Portfolio Management Pathway · Yield Curve Strategies

Bullet, Barbell and Ladder Portfolios and Butterfly Trades

Updated 8 October 2026 · Fact-checked

A bullet concentrates bonds around one maturity, a barbell holds short and long maturities, and a ladder spreads holdings evenly. Choose the structure whose duration, convexity and cash flows fit your yield curve view: parallel shift, slope change (steepener or flattener) or curvature change (butterfly).

Understand Active Strategies: Bullets, Barbells and Butterflies

A yield curve can change in three ways. Level is a parallel shift up or down. Slope is the gap between long and short yields, which can steepen or flatten. Curvature is the change in the middle of the curve relative to the wings, also called a butterfly move.

A bullet puts most holdings near one maturity, for example around 5 years. A barbell holds short and long maturities and little in the middle. A ladder spreads holdings roughly equally across maturities. You can build a bullet and a barbell with the same duration. They still react differently, because their cash flows are spread differently along the curve.

For the same duration, the barbell has more convexity than the bullet, because its cash flows are more dispersed. The bullet usually has a higher yield than the equal-duration barbell. Convexity helps you when yields move a lot in either direction. It costs you if the market has already priced it in as a lower yield on the barbell.

Slope views drive the choice, and the comparison only holds at equal duration. If you expect the curve to steepen (long yields rise relative to short yields), the bullet is favoured over the barbell. If you expect it to flatten, the barbell is favoured over the bullet. So moving from a bullet to a barbell is a flattening trade, and moving from a barbell to a bullet is a steepening trade. Check the weights and the exact exposures.

A butterfly trade combines a short position in one structure with a long position in another so that net duration is about zero. A long butterfly (long the wings, short the body, so long a barbell and short a bullet) gains if the middle yield rises relative to the wings. Body prices fall and wing prices hold up. The curvature measure, 2 × y_middle − (y_short + y_long), increases and the curve becomes more humped. The gain depends on the body yield moving relative to the wings, not on slope. For a pure curvature view, the weights must be duration-neutral and slope-neutral. Otherwise a flattening or steepening of the curve can drive the result. A higher convexity position is a secondary benefit, not the curvature view itself. A short butterfly (short the wings, long the body) is the reverse. A ladder gives balanced exposure and steady reinvestment, so it has less exposure to slope and curvature views and is easier to manage. In liability work, matching cash flows is tighter than matching duration. A barbell may match duration yet leave convexity and cash flow mismatches that must be managed.

Key rules to remember

Portfolio duration: D_P = Σ (w_i × D_i); Weights are market value weights. Use this to size a barbell to equal the bullet's duration.
Two-bond barbell weights: w_short = (D_long − D_target) ÷ (D_long − D_short); w_long = 1 − w_short; Gives a barbell with the same duration as the target bullet.
Duration-neutral butterfly (market value basis): w_short × D_short + w_long × D_long = w_body × D_body; Here w_short and w_long are the long positions in the short and long wings, and w_body is the size of the short position in the body. The body's duration contribution must equal the combined wing contributions, so net duration is about zero. For a market-value-neutral trade, also set w_short + w_long = w_body.
Approximate price change: %ΔP ≈ −D × Δy + ½ × C × (Δy)²; For the same duration, higher convexity means a better result when yield changes are large.
Level, slope, curvature: Slope = y_long − y_short; Curvature = 2 × y_middle − (y_short + y_long); A common way to define the butterfly spread. A rising value means the middle yield rises relative to the wings and the curve becomes more humped. This favours the long butterfly (long wings, short body). A falling value means the opposite.

How to solve Active Strategies: Bullets, Barbells and Butterflies questions

Use this order for any question on bullets, barbells, ladders and butterflies.

1Identify the view: level (parallel), slope (steepen or flatten) or curvature (butterfly).
2Note the client or mandate: liabilities, benchmark duration, convexity needs, liquidity and constraints.
3Set the duration target. Compute weights so the structures being compared have equal duration.
4Compare convexity and yield. For equal duration, barbell has higher convexity and usually lower yield than the bullet.
5Work out the result under the stated scenario: parallel move, slope change or curvature change. Calculate returns if numbers are given.
6Match the structure to the view and state why. Use the command word: calculate, identify, justify or recommend.
7Check the risk left over: convexity cost, non-parallel shifts, and cash flow mismatch against liabilities.

Quickest way: Equal-duration shortcut for barbell versus bullet

When to use it: Use when a question gives yields or durations for short, middle and long bonds and asks which structure wins under a view.

