When comparing two bonds with the same duration, the one with higher convexity will show what when yields fall?

• A. A greater price increase.
• B. A smaller price increase.
• C. No difference.
• D. A greater price decrease.

Answer: (A)

Convexity is about how the price-yield relationship curves. When two bonds have the same duration, the one with higher convexity has a price that bends upward more as yields change. So, if yields fall, the price rise accelerates for the higher-convexity bond.

In practical terms, price changes can be approximated by a formula that combines the first-order duration term and a second-order convexity term: price change ≈ -Duration × Δyield + 0.5 × Convexity × (Δyield)². If yields fall, Δyield is negative, making the first term a positive contribution and the second term also positive (since (Δyield)² is positive). The bond with higher convexity gains more from that second-order effect, leading to a greater overall price increase.

So the higher-convexity bond will show a greater price increase when yields fall.