Curve Trading: Steepeners, Butterflies, and What PCA Reveals
Fixed Income Trading and Risk Management by Alexander Düring (ISBN 9781119756354)
Previous: Trading Principles | Next: Bond Trading
Curve trading sounds like one idea: bet on shape changes. Chapter 31 shows how many distinct bets hide inside that phrase, and how carry and bond idiosyncrasies complicate every one.
Two warnings upfront
- You implement curve views with specific bonds or futures. Individual issues can diverge from the spline segment you had in mind.
- Carry differs by maturity. A steepening view must be measured against the forward curve, not spot. A steepener can win with an unchanged spot curve because forwards are often flatter than spot.
The menu of curve trades
On four points A, B, C, D along a curve:
| Legs | Name | View |
|---|---|---|
| 1 | Outright long/short | Level up/down |
| 2 | Steepener / flattener | Short vs long yields diverge |
| 3 | Butterfly | Bullet vs wings |
| 4 | Condor | Inner spread vs outer spread |
An n-leg trade needs n equations: one sizes risk (PVBP target), the rest neutralize lower-order moves. A butterfly hedges level and steepening so you are pure curvature.
Higher-order moves are smaller in size but trades cost more legs. Lower expected move, higher transaction cost. People still trade them when they have supply/auction information or when hedging creates implicit butterflies.
Sizing and benchmark pitfalls
Steepener: N₁ × PVBP₁ = −N₂ × PVBP₂, with risk R setting notionals. Hedge ratios drift as PVBPs age; forward PVBP matching helps for the intended holding period.
Benchmark spread charts lie when benchmarks roll. Düring’s German example: July 2018 OBL benchmark switch made 2Y-5Y look steeper and 5Y-10Y flatter without any bond price move. Use spline yields for analysis; trade real bonds for execution.
Bond vs swap butterfly quotes differ by sign convention (bullet minus average wings vs twice bullet minus wing sum).
Japan’s kinked 10Y-30Y relationship
Pre-2016 data shows a slope break around 0.75% / 2% driven by domestic life insurers with yield targets supporting the long end in sell-offs. Linear steepener/flattener can behave option-like near the pivot. Post-BoJ QE, operational policy dominates; the old pattern is history for trading purposes.
PCA and intrinsic curve moves
Instead of imposing steepener/flattener labels, PCA on daily yield changes extracts empirical factors. On US and German splines (2014-2018):
- Factor 1: Parallel level (justifies duration as risk measure)
- Factor 2: Slope uncorrelated with factor 1 (bear/bull steepen/flatten)
- Factor 3: Curvature (bullet vs wings)
Residual volatility at 10Y falls as you remove more factors. Factor 1 correlates across US and Germany but regimes shift (ECB QE vs Fed taper changed the relationship).
Factor 3 correlates weakly with VXTYN vol; Vasicek k parameter does not map cleanly to PCA curvature because model parameters correlate and humps move.
Nelson-Siegel β parameters could substitute for PCA factors but λ parameters are volatile and βs are correlated, making hedge mapping awkward.
Why outrights are the hardest alpha
Everyone has a rate view. Higher-order trades often tie to auctions, rolls, or hedging flows where specialized information matters more.
Chapter 31 connects trading craft to the statistics later in the book. Curve trades are not “pick two bonds and hope.” They are systems of equations plus forward carry plus awareness that your spline is a model, not a tradable instrument.