What it means
The yield curve plots the interest rate on bonds of different lengths, from a few months out to 30 years. Analysts picture it as a butterfly, with the short and long ends as the wings and the medium-term section as the body.
A butterfly move changes the curvature of the line rather than lifting or tilting the whole thing. In a positive butterfly, the wings rise faster than the body, so the middle of the curve sags compared with the ends.
The opposite, a negative butterfly, happens when the body rises relative to the wings. Some textbooks define the direction the other way round, so check the convention before relying on a label.
The shift matters to anyone who holds bonds or manages interest-rate risk. A portfolio concentrated in medium-term bonds will do relatively well in a positive butterfly because those yields have lagged, while a portfolio built from short and long bonds suffers more.
Bond managers build butterfly trades that hold the middle against the two ends to profit from changes in curvature. The shift is also a reminder that duration (a measure of how sensitive a bond's price is to interest rate changes) is not the whole story of rate risk.
A parallel shift moves every yield equally, and a steepening or flattening tilts the curve, but a butterfly bends it. Risk reports that look only at one number can miss a bend entirely.
Curvature moves are usually smaller than level or slope moves, yet they can still change bond returns noticeably. Central bank policy, shifts in demand from pension funds for long bonds and changing expectations for growth can all alter the shape of the curve.
Traders often describe butterflies with a three-legged structure. They take opposite positions in the two wings and the body, sized so that the trade is neutral to a parallel move in rates, which isolates the bet on curvature.
If the curve bends the way they expect, the trade profits whether rates go up or down overall.
In practice
Real-world examples.
Example
A bond fund manager expects short and long yields to rise relative to the middle of the curve. She buys 10-year bonds and sells a mix of 2-year and 30-year bonds so that the trade gains if a positive butterfly occurs.
Example
A corporate treasurer holds a ladder of bonds, with maturities from 2 to 30 years. After a positive butterfly, the medium-term bonds lose less value than the others, and she reports the difference to the board.
Example
An insurance company matches liabilities that fall due in 10 years with 10-year bonds. A positive butterfly leaves its matched position in better shape than a competitor that used a barbell of short and long bonds.
Formula
Calculation
Butterfly measure = (2 x Medium-term yield) - Short-term yield - Long-term yield
A positive butterfly shows up as this measure falling, because the body lags the wings.
Before: 2-year yield 4.0%, 10-year yield 4.5%, 30-year yield 5.0%. Measure = (2 x 4.5%) - 4.0% - 5.0% = 9.0% - 9.0% = 0.0%.
After: 2-year yield 4.4%, 10-year yield 4.6%, 30-year yield 5.4%. Measure = (2 x 4.6%) - 4.4% - 5.4% = 9.2% - 9.8% = -0.6%.
The measure fell by 0.6 percentage points, so the wings rose by 0.4% and 0.4% while the body rose by only 0.1%, which is a positive butterfly.Case study
Seen in the real world.
Meridian Annuities is a fictional insurer that tracks its interest-rate risk using the level, slope and curvature of the yield curve. Its risk team noticed that the curvature measure had drifted lower for three consecutive weeks.
Because the firm held a barbell of short and long bonds, it was exposed to a positive butterfly. In this illustrative case the team shifted a small amount into 10-year bonds, and the change reduced the quarterly fall in portfolio value from a projected $1,800,000 to about $900,000.
The team also noted that the move had been driven by heavy issuance at the long end and by banks reducing their holdings of very short bills. Their risk report now shows level, slope and curvature separately each week, so a similar drift would be spotted at the first sign. Management agreed that a single duration number had hidden the problem.
Watch out
Common mistakes.
- Confusing a butterfly with a parallel shift, when a butterfly changes the bend of the curve and not its overall level.
- Assuming every source uses the same sign convention, when some textbooks label the same move a negative butterfly.
- Hedging only duration and ignoring curvature, which leaves the portfolio open to a butterfly move.
Questions
People also ask.
What causes a positive butterfly?
Typically a change in demand or expectations that pushes short and long yields up more than medium-term ones, such as a policy change combined with heavy long-bond issuance.
Is a positive butterfly good or bad?
It depends on what you hold, because medium-term bondholders benefit and holders of the short and long ends lose relatively.
How is a butterfly different from a twist?
A twist rotates the curve around a pivot so that one end rises and the other falls, while a butterfly moves both ends the same way against the middle.
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