Interest-rate risk
Every fixed-rate bond loses value when market yields rise. The size of the loss depends mainly on the time remaining to maturity and the size of the coupon.
Macaulay duration
Macaulay duration is the weighted average time, in years, until the bond's cash flows are received, weighted by their present values. A zero-coupon bond's duration equals its maturity; a coupon bond's duration is shorter than its maturity.
Modified duration
Modified duration converts that into price sensitivity:
A bond with a modified duration of 7 loses about 7% of its value if its yield rises by one percentage point, and gains about 7% if it falls by one percentage point.
DV01
Professional investors often use DV01 (dollar value of one basis point): the change in a position's value for a 0.01% move in yield. It allows risk to be added across bonds and hedged with swaps or futures.
Convexity
Duration is a straight-line approximation. Convexity measures the curvature of the price–yield relationship: for ordinary bonds prices rise more when yields fall than they drop when yields rise by the same amount. Callable bonds can have negative convexity.
Practical points
- Longer maturity means higher duration and more interest-rate risk.
- Lower coupon means higher duration.
- Floating-rate notes have very low interest-rate duration because their coupons reset.
- Holding a bond to maturity removes price risk from rate moves but not the credit risk of the issuer.