When Portfolio Duration Is a Weighted Average of Fund Durations

Summary

The document asks how to combine the durations of two funds held at specified portfolio weights. It states duration as the present-value-weighted average timing of cash flows and proposes taking the weighted average of the funds’ durations. The accepted response confirms that approach under assumptions of a nearly flat yield curve and parallel yield shifts. Under those conditions, portfolio duration is additive across the holdings.

The note also distinguishes cases where those assumptions fail: a non-flat curve or non-parallel yield changes make the analysis more complex. A second response says key rate durations can also be aggregated as weighted averages. The discussion is brief and does not derive the result or work through a numerical example. Its guidance is therefore conditional on the duration measure and yield-shift assumptions; it does not establish that a single weighted-average figure captures all interest-rate exposures in more general settings.

Key ideas

• Portfolio duration can be computed as the weighted average of constituent durations under specified assumptions.
• The stated assumptions are a nearly flat yield curve and parallel shifts in yields.
• Non-flat curves or non-parallel yield moves require a more detailed treatment.
• Key rate durations are also described as aggregating through weighted averages.
• A single portfolio duration may not capture exposures under more complex curve changes.

Tags

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


# 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 $w_{b}=0.6$.

- What is the duration of your portfolio?

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

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

Resources

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

## Answer by Karol J. Piczak (score 6, accepted)

https://quant.stackexchange.com/a/1278

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.

## Answer by Ram Ahluwalia (score 2)

https://quant.stackexchange.com/a/1295

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.