Convexity

It is said that the price-yield relationship for bonds is convex. What does this mean? What role does convexity play in determining the rate of change in a bond price in response to changes in the required yield?

Consider a 15-year 9% bond selling to yield 6%. The modified duration (MD) for this bond is 6.25 years. The convexity measure for the bond is 55. Suppose the required yield increases by 100bp. Determine the approximate percentage change in the price of the bond (dP/P) using the duration formula.

Determine the percentage change in the price of the bond due to convexity. What is the overall effect on the price of the bond?