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Time-Weighted and Money-Weighted Portfolio Returns

Article Quant Q&A · Author: NoNameNo123
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Summary

The document explains two ways to measure a portfolio’s return across periods when the amount invested changes. Compounding each period’s return produces a time-weighted return (TWR), which treats periods equally and is not directly affected by the timing or size of external cash flows. This is useful for evaluating investment performance independently of when capital was added or withdrawn.

For a return measure that reflects the actual amounts invested, the answer recommends internal rate of return (IRR), also called money-weighted return (MWR). It illustrates the distinction with a cash-flow example and gives an IRR that is close to, but differs from, the questioner’s calculation. TWR and MWR therefore answer different questions and need not match. The response does not explain how to handle irregular cash-flow dates or compare alternative IRR conventions, so the example should not be treated as a complete calculation guide.

Key ideas

  • Compounding period returns gives a time-weighted return.
  • Time-weighted return treats each period equally, regardless of the amount invested.
  • Internal rate of return measures returns using the actual investment cash flows.
  • Money-weighted and time-weighted returns can differ because they answer different questions.

Tags

Portfolio constructionStatisticsBacktesting
Full text
# Portfolio return with changing assets over time


# Portfolio return with changing assets over time












I need some feedback on a very basic question regarding the calculation of the portfolio return.

I have created an example of a portfolio with two assets and attempted to calculate the return:

I've calculated the weighted asset returns and from there I would like to calculate the cumulative portfolio return (= the return of the portfolio from Jan 1 to Feb 28). I can't just multiply them (1+r1)*(1+r2)-1, right? The -10% return in January was when the portfolio's value was only $1000 and the same relative decline in asset 1's value in February has a much smaller impact.

So do I simply weigh the returns according to the portfolio values? I've tried it and would appreciate some feedback on my calculation. Did I make a mistake? Is there an easier way to get the result?

## Answer by Alex C (score 1, accepted)

https://quant.stackexchange.com/a/46275

If you calculate (1+r1)*(1+r2)-1 = 11.1435% that gives you the TWR (Time Weighted Return) which is one widely used measure of return. It treats all periods equally, no matter the assets involved.

I am not familiar with the calculation you do in B17 and C18.

If I compute the IRR (internal rate of return) for the cash flows [-1000,-20000,+25810] I get 21.65% per month, which is similar but not identical to your B20 value of 21.9%. The IRR takes into account the actual amounts invested, so is also referred to as a MWR (Money Weighted Return). TWR and MWR are the 2 main ways of computing returns on a portfolio. They do not give the same value.

If you want a money weighted method, I suggest the IRR.

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