Time-Weighted Returns for Portfolios with Cash Flows
Summary
The document explains how portfolio returns can be reported when investors add or withdraw capital. It distinguishes investment performance from changes in account value caused by external cash flows, using an example in which an initial investment grows before another deposit is made. The example also corrects a return calculation: growth from $100 to $200 represents a 100% gain on the original capital.
The main method described is time-weighted return (TWR). It measures returns over intervals without cash flows, then compounds those interval returns; flows occur between intervals, after the portfolio is valued. The discussion notes that this requires reliable valuations at flow dates and that frequent valuations can be costly or operationally difficult, especially across markets in different time zones. It contrasts this approach with simple calculations whose result depends on whether new money arrived before or after a gain. The document offers a conceptual explanation rather than a complete reporting specification: it does not detail linked-return formulas, fee treatment, or other standards funds may follow.
Key ideas
- Time-weighted return separates portfolio performance from the timing and size of external cash flows.
- It calculates returns over periods between deposits or withdrawals and compounds those period returns.
- A gain from $100 to $200 is 100% on the starting capital, before considering later deposits.
- Accurate portfolio valuations are needed when capital flows occur.
- Frequent valuation points can raise cost and create difficulties across markets in different time zones.
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Full text
# How to get returns when investment capital is changing? # 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 However, what if there is new fund deposited or withdrawn?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. ## Answer by nbbo2 (score 0, accepted) https://quant.stackexchange.com/a/77875 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). ## Answer by KaiSqDist (score 0) https://quant.stackexchange.com/a/77874 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: - 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). - 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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