contribution to portfolio duration and contribution to portfolio dollar duration

[sfad]

Why are these different formulas? Why for duration can we not do: duration bond/duration portfolio?
1. Duration
Info: Bond market value = 5m, bond duration = 4.7; portfolio market value =20m; portfolio duration =6.
Contribution of bond to duration of portfolio = (5/20) x 4.7=1.175. Then 1.175/6=19.6
2. Dollar Duration
Info: Bond market value = 5m, bond duration = 4.7; portfolio market value =20m; portfolio duration =6.8.
DD bond = 5mx4.7x0.01=235,000
DD portfolio = 20mx6.8x0.01=1,360,000
Contribution of bond to dollar duration of portfolio = DD of bond / DD of portfolio = 235,000/1,360,000 = 17.3%

 

[S2000magician]

They’re not.
The first is:
(5/20) × (4.7/6)
= (5 × 4.7) / (20 × 6)
= DD of bond / DD of portfolio

 

[June06]

sfad wrote:
Why are these different formulas? Why for duration can we not do: duration bond/duration portfolio?
1. Duration
Info: Bond market value = 5m, bond duration = 4.7; portfolio market value =20m; portfolio duration =6.
Contribution of bond to duration of portfolio = (5/20) x 4.7=1.175. Then 1.175/6=19.6
2. Dollar Duration
Info: Bond market value = 5m, bond duration = 4.7; portfolio market value =20m; portfolio duration =6.8.
DD bond = 5mx4.7x0.01=235,000
DD portfolio = 20mx6.8x0.01=1,360,000
Contribution of bond to dollar duration of portfolio = DD of bond / DD of portfolio = 235,000/1,360,000 = 17.3%

You should get the same answer, no?

 

[kjsgbp]

For a portfolio: Duration is a weighted average, dollar duration is a sum. Thus to calcuate the contribution to duration, you must include the weight of the asset in the portfolio