Why is convexity valuable for bond investors?

Convexity captures the curvature of the price-yield relationship that duration (a linear approximation) misses. Positive convexity means the bond rises more than the duration estimate when yields fall and falls less when yields rise, creating an asymmetric gain for the investor.

What is negative convexity in callable bonds?

Callable bonds exhibit negative convexity at low yields because the call option caps price appreciation. When rates drop, the issuer calls the bond before it rises much above the call price, creating a price ceiling. Duration alone understates the risk of these bonds.

Convexity Second-Order Bond Price Change

Calculate convexity as the second derivative of price with respect to yield, and use it alongside modified duration for a more accurate bond price change estimate: change = -D*dy + 0.5*C*dy^2.

Principal ($)

Annual Rate (%)

Years

Compounding / Year

$ Finance Disclaimer: These calculators are for educational and illustrative purposes only. Results do not constitute financial advice. Consult a licensed financial advisor before making investment or borrowing decisions.

How to Use

Enter the values for the scenario you are assessing. Calculate convexity as the second derivative of price with respect to yield, and use it alongside modified duration for a more accurate bond price change estimate: change = -D*dy + 0.5*C*dy^2. Use the bond convexity result to inform your calculation.

Related Calculators

Modified Duration

Finance Long-tail

DV01 Dollar Duration