DV01 hedging

Immunization matches a whole portfolio to a liability; hedging neutralizes one position's rate risk using a second, more liquid or more convenient instrument, without necessarily selling the first. The arithmetic is a direct application of PVBP: pick a hedge instrument whose own modified duration and price you know (or, for a swap, whose PVBP-per-unit-notional the market simply quotes), and size the hedge so the two PVBPs offset:

Hedge notional (face value, or swap notional) such that PVBP(hedge) = PVBP(position)

Worked Example 2 hedges a $50 million 10-year UST position with a 5-year UST note, computing the exact face value of the 5-year note required. The same logic works with an interest-rate swap instead of a second bond: a desk holding a G-Sec can lay a duration overlay on top of it using an INR OIS referencing the overnight MIBOR fixing, without selling the bond at all, pay fixed on an OIS notional sized so the swap's DV01 offsets however much of the bond's DV01 you want to shed (Worked Example 7). This module teaches you to size the hedge from a given hedge-instrument DV01; DV1.01 teaches you to price that swap or future from scratch and derive its DV01 from first principles. And here is a detail that should reassure you the bump-and-reprice method is not a classroom simplification: CCIL's own published PVBP methodology for INR OIS computes it exactly this way, reprice at the curve +1bp, reprice at −1bp, average the two, the identical arithmetic as this module's effective-duration formula, run on real trades every single day.

{
  "skill": "Scaling a duration/KRD/hedge calculation from one bond to a whole portfolio without losing the by-hand check",
  "use": "Have an AI assistant draft the vectorized version of this module's per-bond formulas — a pandas/numpy routine, or a spreadsheet array formula — that runs across an entire portfolio of bonds at once, so you can see the KRD profile and PVBP of a real book rather than a single position, then validate its portfolio-level output against a hand-computed single-bond case from this module.",
  "tools": ["Code-capable chat assistants with code execution", "Spreadsheet AI add-ins for array/LAMBDA formulas", "Open-source bond-math libraries (e.g., QuantLib) an assistant can wire up for you"],
  "prompt": "Take the single-bond bond_risk function from before and vectorize it with pandas/numpy to run over a DataFrame of bonds (coupon, ytm, years, freq, face, position size per row). Return each bond's modified duration, convexity, and PVBP, plus the portfolio's total PVBP and a simple 2Y/5Y/10Y key-rate duration profile, using each bond's own yield as its key-rate proxy exactly as this module does.",
  "verify": "Portfolio-scale automation multiplies a single silent error by every row in the book. Before trusting the portfolio PVBP or KRD profile, reproduce ONE row by hand — or with this module's own closed-form functions — and confirm it matches to the decimal; only then trust the vectorized run across the rest of the book. This is the by-hand skill this module gates, applied at scale, never replaced by the scale.",
  "diy": "You must already be able to compute a single bond's modified duration, convexity, and PVBP correctly by hand, and already understand why key-rate durations sum to the total effective duration, before vectorizing anything — vectorizing a method you do not yet trust just produces a wrong answer faster and across more positions.",
  "market": "US"
}