# How to get returns when investment capital is changing?

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 However, what if there is new fund deposited or withdrawn?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. • You question does not seem to be formatted properly. Can you edit your question so that it is clear and readable? Commented Jan 1 at 2:57 • 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 Commented Jan 1 at 5:59 • thanks, the edited version got rid of the reformatted characters. Commented Jan 1 at 6:01 • 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. Commented Jan 1 at 11:07 ## 2 Answers 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). • 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. Commented Jan 1 at 21:13 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.

• Oops, yes, 100%, not 200%. Commented Jan 1 at 21:14