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description: "The carry factor strategy buys bonds with the highest carry — the return earned as a bond rolls down the yield curve — combining bond yield income with the roll-down return from the yield curve's slope."
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tags: [fixed-income, factor, carry, roll-down, yield-curve]
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---
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# Carry Factor
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**Section**: 5.11 | **Asset Class**: Fixed Income | **Type**: Factor / Carry
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## Overview
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Carry in fixed income is the return from holding a bond as it "rolls down" the yield curve toward maturity. If the term structure is upward-sloping and stable, a bond's yield declines as its maturity shortens, causing a price appreciation on top of the coupon income. The carry factor strategy buys bonds in the top decile by carry and sells those in the bottom decile.
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## Construction / Mechanics
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**Carry** over horizon Δt for a bond with current maturity T:
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```
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C(t, t+Δt, T) = [P(t+Δt, T) - P(t, T)] / P(t, T) (413)
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```
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Under the assumption that the yield curve shape is constant (R(t,T) = f(T-t) only), the yield at t+Δt is R(t+Δt, T) = R(t, T-Δt), giving:
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```
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C(t, t+Δt, T) = R(t,T)·Δt + C_roll(t, t+Δt, T) (414)
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```
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Two components:
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1. **Yield income**: R(t,T)·Δt — the bond's current yield times the holding period
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2. **Roll-down return**:
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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 the price appreciation as the bond shortens in maturity by Δt along a static yield curve, estimated using modified duration.
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**Portfolio construction**: rank all bonds by C(t, t+Δt, T); long top decile, short bottom decile (zero-cost version).
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## Payoff / Return Profile
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- Earns yield income plus roll-down return when the yield curve is upward-sloping and stable.
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- Roll-down return is greatest in the steepest segments of the yield curve.
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- Underperforms or loses when the yield curve flattens, inverts, or shifts upward unexpectedly.
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## Key Parameters / Signals
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- R(t,T): current yield (income component)
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- ModD(t,T): modified duration (scales the roll-down component)
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- R(t, T-Δt) - R(t, T): slope of the yield curve at maturity T (steeper = more roll-down)
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- Δt: carry horizon (e.g., 1 month)
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## Variations
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- Long-only: buy top decile by carry (no short sales required).
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- Cross-asset carry: extend the same framework to other fixed income markets (government bonds, credit, etc.).
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## Notes
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- The static yield curve assumption simplifies computation; actual carry will differ if the curve shifts.
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- For financed portfolios, R(t,T) is replaced by R(t,T) - r_f (excess yield over the risk-free rate) in the income component, but this does not affect portfolio weights.
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- High-carry bonds tend to have longer maturities in an upward-sloping curve environment, so the carry factor has implicit duration exposure.
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- Carry and roll-down are sometimes separated as distinct signals; roll-down alone favors bonds in the steepest curve segments regardless of yield level.
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