Bond Barbell vs. Bullet Calculator
Enter the short, long, and intermediate bond terms to solve the barbell weights that match the bullet bond duration. The result shows allocations, executable bond counts, convexity, and exact price returns for parallel rate shocks.
Duration-matched allocation57.16% short / 42.84% long
- Short-bond allocation
- $57,159.89
- Long-bond allocation
- $42,840.11
- Estimated whole bonds to buy
- 57 short and 42 long
- Residual cash
- $1,539.33
- Barbell modified duration
- 4.42 years
- Bullet modified duration
- 4.42 years
- Executable duration gap
- -0.01 years
- Annual coupon income
- $4,450.24 barbell vs. $4,550.10 bullet
- Barbell convexity
- 34.17
- Bullet convexity
- 22.97
- Price return if rates rise
- Barbell -4.26% vs. bullet -4.31%
- Price return if rates fall
- Barbell 4.6% vs. bullet 4.54%
- Convexity advantage
- Barbell: it loses less when rates rise and gains more when rates fall.
Bond math by component
| Component | Price | Modified duration | Convexity | Annual coupon |
|---|---|---|---|---|
| Short bond | $990.54 | 1.9 years | 4.6 | $40.00 |
| Long bond | $1,000.00 | 7.79 years | 73.63 | $50.00 |
| Bullet bond | $988.99 | 4.42 years | 22.97 | $45.00 |
Assumes fixed-rate, option-free bonds with prices based only on the entered yield, coupon, maturity, frequency, and face value.
Odd final coupon periods are simplified by placing the final coupon and principal at the exact entered maturity.
How to use this calculator
- Enter the amount to invest, face value, and coupon frequency shared by the comparison.
- Enter the maturity, coupon rate, and yield for the short and long barbell bonds.
- Enter the maturity, coupon rate, and yield for the bullet bond.
- Choose the parallel rate shock, then compare allocations, duration, convexity, and shocked price returns.
How the duration-matched barbell is calculated
A bond barbell holds a shorter bond and a longer bond. A bullet strategy puts the same market value into one intermediate bond. This calculator first prices all three bonds from their coupon, maturity, yield, face value, and coupon frequency. It then solves the short-bond and long-bond market-value weights that make the barbell's modified duration equal the bullet bond's modified duration.
For each bond, let F be face value, m be coupon payments per year, T be maturity in years, c be the annual coupon rate, y be yield to maturity, r = y / m, and C = F * c / m. The price is:
P = sum(C / (1 + r)^t) + F / (1 + r)^N
The duration calculation weights each discounted cash flow by its payment time. Macaulay duration is divided by 1 + r to get modified duration. Convexity is calculated from the same discounted cash flows as sum(CF * t * (t + 1) / (1 + r)^(t + 2)) / (P * m^2).
Once the short, long, and bullet modified durations are known, the short-bond weight is:
wS = (DModL - DModB) / (DModL - DModS)
The long-bond weight is 1 - wS. If the bullet duration is not between the short and long durations, an unlevered duration-matched mix cannot be solved from those two bonds.
What the comparison shows
The calculator reports the theoretical market-value allocation and then rounds each side down to whole bonds using the calculated full price. Residual cash is the amount left after those whole-bond purchases. The executable duration gap shows how much whole-bond rounding moved the actual portfolio away from the bullet bond's modified duration.
The price-shock rows reprice every component bond after adding and subtracting the selected parallel yield shock. They do not use the duration approximation. This matters because a barbell often has more convexity than a bullet with the same duration, so its exact price response can be different for larger moves.
What this calculator leaves out
The model assumes fixed-rate, option-free bonds with no default. It excludes accrued interest, bid-ask spreads, commissions, taxes, settlement calendars, day-count conventions, call features, sinking funds, credit migration, and coupon reinvestment. Odd final coupon periods are simplified by placing the final coupon and principal at the entered maturity rather than applying market-specific stub-period rules.
Worked example
With the default entries, the $100,000 portfolio is matched to a five-year bullet bond. The calculator prices the two-year short bond at about $990.54, the ten-year long bond at about $1,000.00, and the five-year bullet at about $988.99.
The solved barbell allocation is about 57.16% short bonds and 42.84% long bonds, or roughly $57,160 in the short bond and $42,840 in the long bond. Rounded to whole bonds, that buys 57 short bonds and 42 long bonds, leaving about $1,539 in residual cash.
The theoretical barbell modified duration matches the bullet at about 4.42 years. Its convexity is about 34.17 versus 22.97 for the bullet. For a 100 bp parallel rate rise, the exact price return is about -4.26% for the barbell and -4.31% for the bullet; for a 100 bp fall, it is about 4.60% for the barbell and 4.54% for the bullet.
Common questions
What is the difference between a barbell and a bullet bond strategy?
A barbell strategy splits money between shorter and longer maturities. A bullet strategy concentrates the money in one intermediate maturity. This calculator compares them after matching modified duration, so the rate sensitivity is similar at the starting point.
Why should the portfolios be duration matched?
Duration matching makes the comparison focus on shape and convexity rather than simply comparing a short portfolio with a long one. Without matching duration, the portfolio with the longer duration would usually show larger price moves for ordinary rate shocks.
Why does a barbell usually have more convexity?
Longer cash flows add convexity quickly, and a barbell deliberately includes a long bond while offsetting its duration with a short bond. That mix can produce more curvature than a single intermediate bond with the same modified duration.
How do whole-bond purchase increments affect the match?
The duration match is solved with fractional market-value weights. Real purchases may need whole bonds, so the rounded portfolio can leave residual cash and a duration gap. The executable duration gap shows the size and direction of that rounding effect.
Does higher convexity always mean better performance?
No. Convexity helps for parallel rate moves when duration is closely matched, but yield differences, curve steepening or flattening, credit changes, taxes, transaction costs, and reinvestment returns can dominate the realized result.