Bond convexity is a direct measure of the duration sensitivity of a bond when its interest rate is changing. There is one key thing to remember here, as bond yields go higher, the price of them goes lower. In essence, the relationship this statement has, between price and yield, it has a convex structure in nature. You won’t be surprised to hear that this relationship is otherwise known as convexity. For any type of bond, a graph of the direct relationship between its price and yield is convex. As we have already mentioned, this means the graph forms a curve rather than a straight-line which would be called linear. Just how curved a graph is shows how much a bond’s yield changes in response to changes in price.

What is the bond convexity calculation?

As we have already discussed, convexity is a direct measure of the curvature or 2nd derivative of how the price of a bond varies with a specific interest rate. In more simplistic terms, this means how the duration of a bond changes as the interest rate also changes. We will assume in this example that the interest rate of the bond does not change or at least for the life of the bond, it remains static. A duration can therefore be formulated as the first derivative of the price of the bond. Using convexity methods, the 2nd derivative can be used with the interest rate.

What are the factors that affect bond convexity?

• Callable bonds negate convexity at particular price-yield combinations (ie; As market yields decrease so to does duration).
• The higher the coupon rate the lower the convexity of a bond (Zero-coupon bonds are the bonds with the highest convexity).
• Price yield relationship shows us that price-yield curve will increase as yield decreases. (ie; As market yields decrease the duration increases).

What is the bond convexity formula?

We attempted to produce a guide explaining the bond convexity formula but we just couldn’t do it justice and would recommend you see the contribution at Wikipedia which you can find here.