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Why XIRR Cannot Be Additively Split into Return Sources

Article Quant Q&A · Author: Cheok Yan Cheng
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Summary

The document asks how to divide an annualized XIRR among dividends and stock-sale gains, using an example with an initial stock purchase, an interim dividend, and a later sale. The replies distinguish calculating an overall money-weighted return from measuring separate sources of profit. A proposed approach is to recompute returns for selected cash-flow subsets, such as dividend income while excluding sale profit, but the document does not establish this as a unique attribution method.

Key ideas

  • XIRR compresses dated cash flows into a single annualized return measure.
  • That single result does not uniquely identify how much return came from each cash-flow source.
  • Separate cash-flow subsets can be analyzed, but their reported returns depend on the chosen treatment and dates.
  • A portfolio chart should define its attribution method rather than assume XIRR components add up.

Tags

StatisticsPortfolio constructionEquities
Full text
# Break down XIRR to different segments


# Break down XIRR to different segments












Currently, I have the following transactions.

```
01/01/2000 I used $1000 to purchase stocks
30/05/2000 I received $100 stock dividend.
31/12/2000 I sold all stocks for $2000.
```

Hence, if I use XIRR to calculate

```
01/01/2000  -1000 (Invest in stock)
30/05/2000  100 (Received dividend)
31/12/2000  2000 (Sales in stock)
```

My yearly return is 1.157284223 (115.73%)

From the above calculated XIRR, may I know how much % does the received dividend contribute to the total XIRR? Is there any proper formula to calculate so?

I wish to get x & y figure.

> I am having annualized return 115.73%. Out of this 115.73% annualized return, x% is contributed by dividend gain, y% is contributed by stock sales.

The reason I ask so, as I'm currently building a portfolio performance chart.

I need to break down my yearly XIRR to different segments (dividend, sales gain, paper gain)

## Answer by tario (score 1)

https://quant.stackexchange.com/a/14022

Not 100% sure but does the following work?

Dividend gain:

-1000 purchase 100 dividend 1000 sell (ignoring sell profit)

Sell profit: -1000 purchase 2000 sell

## Answer by Lucas Morin (score 0)

https://quant.stackexchange.com/a/14020

You use 4 number (dividend/investment at first date, sales/investment at second date) to build one number.

There is an infinite number of possibilities to obtain a given results so no you can't give the dividend part with only XIRR.

If you have the investments/dividends/sales/dates well you can remove the sales and use only the dividends if you want the dividends part.

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.