Understanding Duration Exposure in Constant Maturity Swaps
Summary
This exchange challenges the claim that a Constant Maturity Swap keeps a company’s debt duration near the tenor of its CMS index throughout the life of the trade. CMS names the rate used to reset a leg, such as the prevailing five-year swap rate; it does not mean the whole position has exposure only to that curve point. Each upcoming reset has rate exposure, and later reset dates embed forward swaps whose sensitivities span multiple curve maturities.
The main example considers a fixed-versus-five-year-CMS swap with quarterly resets. A near reset can resemble a small-notional five-year swap, but a reset far in the future behaves more like a forward swap, decomposable into offsetting exposures at longer and shorter maturities. Thus assigning the entire position to the five-year bucket is misleading. Another response offers the intuition that reset rates concentrate duration near the index tenor, but the fuller explanation cautions that whole-trade duration depends on all future cash flows and can vary with the trade’s value.
Key ideas
- CMS identifies the rate index used for resets; it does not specify the duration of the entire swap.
- A near CMS reset can resemble a small-notional swap at the index tenor.
- Future reset payments embed forward swaps with exposures across multiple yield-curve maturities.
- Representing the whole CMS position in a single tenor bucket can misstate its risk.
- Total duration depends on the complete set of future cash flows and market value.
Tags
Full text
# duration of a cms swap # duration of a cms swap in the linked paper kwok_part2_exotic_swaps it says the following: A Swedish company has recently embraced the concept of duration and is keen to manage the duration of its debt portfolio. In the past, the company has used the Interest Rate Swap market to convert LIBOR based funding into fixed rate and as swap transactions mature has sought to replace them with new 3, 5 and 7yr swaps. The debt duration of the company is therefore quite volatile as it continues to shorten until new transactions are booked when it jumps higher. The Constant Maturity Swap can be used to alleviate this problem. If the company is seeking to maintain duration at the same level as say a 5 year swap, instead of entering into a 5 yr swap, they can enter the following Constant Maturity swap: The tenor of the swap is not as relevant, and in this case could be for say 5 years. The "duration" of the transaction is almost always at the same level as a 5yr swap and as time goes by, the duration remains the same unlike the traditional swap. So here, the duration will remain around 5yrs for the life of the Constant Maturity Swap, regardless of the tenor of the transaction. it is not clear to me how this can be true. i think that both the net (outright) duration, and the key rate duration on the 5y rate will still be proportionate to how much life is left in the swap, and so on a swap with term of 10y, it would be 10 times higher than on a swap with term 1y. Any explanation much appreciated! ## Answer by dm63 (score 2) https://quant.stackexchange.com/a/33250 Your intuition is correct and the paper seems to misunderstand the exposure of a swap based on CMS. The term "Constant Maturity Swap" or CMS, refers to the name of an index (the prevailing swap rate at the time of observation). A swap based on the CMS can be versus either a fixed rate or Libor. In the context of this question, consider a USD100mm 5yr swap consisting of a fixed rate versus 5 year CMS. Each quarter, the company will pay fixed and receive 5 yr CMS. For a given swaplet (say the one with the next upcoming reset date), indeed the exposure is approximately the same as a 5 year swap with a notional equal to 0.25/5 *USD100mm. However the swap also has future reset dates. Looking at the reset date in 5 years' time, this is economically equivalent to a forward swap, in 5 years for 5 years, on the same adjusted notional. But this forward swap is equivalent to being short 10 year duration versus long 5 year duration, which does not necessarily behave like a simple 5 year liability at all. Representing the exposure of a swap on 5yr CMS as wholly in the 5 year bucket is wrong. ## Answer by msitt (score 1) https://quant.stackexchange.com/a/33285 The cash flows on CMS leg reset based on some index, let's say the 5y swap rate. Duration measures sensitivity to different parts of the yield curve. The amount paid is based on that rate as of the last reset date, so essentially your duration should be close to 5 as your exposure is concentrated at the 5yr point on the yield curve (could be a bit higher/lower as the swap gains/loses premium).
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