Consider a 4 years 10% coupon bond with annual coupons and face value of 1000.

• Price it at 10% YTM (An. Comp.) and calculate its Macaulay duration

• Calculate the change in bonds value when YTM goes up to 11%(An. Comp.)
• How could you estimate (or approximate) the change in bonds value without calculating the actual value of the bond (at 11% YTM). What is the size approximation error ?
• Now repeat all above calculations should YTM go up from 10% to 10.01% (rather than to 11%). Compare size approximation error and conclude that duration approximation works better for small changes in rates .