long-t...

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**Vanilla swap vs CMS:**

| Feature | Vanilla Swap | CMS |
|---|---|---|
| Floating leg reference | SOFR (overnight) | 10-year swap rate |
| Reset frequency | Quarterly | Quarterly (but references 10yr rate) |
| Exposure | Short end of the curve | Long end of the curve |
| Convexity | Minimal | Significant convexity adjustment needed |

**Mechanics -- Example:**

Brightwater Capital enters a 5-year CMS receiver swap (fictional):
- **Receives:** 10-year CMS rate (reset quarterly to prevailing 10-year swap rate)
- **Pays:** SOFR + 50 bps
- **Notional:** $50M

Every quarter, Brightwater receives the then-current 10-year swap rate and pays SOFR + 50 bps. If the 10-year rate is 4.5% and SOFR is 3.8%, Brightwater receives 4.5% - 4.3% = 0.2% net on $50M = $25,000 that quarter.

**Why CMS requires a convexity adjustment:**

The 10-year swap rate is itself a function of the yield curve. When rates rise, the present value of the higher CMS payments is discounted more heavily, creating an asymmetry. This means the expected value of the CMS rate under the pricing measure is NOT equal to the forward rate -- a convexity correction is needed, typically making CMS rates slightly higher than forward rates.

**Use cases:**
- **Yield curve views** -- CMS receivers profit from a steep curve; CMS payers profit from flattening
- **Liability management** -- Insurance companies with long-duration liabilities use CMS to match their exposure to long-term rates
- **Structured notes** -- Banks embed CMS in retail products offering enhanced coupons linked to long-term rates

What is a constant maturity swap (CMS) and how does it differ from a standard interest rate swap?

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