A 30-year maturity bond making annual coupon payments with a coupon rate of 15.3
ID: 2725804 • Letter: A
Question
A 30-year maturity bond making annual coupon payments with a coupon rate of 15.3% has duration of 9.97 years and convexity of 144.9. The bond currently sells at a yield to maturity of 10%.
Price of the bond $1647.24
price predicted by the duration rule: $1796.54
c. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $
d-1. What is the percent error for each rule? (Enter your answer as a positive value. Do not round intermediate calculations. Round "Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal places.)
Percent Error
e-1. Find the price of the bond if it's yield to maturity rises to 11%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Price of the bond $
e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $
e-3. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $
e-4. 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
Percent Error
YTM Duration Rule Duration-with-Convexity Rule 9% % %
Explanation / Answer
Answer
Answer e-1
Figures in $
Year
Interest
Redemption Price
Cash flow
Disc rate 11%
Present value
A
B
C
D
A+B
C*D
1
153
153
0.901
137.84
2
153
153
0.812
124.18
3
153
153
0.731
111.87
4
153
153
0.659
100.79
5
153
153
0.593
90.80
6
153
153
0.535
81.80
7
153
153
0.482
73.69
8
153
153
0.434
66.39
9
153
153
0.391
59.81
10
153
153
0.352
53.88
11
153
153
0.317
48.54
12
153
153
0.286
43.73
13
153
153
0.258
39.40
14
153
153
0.232
35.50
15
153
153
0.209
31.98
16
153
153
0.188
28.81
17
153
153
0.170
25.95
18
153
153
0.153
23.38
19
153
153
0.138
21.06
20
153
153
0.124
18.98
21
153
153
0.112
17.10
22
153
153
0.101
15.40
23
153
153
0.091
13.88
24
153
153
0.082
12.50
25
153
153
0.074
11.26
26
153
153
0.066
10.15
27
153
153
0.060
9.14
28
153
153
0.054
8.23
29
153
153
0.048
7.42
30
153
1000
1153
0.044
50.37
Present value
1373.83
Answer : if it's yield to maturity rises to 11%, the price of the bond will be $ 1373.83
Answer e-2
Modified Duration = Duration / (1 + YTM)
= 9.97 / (1 + 0.10)
= 9.97 / (1.10)
= 9.0636
% change in bond price = - modified duration * % change in Interest rate
= - 9.0636 * (11% - 10%)
= - 9.0636 * (1%)
=- 9.0636 %
New price of the bond = Old price – (Old price * % change in bond price)
= $1647.24 - ($1647.24 *- 9.0636 %)
= $1647.24 - $ 149.30
= $ 1497.94
Answer : Price predicted by the duration rule would be $ 1497.94
Figures in $
Year
Interest
Redemption Price
Cash flow
Disc rate 11%
Present value
A
B
C
D
A+B
C*D
1
153
153
0.901
137.84
2
153
153
0.812
124.18
3
153
153
0.731
111.87
4
153
153
0.659
100.79
5
153
153
0.593
90.80
6
153
153
0.535
81.80
7
153
153
0.482
73.69
8
153
153
0.434
66.39
9
153
153
0.391
59.81
10
153
153
0.352
53.88
11
153
153
0.317
48.54
12
153
153
0.286
43.73
13
153
153
0.258
39.40
14
153
153
0.232
35.50
15
153
153
0.209
31.98
16
153
153
0.188
28.81
17
153
153
0.170
25.95
18
153
153
0.153
23.38
19
153
153
0.138
21.06
20
153
153
0.124
18.98
21
153
153
0.112
17.10
22
153
153
0.101
15.40
23
153
153
0.091
13.88
24
153
153
0.082
12.50
25
153
153
0.074
11.26
26
153
153
0.066
10.15
27
153
153
0.060
9.14
28
153
153
0.054
8.23
29
153
153
0.048
7.42
30
153
1000
1153
0.044
50.37
Present value
1373.83
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.