Introductory Context
"Duration-neutral three-legged sovereign bond butterfly exploiting mean-reverting curvature in the Indian 2Y-5Y-10Y G-Sec yield curve."
Yield Curve Curvature: The Bond Butterfly Anomaly
While level (parallel shifts) and slope (steepening/flattening) account for over 90% of yield curve movements, the remaining variance is driven by Curvature: local humps or valleys where intermediate maturities (e.g. 5-year G-Secs) become rich or cheap relative to the short (2-year) and long (10-year) wings of the curve.
The Dollar Duration Neutral Bond Butterfly constructs a three-legged sovereign portfolio (Short Wing, Body, Long Wing) engineered to be completely immune to both parallel yield shifts (zero DV01) and curve slope tilts (zero slope duration), isolating pure mean-reverting yield curvature alpha.
• The Bond Butterfly Rule in One Sentence
Calculate the Butterfly Spread (2 × Yield5Y - Yield2Y - Yield10Y); when curvature is abnormally wide (> +1.5σ), sell the rich 5Y body and buy the 2Y and 10Y wings in exact dollar duration and slope-neutral weighting.
Mathematical Formulation: DV01 & Slope Neutrality
Let y1, y2, y3 be the yields of the Short Wing (2Y), Body (5Y), and Long Wing (10Y) Government of India (GoI) benchmark bonds. The raw butterfly spread is:
To ensure perfect duration immunity, position notionals (N1, N2, N3) must satisfy two simultaneous linear constraints:
- Long Butterfly (Cheap Body): Buy 5Y Body, Sell 2Y Wing, Sell 10Y Wing (entered when 5Y yield is abnormally elevated above the wing chord).
- Short Butterfly (Rich Body): Sell 5Y Body, Buy 2Y Wing, Buy 10Y Wing (entered when 5Y yield is depressed due to structural institutional buying).
- Indian Market Venue: Executed on RBI NDS-OM and CCIL interbank sovereign markets using benchmark 2Y, 5Y, and 10Y G-Secs.