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This question came out of the Kelly rule. Curious how returns are calculated when allocated investment is changing on the course.

Let's say an investment start with \$100, if the investment hasn't changed over time, then its return would be just be based on the \$100. However, what if there is new fund deposited or withdrawn? For example, when the \$100 has grown to \$200 from the original $100 capital (200% over time), there is additional \$100 deposited. Should the 200% be recalibrated based on \$300? Similarly what happen when there are withdraws? A practical use of this question is what methods funds report their returns.

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  • $\begingroup$ You question does not seem to be formatted properly. Can you edit your question so that it is clear and readable? $\endgroup$
    – KaiSqDist
    Commented Jan 1 at 2:57
  • $\begingroup$ oh, I see the problem in the post. For some reasons, my original text got reformatted. I didn't think I used special format, just plain text. Let me see if I need to re-write it $\endgroup$
    – user70540
    Commented Jan 1 at 5:59
  • $\begingroup$ thanks, the edited version got rid of the reformatted characters. $\endgroup$
    – user70540
    Commented Jan 1 at 6:01
  • $\begingroup$ The dollar sign is a a formatting character, to just have a plain dollar sign in your text you have to 'escape it' by preceding it with a backslash. $\endgroup$
    – nbbo2
    Commented Jan 1 at 11:07

2 Answers 2

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You ask "what methods funds report their returns". In the US they generally use the TWR (time weighted return) method. Essentially returns are measured over short periods (as short as 1 day) where there is no cash inflo/outflow during the period, and then these periods returns are chained together by compounding. Inflows/ouflows take place at the instant between a period end and the next period beginning (ex: in hedge funds you are only allowed to add money at the end of the month, in mutual funds only at the end of a day). At an inflow/outflo point you need a full and accurate valuation of the existing portfolio (which makes it too costly to allow inflows/outflows every second, it also makes problems for global funds that trade in different time zones in markets that may not all be open at a specific time).

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  • $\begingroup$ Thanks for pointing out the dollar sign is a special character. First time post so wasn't aware of it. I marked your answer as the solution as it explained fund inflow/outflow duration and compounding. I think actual cases may be more complicated, as Kai pointed out about dividends etc. $\endgroup$
    – user70540
    Commented Jan 1 at 21:13
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TBH your explanation is still a bit confusing, are you saying that an initial investment of \$100 grows to \$200? (this is 100% return not 200% btw). After that, there is an additional \$100 deposited? This results in the final \$300 I suppose?

Unless you are saying that you are attributing the 200% return to both the return of \$100 and additional \$100 deposit? I think this computation of return does not make sense as returns are attributed to dividends/coupons or the appreciation of assets and not capital inflows.

To me, it only comes down to 2 cases:

  1. The \$100 is deposited after the \$100 return - this is a 100% return as the return is based on the initial \$100 capital (\$200/\$100 - 1 = 100% return).
  2. The \$100 is deposited before the \$100 return - this is a 50% return as the return is based on the \$200 capital (\$300/\$100 - 1 = 50% return).

I think funds themselves have a way of computing returns such that they adjust for the timing of capital inflows/outflows such that they only compute returns based on dividends/coupons or the appreciation of assets.

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  • $\begingroup$ Oops, yes, 100%, not 200%. $\endgroup$
    – user70540
    Commented Jan 1 at 21:14

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