A butterfly spread is a yield curve trade involving three maturities: a short and long maturity (the "wings") and an intermediate maturity (the "belly"). It isolates the curvature component of the yield curve. Weighted so the wing DV01 offsets the belly DV01, it is neutral to parallel shifts; full neutrality to slope changes takes an additional maturity-weighting step (see Building the Trade below).
A long butterfly (long the wings, short the belly) profits when the curve becomes more humped, meaning the belly cheapens relative to the wings. A short butterfly profits when the belly richens.
Example: the classic 2s/5s/10s butterfly:
Butterfly spreads are quoted in basis points as:
Butterfly = (wing1 yield + wing2 yield) / 2 - belly yield
Positive values mean the belly is rich (low yield, expensive price) relative to the wings. Negative values mean the belly is cheap (high yield, inexpensive price).
Butterfly trades are used for:
The blog post "Ten Treasury Curve Snapshots That Tell the Story of a Generation" discusses how butterfly spreads shift across major market events.
A butterfly is quoted as a single number in basis points, and the sign carries the whole message. It is also the part that trips people up, because desks do not all quote it the same way.
Under the convention above, the spread is the average of the two wing yields minus the belly yield. A positive number means the belly yields less than the wings, so the belly is rich. A negative number means the belly yields more than the wings, so the belly is cheap.
Other desks quote the mirror image, taking the belly minus the wings, which flips every sign. Neither is wrong. The lesson is to confirm the convention before acting on a number, because a fly quoted the other way turns a rich signal into a cheap one.
Naming is a second trap, because two conventions are in use. Some desks name the trade after the wings, which is the convention used above, so a long butterfly is long the wings and short the belly. Others name it after the belly, so the same structure is a short belly fly. The structure is identical either way. Say which leg you mean rather than relying on the label.
A butterfly is only a curvature trade if both other risks are removed first. That takes two conditions, and the second one is what makes the structure work.
The trade must be neutral to a parallel shift. The DV01 of the belly leg must equal the combined DV01 of the two wing legs.
The wing risk is then split between the two wings rather than put into one. In the common equally weighted form, each wing carries half the belly's risk.
Work through a 2s5s10s fly with round figures. Assume DV01 per million of 195 for the 2 Yr, 450 for the 5 Yr, and 820 for the 10 Yr.
The face amounts look lopsided and should. Risk is what is being matched, not size. The 2 Yr leg needs roughly four times the notional of the 10 Yr leg to carry the same risk.
Equal weighting removes the parallel shift and leaves some slope exposure behind. Using the figures above, the position still gains or loses if the curve tilts, because the 10 Yr leg sits further out along the curve than the 2 Yr leg. Removing that as well requires weighting the wings by maturity rather than splitting the risk evenly, which shifts risk toward the near wing. Desks that want a purer curvature trade weight the wings by how each has historically moved against the belly. That improves the hedge and adds a model, and the model can be wrong.
A slope trade compares two points. It answers whether the curve is steep or flat between them. A butterfly compares three points, so it answers a different question. It asks whether the middle of the curve is priced correctly given the two ends.
This matters because the belly is where policy expectations concentrate. The front end tracks the current policy rate closely. The long end tracks inflation and term premium. The belly is where the market prices the path between them, including how fast a tightening or easing cycle will run and where it will stop.
A cheapening belly therefore often signals that the market has changed its view of the policy path without changing its view of the destination. A curve trade between 2 Yr and 10 Yr would show none of this, because a change concentrated in the 5 Yr sector can leave the 2s10s spread almost unmoved.
Butterflies are also the natural home for relative value between neighboring issues. Comparing one bond to a fitted curve is a butterfly in disguise, with the two nearest bonds acting as the wings.
Because curvature is defined by three points. Two points can only describe a level and a slope. Adding a third point makes it possible to ask whether the line between the outer two passes above or below the middle one, which is what curvature measures.
It is hedged against a parallel shift once the wing DV01 offsets the belly DV01. Hedging a change in slope too takes an additional maturity-weighting step (see Building the Trade). It is not riskless. The trade is fully exposed to the belly moving against the wings, which is the exposure it was built to take. It also carries funding cost, and the three legs may finance at different rates.
It depends on the sign convention in use, so the convention has to be stated before the answer means anything. Where the spread is quoted as the average of the wing yields minus the belly yield, a widening spread means the belly is richening relative to the wings. The middle of the curve is then falling in yield faster than the two ends, or rising more slowly. This often happens when the market pulls forward its expectation of a change in policy.