Question

1. There is a 10%, 13 year note bond which has a ytm of 9%. The ytm alters by half a percent down. By how much does the price alter? If the ytm drops by 3%, by how much does the price change, if the convexity is 40? Use formula to show work

Answer 1

Bond price = sigma^n_t = 1 coupon payments/(1 + r)^t + Matunity value/(1 + r)^n = 100/(1.09) + 100/(1.09)^2 + ... + 100/(1.09)^2 + 1100/(1.09)^13 = $1,074.87 Mocaulay Duration = sigma^n_t = 1 tC/(1 + y)^t + nM/(1 + y)^n/p where t = period in which the coupon is recieved C = periodic coupon payment y = periodic 4TM \r\n n = No.of periods m = Maturity value (in $) p = Market price of bond mocaulay Duration = 8,593.80/1074.87 = 8 modified Duration = Macaulay Duration/(1 + 4TM/n) = 8/1.09 = 7.335 i) Delta is price = duration times charge in yield = -7.333 times - 0.005 = 3.6790 so, If the yield drops by 0.570 there , price increase by 3.6790 ii) change in price = (-Duration times change in yield times 100) + (converity times change in yield squared times 100) = [-7.335 times (-0.003) times 100] + [40 times (0.03)^2 times 100) = 22.005 + 3.60 = 25.605 so if rates decrease by 320,the price will increase by 25.60590