True time-weighted rate of return

The time-weighted return (TWR) (or true time-weighted rate of return (TWRR)) is a method of calculating investment return. To apply the time-weighted return method, combine the return over sub-periods, by compounding them together, resulting in the overall period return. The rate of return over each different sub-period is weighted according to the duration of the sub-period.

The time-weighted method differs from other methods of calculating investment return only in the particular way it compensates for external flows - see below.

For an understanding of why this method is called "time weighted", consider an example where we are tasked with calculating the annualized rate of return over a five-year period of an investment which returns 10% p.a. for two of the five years, and -3% p.a. for the other three. The time-weighted return over the five-year period is:

and after annualization, the rate of return is:

The reason why this is called "time-weighted" can be partly understood by observing that the length of time over which the rate of return was 10% was two years, and the two-year "weight" appears in the power of two on the 1.1 factor:

Likewise, the rate of return was -3% for three years, and the three-year "weight" appears in the power of three on the 0.97 factor. The result is then annualized over the overall five-year period.

More generally, if an annualized rate of return ${\displaystyle r_{1}}$ applies over a period of ${\displaystyle t_{1}}$ measured in years, ${\displaystyle r_{2}}$ over another period of ${\displaystyle t_{2}}$ years, etc. then the time-weighted return over the overall period of ${\displaystyle T=t_{1}+t_{2}+t_{3}+...+t_{n}}$ years is:

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