What is the approximate formula for convexity?

Convexity is an important concept in the analysis of fixed-income securities, reflecting how the duration of a bond changes as interest rates change. The formula for convexity provides insights into how a bond's price will change as interest rates fluctuate, and it helps investors understand the potential price volatility of a bond portfolio.

The correct response regarding the approximation of convexity is derived from the principle that convexity measures the degree of curvature in the price-yield relationship of a bond. While duration provides a linear approximation of price sensitivity to interest rate changes, convexity captures the non-linear effects.

The formula typically used to calculate convexity involves the second derivative of price with respect to interest rates and the various cash flows associated with the bond. A simplified way to understand the contribution of cash flows and duration in the context of convexity is through the relationship where duration is factored into the convexity calculation.

In this context, duration squared is employed in certain convexity approximations, illustrating that as duration increases, the sensitivity of the bond's price to interest rate changes (and hence its convexity) rises more than linearly. This aligns with the understanding that convexity is influenced by the shape of the price-yield curve, which becomes more pronounced with higher