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

This measure is often used to compare the returns of investment managers because it eliminates the distorting effects on growth rates created by inflows and outflows of money.

#### Time-Weighted Rate of Return

### BREAKING DOWN Time-Weighted Rate of Return

The figure is found by multiplying the number of holding-period returns that are linked together or compounded over time.

When calculating the time-weighted rate of return, it is assumed that all cash distributions are reinvested in the portfolio. Daily portfolio valuations are needed whenever there is an external cash flow, such as a deposit or a withdrawal, which would denote the start of a new sub-period. In addition, sub-periods must be the same to compare returns of different portfolios or investments. These periods are then geometrically linked to find the time-weighted rate of return.

The time-weighted rate of return of an investment can be calculated using the following formula, where:

- N = Number of sub-periods
- HPR = (End Value - Initial Value + Cash Flow) / (Initial Value + Cash Flow)
- HPR
_{N}= Return for sub-period N

Time-Weighted Rate of Return = **[(1 + HPR _{1}) * (1 + HPR_{2})... * (1 + HPR_{N})] - 1**

Because investment managers that deal in publicly traded securities do not typically have control over fund investors' cash flows, the time-weighted rate of return is a popular performance measure for these types of funds as opposed to the internal rate of return (IRR), which is more sensitive to cash-flow movements.

### 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 holding-period return for the first period, from December 31 to August 15, would be calculated as:
- Return = ($1,162,484 - $1,000,000) / $1,000,000 = 16.25%

- The holding-period return for the second period, 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 return over the two time periods is calculated by geometrically linking these two returns:
- 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 holding-period return for the first period, from December 31 to August 15, would be calculated as:
- Return = ($1,162,484 - $1,000,000) / $1,000,000 = 16.25%

- The holding-period return for the second period, 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 return over the two time periods is calculated by geometrically linking these two returns:
- 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.