Shape of the bond price versus yield curve

Question

Draw the relationship between a plain fixed-coupon bond's price and its yield to maturity. What does the curvature of this graph mean, and why does it matter?

Short answer

A downward-sloping curve that bends towards the origin (convex). Price falls as yield rises, but each extra basis point moves the price less at higher yields and more at lower yields. So for an option-free bond a fall in yields lifts the price by more than an equal rise lowers it; duration alone (the tangent line) understates the price, and the curvature is measured by convexity.

Adapted from Crack, Heard on the Street, Q3.6, p.34; question and answer rewritten by SelfMadeQuant.com.

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