What does convexity measure?

What does convexity measure?

• A. The curvature of the price-yield relationship, providing second-order sensitivity beyond duration.
• B. The issuer's credit quality
• C. The bond's coupon rate
• D. The time to maturity.

Answer: (A)

Convexity measures the curvature of the price-yield relationship, i.e., the second-order sensitivity of a bond’s price to changes in yield beyond what duration captures. It comes from the second derivative of price with respect to yield, and it explains why price movements aren’t perfectly linear when yields change. In a Taylor expansion, price change is approximated by minus duration times the yield change plus one-half times convexity times the yield change squared. Because of positive convexity in most plain-vanilla bonds, prices rise more when yields fall and fall less when yields rise, compared with what duration alone would predict. This makes convexity a valuable tool for assessing price risk, especially for larger yield moves. The other options don’t describe this curvature aspect: convexity isn’t a measure of credit quality, coupon rate, or simply time to maturity (though those factors influence convexity, they don’t define what convexity itself measures).

Convexity measures the curvature of the price-yield relationship, i.e., the second-order sensitivity of a bond’s price to changes in yield beyond what duration captures. It comes from the second derivative of price with respect to yield, and it explains why price movements aren’t perfectly linear when yields change. In a Taylor expansion, price change is approximated by minus duration times the yield change plus one-half times convexity times the yield change squared. Because of positive convexity in most plain-vanilla bonds, prices rise more when yields fall and fall less when yields rise, compared with what duration alone would predict. This makes convexity a valuable tool for assessing price risk, especially for larger yield moves. The other options don’t describe this curvature aspect: convexity isn’t a measure of credit quality, coupon rate, or simply time to maturity (though those factors influence convexity, they don’t define what convexity itself measures).