Every bond investor learns the first rule quickly: when interest rates rise, existing bonds fall in price. The rule that separates a beginner from someone who understands fixed income is the second one — by how much? The answer is duration, and the refinement that makes it accurate for big moves is convexity.
Modified duration: the price move per 1% in yield
The most practical measure, modified duration, is simply the approximate percentage a bond’s price changes for a 1% change in yield. A modified duration of 4 means a 1% rise in yields knocks about 4% off the price, and a 1% fall adds about 4%. It compresses a bond’s entire interest-rate risk into one number — and crucially, it depends on far more than maturity: a bond’s coupon and yield shape it too.
Set the coupon, maturity and yield, and read the modified duration — then change the yield and watch the price move. Lengthen the maturity or cut the coupon and see duration, and the swing, grow.
Convexity: the curve duration misses
Duration draws a straight line, but the real relationship between price and yield is a curve. For small yield changes the line and the curve agree; for large ones they diverge — and always in your favour. When yields fall, a bond’s price rises more than duration predicts; when yields rise, it falls less. That helpful curvature is convexity, and a more convex bond is worth a little extra because it cushions losses and amplifies gains beyond the duration estimate.
Two government bonds have no default risk. Bond A has a modified duration of 2; Bond B has 9. Rates rise sharply. What happens?
Sab jaante hain rate badhne pe bond ka bhaav girta hai — par kitna? Yeh duration batata hai. Modified duration 4 matlab yield 1% badha toh price ~4% gira. Lambi maturity aur kam coupon = zyada duration = zyada jhatka, kyunki paisa door future mein phasa hota hai. Isiliye "safe" gilt debt fund bhi rate badhne pe nuksaan de sakta hai — default risk nahi, duration ki wajah se. Bade move pe duration seedhi line maanta hai; asli curve (convexity) hamesha aapke haq mein mudta hai.
- Modified duration is the approximate % price change for a 1% change in yield.
- Longer maturity and lower coupons both raise duration and interest-rate risk.
- Duration, not maturity alone, is the true measure of a bond’s price sensitivity.
- Convexity corrects duration’s straight-line estimate for large moves, always in the holder’s favour.
- Debt funds lose money when rates rise via duration, even with zero default risk — check their duration.
Mark it done to track your progress through the curriculum.
Common questions
Short, direct answers to what people ask about this topic.
- what is bond duration
- Bond duration measures how sensitive a bond’s price is to a change in interest rates, expressed in years. The most useful form, modified duration, tells you the approximate percentage change in a bond’s price for a 1% change in yield: a modified duration of 4 means the price falls about 4% if yields rise 1%, and rises about 4% if yields fall 1%. It captures a bond’s interest-rate risk in a single number, which is why it matters far more than a bond’s maturity alone when you are judging how much its price can swing.
- why do longer-maturity bonds have higher duration
- Because more of their cash is locked up further in the future, where a change in the discount rate has a bigger compounding effect. A long bond returns most of its value years from now, so re-pricing all those distant cash flows at a new yield moves the price a lot; a short bond returns your money soon, giving rates little time to bite. Lower coupons work the same way — they push more of the return to the final principal payment — so long-dated, low-coupon bonds have the highest duration and the most price sensitivity to rates.
- what is the difference between duration and convexity
- Duration is a straight-line estimate of how a bond’s price moves with yields, while convexity is the correction for the fact that the true relationship is curved, not straight. For small yield changes duration alone is accurate, but for large moves it becomes wrong, and always in the bondholder’s favour: prices rise more than duration predicts when yields fall, and fall less than predicted when yields rise. Convexity measures that curvature, so a high-convexity bond is more attractive because it cushions losses and amplifies gains relative to the duration estimate.
- why do debt funds lose money when interest rates rise
- Because a debt fund holds bonds, and existing bonds fall in price when rates rise — the higher the fund’s average duration, the larger that fall. A long-duration gilt fund can post real, visible losses in a rate-rising period even though its bonds are perfectly safe from default, purely from this price effect. This is why a fund’s duration, not just its credit quality, tells you how much its value can drop, and why short-duration funds are steadier when rates are climbing.