Force equal duration first. Never compare structures with different durations.
Parallel shift, large move: barbell wins on convexity. Small move: bullet wins on yield.
At equal duration, steepening favours the bullet and flattening favours the barbell.
Curvature: long butterfly (long wings, short body) wins if the middle yield rises relative to the wings; short butterfly wins if the middle falls.
If liabilities are fixed, prefer cash flow matching over duration matching, since the barbell leaves cash flow gaps.

Common mistakes in Active Strategies: Bullets, Barbells and Butterflies

Comparing a barbell and a bullet with different durations.
Students compare yields and convexity without equalising the interest rate sensitivity.
Fix: Solve for weights that give equal duration before drawing any conclusion.
Saying the barbell always outperforms because it has more convexity.
Convexity is remembered as always good.
Fix: The barbell usually gives up yield. It wins only if yield moves are big enough, or the curve changes in its favour.
Mixing up steepener and flattener positions.
Students focus on price direction instead of which yields move.
Fix: Steepener: long-short spread widens, so at equal duration the bullet is favoured. Flattener: spread narrows, so at equal duration the barbell is favoured. Then check weights.
Treating a ladder as a pure slope or curvature view.
Ladder is confused with a barbell.
Fix: A ladder is spread evenly with a neutral stance. It diversifies reinvestment risk and has less exposure to slope or curvature changes.
Assuming duration matching removes all risk for a liability.
Duration is seen as the only risk measure.
Fix: Duration matching handles small parallel shifts only. A barbell can leave convexity and cash flow mismatch, so cash flow matching is tighter.
Using par amounts instead of market values for butterfly weights.
Quick calculation shortcuts.
Fix: Use market value weights unless the question states duration contributions or DV01 weights.

Worked examples

Example 1

A manager wants a barbell of 2-year and 10-year bonds to match a 5-year bullet with modified duration 4.5. The 2-year bond has duration 1.9 and the 10-year bond has duration 8.1. Find the market value weight in each bond.

Show the solution

Target duration is 4.5.
w_short = (D_long − D_target) ÷ (D_long − D_short) = (8.1 − 4.5) ÷ (8.1 − 1.9).
w_short = 3.6 ÷ 6.2 = 0.5806.
w_long = 1 − 0.5806 = 0.4194.
Check: 0.5806 × 1.9 + 0.4194 × 8.1 = 1.1032 + 3.3971 = 4.5003, which is about 4.5.

Answer: About 58.1% in the 2-year bond and 41.9% in the 10-year bond.

Example 2

A portfolio holds a duration-matched barbell and a bullet. The manager expects a large parallel fall in yields and no change in slope. The barbell has higher convexity but a lower yield than the bullet. Which should the manager hold, and what is the main risk?

Show the solution

Both structures have equal duration, so first-order sensitivity to a parallel move is the same.
The view is a large parallel move, so the convexity term ½ × C × (Δy)² matters.
The barbell has higher convexity, so it gains more when yields fall by a large amount.
The cost is the lower yield, which reduces return if yields barely move.
The view also assumes a parallel shift. If the curve steepens, the bullet is favoured and the barbell's advantage shrinks.

Answer: Hold the barbell. It benefits from higher convexity in a large move. The main risk is the yield give-up if yields stay stable, and non-parallel shifts in the curve.

Exam tips

Command words matter. For calculate, show the weight formula and the number. For justify, give the view, the structure and one reason.
Always state that duration is equalised before comparing convexity.
Tie the choice to the client: a liability-driven client may need cash flow matching, not a convexity bet.
Write the direction of the spread in words, such as long-short spread widens, to avoid steepener and flattener mix-ups.
In item sets, read the scenario for whether the move is parallel, slope or curvature before looking at the answer options.

Active Strategies: Bullets, Barbells and Butterflies in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Active Strategies: Bullets, Barbells and Butterflies: frequently asked questions

What is the difference between a barbell and a bullet strategy?

A bullet holds bonds concentrated around one maturity. A barbell holds short and long maturities with little in between. With equal duration, the barbell has higher convexity and usually lower yield.

What is a duration-neutral butterfly trade?

It combines positions in short, middle and long bonds so net duration is about zero. A long butterfly is long the wings and short the body. It expresses a view on curvature, not on the level of rates.

When does a steepener or flattener trade make sense?

Use a steepener when you expect the long-short yield spread to widen and a flattener when you expect it to narrow. Size the legs so duration is neutral if you want a pure slope view.

Why is cash flow matching tighter than duration matching for a barbell?

Cash flow matching aligns bond cash flows with each liability payment. Duration matching only equalises sensitivity, so a barbell can leave convexity and timing gaps that need rebalancing.