What it means
The yield curve plots the yields of bonds against their maturity, such as two, five and ten years. It can move up or down, tilt steeper or flatter, or change its curvature, which is the shape of the bend in the middle.
A butterfly describes a move in that curvature, in which the three points, short, medium and long, change by different amounts. The name comes from the shape of a butterfly spread, a position that combines the short and long maturities (the wings) against the medium maturity (the body).
A common measure is the sum of the wing yields minus twice the body yield. The sign convention differs between sources, so it is important to check how a given report defines it.
In the convention used here, a negative butterfly means the body yield has risen relative to the wings, so the measure falls and the curve becomes more humped. A positive butterfly is the opposite, with the body yield falling relative to the wings.
Fixed-income investors use butterfly moves to design trades. If they expect medium-term yields to rise more than short and long ones, they can arrange a portfolio that benefits from that change while staying roughly neutral to a parallel shift in rates, which separates the view on shape from the view on direction.
Butterfly changes often follow shifts in central bank expectations. Policy announcements may affect the shorter maturities, long-term inflation views affect the longer maturities, and the middle responds to expectations of how quickly the central bank will move, so the curvature records those competing forces.
For corporate treasurers the practical point is limited. Most borrowing and hedging decisions focus on the level and slope of rates, but a large butterfly change can alter the cost of borrowing at specific maturities, such as five years.
In practice
Real-world examples.
Example
A bond portfolio manager expects medium-term yields to rise as the central bank signals fewer cuts. She sells five-year bonds and buys two-year and ten-year bonds in proportions that keep her sensitivity to a parallel rate move close to zero.
Example
A risk analyst on a bank's treasury desk reports that the five-year yield rose 30 basis points while the two and ten-year yields were unchanged. She explains that the curve became more humped and that the bank's five-year hedges lost value.
Example
An insurance company comparing its asset and liability maturities notices that a negative butterfly has made its five-year liabilities more expensive to match than longer ones.
Formula
Calculation
Butterfly measure = (Short yield + Long yield) - 2 x Medium yield
A negative butterfly is a fall in this measure.
Worked example: yields at the start of the period are 2-year 4.00%, 5-year 4.20% and 10-year 4.60%.
Initial measure = (4.00% + 4.60%) - 2 x 4.20% = 8.60% - 8.40% = 0.20%
Later, the 5-year yield rises to 4.50% while the others stay unchanged.
New measure = (4.00% + 4.60%) - 2 x 4.50% = 8.60% - 9.00% = -0.40%
Change in the measure = -0.40% - 0.20% = -0.60%, or -60 basis points, which is a negative butterfly because the middle of the curve rose relative to the wings.Case study
Seen in the real world.
Cedarwood Asset Management is an illustrative, fictional manager with a bond fund that held most of its holdings in five-year bonds. The portfolio manager noticed that the five-year yield had been unusually low relative to two-year and ten-year yields.
She expected the gap to correct and positioned the fund to benefit from a negative butterfly by reducing the five-year bonds and holding more in the wings. When the five-year yield rose by 30 basis points over the next quarter while the other yields were steady, the fund outperformed its benchmark.
In this illustrative story, the manager also noted that the trade could have lost money if the curve had become less humped, and she kept the position small. The firm's risk committee reviewed the trade against its limits.
Watch out
Common mistakes.
- Confusing a butterfly move with a parallel shift or a steepening, when it concerns curvature.
- Assuming every source uses the same sign convention.
- Ignoring weighting, when a proper butterfly trade must balance the sensitivities of each leg.
Questions
People also ask.
What is the difference between a butterfly and a twist?
A twist changes the slope, with short and long yields moving in opposite directions, whereas a butterfly changes the curvature of the middle against the ends.
Who uses butterfly measures?
Mostly bond traders, fund managers and risk analysts, who use them to express views and measure risk.
Is a negative butterfly good or bad?
It is neither by itself, since the outcome for a portfolio depends on how its holdings are spread across maturities.
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