A 30-year maturity bond making annual coupon payments with a coupon rate of 16.5% has
duration of 11.19 years and convexity of 180.9. The bond currently sells at a yield to maturity of
8%.
Find the price of the bond if its yield to maturity falls to 7% or rises to 9%. (Do not round
intermediate calculations.Round your answers to 2 decimal places.)
What prices for the bond at these new yields would be predicted by the duration rule and the
duration-with-convexity rule? (Do not round intermediate calculations.Round your answers to 2
decimal places.)
What is the percent error for each rule? (Do not round intermediate calculations. Round
\"Duration Rule\" to 2 decimal places and \"Duration-with-Convexity Rule\" to 3 decimal
places.)
Percent Error
A 30-year maturity bond making annual coupon payments with a coupon rate of 16.5% has
duration of 11.19 years and convexity of 180.9. The bond currently sells at a yield to maturity of
8%.
Solution
Assume Bond par value =1000 Bond Duration=11.19 years Bond Convexity=180.9
Maturity 30 years Coupon per year=165 Current Bond price Year
Interest+Maturity PV Factor @8% PV of cash flows PV Factor @9% PV of cash flows PV
Factor @7% PV of cash flows 1.00 165.00
0.93 152.78 0.92 151.38 0.93 154.21
2.00 165.00 0.86 141.46
0.84 138.88 0.87 144.12 3.00
165.00 0.79 130.98 0.77 127.41 0.82 134.69
4.00 165.00 0.74 121.28
0.71 116.89 0.76 125.88 5.00
165.00 0.68 112.30 0.65 107.24 0.71 117.64
6.00 165.00 0.63 103.98
0.60 98.38 0.67 109.95 7.00
165.00 0.58 96.28 0.55 90.26 0.62 102.75
8.00 165.00 0.54 89.14
0.50 82.81 0.58 96.03 9.00
165.00 0.50 82.54 0.46 75.97 0.54
89.75 10.00 165.00 0.46
76.43 0.42 69.70 0.51 83.88 11.00
165.00 0.43 70.77 0.39 63.94 0.48
78.39 12.00 165.00 0.40
65.52 0.36 58.66 0.44 73.26 13.00
165.00 0.37 60.67 0.33 53.82 0.41
68.47 14.00 165.00 0.34
56.18 0.30 49.38 0.39 63.99 15.00
165.00 0.32 52.01 0.27 45.30 0.36
59.80 16.00 165.00 0.29
48.16 0.25 41.56 0.34 55.89 17.00
165.00 0.27 44.59 0.23 38.13 0.32
52.23 18.00 165.00 0.25
41.29 0.21 34.98 0.30 48.82 19.00
165.00 0.23 38.23 0.19 32.09 0.28
45.62 20.00 165.00 0.21
35.40 0.18 29.44 0.26 42.64 21.00
165.00 0.20 32.78 0.16 27.01 0.24
39.85 22.00 165.00 0.18
30.35 0.15 24.78 0.23 37.24 23.00
165.00 0.17 28.10 0.14 22.73 0.21
34.81 24.00 165.00 0.16
26.02 0.13 20.86 0.20 32.53 25.00
165.00 0.15 24.09 0.12 19.13 0.18
30.40 26.00 165.00 0.14
22.31 0.11 17.55 0.17 28.41 27.00
165.00 0.13 20.66 0.10 16.11 0.16
26.55 28.00 165.00 0.12
19.13 0.09 14.78 0.15 24.82 29.00
165.00 0.11 17.71 0.08 13.56 0.14
23.19 30.00 1,165.00 0.10
115.77 0.08 87.81 0.13 153.04 1,956.91 1,770.52 2,178.86
So current Bond Value = $ 1,956.91 As per Duration +Convexity rule %
change in Bond price=-Modified duration*change in interest rate+1/2*Convexity*(interest
cahnge)^2 At 7% YTM , interest rate change =-1% So % Price change =-11.19*-
0.01+1/2*(-0.01)^2 *180.9= 12.09% So Changed Bond price= 1956.91*1.1209=
$ 2,193.50 When YTM = 9% Interest change =1% So % Price
change =-11.19*.
Measures of Dispersion and Variability: Range, QD, AD and SD
A 30-year maturity bond making annual coupon payments with a coupon .pdf
1. A 30-year maturity bond making annual coupon payments with a coupon rate of 16.5% has
duration of 11.19 years and convexity of 180.9. The bond currently sells at a yield to maturity of
8%.
Find the price of the bond if its yield to maturity falls to 7% or rises to 9%. (Do not round
intermediate calculations.Round your answers to 2 decimal places.)
What prices for the bond at these new yields would be predicted by the duration rule and the
duration-with-convexity rule? (Do not round intermediate calculations.Round your answers to 2
decimal places.)
What is the percent error for each rule? (Do not round intermediate calculations. Round
"Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal
places.)
Percent Error
A 30-year maturity bond making annual coupon payments with a coupon rate of 16.5% has
duration of 11.19 years and convexity of 180.9. The bond currently sells at a yield to maturity of
8%.
Solution
Assume Bond par value =1000 Bond Duration=11.19 years Bond Convexity=180.9
Maturity 30 years Coupon per year=165 Current Bond price Year
Interest+Maturity PV Factor @8% PV of cash flows PV Factor @9% PV of cash flows PV
Factor @7% PV of cash flows 1.00 165.00
0.93 152.78 0.92 151.38 0.93 154.21
2.00 165.00 0.86 141.46
3. 22.31 0.11 17.55 0.17 28.41 27.00
165.00 0.13 20.66 0.10 16.11 0.16
26.55 28.00 165.00 0.12
19.13 0.09 14.78 0.15 24.82 29.00
165.00 0.11 17.71 0.08 13.56 0.14
23.19 30.00 1,165.00 0.10
115.77 0.08 87.81 0.13 153.04 1,956.91 1,770.52 2,178.86
So current Bond Value = $ 1,956.91 As per Duration +Convexity rule %
change in Bond price=-Modified duration*change in interest rate+1/2*Convexity*(interest
cahnge)^2 At 7% YTM , interest rate change =-1% So % Price change =-11.19*-
0.01+1/2*(-0.01)^2 *180.9= 12.09% So Changed Bond price= 1956.91*1.1209=
$ 2,193.50 When YTM = 9% Interest change =1% So % Price
change =-11.19*0.01+1/2*(0.01)^2*180.9 = -10.3% So Changed Bond price= 1956.91*(1-
.1030)= $ 1,755.35 As per duration rule % change in Bond price=-
Modified duration*change in interest rate At 7% YTM , interest rate change =-1%
So % Price change =-11.19*-0.01 11.19% So Changed Bond price= 1956.91*1.1190=
$ 2,189.78 When YTM = 9% Interest change =1% So % Price
change =-11.19*0.01 -11.19% So Changed Bond price= 1956.91*(1-.1190)= $
1,724.04 Bond price As per calculation As per duration As per duration
+convexity % errorAs per duration % error As per duration +convexity YTM 9%
1,770.52 1,724.04 1,755.35 2.63% 0.86% YTM 7% 2,178.86
2,189.78 2,193.50 -0.50% -0.67%
