Question

Bond J has a coupon rate of 5 percent. Bond K has a coupon rate of 11 percent. Both bonds have 8 years to maturity, make semiannual payments, and have a YTM of 6 percent.

  

	If interest rates suddenly rise by 5 percent, what is the percentage price change of Bond J?

  

	If interest rates suddenly rise by 5 percent, what is the percentage price change of Bond K?

  

	If interest rates suddenly fall by 5 percent, what is the percentage price change of Bond J?

  

	If interest rates suddenly fall by 5 percent, what is the percentage price change of Bond K?

Answer 1

Bond J

Number of periods = n = 8*2 = 16 semiannual periods

Yield I/Y= 6%/2 = 3% or 0.03 semiannual

Let Face Value of the bond = FV = $1000

Semiannual Payment P = 5%*1000/2 = $25

Hence, PV = P/(1+r) + P/(1+r)² + .... + P/(1+r)ⁿ + FV/(1+r)ⁿ

= P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ = 25(1 - 1.03^-16)/0.03 + 1000/1.03¹⁶ = $937.19

Bond K

Number of periods = n = 8*2 = 16 semiannual periods

Yield I/Y= 6%/2 = 3% or 0.03 semiannual

Let Face Value of the bond = FV = $1000

Semiannual Payment P = 11%*1000/2 = $55

Hence, PV = P/(1+r) + P/(1+r)² + .... + P/(1+r)ⁿ + FV/(1+r)ⁿ

= P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ = 55(1 - 1.03^-16)/0.03 + 1000/1.03¹⁶ = $1314.03

(a) For Bond J, If interest Rate increases by 5%, net Interest Rate = 11%

=> Yield I/Y= 11%/2 = 5.5% or 0.055 semiannual

Hence, PV = 25(1 - 1.055^-16)/0.055 + 1000/1.055¹⁶ = $686.14

%Change in Price = (686.14 - 937.19)/937.19 *100% = -26.79%

(b) For Bond K, If interest Rate increases by 5%, net Interest Rate = 11%

=> Yield I/Y= 11%/2 = 5.5% or 0.055 semiannual

Hence, PV = 55(1 - 1.055^-16)/0.055 + 1000/1.055¹⁶ = $1000

%Change in Price = (1000 - 1314.03)/1314.03 *100% = -23.90%

(c) For Bond J, If interest Rate decrease by 5%, net Interest Rate = 1%

=> Yield I/Y= 1%/2 = 0.5% or 0.005 semiannual

Hence, PV = 25(1 - 1.005^-16)/0.005 + 1000/1.005¹⁶ = $1306.80

%Change in Price = (1306.80 - 937.19)/937.19 *100% = 39.44%

(c) For Bond K, If interest Rate decrease by 5%, net Interest Rate = 1%

=> Yield I/Y= 1%/2 = 0.5% or 0.005 semiannual

Hence, PV = 55(1 - 1.005^-16)/0.005 + 1000/1.005¹⁶ = $1767

%Change in Price = (1767 - 1314.03)/1314.03 *100% = 34.47%