# Is duration additive? $C_{newDur}=A_{fundDur}w_{a} + B_{fundDur}w_{b}$?

Suppose quantified duration (like Macaulay duration with changing intervals) $Dur = \frac{\sum t_{i} PV_{i}}{\sum PV_{i}}$ and two funds having durations $D_{a}$ and $D_{b}$. You own them in the proportion $w_{a}=0.4$ and $w_{b}=0.6$.

1. What is the duration of your portfolio?

2. Is it the following? $C_{newDur}=A_{fundDur}w_{a} + B_{fundDur}w_{b}$

3. Is duration combinations always sumproduct (like above, presupposing right not sure) or does it vary between different definitions of duration?

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Yes, you are correct. Duration is additive, so your aggregate portfolio duration is the weighted average of your individual durations as you present in point 2.

That holds assuming a close to flat yield curve and parallel (additive) shifts.

If that's not the case, the situation gets a bit more complex. Unfortunately, right now I couldn't find any interesting and freely accessible paper that would deal with non-additive shifts or non-flat yield curve.

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Did you ever end up finding something ? – Alexandre Cassagne Mar 20 at 21:49
I don't remember much due to the time span, but I think most textbooks just blatantly assume this is the case, while non-additive shifts seem to pose a not so trivial research problem. I'm sorry I don't feel competent enough to delve into the subject right now, as I've mostly switched fields completely. Maybe someone more versed will be able to chime in. – Karol Piczak Mar 21 at 16:10

Duration is also additive if you are dealing with key rate durations. In this case, Effective Duration is the weighted average of your key rate durations.

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