What it means
The word constant refers to the maturity, not the rate. Each quarter the swap looks up the current ten year rate, so the maturity being referenced is always ten years even though the rate itself moves at every reset.
The economic exposure is therefore the gap between long and short rates. A party receiving the long rate and paying the short rate profits from a steep curve, where long rates sit well above short ones, and loses when the curve flattens or inverts.
Insurers and pension funds are natural users, because their liabilities behave like long dated bonds while much of their income is short dated. A constant maturity swap lets them import long rate exposure without buying and rolling actual long bonds.
The instrument also sits inside retail structured products. A note paying a coupon linked to the ten year rate, or to the spread between the ten year and the two year rate, is a constant maturity swap wrapped in a bond, and the buyer usually carries more curve risk than the marketing suggests.
Pricing is genuinely harder than for a plain swap. Because the payment depends on a long rate rather than the rate matching the payment period, the valuation requires a convexity adjustment, which is why these trades are priced by specialist desks rather than lifted from a screen.
In practice
Real-world examples.
Example
A life insurer with liabilities stretching forty years receives the ten year rate and pays a short term rate on $200,000,000 of notional. The trade lifts the interest rate sensitivity of its assets closer to that of its liabilities without forcing it to sell equities to buy long bonds.
Example
A property developer with floating rate debt worries that short rates will rise faster than long ones. It enters a constant maturity swap receiving the short rate and paying the ten year rate, which pays off if the curve flattens as it fears.
Example
A private bank sells clients a five year note whose annual coupon equals the ten year swap rate plus 0.25%, capped at 6%. The issuing desk offsets its exposure with a constant maturity swap, and the client, in effect, holds one indirectly.
Formula
Calculation
Net payment = notional x (rate received - rate paid) x (days in the period / day count basis)
A company enters a $50,000,000 constant maturity swap on which it receives the ten year swap rate and pays the three month reference rate plus 0.50%, settling quarterly on a 90 day quarter and a 360 day year.
At the first reset the ten year swap rate is 4.20% and the three month rate is 3.00%. The company pays 3.00% + 0.50% = 3.50% and receives 4.20%, a net 4.20% - 3.50% = 0.70% in its favour, so it collects $50,000,000 x 0.70% x (90 / 360) = $87,500 for the quarter, roughly 4 x $87,500 = $350,000 a year if the curve held still.
A quarter later the curve has flattened. The ten year rate falls to 3.80% while the three month rate rises to 3.60%, so the company now pays 3.60% + 0.50% = 4.10% and receives 3.80%, a net cost of 0.30%. It hands over $50,000,000 x 0.30% x (90 / 360) = $37,500, and the swing of $87,500 + $37,500 = $125,000 per quarter came entirely from the shape of the curve, not its level.Case study
Seen in the real world.
The following is an illustrative and entirely fictional example. Kelbridge Life Assurance, an invented insurer, was earning short term money market returns on $400,000,000 of assets while its annuity promises behaved like thirty year bonds. Every fall in long rates raised the value of those promises without raising the value of the assets backing them.
Rather than sell its portfolio, Kelbridge entered constant maturity swaps on $150,000,000 of notional, receiving the ten year rate and paying the three month rate. In the first year the curve was steep, with the ten year rate near 4.20% and the three month rate near 3.00%, and the trade produced a positive net flow while narrowing the mismatch.
The following year the curve inverted and the swaps became a cost. The fictional insurer's risk committee had approved the trade specifically as a hedge rather than as a source of income, so the loss was measured against the fall in its liability value rather than judged in isolation, which is exactly how a hedge should be assessed.
Watch out
Common mistakes.
- Reading the word constant as meaning a fixed rate, when it is the ten year maturity that stays constant while the rate resets at every payment date.
- Treating a constant maturity swap as a bet on rates going up or down, when the real exposure is to the gap between long and short rates.
- Valuing one with a plain vanilla swap model and skipping the convexity adjustment, which produces a price that is systematically wrong.
Questions
People also ask.
How is this different from an ordinary interest rate swap?
An ordinary swap pays a rate matching its payment period, such as three month money every three months, whereas this one pays a ten year rate every three months.
What is a CMS spread trade?
It is a position on the difference between two constant maturity rates, most often the ten year and the two year, so it profits purely from the curve steepening or flattening.
Who should not use one?
Any borrower simply wanting protection against rising rates, since a plain fixed for floating swap or a cap does that job more cheaply and with far less curve risk.
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