Given the following bonds, compute the respective bond portfolio’s duration and
ID: 2793489 • Letter: G
Question
Given the following bonds, compute the respective bond portfolio’s duration and yield.
Bond
Coupon
Maturity Yr
Price $
YTM
Duration
Ajax
1.50%
2
99.02
2.00%
1.96
Bounty
2.50%
5
97.69
3.00%
4.66
Champ
3.50%
10
95.91
4.00%
8.32
Dino
4.50%
15
94.77
5.00%
10.67
Elf
5.00%
20
88.44
6.00%
12.01
Figleaf
6.00%
25
88.27
7.00%
12.09
Ladder (equal weighting for all bond). Duration:______ YTM:_____
Bullet (50% weighting of the each of the two middle maturity bonds – Champ and Dino). Duration:______ YTM:_____
Barbell (50% weighting of the lowest and highest maturity bonds – Ajax and Figleaf). Duration:______ YTM:_____
Please Show Work and Explain!
Bond
Coupon
Maturity Yr
Price $
YTM
Duration
Ajax
1.50%
2
99.02
2.00%
1.96
Bounty
2.50%
5
97.69
3.00%
4.66
Champ
3.50%
10
95.91
4.00%
8.32
Dino
4.50%
15
94.77
5.00%
10.67
Elf
5.00%
20
88.44
6.00%
12.01
Figleaf
6.00%
25
88.27
7.00%
12.09
Explanation / Answer
1) Ladder (equal weighing for all bond)
Duration -
The portfolio duration is equivalent to the weighted average of the duration for bonds.
Formula -
Duration of Portfolio = Weight of Bond x Duration of the Bond
Calculation -
As there are 6 bonds so equal weights will be 100 % divided by 6 bonds which means 1/6th for each bond.
Duration of Portfolio will be -
= 1/6(1.96) +1/6(4.66) + 1/6(8.32) +1/6(10.67) +1/6(12.01) +1/6(12.09)
= 0.3267 + 0.7767 + 1.3867 + 1.7783 + 2.0017 + 2.015
Duration = 8.2851
Yield to Maturity (YTM) -
Formula -
YTM of a portfolio = Average of all the Coupon rate
Calculation -
YTM of a portfolio =
= (1.50% + 2.50% + 3.50% + 4.50% + 5.00% + 6.00%) / 6
= 23.00% / 6
YTM of a portfolio = 3.83%
2) Bullet (50% weighting of each of the two middle maturity bonds - Champ and Dino) -
Duration
Formula -
Duration = Weight of Bond x Duration of the Bond
Calculation -
As there are 2 bonds so equal weights will be 100 % divided by 2 bonds which means 1/2th for each bond.
Duration will be -
= 1/2(8.32) + 1/2(10.67)
= 4.16 + 5.335
Duration = 9.495
Yield to Maturity (YTM) -
Formula -
YTM = Average of the Coupon rate of Champ and Dino
Calculation -
YTM = (3.50% + 4.50%) / 2
= 8.00% / 2
YTM = 4.00%
3) Barbell (50% weighting of the lowest and highest maturity bonds – Ajax and Figleaf) -
Duration
Formula -
Duration = Weight of Bond x Duration of the Bond
Calculation -
As there are 2 bonds so equal weights will be 100 % divided by 2 bonds which means 1/2th for each bond.
Duration will be -
= 1/2(1.96) + 1/2(12.09)
= 0.98 + 6.045
Duration = 7.025
Yield to Maturity (YTM) -
Formula -
YTM = Average of the Coupon rate of Ajax and Figleaf
Calculation -
YTM = (1.50% + 6.00%) / 2
= 7.50% / 2
YTM = 3.75%
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