Question

Bond J has a coupon rate of 3 percent. Bond K has a coupon rate of 9 percent. Both bonds have 14 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 2 percent, what is the price change of these bonds? What if rates suddenly fall by 2 percent instead?

Answer 1

Bond J:

Current price of the bond = $ 1,000 x 3 % x 1/2 x [ { 1 - ( 1 / 1.03 ) ²⁸ } / 0.03 ] + $ 1,000 x ( 1 / 1.03 ) ²⁸ = $ 281.46 + $ 437.10 = $ 718.56

If the interest rates rise by 2 %, YTM is 8 %.

Price of Bond J = $ 15 x 16.6631 + $ 1,000 x 0.3335 = $ 583.45

Change in price = $ 583.45 - $ 718.56 = - $ 135.11

Percentage change in price = - $ 135.11 / $ 718.56 = - 18.80 %

If the rates rates were to decrease by 2 %, YTM is 4 %

Price of Bond J = $ 15 x 21.2813 + $ 1,000 x 0.5744 = $ 893.62

Change in price = $ 893.62 - $ 718.56 = + $ 175.06

Percentage change in price = $ 175.06 / $ 718.56 = 24.36 %

Bond K :

At the current YTM of 6 %,

Current price of Bond K = $ 1,000 x 9% x 1/2 x [ { 1 - ( 1 / 1.03) ²⁸ } / 0.03 ] + $ 1,000 ( 1 / 1.03 ) ²⁸ = $ 844.38 + $ 437.10 = $ 1,281.48

If there is a 2 % increase in interest rate, YTM is 8%.

Present value of the bond = $ 1,000 x 9% x 1/2 x [ { 1 - ( 1 / 1.04 ) ²⁸ } / 0.04 ] + $ 1,000 x ( 1 / 1.04 ) ²⁸ = 749.84 + 333.50 = $ 1,083.34

Price change in the bond = $ 1,083.34 - $ 1,281.48 = - $ 198.14

Percentage change in price = - $ 198.14 / $ 1,281.48 = - 15.46 %

If there is a 2 % decrease in interest rates, YTM is 4 %.

Present value of Bond K at 2% for 28 periods = $ 45 x 21.2813 + $ 1,000 x 0.5744 = $ 1,532.06

Change in price = $ 1,532.06 - $ 1,281.48 = + $ 250.58

Percentage change in price = $ 250.58 / $ 1,281.48 = + 19.55 %