Barbell and bullet are the two fundamental ways to structure a fixed-income portfolio along the maturity spectrum while maintaining the same overall duration.
A barbell concentrates holdings in the short and long ends of the curve, for example 2-year and 30-year bonds. A bullet concentrates holdings in a single intermediate maturity, for example the 10-year. Both can be constructed to have the same duration, but they respond differently to curve movements and yield volatility regimes.
Three forces separate the two structures at equivalent duration:
Assume a flat 4.0% yield environment. A 10-year Treasury at par carries a modified duration of approximately 8.1 years. Call it 8.0 for round numbers.
To match that with a barbell, allocate 50% to the 2-year (modified duration 1.9 years) and 50% to the 30-year (modified duration 18.0 years at 4%):
Portfolio duration = 0.50 * 1.9 + 0.50 * 18.0 = 9.95 years.
That overshoots. In practice you shade toward the short end: roughly 55% in the 2-year and 45% in the 30-year gives 0.55 * 1.9 + 0.45 * 18.0 = 9.1 years, still high. The point is that matching duration to 8.0 years requires a meaningful allocation to the short bond to offset the long wing. Once you do, convexity tells the real story.
Convexity scales approximately with the square of duration. A 30-year bond at 4% carries convexity near 360, while a 10-year carries roughly 80. The 2-year contributes near 4. A barbell with 42% in the 2-year and 58% in the 30-year, duration-matched to 8.0 years, has portfolio convexity of approximately 0.42 * 4 + 0.58 * 360 = 210, versus 80 for the 10-year bullet. That is a 2.6x convexity advantage for the barbell. For a 50 bp parallel shift down, the convexity correction is +0.5 * 210 * (0.005)^2 = 0.26% for the barbell versus +0.5 * 80 * (0.005)^2 = 0.10% for the bullet. The barbell captures an extra 16 bps of price gain purely from convexity.
In an upward-sloping curve, the 10-year bullet yields more than the average of the 2-year and 30-year wings on a carry-adjusted basis. The 2-year bond financed at repo earns minimal net carry, often 10 to 30 bps per year above the overnight rate. The 30-year adds rolldown but that gain is concentrated far from the short end. The 10-year sits at the inflection point where rolldown per unit of duration is often highest. In a normal curve environment, the barbell sacrifices 20 to 40 bps per year in carry relative to the bullet.
The barbell wins above a yield volatility threshold. The carry disadvantage divided by the convexity advantage gives the breakeven in yield-move terms. If the barbell gives up 30 bps per year in carry and gains 0.5 * (210 - 80) * (dy)^2 in convexity P&L, setting 0.5 * 130 * (dy)^2 = 0.0030 solves to dy = 0.0215, or roughly 215 bps annualized yield volatility. In practice, 10-year implied vol runs 80 to 140 bps in normal markets and spiked above 200 bps during 2022. When realized vol approaches or exceeds that threshold, the barbell outperforms.
The 2022 quantitative tightening cycle provided a clear barbell case study. The Fed raised rates 425 bps from March through December 2022, and the curve bear-flattened aggressively. Long-end convexity provided partial price offset as rates spiked. Managers positioned in barbells captured that convexity cushion on down-price days, which reduced drawdown versus duration-matched bullets. Conversely, in 2021 the curve was steep, realized volatility was low, and carry dominated. Bullet holders in the 7-to-10-year sector earned consistent roll-down with minimal convexity competition. You can track current curve shape and roll-down on the /curves page, and examine duration profiles across tenors on the /duration pages.
Choose the bullet when: the curve is steep, carry is high relative to volatility, and you expect stable rates or moderate steepening. The 2021 environment was archetypal.
Choose the barbell when: realized or implied yield volatility is elevated, the curve is flat or inverting, or you want convexity protection without extending average maturity. The 2022 bear-flat environment rewarded this posture.
A barbell-bullet trade, long the barbell and short the bullet at equal duration, is equivalent to a butterfly spread and isolates exposure to yield curve curvature. It expresses a view on the belly of the curve relative to the wings without taking an outright rate directional position.
Is the barbell always more convex than the bullet at the same duration?
Yes, for standard non-callable bonds. Convexity is always positive and scales with the square of maturity. Spreading duration across short and long maturities captures more of that squared relationship than concentrating it in a single intermediate maturity.
Does the barbell always underperform in carry?
In a positively sloped curve, yes. The 2-year wing earns minimal carry above repo, and the average of the two wings is typically below what the intermediate bullet earns. In an inverted curve the relationship can reverse, but inversion also compresses the incentive to extend duration at all.
How does this relate to the butterfly spread?
A long barbell, short bullet trade at duration-neutral weights is a butterfly spread. It is long the wings and short the belly. If the belly cheapens relative to the wings (the curve flattens or the butterfly widens), the trade profits. Use the /curves page to monitor the curvature in real time.