How do I compute the duration effect in fixed income attribution?

Question

AcadiFi · Accepted Answer

The duration effect captures return attributable to the portfolio's interest rate sensitivity deviation from the benchmark, assuming parallel yield shifts.

Halcyon Bond Fund duration effect:
- Portfolio duration: 6.2 years
- Benchmark duration: 5.8 years
- Active duration bet: +0.4 years (long duration)
- Yield change (parallel): -40 bps
- Duration effect = -(Portfolio Duration - Benchmark Duration) x Yield Change
- Duration effect = -(6.2 - 5.8) x (-0.40%) = -0.4 x -0.40% = +0.16% or 16 bps

The manager correctly added duration before a rally — this bet earned 16bps vs the benchmark.

Formula variations:
- Simple: -ΔD x Δy (captures first-order effect)
- With convexity: -ΔD x Δy + 0.5 x ΔC x (Δy)^2
- Key-rate duration version: sum of key-rate contributions for non-parallel shifts

```mermaid
flowchart TD
    A[Active Duration +0.4] --> B[Parallel Shift -40bps]
    B --> C[Duration Effect +16bps]
    A --> D[Convexity Bet?]
    D --> E[Convexity Effect]
    C --> F[Total Active Return]
    E --> F
```

Decomposition levels in fixed income attribution:
1. Duration/interest rate effect
2. Yield curve effect (slope/curvature changes)
3. Spread effect (credit, swap spreads)
4. Currency effect (for multi-currency portfolios)
5. Selection effect (security-specific alpha)
6. Residual

Caveats:
- Duration effect formula assumes parallel shift — actual curves rarely move parallel
- For non-parallel moves, duration effect must decompose into level vs twist components
- Convexity effect can dominate in volatile environments (particularly for callable/MBS)
- Spread duration separate from treasury duration for credit portfolios

Practical application: Halcyon's +16bps duration effect is one component; total active return might be -5bps if negative selection or curve effects offset. The full attribution story requires all six components to explain the alpha/beta breakdown convincingly for investor reporting.

How do I compute the duration effect in fixed income attribution?

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