PVBP Hedge Ratios Between Bonds

Suppose a desk owns $10 million face of a 10-year bond and wants to hedge its rate risk using a 5-year bond. Shorting $10 million face of the 5-year is the wrong hedge — face amount has nothing to do with how much each bond's price actually moves per basis point of yield. What has to match is dollar sensitivity, not notional, and the tool for that match is the price value of a basis point (PVBP), also called DV01.

Building the hedge ratio

PVBP is the dollar price change of a position for a one-basis-point (0.01%) move in yield:

$$PVBP = -\frac{D_{mod} \times P \times 0.0001}{1}$$

In words: modified duration times price gives percentage sensitivity per unit yield change; multiplying by 0.0001 converts that into dollars per one-basis-point move, and the position size scales the whole thing up to the actual holding.

To hedge, the hedge ratio $HR$ is simply the ratio of the position's total PVBP to the hedging instrument's PVBP per unit (per bond, per contract, or per $1 million face):

$$HR = \frac{PVBP_{position}}{PVBP_{hedge, per unit}}$$

In words: divide how many dollars per basis point you need to offset by how many dollars per basis point one unit of the hedge provides — the result is how many units of the hedge to trade.

Worked example

A desk holds $10 million face of a 10-year bond with a PVBP of $920 per $1 million face (so $9,200 total). It wants to hedge using a 5-year bond with a PVBP of $460 per $1 million face.

1. Total position PVBP: $920 × 10 = $9,200.
2. Hedge PVBP per $1 million face: $460.
3. Hedge ratio: $HR = 9200 / 460 = 20$, meaning the desk needs $20 million face of the 5-year bond, sold short, to offset the position.
4. Check: $20 million × $460 per $1 million = $9,200 — matches the position's PVBP exactly, so a 1 bp parallel move changes both legs by the same $9,200, in opposite directions, leaving the hedged book flat.

What this means in practice

PVBP hedge ratios are the everyday tool for relative-value and curve trades: hedging a corporate bond with Treasury futures, hedging one point on the curve with another, or flattening a swap book's rate exposure. Because PVBP already bakes in each instrument's price and duration, it lets a desk hedge across bonds with completely different coupons, maturities, and prices using one consistent unit — dollars per basis point.