# Time-Weighted Rate of Return

## What is the 'Time-Weighted Rate of Return'

The time-weighted rate of return is a measure of the compound rate of growth in a portfolio. Because this method eliminates the distorting effects created by inflows of new money, it is used to compare the returns of investment managers.

This is also called the geometric mean return, as the reinvestment is captured by using the geometric total and mean, rather than the arithmetic total and mean.

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## BREAKING DOWN 'Time-Weighted Rate of Return'

It is assumed that all cash distributions are reinvested in the portfolio and the exact same periods are used for comparisons. When calculating time-weighted rate of return, daily portfolio valuations are needed whenever there is an external cash flow, such as a deposit or a withdrawal. These periods are then geometrically linked to find the time-weighted rate of return.

## Calculation Examples

As noted, the time-weighted return eliminates the effects of portfolio cash flows on returns. To see this how it works, consider the following two investor scenarios:

Investor 1 invests \$1 million into Mutual Fund A on December 31. On August 15 of the following year, his portfolio is valued at \$1,162,484. At that point, he adds \$100,000 to Mutual Fund A, bringing the total value to \$1,262,484. By the end of the year, the portfolio has decreased in value to \$1,192,328.

The first period return, from December 31 to August 15, would be calculated as follows:

Return = (\$1,162,484 - \$1,000,000) / \$1,000,000 = 16.25%

The second period return, from August 15 to December 31, would be calculated as:

Return = (\$1,192,328 - (\$1,162,484 + \$100,000)) / (\$1,162,484 + \$100,000) = -5.56%

The time-weighted over the two time periods is calculated by geometrically linking these two returns as follows:

Time-weighted return = (1 + 16.25%) x (1 + (-5.56%)) - 1 = 9.79%

Investor 2 invests \$1 million into Mutual Fund A on December 31. On August 15 of the following year, her portfolio is valued at \$1,162,484. At that point, she withdraws \$100,000 from Mutual Fund A, bringing the total value down to \$1,062,484. By the end of the year the portfolio has decreased in value to \$1,003,440.

The first period return, from December 31 to August 15, would be calculated as follows:

Return = (\$1,162,484 - \$1,000,000) / \$1,000,000 = 16.25%

The second period return, from August 15 to December 31, would be calculated as:

Return = (\$1,003,440 - (\$1,162,484 - \$100,000)) / (\$1,162,484 - \$100,000) = -5.56%

The time-weighted over the two time periods is calculated by geometrically linking these two returns as follows:

Time-weighted return = (1 + 16.25%) x (1 + (-5.56%)) - 1 = 9.79%

As expected, both investors received the same 9.79% time-weighted return, even though one added money and the other withdrew money. Eliminating the cash flow effects is precisely why time-weighted return is an important concept that allows investors to compare the investment returns of their portfolios and any financial product.

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