How would you explain duration and convexity in bond pricing?

• A. Duration measures price sensitivity to yield changes; convexity adjusts for non-linear price movement; higher duration equals higher interest-rate risk.
• B. Duration measures credit risk.
• C. Convexity measures liquidity risk.
• D. Higher duration reduces interest-rate risk.

Answer: (C)

Duration and convexity describe how bond prices respond to changes in interest rates. Duration is the first-order measure of price sensitivity, telling you how much the price will move for a small change in yield. Convexity captures the curvature of the price–yield relationship, giving a better estimate when yields move more than a tiny amount.

In practice, the price change from a small yield shift is roughly the negative of the modified duration times the yield change. For larger moves, you add one-half times the convexity times the square of the yield change. So, duration handles the linear part of the response, and convexity accounts for the non-linear bend.

A longer duration means greater sensitivity to interest-rate moves, hence higher interest-rate risk. Convexity is typically positive, so prices rise a bit more when yields fall and fall a bit less when yields rise, making the price response less extreme than a purely linear model would suggest.

Duration isn’t a measure of credit risk, and convexity isn’t a measure of liquidity risk; together they describe interest-rate risk in a bond’s price.