Question

Both Bond A and Bond B have 7.8 percent coupons and are priced at par value....

Both Bond A and Bond B have 7.8 percent coupons and are priced at par value. Bond A has 8 years to maturity, while Bond B has 18 years to maturity. If interest rates suddenly rise by 1 percentage points, what is the difference in percentage changes in prices of Bond A and Bond B? (i.e., Bond A - Bond B).  The bonds pay coupons twice a year.

Homework Answers

Answer #1
YTM = [Annual interest +(Face value-Current price)/n]/(Face value + 2*Current Price)/3
Bond A Bond B
Maturity Years =n 8 18
Face value -suppose 100 100
Market value 100 100
Annual Interest amount 7.8 7.8
Yield to maturity 7.80% 7.80%
Bond A =[7.8+0/8](100+200)/3=7.8/100=7.8%
Bond B=[7.8+0/18]/(100+200)/3=7.8/100=7.8%
Caculation of Modified Duration of Bond A
Period Cash Flow Discount factor @3.9% semi annually PV cash floW Time period*Cash flow PV of time adjusted cash flow
1 3.9 0.962 3.7518 3.9 3.7518
2 3.9 0.926 3.6114 7.8 7.2228
3 3.9 0.892 3.4788 11.7 10.4364
4 3.9 0.858 3.3462 15.6 13.3848
5 3.9 0.826 3.2214 19.5 16.107
6 3.9 0.795 3.1005 23.4 18.603
7 3.9 0.765 2.9835 27.3 20.8845
8 3.9 0.736 2.8704 31.2 22.9632
9 3.9 0.709 2.7651 35.1 24.8859
10 3.9 0.682 2.6598 39 26.598
11 3.9 0.656 2.5584 42.9 28.1424
12 3.9 0.632 2.4648 46.8 29.5776
13 3.9 0.608 2.3712 50.7 30.8256
14 3.9 0.585 2.2815 54.6 31.941
15 3.9 0.563 2.1957 58.5 32.9355
16 103.9 0.542 56.3138 1662.4 901.0208
Total= 100.0 1219.2803
Macaulays duration= sum of PV of time adjusted cash flow/ Sum of PV of cash flows= 12.19593736
Modified duration =Macaulay's duration/(1+YTN/n) 11.73814952
n= no of coupon payment per year
% change in Price = - modified Duration*% interest change
Interest rate rise 1%
So change in Price in Bond A=-11.73*1%=-11.73%
Caculation of Modified Duration of Bond A
Period Cash Flow Discount factor @3.9% semi annually PV cash floW Time period*Cash flow PV of time adjusted cash flow
1 3.9 0.962 3.7518 3.9 3.7518
2 3.9 0.926 3.6114 7.8 7.2228
3 3.9 0.892 3.4788 11.7 10.4364
4 3.9 0.858 3.3462 15.6 13.3848
5 3.9 0.826 3.2214 19.5 16.107
6 3.9 0.795 3.1005 23.4 18.603
7 3.9 0.765 2.9835 27.3 20.8845
8 3.9 0.736 2.8704 31.2 22.9632
9 3.9 0.709 2.7651 35.1 24.8859
10 3.9 0.682 2.6598 39 26.598
11 3.9 0.656 2.5584 42.9 28.1424
12 3.9 0.632 2.4648 46.8 29.5776
13 3.9 0.608 2.3712 50.7 30.8256
14 3.9 0.585 2.2815 54.6 31.941
15 3.9 0.563 2.1957 58.5 32.9355
16 3.9 0.542 2.1138 62.4 33.8208
17 3.9 0.522 2.0358 66.3 34.6086
18 3.9 0.502 1.9578 70.2 35.2404
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