A deep-dive into butterfly trades, from curve shape to carry and forward risk.

What is a Butterfly Trade?

A butterfly trade has three legs; two wings and a belly. The standard definition of a swap butterfly is:

where S_t denotes the fixed rate of a swap with maturity t. The equation shows us that:

• The price for a swap butterfly is equivalent to 2 times the fixed rate on the “belly” swap, minus each of the wings.
• The structure is DV01 neutral and is a so-called “relative value” strategy.
• The butterfly is quoted in basis points, so we will typically multiply the above by 100.
• Mathematically, the same trade can also be expressed as:

This formulation makes it explicit that we are comparing one spread versus another spread. That can make it easier to understand why butterflies are traded in the first place.

Why Trade Butterflies?

A steepener or flattener (e.g. 2y10y, 10y30y) expresses a view on the “slope” of the interest rate curve.

A butterfly expresses a view on the shape of the curve.

More precisely;

• The underlying view is that one area of the curve will steepen (flatten) more than another area.
• The belly of the butterfly is the pivot point around which the curve reshapes.
• It is a relative value trade and can help pinpoint distortions caused by flow, issuance or positioning.

An Example: 2Y-5Y-10Y on the USD SOFR curve

Consider the USD SOFR swap curve in early 2026:

Showing;

• The USD swaps curve in January 2026.
• The chart plots the par coupons of spot starting SOFR swaps.
• Current pricing expects USD rates to bottom out in about two years time. A chart of 3 month forwards implied from these spot starting swaps confirms this:

Whilst pricing implies that rates bottom out in roughly two years time, I do not pretend to know whether that will be true or not. But I can observe that;

• Paying two-year swaps offers very attractive positive carry!
• New Issuance has been exceptionally heavy so far this year. That puts receiving (downward) pressure on the belly of the curve as issuers come in and receive fixed, typically in the 4y-10y area.
• The Fed’s independence is being threatened. There are more and more doves on the board. There is a lack of fiscal responsibility on both sides of the aisle. All of these reasons cause me to be “bearish” on 10Y bonds and think that longer tenor swaps will trend higher.

To express those views, I could potentially look at a 5s10s steepener. But that feels too directional in a headline driven world – or what if long-end flow overwhelms issuance?

I would prefer to be directionally neutral and pick-up positive carry from paying 2Y.

I want a solution that neutralises directionality and isolates a view on the shape of the curve. That leads me to the 2Y-5Y-10Y butterfly.

Trade Structure and DV01 Neutrality

Most of the butterflies that I traded were DV01 neutral. This means that the DV01 exposure in the belly equals the sum of the DV01s of the two wings. For example, the risk on a 2Y-5Y-10Y butterfly looks like the below:

Showing;

• A paid position in $50k of 2Y and 10Y swaps versus a received position of $100k DV01 in 5Y swaps.
• In terms of directionality, we speak in terms of the belly position: “I have “sold” the ‘fly. I have received the ‘fly. I am receiving in the belly.”
• Using the par coupons on the curve, the butterfly is marked at a price of -12.1 basis points.

Carry on Butterfly Trades

Because butterflies are relative value trades they do not move very much.

A “spread of spreads” is naturally less volatile than a spread, which is less volatile than an outright. Butterflies can end up eating up risk allowances whilst not really moving. That can be attractive from a hedging perspective (or just a “keeping your toe in” experience), but not great as a PnL driver.

Carry is therefore a vital component of returns when trading ‘flies.

A negative carry butterfly can destroy your PnL. If it doesn’t move much and has negative time decay, it is a killer.

The 2Y-5Y-10Y is a good illustration at the moment. Look at the optics:

Showing;

• Today’s coupons and what those swaps will decay to in one year if the market doesn’t move.
• 2Y-5Y-10Y is at -12 basis points, whilst the 1Y-4Y-9Y butterfly is at -53 basis points.
• Receiving the ‘fly yields over 3.4 basis points of positive carry each month.
• Thanks to the ratio of notionals ($270m 2Y vs $218m 5y and $60m 10Y), the coupons also accrue at a positive rate each month (an easily forgotten element of carry for spot starting swaps).

This is great if you are receiving 2Y vs 5Y vs 10Y.

But what if you want to pay it?

Forward Butterflies

This is where forward space matters.

2Y-5Y-10Y that starts 1Y forward looks very different to the spot equivalent thanks to the shape of the curve. The DV01 risk ladder of this forward starting 2Y-5Y-10Y trade is shown below:

Showing risk in the 1Y bucket (due to the forward start) and then the butterfly lives in the 3Y, 6Y and 11Y buckets. (Because I don’t have an 11Y point on my curve and I have used “smooth forwards” to construct the long-end, I end up with quite a mess beyond 10Y in my risk buckets. Eurgh.)

In the current curve environment, a 1Y-forward 2Y-5Y-10Y butterfly will decay from -8bp to -12bp over a year. This is an order of magnitude less than the spot trade!

The conclusion is simple:

• Bearish on the fly? Sell the butterfly value spot and harvest the carry.
• Bullish on the fly? Pay the fly with a 1Y forward start and avoid most of the carry killer.

Why This Matters

This is why swap markets are so powerful.

Opposing views can be expressed using almost identical structures, differentiated only by forward start and carry profile.

And it all reduces to simple algebra:

• spreads,
• spreads of spreads,
• and time.

That is the quiet beauty of relative value trading. In this case, expressed via butterflies.