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Measuring Portfolio Returns with External Cash Flows

Article Quant Q&A · Author: Vinícius Lopes Simões
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Summary

The document asks how to measure a portfolio’s overall return when it receives contributions and withdrawals, without treating those cash flows as investment gains or losses. It mentions a unitization approach, in which the portfolio is represented by units with a changing value, but does not identify or explain that method in detail.

The answer recommends internal rate of return: solve for the rate that equates the present value of cash inflows and outflows. It treats the portfolio’s starting value as an initial inflow and its ending value as a liquidation outflow, with contributions and withdrawals represented as intermediate cash flows. This provides a money-weighted measure, so results depend on the timing and size of external flows. The brief exchange gives no worked example or comparison with time-weighted return, which may be more suitable when evaluating investment performance independently of cash-flow timing.

Key ideas

  • External contributions and withdrawals should be represented as cash flows rather than investment gains or losses.
  • Internal rate of return is proposed as the portfolio’s money-weighted return measure.
  • The calculation includes the starting portfolio value and an assumed liquidation at the end date.
  • The answer does not compare internal rate of return with time-weighted performance measurement.

Tags

Portfolio constructionStatistics
Full text
# How to adjust a portfolio's rate of return for contributions and withdrawals?


# How to adjust a portfolio's rate of return for contributions and withdrawals?












Suppose we have a portfolio with many assets.

Since this portfolio receives monthly contributions and withdrawals, what is the best method to evaluate its global rate of return and avoid computing these contributions as a "profit" and withdrawals as "losses"?

I've already seen some people using abstract entities (e.g.: we may define that we start with 100 entities, and, for a \$100 portfolio, each entity would cost \$1), but I don't know the name of this method in English.

## Answer by kurtosis (score 1)

https://quant.stackexchange.com/a/57293

Usually this would be evaluated using an internal rate of return, the rate $r$ which makes the PV of inflows and outflows equal -- assuming a starting inflow of portfolio value at the start date and an outflow as though the portfolio were liquidated at the end date.

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.