Given the following bonds, compute the respective bond portfolio’s duration and

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 Explain and Show Work!

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

A portfio is a combination of various bonds. So calculation of duration or yield for portfolio is nothing but calculating the weighted average of individual bond values that are taken into the porfolio.

For example........

Duration of Bond portfolio = W1*D1 + W2*D2 + W3*D3 + ................Wk*Dk

Yield of Bond portfolio = W1*Y1 + W2*Y2 + W3*Y3 + ................Wk*Yk

Ladder

Duration = 8.285 and YTM = 4.5

Bullet (50% weighting of the each of the two middle maturity bonds – Champ and Dino).

Duration = 9.495    and YTM = 4.5

Barbell (50% weighting of the lowest and highest maturity bonds – Ajax and Figleaf).

Duration = 7.025    and YTM = 4.5

Bond W D Y WD WY Ajax 0.166667 1.96 2 0.3266667 0.333333 Bounty 0.166667 4.66 3 0.7766667 0.5 Champ 0.166667 8.32 4 1.3866667 0.666667 Dino 0.166667 10.67 5 1.7783333 0.833333 Elf 0.166667 12.01 6 2.0016667 1 Figleaf 0.166667 12.09 7 2.015 1.166667 8.285 4.5

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