Dollar Duration
Dollar Duration
Modified duration times price: the dollar change in a bond's price for a one-unit (100 percentage point) change in yield. Scale by the actual yield move to get the price move; DV01 is this divided by 10,000.
When to use: Use when hedging or sizing positions in dollars rather than percentages, and to compare rate exposure across bonds of different prices.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| DollarDur | Dollar Duration | Price change per unit change in yield | $ |
| ModDur | Modified Duration | Price sensitivity coefficient: −(1/P)(dP/dy), in years | years |
| P | Bond Price | Market price of the bond per face value unit | $ |
Real-Life Examples
Example 1: Discount Bond
A bond priced at $925.60 with a modified duration of 7.5 years.
Given
Step-by-Step
A 1% (0.01) rise in yield moves the price by about 0.01 × $6,942 = $69.42, or $0.69 per basis point (the DV01).
Example 2: Premium Bond
A bond priced at $1,050 with a modified duration of 4.2 years.
Given
Step-by-Step
Despite the higher price, the shorter duration makes this bond less exposed in dollar terms than the first: $44.10 per 1% move versus $69.42.
Frequently Asked Questions
DV01 is the dollar price change for a one-basis-point move, so DV01 = dollar duration / 10,000.
Two positions with equal dollar duration have equal dollar exposure to a parallel rate move regardless of their prices or sizes, which is what a hedge has to match.