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Why IRR Does Not Track Daily Changes in Cumulative Cash Flow

Article Quant Q&A · Author: Revious
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Summary

The discussion asks how internal rate of return relates to the discrete change in a cumulative cash-flow curve. The response advises using XIRR when cash flows occur on dated, potentially irregular intervals, since ordinary IRR does not account for the actual dates.

It explains that abrupt daily cash-flow changes can create visible jumps in the cumulative series while the period-wide IRR responds less sharply. Over longer periods and with more observations, the two curves may show more similar broad behavior, but they are not direct counterparts: IRR summarizes cash flows across the measurement window. The response also cautions that the displayed graph may omit early flows, which could affect interpretation. It offers no formula for the relationship or quantitative evidence, so its account is qualitative and dependent on the cash-flow series and chosen interval.

Key ideas

  • Use XIRR when cash flows occur at irregular dates because timing matters to the return calculation.
  • A cumulative cash-flow curve shows accumulated amounts, while IRR summarizes the full dated cash-flow stream over a selected period.
  • Large short-term cash-flow jumps may not produce equally large movements in period-wide IRR.
  • Missing early cash flows or changing the measurement window can alter the apparent relationship between the curves.

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StatisticsPortfolio construction
Full text
# Which relation stands between IRR and the cumulative profits?


# Which relation stands between IRR and the cumulative profits?












In the graph below you can see an irregular Cash Flow.

```
The graph is cumulative, on the y axes there are moneys, on the x the dates.
```

In the second graph the IRR (calculated from the beginning to the last day x). I was expecting the IRR to be correlated to the discrete derivative of the first graph, but I was wrong.

Can you help me to understand the relationship between the two curves?

## Answer by Sergejs Millers (score 1, accepted)

https://quant.stackexchange.com/a/58830

As you have series of dates the XIRR should be applied. I suppose you did so. In regard to the graphs correlation. The longer the period and the larger the amount of data, the more the same behavior of the graphs should be. Seems the graph does not present all cash flows/period, the beginning part I mean. Relatively high fluctuations, jumps, in a daily cash flow data will cause a difference between graphs on that dates. The IRR will react less. It could be observed from the graph attached for the shorter period. I am sure, there is a formula could be found for calculating of relationship and deviation value.

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