What is bond duration?
A plain-language guide to Macaulay duration, modified duration, convexity and DV01, and how they measure a bond's interest rate risk.
Duration in one sentence
Duration measures how long, on average, you wait to be repaid by a bond, and by extension how much its price will move when interest rates change. A bond with a duration of seven will lose roughly seven percent of its value if yields rise by one percentage point, and gain roughly seven percent if yields fall by the same amount.
Macaulay versus modified
Macaulay duration is a time, measured in years. It weights each cash flow date by the share of the bond's price that flow represents. Modified duration rescales that number into a price sensitivity by dividing by one plus the periodic yield. In practice modified duration is the figure traders quote when they talk about a bond moving a certain percent per one percent change in yield.
Why convexity matters
Because duration is a straight-line estimate, it understates the gain when yields fall and overstates the loss when yields rise. Convexity is the second-order correction that captures the curve. For most plain bonds convexity is positive, which is good for the holder: it cushions losses and amplifies gains. Long, low-coupon bonds have the most convexity.
Putting it to work with DV01
DV01 turns duration into dollars. It tells you how much one bond, or a whole portfolio, gains or loses for a single basis point move in yield. Risk desks add up the DV01 across positions to see their total exposure and to work out how many bonds or futures to trade to hedge it.