Tim Olson
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53 lines
3.0 KiB
Markdown
53 lines
3.0 KiB
Markdown
---
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description: "Rolling down the yield curve buys long- or medium-term bonds in the steepest segment of the yield curve and holds them while they appreciate as they shorten in maturity, then reinvests proceeds into new steepest-segment bonds."
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tags: [fixed-income, roll-down, yield-curve, carry, duration]
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---
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# Rolling Down the Yield Curve
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**Section**: 5.12 | **Asset Class**: Fixed Income | **Type**: Carry / Roll-Down
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## Overview
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The rolling down the yield curve strategy captures the roll-down component C_roll of bond returns by purchasing bonds in the steepest segments of the yield curve and holding them while their maturity shortens, causing price appreciation. Bonds are sold before maturity and the proceeds reinvested in new long/medium-term bonds from the same steep segment.
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## Construction / Mechanics
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The roll-down return over horizon Δt:
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```
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C_roll(t, t+Δt, T) ≈ -ModD(t,T) · [R(t, T-Δt) - R(t, T)] (415)
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```
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This is maximized when:
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- **ModD(t,T)** is large (longer-maturity bonds have higher duration)
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- **R(t, T-Δt) - R(t, T) < 0** (yield declines as maturity shortens — upward-sloping curve)
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- The magnitude |R(t, T-Δt) - R(t, T)| is large (steep segment of the curve)
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**Strategy mechanics**:
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1. Identify the steepest segment(s) of the yield curve.
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2. Buy long- or medium-term bonds from those segments.
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3. Hold while they "roll down" the curve (their maturity shrinks and yield declines).
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4. Sell before maturity approaches (before they enter a flatter/shorter segment).
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5. Reinvest proceeds into new long/medium-term bonds from the steep segment.
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## Payoff / Return Profile
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- Earns roll-down return C_roll in addition to yield income R(t,T)·Δt.
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- Total carry C(t, t+Δt, T) = R(t,T)·Δt + C_roll(t, t+Δt, T).
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- Profits maximized in steeply upward-sloping yield curves.
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- Loses money when the yield curve flattens, inverts, or when long-end yields rise (parallel upward shift).
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## Key Parameters / Signals
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- Yield curve slope: identifies which segments offer the most roll-down return
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- Modified duration: amplifies the roll-down return
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- Holding horizon Δt: determines how far down the curve the bond rolls before sale
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- Curve stability: strategy depends on curve shape remaining approximately stable
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## Variations
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- Pure roll-down: focus exclusively on C_roll, ignoring yield income (selects steepest curve segments regardless of absolute yield level).
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- Combined carry + roll: as in the carry factor strategy (5.11), which uses total C as the signal.
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## Notes
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- The yield curve must be upward-sloping for roll-down to be positive; in a flat or inverted curve the roll-down may be zero or negative.
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- Transaction costs from repeated roll-overs must be weighed against the roll-down income.
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- The strategy has implicit duration risk: long/medium bonds lose value in a rising rate environment, which can more than offset the roll-down gain.
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- Steepest curve segments often occur at the short to medium end (e.g., 2-10 year part of the Treasury curve) and can shift over time with monetary policy.
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