---
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."
tags: [fixed-income, duration, ladder, diversification, yield-curve]
---

# Ladders

**Section**: 5.4 | **Asset Class**: Fixed Income | **Type**: Duration-Targeting / Diversification

## Overview
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.

## Construction / Mechanics
- Allocate roughly equal capital to each rung T_i, i = 1,...,n (n is sizable, e.g., n = 10).
- Equidistant maturities: T_{i+1} = T_i + δ.
- Average (effective) maturity of the portfolio:

```
T = (1/n) Σ_{i=1}^n T_i                                             (395)
```

- As the shortest rung approaches maturity, sell it and purchase a new bond at the longest maturity, maintaining the ladder structure.
- Also generates regular income from coupon payments across all rungs.

## Payoff / Return Profile
- Higher average maturity T → higher income (upward-sloping yield curve), but also higher interest rate risk.
- Rolling shorter bonds into longer bonds continuously captures roll-down return.
- 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.

## Key Parameters / Signals
- n: number of rungs (more rungs = more diversification)
- δ: spacing between maturities
- T (average maturity): determines the income/risk trade-off
- Equal capital allocation per rung: ensures no concentration at any maturity

## Variations
- Unequal allocations tilting toward shorter or longer maturities (incorporating a partial bullet or barbell bias).

## Notes
- The ladder avoids the concentration risk of bullets and barbells, making it suitable for investors uncertain about the rate environment.
- The constant-duration property is approximate; exact duration changes as bonds age and are replaced.
- Reinvestment risk is diversified: proceeds from maturing bonds are spread across the yield curve over time rather than all reinvested at once.
- Transaction costs from regular rolling must be weighed against the diversification and roll-down benefits.