DV01

DV01, short for dollar value of an 01, is a fixed-income risk metric that expresses the dollar change in the price of a bond or bond portfolio resulting from a one-basis-point (0.01 percentage point) change in yield. It is commonly quoted per unit of price or per $100 of face value and is used in hedging and risk management to gauge interest-rate sensitivity.

Calculation and interpretation: For a bond with price P and modified duration D_mod, the approximate price change from a 1 bp yield shift dy = 0.0001 is ΔP ≈ -D_mod × P × dy. Therefore DV01 ≈ -D_mod × P × 0.0001. In practice, some sources compute DV01 by evaluating prices at y and y+0.0001 and taking the difference. Units depend on convention, typically dollars of price per bond or per $100 of par.

Relation to duration and convexity: DV01 is a first-order sensitivity linked to duration. Yields rising generally lower price, so DV01 is usually negative in sign, though practitioners often report the absolute magnitude. For larger moves, convexity accounts for curvature: ΔP ≈ -D_mod × P × dy + 0.5 × Convexity × P × dy^2.

Applications and limitations: Across a portfolio, DV01 is the sum of individual DV01s and is used to hedge risk, for example by balancing DV01 with futures or swaps. Limitations include the assumption of parallel yield changes and small moves; DV01 is less accurate for large, non-parallel shifts or for instruments with complex cash flows.

Example: A bond priced at 102 with D_mod = 6 would have DV01 ≈ -6 × 102 × 0.0001 ≈ -0.0612, meaning about a 6-cent price drop for a 1 bp increase in yield.