Tim Olson
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44 lines
2.6 KiB
Markdown
44 lines
2.6 KiB
Markdown
---
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description: "A ladder portfolio holds bonds spread evenly across n equidistant maturities to diversify interest rate and reinvestment risk while maintaining an approximately constant duration through systematic roll-down."
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tags: [fixed-income, duration, ladder, diversification, yield-curve]
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---
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# Ladders
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**Section**: 5.4 | **Asset Class**: Fixed Income | **Type**: Duration-Targeting / Diversification
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## Overview
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A ladder holds bonds with (roughly) equal capital allocations across n different maturities T_i (i = 1,...,n), where maturities are equidistant: T_{i+1} = T_i + δ. The strategy maintains an approximately constant duration by selling shorter-maturity bonds as they near maturity and replacing them with new longer-maturity bonds. It diversifies both interest rate risk and reinvestment risk.
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## Construction / Mechanics
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- Allocate roughly equal capital to each rung T_i, i = 1,...,n (n is sizable, e.g., n = 10).
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- Equidistant maturities: T_{i+1} = T_i + δ.
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- Average (effective) maturity of the portfolio:
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```
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T = (1/n) Σ_{i=1}^n T_i (395)
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```
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- As the shortest rung approaches maturity, sell it and purchase a new bond at the longest maturity, maintaining the ladder structure.
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- Also generates regular income from coupon payments across all rungs.
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## Payoff / Return Profile
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- Higher average maturity T → higher income (upward-sloping yield curve), but also higher interest rate risk.
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- Rolling shorter bonds into longer bonds continuously captures roll-down return.
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- Diversification across maturities smooths the impact of rate moves: if rates rise, maturing short bonds are reinvested at higher rates; if rates fall, longer bonds appreciate.
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## Key Parameters / Signals
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- n: number of rungs (more rungs = more diversification)
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- δ: spacing between maturities
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- T (average maturity): determines the income/risk trade-off
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- Equal capital allocation per rung: ensures no concentration at any maturity
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## Variations
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- Unequal allocations tilting toward shorter or longer maturities (incorporating a partial bullet or barbell bias).
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## Notes
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- The ladder avoids the concentration risk of bullets and barbells, making it suitable for investors uncertain about the rate environment.
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- The constant-duration property is approximate; exact duration changes as bonds age and are replaced.
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- Reinvestment risk is diversified: proceeds from maturing bonds are spread across the yield curve over time rather than all reinvested at once.
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- Transaction costs from regular rolling must be weighed against the diversification and roll-down benefits.
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