# 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?

Resources

1. page 61 about parallel shift, page 73 about traditional immunization, page 79 about multivariate immunization (1990), here.