Portfolio Construction
Duration Matching
Convexity Advantage
Barbell vs. Bullet Bond Strategy Lab
Construct duration-matched barbell and bullet fixed income portfolios, analyze the barbell convexity premium, model yield giveup drag, and simulate returns across curve steepening, flattening, and butterfly twists.
Duration Matching: w_S D_S + w_L D_L = D_{\text{bullet}} |
Convexity Advantage: \Delta C = (w_S C_S + w_L C_L) - C_{\text{bullet}} > 0 |
Taylor Return: \frac{\Delta P}{P} \approx -D_{\text{mod}} \Delta y + \frac{1}{2} C (\Delta y)^2
Curve Scenarios:
Portfolio Parameters
Y
Y
Y
Initial Yield Curve (YTM, %)
%
%
%
Yield Curve Shift Scenario (Δy, bps)
bps
bps
bps
Barbell Outperformance Regime
Higher convexity cushions downside loss during parallel rate shocks.
BARBELL CONVEXITY
112.4
Advantage: +39.9
BULLET CONVEXITY
72.5
Duration: 7.95 Y (Matched)
BARBELL RETURN
-10.66%
P&L vs Bullet: +0.45%
BULLET RETURN
-11.11%
Initial YTM: 4.25%
Portfolio Weights & Performance Attribution
| Portfolio Component | Weight | Tenor | Mod. Duration | Convexity | YTM | Shock Return |
|---|---|---|---|---|---|---|
| Barbell: Short Leg | 71.4% | 2.0 Y | 1.89 Y | 4.5 | 4.50% | -2.78% |
| Barbell: Long Leg | 28.6% | 30.0 Y | 16.85 Y | 381.2 | 4.60% | -21.02% |
| Barbell Combined | 100.0% | Blended | 7.95 Y | 112.4 | 4.53% | -10.66% |
| Bullet Benchmark | 100.0% | 10.0 Y | 7.95 Y | 72.5 | 4.25% | -11.11% |
Performance curve comparing duration-matched Barbell vs. Bullet returns across parallel interest rate shocks.
Rate Shock vs. Long Leg Tenor on Barbell Excess Return (%)
Rows: Rate Shock (bps), Columns: Long Leg Tenor (Y). Shows how wider barbell maturity dispersion magnifies the convexity spread.
Curve Twist (Long - Short bps) vs. Belly Shock on Barbell Advantage (%)
Rows: Slope Twist (Δy Long - Δy Short bps), Columns: Belly Shock (bps). Steepening favors bullet; flattening favors barbell.
Barbell vs. Bullet Strategy Mastery Self-Assessment
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Frequently Asked Questions: Barbell vs. Bullet Portfolios
A bullet portfolio concentrates its capital in bonds maturing around a single intermediate maturity (such as a 10-year Treasury). A barbell portfolio splits its capital between short-term bonds (e.g., 2-year) and long-term bonds (e.g., 30-year), calibrated so that the overall portfolio has the exact same duration as the bullet portfolio.
Convexity increases exponentially with maturity (approximately proportional to duration squared). Because the barbell holds long-maturity bonds whose convexity is vastly higher than intermediate bonds, the weighted-average convexity of the barbell exceeds that of the bullet (C_barbell > C_bullet), giving the barbell superior curvature protection against large rate swings.
Because markets price in the value of superior convexity, an upward-sloping or normal yield curve typically causes a barbell portfolio to deliver a lower weighted-average running yield compared to an intermediate bullet. This difference in carry is called yield giveup. If interest rates remain stable, the bullet outperforms by earning higher coupon income.
When the yield curve flattens (long rates fall relative to short rates), the barbell tends to outperform because its long-duration leg experiences massive capital gains. When the yield curve steepens (long rates rise relative to short rates), the bullet outperforms because the barbell's long leg suffers heavy duration losses.
Managers favor a barbell when they expect high interest rate volatility, large rate moves in either direction, yield curve flattening, or when short-term liquidity is needed while maintaining long-term duration exposure. Managers choose a bullet when they anticipate stable rates, low volatility, or curve steepening to maximize running coupon carry.