Question

A five-year bond with a yield of 7% (continuously compounded) pays an 8% coupon at the end of each year.

a) What is the bond’s price?

b) What is the bond’s duration?

c) Use the duration to calculate the effect on the bond’s price of a 0.2% decrease in its yield.

d) Recalculate the bond’s price on the basis of a 6.8% per annum yield and verify that the result is in agreement with your answer to (c).

Answer 1

ra (a) bet loud Parce 1000 Let bond face value - 1000 cov) coup on rate a 87 (5) yield = 7) (9) Coupon - 1000 x 8) = 0 Price = formula Bond 1 1 = Coupon x 1 (1+r)n 1 + ne no of years Price = 0 so, Bond ооо t (1.07) or (107)5 L 0.07 = 328.015 + 1o Bord Price & 7 12.986 1041.001 / 167 Bond Duration sont thice

Duration (6) Bond founda = (PV, 1) + (PV 2 x 2) + (P ve x 3) + (Pv4 x 4) + (PVS XS). Pr + PV2 + PV2 + PV y + PV5 PV = Present Present value of cash aufteros Dhows Brand amations PV, 2 coupon = 80 = 74.767 (1.07) PV coupon (1+r)2 = 0.0272 = 69.875 PV = Coupon = 80 a 65.303 (1+r) - 71.0773 - coupon = 80 6/03/ 4 - Titr) 4 = 11.07) 4. 67 coupon + FV 280+1000 = 770.025 11+55 (107) Rond Duration - (74.767x0) +69.87542) +65130383) + (61.03184) + (270.02585) PV5 - +69.875+ 65 303+ €1.011 + 720.00 Bonden = 45o4.675 1041.001 duration = 4.327 Rond years a

a change in Lond's luu Potion Dmac & Bond duration or Macaulay's dy = change in yold y - original yold dy = 0.2% mac = 4.32 years Change in Bond suce - - 4327 x(-0:21.) 01 +0.07) = (0.00808 808/1 = 10.808% New Yield = 6.8%. Bord EN 1000 coupon = 81. sond fuce = coupon x 1-1 n . (tr) n + kr. (1+rin 7000 2 80 x & 1-1 (1.06875 0.068 (1.06875

| لنا = 329.779719.687 News and Price & 11049.466] % change in Price = 1049.466 - 1047.00) 70 4.001 X 700 which same as is in approx (c) MD PROES