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The Math of the Time-Weighted Return (TWR)
The one thing we know for sure is the claim that the lone investor will have at the end of
the period. The investor will look at how much the pot grew between the point of the
investment and the end of the period: it grew from
V_{2} + I
to V_{3}, that is, by a factor of

Therefore, the total claim of all the other investors at the end of the period is what's left:

This means that the other investors' claim has grown
from V_{1} to

over the course of the period. It has thus grown by a factor of

The return that the fund must publish for that period is that factor minus 1:

Inspecting the expression

in there, that is, the factor by which the investors' claim grew over the course of the
period, we see that this is in fact the result of a compounding. The first
part, V_{2}/V_{1},
describes the return of the fund from the beginning of the period to the point just prior to
the investment. The second part,

describes the return of the fund from the point just after the investment to the end of the period.

Assume that there was just a single redemption during the reporting period. The data that we need for the calculation of the time-weighted return is the analogue of what we needed in the case of a single investment: