Time Weighted Return

Method of calculation to account for external flows in a portfolio (deposits, withdrawals). It does so by considering internal timeframes and calculating the return in each timeframe, then compounding them together.

Suppose that the portfolio is valued immediately after each external flow. The value of the portfolio at the end of each sub-period is adjusted for the external flow which takes place immediately before. External flows into the portfolio are considered positive, and flows out of the portfolio are negative.

$1+R=\frac{M_1-C_1}{M_0}\times \frac{M_2-C_2}{M_1}\times \frac{M_3-C_3}{M_2}\times \cdots \times \frac{M_{n-1}-C_{n-1}}{M_{n-2}}\times \frac{M_n-C_n}{M_{n-1}}$ where

$R$ is the time-weighted return of the portfolio,

$M_0$ is the initial portfolio value,

$M_t$ is the portfolio value at the end of sub-period $t$, immediately after external flow $C_t$,

$M_n$ is the final portfolio value,

$C_t$ is the net external flow into the portfolio which occurs just before the end of sub-period $t$,

and

$n$ is the number of sub-periods.

Source: https://en.wikipedia.org/wiki/Time-weighted_return

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