there is defintely talk of economic surplus…recall contingent immunization?

the surplus efficient frontier?

For OP:

REfer to the following diagram to follow along:

https://www.google.ca/search?q=convexity+bond+price&espv=2&biw=1600&bih=957&source=lnms&tbm=isch&sa=X&ei=DxdtVdSwAfPIsATen4K4CQ&ved=0CAcQ_AUoAg#imgrc=f7UAVGwEFEIGpM%3A%3B68FJosm-wwep2M%3Bhttp%3A%2F%2Fi.investopedia.com%2Finv%2Ftutorials%2Fsite%2Fadvancedbond%2Fconvexity.gif%3Bhttp%3A%2F%2Fwww.investopedia.com%2Funiversity%2Fadvancedbond%2Fadvancedbond6.asp%3B324%3B238

If you look at a diagram where the x axis is interest rate and the y axis is the bond price, this graph will be convex to the origin.

So if you draw a tangent line to the curve, that will be the bond duration at that point.

The distance between the duration line and the bond price curve is the convexity adjustment.

If rates move down, the duration has underestimated the bond price increase (as seen by the distance between the tangent and the curve), and there will be an positive convexity adjustment to the bond price (resulting in a higher price_

If rates move up, the duration has overestimated the price decline (as seen by the distance between…), and there will be a positive convexity adjustment (resulting in a higher price than what was estimated by the duration).