### What is Time-Weighted Rate of Return – TWR?

The time-weighted rate of return (TWR) is a measure of the compound rate of growth in a portfolio. The TWR 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. The time-weighted return breaks up the return on an investment portfolio into separate intervals based on whether money was added or withdrawn from the fund.

The time-weighted return measure is also called the geometric mean return, which is a complicated way of stating that the returns for each sub-period are multiplied by each other.

### Formula for TWR

Use this formula to determine the compounded rate of growth of you portfolio holdings.

﻿\begin{aligned} &TWR = \left [(1 + HP_{1})\times(1 + HP_{2})\times\dots\times(1 + HP_{n}) \right ] - 1\\ &\textbf{where:}\\ &TWR = \text{ Time-weighted return}\\ &n = \text{ Number of sub-periods}\\ &HP =\ \dfrac{\text{End Value} - \text{Initial Value} + \text{Cash Flow}}{\text{Initial Value} + \text{Cash Flow}}\\ &HP_{n} = \text{ Return for sub-period }n\\ \end{aligned}﻿

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### How to Calculate TWR

1. Calculate the rate of return for each sub-period by subtracting the beginning balance of the period from the ending balance of the period and divide the result by the beginning balance of the period.
2. Create a new sub-period for each period that there is a change in cash flow, whether it's a withdrawal or deposit. You'll be left with multiple periods, each with a rate of return. Add 1 to each rate of return, which simply makes negative returns easier to calculate.
3. Multiply the rate of return for each sub-period by each other. Subtract the result by 1 to achieve the TWR.

### What Does TWR Tell You?

It can be difficult to determine how much money was earned on a portfolio when there are multiple deposits and withdrawals made over time. Investors can't simply subtract the beginning balance, after the initial deposit, from the ending balance since the ending balance reflects both the rate of return on the investments and any deposits or withdrawals during the time invested in the fund. In other words, deposits and withdrawals distort the value of the return on the portfolio.

The time-weighted return breaks up the return on an investment portfolio into separate intervals based on whether money was added or withdrawn from the fund. The TWR provides the rate of return for each sub-period or interval that had cash flow changes. By isolating the returns that had cash flow changes, the result is more accurate than simply taking the beginning balance and ending balance of the time invested in a fund. The time-weighted return multiplies the returns for each sub-period or holding-period, which links them together showing how the returns are 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 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 the returns of different portfolios or investments. These periods are then geometrically linked to determine the time-weighted rate of return.

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.

### Key Takeaways

• The time-weighted return (TWR) multiplies the returns for each sub-period or holding-period, which links them together showing how the returns are compounded over time.
• ﻿The time-weighted return (TWR) helps eliminate the distorting effects on growth rates created by inflows and outflows of money.

### Examples of Using the TWR

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:

#### Scenario 1

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 (August 15), 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 second sub-period is created following the$100,000 deposit so that the rate of return is calculated reflecting that deposit with its new starting balance of $1,262,484 or ($1,162,484 + $100,000). The time-weighted return for the two time periods is calculated by multiplying each subperiod's rate of return by each other. The first period is the period leading up to the deposit, and the second period is after the$100,000 deposit.

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

#### Scenario 2

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 (August 15), 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 multiplying or 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.

### Difference Between TWR and ROR

A rate of return (ROR) is the net gain or loss on an investment over a specified time period, expressed as a percentage of the investment’s initial cost. Gains on investments are defined as income received plus any capital gains realized on the sale of the investment.

However, the rate of return calculation does not account for the cash flow differences in the portfolio, whereas the TWR accounts for all deposits and withdrawals in determining the rate of return.

### Limitations of the TWR

Due to changing cash flows in and out of funds on a daily basis, the TWR can be an extremely cumbersome way to calculate and keep track of the cash flows. It's best to use an online calculator or computational software. Another often-used rate of return calculation is the money-weighted rate of return.