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The Daily Capital
INVESTING 201 · Lesson 71

Convexity: why duration understates what a big rate move does

Daily Desk · Editorial5 min read
Duration draws a straight line through a curved relationship. Over 25 basis points nobody notices. Over 300, the line is off by several percent — and for a normal bond, it's off in your favor.

Take a 10-year bond with a 4% annual coupon, priced at par when yields are 4%. Its modified duration is about 8.1, so duration says a 3-point rise in yields costs you 24.3%, and a 3-point fall gains you 24.3%. Price the bond properly and the truth is asymmetric: it falls about 21% when yields go to 7%, and rises about 28% when they go to 1%. Duration was wrong both times, and both times in the bondholder's favor.

Educational, not financial advice.