Butterfly Trades
Trading relative value across three points on the curve.
The Belly Looked Too Cheap
It was March 2020. The world was shutting down. The Fed had just slashed rates to zero. Everyone was scrambling for safety. But in the chaos, something strange happened to the 5-year Treasury.
The 2-year yield collapsed to 0.49%. The 10-year dropped to 0.54%. But the 5-year? It was stuck at 0.69%. On a straight line between 2Y and 10Y, the 5-year "should" have been around 0.51%. Instead, it was 35 basis points higher.
The belly was cheap. In rates trader parlance, the 5-year was dislocated. It was a textbook butterfly opportunity.
Professional traders pounced. They bought the 5-year and sold the wings (2Y and 10Y) in a duration-neutral structure. Over the following months, as the curve normalized, they captured 20-30 basis points of spread compression.
This is what butterflies are for: betting on the relative value of one point on the curve versus its neighbors, without taking a directional view on rates.
Learn From History
Butterfly opportunities arise when one part of the curve gets dislocated from its neighbors. Study these moments:
COVID Panic - Belly Cheap
Butterfly: +35 bpsThe Setup
The Fed slashed rates to zero. Flight to quality crushed front-end and long-end yields. But the 5Y got left behind - it was 35bps cheap to the 2s10s line. Classic belly dislocation.
What Happened Next
Butterfly buyers (long 5Y, short wings) made 20-30bps as the curve normalized over the following months. The belly richened as panic subsided.
How to Construct a Butterfly
A butterfly trade has three legs: two "wings" (usually the short and long ends) and a "belly" (the middle tenor). The key is making it duration-neutral so parallel rate moves don't affect you.
Choose Your Tenors
Classic butterflies use 2s5s10s (2-year, 5-year, 10-year). But you can construct butterflies anywhere: 3s5s7s, 5s10s30s, etc. The "belly" is what you're betting on.
Calculate the Theoretical Yield
Draw a straight line between the wing yields. Where does the belly "should" be? The butterfly spread is: actual belly yield minus theoretical yield. Positive = belly is cheap. Negative = belly is rich.
Weight by DV01
To be duration-neutral, the DV01 of your belly position must equal the combined DV01 of your wing positions. Typically, split the wing risk 50/50 between short and long wings.
DV01 Weighting Example
Notice how the belly DV01 (~$4,465) roughly equals the sum of the wing DV01s. This makes the position neutral to parallel rate moves.
When Butterflies Work (And When They Blow Up)
Butterflies Work When...
- Dislocations are extreme: 30+ bps butterfly spreads tend to mean-revert. Small mispricings can persist forever.
- There's a catalyst: Fed meetings, auctions, or macro events can trigger curve normalization.
- You can wait: Butterflies can take weeks or months to normalize. Patience is essential.
- Carry supports you: If you earn positive carry while waiting, time is on your side.
Best environment: March 2020 COVID panic. Extreme dislocations, clear catalyst (Fed intervention), and eventual normalization made belly-cheap butterflies highly profitable.
Butterflies Blow Up When...
- The dislocation is fundamental: Sometimes the belly IS supposed to be cheap/rich. Fed policy can make it persist.
- Carry bleeds you: Negative carry butterflies need quick resolution or you lose money waiting.
- You size too big: Even duration-neutral positions have convexity risk. Huge moves can hurt.
- Liquidity dries up: In a crisis, you might not be able to exit at fair prices.
Worst environment: 2022-2023 inversion. The belly stayed rich for over a year. Traders who sold butterflies expecting quick normalization bled carry for months.
Types of Butterfly Trades
Cash Butterfly
Trade using actual Treasury bonds
Execution: Buy/sell the actual Treasury securities. Most straightforward but capital-intensive.
Funding: Each leg needs repo financing. You receive repo on longs, pay on shorts. Net financing depends on whether bonds trade special.
Considerations: Settlement dates, accrued interest, and specific issue selection matter. On-the-run vs off-the-run can affect pricing.
Futures Butterfly
Trade using Treasury futures (TU, FV, TY, US)
Execution: Use 2Y (TU), 5Y (FV), 10Y (TY), or Ultra (US) futures. More capital efficient than cash.
Funding: Only margin required, not full notional. No repo complexities. But you're exposed to CTD (cheapest-to-deliver) basis.
Considerations: Futures roll every quarter. The CTD bond can change, affecting your hedge ratios. Need to adjust for conversion factors.
Swap Butterfly
Trade using interest rate swaps
Execution: Enter 2Y, 5Y, and 10Y swaps. Pay fixed on some legs, receive fixed on others.
