2s5s10s Butterfly Trade: Yield Curve Curvature

Key Takeaways

• Butterfly spread = 2 × belly yield minus both wing yields; a negative spread means the belly is cheap relative to the wings.
• A long-belly butterfly goes long the 5-year and short both wings, sized so each wing contributes half the belly DV01.
• Different weighting schemes (50-50, regression, PCA) hedge different amounts of residual slope risk.
• Butterfly spreads can trend persistently; mean reversion is slower and less certain than in simpler spread trades.

What It Is

The trade has two wings and one belly. In a standard 2s5s10s structure the 2-year and 10-year Treasuries are the wings, and the 5-year Treasury is the belly. A long belly (also called buying the butterfly) position is long the 5-year and short both the 2-year and the 10-year, with notionals sized so the position is DV01-neutral.

Curvature itself is usually measured as twice the belly yield minus the two wing yields:

Butterfly spread = 2 x Y(5Y) - Y(2Y) - Y(10Y)

If the belly cheapens relative to the wings, the butterfly spread falls (becomes more negative). A long-belly trade loses. If the belly richens, the butterfly spread rises and the long-belly trade gains.

The Intuition

Yield curves do three things: shift, steepen or flatten, and bend. Outright bond trades capture shift. Steepeners and flatteners capture slope. The butterfly captures the third mode, curvature, which is whatever is left after level and slope are taken out.

Bellies often cheapen when issuance is concentrated there, when a duration-sensitive investor like a pension fund sells intermediate maturities, or when the market is pricing a specific macro horizon (for example, the Fed cutting in eighteen months). Traders who think the belly has overshot fair value relative to the wings put on a long-belly butterfly.

Because the trade is hedged against both level and slope, it tends to have lower volatility than a directional bet on any single maturity. That makes it a favored relative-value trade, though also a crowded one.

How It Works

The hedge ratios come from DV01. Let D2, D5, and D10 be the DV01s of the three legs. A DV01-neutral long-belly butterfly with one unit of notional in the 5-year buys and sells wings so that:

Wing DV01 on each side = 0.5 x belly DV01
Notional(2Y)  = 0.5 x D5 / D2
Notional(10Y) = 0.5 x D5 / D10
2Y notional + 10Y notional (in DV01 terms) = belly DV01

This is called 50-50 weighting: each wing contributes half the belly's risk. Other weighting schemes exist. Regression weights replace 50-50 with historical betas of the 2-year and 10-year to the 5-year. Cash-neutral structures equalize dollar amounts rather than risk. PCA-weighted butterflies use the loadings on the third principal component of the curve so that the trade is genuinely orthogonal to level and slope.

Worked Example

Assume the 2-year yields 4.00 percent, the 5-year yields 4.10 percent, and the 10-year yields 4.40 percent. The butterfly spread is 2 x 4.10 - 4.00 - 4.40 = -0.20 percent, or -20 bps. That is, the belly is 20 bps cheap to the average of the wings.

A trader believes the belly is too cheap and will richen back toward zero. They buy the butterfly: long 100 million of 5-year (DV01 roughly 0.045 per dollar), short 2-year and 10-year wings each sized to contribute half the 5-year DV01. The 2-year DV01 is 0.019; the 10-year DV01 is 0.087. The short legs become 118 million of 2-year (0.5 x 0.045 / 0.019 x 100) and 26 million of 10-year (0.5 x 0.045 / 0.087 x 100).

If the butterfly spread tightens from -20 bps to 0 bps through a 10 bp rally in the 5-year and no move in the wings, the trade earns approximately the belly DV01 times 10, regardless of whether all yields shift in parallel.

Common Mistakes

• Assuming the trade is risk-free. Zero DV01 does not mean zero volatility. Butterfly spreads can trend for months, and mean reversion is slower than traders expect.
• Using one weighting scheme blindly. A 50-50 weighted butterfly is exposed to slope changes that a regression-weighted or PCA-weighted butterfly would hedge. Know which shape risk the chosen scheme is actually hedging.
• Ignoring carry. The belly often yields less than the average of the wings in upward-sloping curves, so a long-belly trade can be negative-carry. Paying daily for a slow mean reversion is a real cost.
• Forgetting cheapest-to-deliver drift in futures. When the trade is implemented in Treasury futures, CTD changes on the 5-year or 10-year contracts alter the effective DV01 and the trade becomes mis-hedged.
• Treating historical ranges as stable. Butterfly spreads reset when the shape of the curve regime changes, for instance when the Fed goes from hiking to cutting. Old ranges stop being informative.

Frequently Asked Questions

Why is this called a butterfly trade? The name comes from the visual shape of the position when mapped on a yield curve chart. The belly (the middle bond) appears to be the body of the butterfly, with the two wing positions fanning out on either side at shorter and longer maturities. The same three-legged relative-value structure is used across many markets and asset classes, and the butterfly metaphor has stuck.

What is the difference between a 50-50 weighted and a regression-weighted butterfly? A 50-50 weighted butterfly assigns equal DV01 risk to each wing. This is simple but leaves residual slope exposure because the 2-year and 10-year respond differently to slope moves. A regression-weighted butterfly uses historical betas to calibrate how much of each wing to hold so that the position is empirically hedged against slope changes, leaving only curvature. The two methods can produce meaningfully different P&L in trending slope environments.

What macro scenarios cause the belly to cheapen relative to the wings? The belly often cheapens when Treasury supply is concentrated in the 5–7 year sector, when pension funds or insurance companies rebalance away from intermediate duration, or when markets price a specific rate-cutting horizon that makes the 5-year the focal point of expectations. Uncertainty about the Fed's path at an intermediate horizon can make the belly volatile relative to the more anchored short and long ends.

How does carry affect a long-belly butterfly position? In an upward-sloping curve, the 5-year typically yields less than the 10-year but more than the 2-year. The long-belly trade is long the moderate-yielding belly and short both the low-yielding front wing and the high-yielding back wing. The net carry depends on the specific yield levels and DV01 weighting but can be modestly negative if the 10-year yield is high enough to make the short position's carry outweigh the belly's income.

How often do butterfly spreads revert to historical averages? Mean reversion in butterfly spreads is slower and less reliable than in simpler curve relationships. Because the butterfly measures the third mode of curve movement, catalysts for reversion are less frequent and more macro-dependent. Traders typically model historical mean and standard deviation as initial reference points but accept that regime changes in Fed policy or Treasury supply can shift the equilibrium spread for years.

Sources

1. Montreal Exchange. Understanding 2-5-10 Butterfly Trades in Futures. https://www.m-x.ca/f_publications_en/understanding_2_5_10_in_futures_en.pdf
2. CFA Institute. Yield Curve Strategies (2026 refresher reading). https://www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/yield-curve-strategies
3. CME Group. Yield Curve Spread Trades: Opportunities and Applications. https://www.cmegroup.com/education/files/yield-curve-spread-trades.pdf
4. Clarus Financial Technology. Mechanics and Definitions of Spread and Butterfly Swap Packages. https://www.clarusft.com/mechanics-and-definitions-of-spread-and-butterfly-swap-packages/

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.