How do I manage curve risk beyond parallel-shift duration?

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AcadiFi · Accepted Answer

Duration captures parallel-shift risk only. Yield curves rarely move in parallel — they steepen, flatten, bull-steepen, bear-flatten, hump, and twist. Two portfolios with identical parallel duration can have vastly different sensitivities to non-parallel moves. **Key types of non-parallel moves**: 1. **Steepening**: Long rates rise more than short (bear-steepen) or short rates fall more than long (bull-steepen). 2. **Flattening**: Opposite. 3. **Butterfly / curvature**: Belly (intermediate) moves opposite to wings. 'Body sell-off' or 'belly rally'. **Measurement: Key Rate Duration (KRD)** KRD for a key point (say 5yr) = sensitivity of portfolio to a 1bp shift in the 5yr rate holding other key points fixed, with linear interpolation between. Typical key points: 3m, 2yr, 5yr, 10yr, 20yr, 30yr. Sum of KRDs ≈ parallel duration. For your portfolio crushed by 2s10s steepening of 40bps: the portfolio was likely long duration concentrated at the long end (barbell or bullet at 10yr+) so the steepening (10yr selling off more than 2yr) caused larger losses than parallel duration predicted. ```mermaid flowchart TD A[Curve Move] --> B{Shape Change?} B -->|Parallel| C[Duration
Sufficient] B -->|Non-Parallel| D[Need KRDs] D --> E[2yr KRD] D --> F[5yr KRD] D --> G[10yr KRD] D --> H[30yr KRD] ``` **Attribution example**: Parallel duration 7, but KRDs: 2yr=0.5, 5yr=1.0, 10yr=2.5, 30yr=3.0 (sums to 7). A steepening where 2s rally 10bps and 10s sell off 30bps: - 2yr effect: +0.5 × 0.10% = +0.05% - 10yr effect: −2.5 × 0.30% = −0.75% - Net: −0.70% A parallel-shift measure would have predicted zero P&L (since ave yield ≈ unchanged). The KRD framework reveals the real risk. **Hedging curve risk**: Use multiple hedges at different maturities. To immunize against both parallel and 2s10s moves, you need at least two hedging instruments with KRDs at those points. Regression-based 'curve trades' often use 3 futures (2, 10, 30) weighted to zero out duration while expressing a view on the shape. **Principal Component Analysis (PCA)**: In practice, ~95% of curve variance is captured by three factors: level (parallel), slope (steepening/flattening), and curvature (butterfly). Sophisticated shops hedge level and slope separately, accepting curvature residual. **Lesson for your portfolio**: Go back and compute KRDs. Match not just parallel duration to the benchmark but also KRDs at the major nodes. Alternatively, specify a curve-beta target and hedge slope risk explicitly.

How do I manage curve risk beyond parallel-shift duration?

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