Funding: Initial margin only. Swap spreads introduce additional complexity - you're trading both the curve shape AND the swap spread at each tenor.
Considerations: Swap butterfly = Treasury butterfly + swap spread differences. You might be right on the Treasury butterfly but wrong on swap spreads.
Build a Butterfly Position
Trade Legs
Combined Position
Payoff Profile
P&L across parallel yield curve shifts (all tenors move equally):
Risk Summary
Position is short duration ($-4K DV01). Profits when rates rise, loses when rates fall.
Significant curve exposure between 2Y and 10Y. Sensitive to steepening/flattening.
Trade Examples (Simple)
Here are three butterfly trades explained clearly:
Example 1: The Belly Cheap Trade
5Y yields 4.30%. 2Y yields 4.20%. 10Y yields 4.10%. Drawing a line from 2Y to 10Y, the 5Y "should" yield 4.15%. But it's yielding 4.30% - that's 15bps cheap to the line.
Buy $10M 5Y (the cheap belly)
Sell $20M 2Y (short wing)
Sell $6.5M 10Y (long wing)
Net DV01 ≈ $0
You repo-finance your $10M long 5Y position. You borrow the 2Y and 10Y bonds via reverse repo to sell them short. Total capital required is margin on all three legs, maybe $1-2M. Carry depends on relative repo rates - often close to neutral.
Over the next month, the curve normalizes. 5Y drops to 4.20% while wings stay put. The butterfly spread compresses 10bps.
10bps on your belly position x duration x notional. On $10M with ~4.5 year duration, that's roughly +$45,000 from the butterfly normalizing.
You spotted that the 5Y was too cheap relative to its neighbors. You bought it and hedged out the rate risk by selling the wings. When the curve normalized, you made money without needing to predict rate direction.
Example 2: The Wings Cheap Trade (Sell the Butterfly)
Inverted curve. 5Y yields 4.00%. 2Y yields 4.50%. 10Y yields 3.80%. The 5Y "should" yield 4.15% on the line. But it's at 4.00% - that's 15bps RICH to the line.
Sell $10M 5Y (the rich belly)
Buy $20M 2Y (long wing)
Buy $6.5M 10Y (long wing)
Net DV01 ≈ $0
You borrow and short the 5Y via reverse repo. You repo-finance your long 2Y and 10Y positions. On an inverted curve, this trade often has NEGATIVE carry - the wings yield less than financing costs. You're paying to hold this position.
Over 3 months, the butterfly normalizes. 5Y yield rises 10bps while the wings stay put.
10bps gain from butterfly spread widening. But you lost 15bps in carry over 3 months. Net: -$15,000 or so. You were right on direction but carry killed you.
On inverted curves, selling butterflies often means negative carry. Even if you're right about the mispricing, you might lose money waiting for it to correct. Timing matters enormously.
Example 3: The Carry Butterfly
Steep curve. The butterfly spread is near zero (no obvious mispricing). But the belly of the curve has much better roll-down than the wings. You're not betting on mispricing - you're positioning for differential roll.
Buy $10M 7Y (best roll-down sector)
Sell $25M 2Y (minimal roll-down)
Sell $5M 30Y (flat curve at long end)
Net DV01 ≈ $0
Standard repo/reverse repo. On a steep curve, you're likely earning positive carry: the belly coupon exceeds financing, while short positions are cheap to fund. You might earn 20-30bps annualized just from carry.
You hold for 1 year. The curve doesn't change shape.
Carry: +25bps. Roll-down differential: +15bps (7Y rolls faster than 2Y or 30Y). Total: +40bps or ~$40,000 without any directional call.
Not all butterflies are about mispricing. Sometimes you structure a butterfly to capture differential carry and roll across the curve. It's a more passive approach but can generate steady returns on steep curves.
Funding a 3-Leg Trade
Butterflies are more complex to fund than simple long/short trades because you have three positions to finance:
Long Belly Position
Financed via repo. You buy the bond, then immediately repo it out (borrow against it). You pay the repo rate, receive the coupon. Net = carry on the long.
Short Wing Positions
Financed via reverse repo. You borrow the bonds and sell them. You pay the coupon on borrowed bonds, receive repo rate on cash. Short positions have "negative carry" in normal environments.
Net Funding Impact
The butterfly's net carry depends on:
- Curve shape (steep = positive carry on longs, inverted = negative)
- Whether any bonds trade "special" in repo
- The relative notional sizes of each leg
In general: steep curves favor buying butterflies (long belly), while inverted curves favor selling butterflies (short belly) from a carry perspective.