Problem 2 (a) Let Ay be a small change in a bond yield and let AP= P(y+Ay) P(y) be the corresponding change in the price of the bond (note that P(y) means that the price P is a function of the yield y). Show that the return can be approximated as: ~-AyD Hint: Use Taylor approximation. (b) Establish the following relationship between duration and convexity: C = D2 - OD Problem 2 (a) Let Ay be a small change in a bond yield and let AP= P(y+Ay) P(y) be the corresponding change in the price of the bond (note that P(y) means that the price P is a function of the yield y). Show that the return can be approximated as: ~-AyD Hint: Use Taylor approximation. (b) Establish the following relationship between duration and convexity: C = D2 - OD