What Is a Constant Maturity Swap?
Constant maturity swap is a swap in which one leg resets periodically to a long-dated market rate — a ten-year swap rate, say — rather than to a short-term rate. That makes its value depend on the slope of the yield curve rather than on the level of short rates alone.
An ordinary swap’s floating leg resets to a short rate. A constant maturity swap resets to a long one, and that single substitution changes what the contract is a position on.
How it works
Every reset takes the current ten-year swap rate — or whatever tenor is specified — rather than the current three-month rate.
The maturity referenced stays constant. Six months later it resets to the ten-year rate again — a different ten-year period, always ten years out from that moment, which is where the name comes from.
So what matters is the gap between long and short rates. A receiver of the long rate paying a short one profits when the yield curve is steep and loses when it flattens.
Level versus shape
Rates can all rise together and this position barely moves. Both legs rise, the spread between them is unchanged, and the swap’s value is roughly where it was.
Rates can be unchanged and the position move a great deal. If short rates rise while long ones do not, the curve flattens and the receiver loses without any change in the general level.
Which is why it cannot be hedged with an ordinary swap. The two instruments respond to different variables, and offsetting the level leaves the shape exposure entirely intact.
A worked example
A receiver takes the ten-year rate and pays three-month. At the start the ten-year is 4% and the three-month is 2% — a 2% spread in their favour.
Central banks raise short rates to 4% while long rates stay at 4%. The curve is now flat, the spread is zero, and the receiver’s income has vanished.
The general level of rates rose by exactly nothing on the leg they receive. Nothing they were paid on moved, and the position went from comfortable to worthless on a variable most people do not track.
And it can go further. An inverted curve puts short rates above long ones, so the receiver pays more than they receive on every period — a position that was earning carry now costs it.
The convexity adjustment
A CMS rate is not simply the forward swap rate. The payoff is linear in the swap rate, while the value of a swap is not linear in its own rate, and that mismatch has to be priced.
The correction is called the convexity adjustment, it is always positive for the receiver, and it grows with the tenor referenced and with rate volatility.
Which means CMS pricing requires a volatility input. An instrument that appears to be about the curve’s shape also carries an exposure to how much rates move, and that exposure is not obvious from the contract terms.
That is the practical reason this product belongs to institutions. Pricing it requires a model, models require assumptions, and the assumptions are where the value ends up sitting — which is a general truth about structured rate products and is unusually visible here.
The original data
On this site’s thirty-year fee measurement: 5 basis points costs 1.5% of the final balance, 20 costs 5.8%, 75 costs 20.2%, 150 costs 36.5%.
That table is the scale against which a curve spread should be judged. A 2% spread between long and short rates is a very large number in a world where 75 basis points of annual cost consumes a fifth of a thirty-year balance — which is exactly why products paying that spread find buyers.
And direction runs average 2.01 bars with a longest of 11 on this site’s series. A curve can stay flat or inverted for far longer than that in real markets, and a position carrying negative income does not survive on the expectation that shapes revert.
Where it actually shows up
In structured notes sold to investors. A retail or private-bank note paying a coupon linked to a curve spread is a CMS position wrapped in a different label.
In insurance and pension hedging, where liabilities are long-dated and a long rate is the relevant reference rather than a short one.
And in relative-value trading, where a CMS spread is the cleanest way to express a view on the curve without holding bonds.
The structured-note case is the one worth flagging. A note advertised on its coupon is a leveraged view on curve shape, and a buyer attracted by the headline rate is usually not told that a flattening curve — common, and driven by central bank policy — is what turns the coupon off.
When it fails
The characteristic failure is buying the coupon and inheriting the curve. A structured note pays an attractive rate linked to a long-minus-short spread, and the buyer reads it as a high-yield deposit. Then short rates rise, the curve flattens, and the coupon falls to nothing or the note’s value drops sharply. Nothing was misrepresented in the documentation. The buyer took a position on the shape of the yield curve without ever framing it that way, and shape is a variable that central bank policy moves deliberately.
A second failure is hedging it with a vanilla swap. The two respond to different variables and do not offset.
A third is ignoring the convexity adjustment, which is a real cost and requires a volatility view to evaluate.
A fourth is assuming a curve must re-steepen. Curves stay flat and inverted for extended periods, and carry accrues against you throughout.
And a fifth is treating it as a rates position. It is a curve position, and the difference is the whole instrument.
Related
Interest rate swap covers the vanilla version this modifies. Yield curve covers the shape it is a position on. And basis swap covers another floating-leg variation and the spread it trades.
This is where interest rate products stop being about whether rates go up or down and start being about the shape of the curve. That is a genuinely different variable, and a lot of people have discovered the difference the expensive way.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.