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What makes some bonds have higher convexity than others？How are duration and convexity related？

What makes some bonds have higher convexity than others？How are duration and convexity related？
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Bond convexity :

The relationship between the price and yield of the bond is measured in terms of a non -- linear curve (convex curve). The bond price and the yield are inversely related ; if yield increases the price decreases. Convexity also measures how the duration changes with a change in yield of the bond.

  zero coupon bonds have the highest convexity showing its prices most sensitive to changes in yield. The price of bond changes drastically with a very small change in interest rate because of its high convexity. Usually a bond with high convexity is chosen for investment purposes.

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