Round to the nearest cent for the dollar, e.g., for $101.5476, round to $101.55.
⢠For percentages such as 2.5786%, round to four decimal places, e.g., 0.0258, or 2.58%.
1. In order to find the duration and convexity of a 5% coupon bond making semiannual coupon payments if it has three years until maturity and a yield to maturity of 6%, we conduct calculations in the following table.
Period
Time until payment
Payment
Payment discounted at 3%
weight
Time x weight
Time x Next Time x weight
(t)
(CFt)
PMT/(1 + y/2)t
(wt = discounted pmt/P)
(t)(wt)
(t)(t+(1/2))(wt)
1
0.5
$25
24.2718
0.0249
0.0125
0.0125
2
1.0
$25
23.5649
0.0242
0.0242
0.0363
3
1.5
$25
22.8785
0.0235
0.0353
0.0705
4
2.0
$25
22.2122
0.0228
0.0457
0.1142
5
2.5
$25
21.5652
0.0222
0.0554
0.1662
6
3.0
$1,025
858.4214
0.8823
2.6470
9.2644
Sums
972.91
1
2.8200
9.5448
Divide by 1 + y/2
2.7379
9.2668
(1) Find the (Macaulay) bond duration.
(2) What is the modified duration?
(3) If the bond YTM decreases from 6% to 5%, what is the percent change in the bond price estimated based on the modified duration rule?
(4) If the bond YTM decreases 6% to 5%, what is the percent change in the bond price estimated based on the convexity rule?
(5) Calculate the actual bond price with 5% semiannual coupon payments, YTM of 5%, and 3 year maturity. What is the actual percent change in the price?
Round to the nearest cent for the dollar, e.g., for $101.5476, round to $101.55.
⢠For percentages such as 2.5786%, round to four decimal places, e.g., 0.0258, or 2.58%.
1. In order to find the duration and convexity of a 5% coupon bond making semiannual coupon payments if it has three years until maturity and a yield to maturity of 6%, we conduct calculations in the following table.
| Period | Time until payment | Payment | Payment discounted at 3% | weight | Time x weight | Time x Next Time x weight | |||||||||
| (t) | (CFt) | PMT/(1 + y/2)t | (wt = discounted pmt/P) | (t)(wt) | (t)(t+(1/2))(wt) | ||||||||||
| 1 | 0.5 | $25 | 24.2718 | 0.0249 | 0.0125 | 0.0125 | |||||||||
| 2 | 1.0 | $25 | 23.5649 | 0.0242 | 0.0242 | 0.0363 | |||||||||
| 3 | 1.5 | $25 | 22.8785 | 0.0235 | 0.0353 | 0.0705 | |||||||||
| 4 | 2.0 | $25 | 22.2122 | 0.0228 | 0.0457 | 0.1142 | |||||||||
| 5 | 2.5 | $25 | 21.5652 | 0.0222 | 0.0554 | 0.1662 | |||||||||
| 6 | 3.0 | $1,025 | 858.4214 | 0.8823 | 2.6470 | 9.2644 | |||||||||
| Sums | 972.91 | 1 | 2.8200 | 9.5448 | |||||||||||
| Divide by 1 + y/2 | 2.7379 | 9.2668 | |||||||||||||
(1) Find the (Macaulay) bond duration.
(2) What is the modified duration?
(3) If the bond YTM decreases from 6% to 5%, what is the percent change in the bond price estimated based on the modified duration rule?
(4) If the bond YTM decreases 6% to 5%, what is the percent change in the bond price estimated based on the convexity rule?
(5) Calculate the actual bond price with 5% semiannual coupon payments, YTM of 5%, and 3 year maturity. What is the actual percent change in the price?
