# What is Time-Weighted Rate of Return?

Definition: The time-weighted rate of return (TWRR), also known as a geometric mean return, is a portfolio performance benchmark that calculates the compound rate of return of \$1 invested over a period of time.

## What Does Time Weighted Rate of Return Mean?

What is the definition of time-weighted return? Analysts use the WTRR to calculate the rate of return over multiple periods because the formula attributes equal weight to each sub-period returns. The benchmark takes into account external cash flow periods, and it splits these periods into sub-periods, which are compounded to produce the WTRR over the specified period.

The time-weighted rate of return formula is calculated using the beginning value (V0) and the ending value (V1) of a portfolio.

Let’s look at an example.

## Example

Matthew invested \$300,000 in December 2016. In October 2017, his portfolio value was \$292,897 and he made a contribution of \$18,555. In December 2017, the portfolio value was \$298,984. How can Matthew calculate the time-weighted rate of return of his portfolio for the period January 1 to December 31, 2017?

Matthew needs to calculate first the portfolio return of the first sub-period from December 2016 to October 2017 during which no external cash flow (contribution or withdrawal) occurred.

TWRR1 = (V1 – V0) / V0 = (\$341,897 – \$300,000) / \$300,000 = 0.1397

Then, Matthew needs to calculate the portfolio return of the second sub-period from October 2016 to December 2017 during which external cash flows occurred.

TWRR2 = (V1 – V0) / V0 = ((\$298,984 – (\$292,897 + \$18,555)) / (\$292,897 + \$18,555) = (\$298,984 – \$311,542) / \$311,542 = -0.040

Now that the returns of both sub-periods are calculated, Matthew can calculate the time-weighted rate of return of his portfolio over the entire period January 1 to December 31, 2017 by linking the sub-period returns.

TWWR = (1+TWRR1) x (1+TWWR2) – 1 = ((1+0.1397) x (1-0.040)) – 1 = (1.1397 x 0.960) – 1 = 1.094 – 1 = 0.094 = 9.4%

## Summary Definition

Define Time-Weighted Rate of Return: TWRR is an investment measurement that calculates the value of an investment adjusted for compound interest over time.

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