What Is Time-Weighted Rate of Return (TWR)?

Definition and Examples of Time-Weighted Rate of Return (TWR)

Investors and analysts can use multiple measurements to calculate the rate of return on a particular investment or portfolio. Some measurements can provide distorted results due to the effects of incoming and outgoing cash flow. The time-weighted rate of return (TWR) uses a unique formula that eliminates these misleading effects.

TWR might be used when comparing the performance of multiple mutual funds. Fund managers aren’t responsible for the cash flows into and out of the mutual fund. So to include those cash flows in the returns would provide misleading results. This measurement helps calculate returns separate from those cash flows.

• Alternative name: Geometric mean, geometric average
• Abbreviation: TWR, TWRR

How Does Time-Weighted Rate of Return Work?

TWR calculates the rate of return for multiple sub-periods based on changes in cash flow. It’s essentially a calculation of the investment returns that a manager generates over specific time periods that are geometrically linked or compounded. The formula used to calculate the time-weighted rate of return looks like this:

TWR = [(1+HP1) x (1+HP2) x (1+HPn)] – 1

In this formula:

• n = the number of sub-periods
• HP = (End Value - (Beginning Value + Cash Flow)) / (Beginning Value + Cash Flow)
• HPn = Return for sub-period n

To calculate TWR, you must find the return for each sub-period by subtracting the sum of the starting balance and the cash flow from the ending balance. Then you divide the result by the sum of the starting balance and cash flow.

Any time new cash flow moves into or out of the fund, a new sub-period begins. After adding the cash flow to each HP value, it is multiplied by other cash flows.

Let’s use this formula to look at a more realistic example. Suppose you wanted to use TWR to calculate the performance of a mutual fund. You initially invest with a contribution of $100,000, and at the end of the first month, your portfolio is valued at $100,850. You would run the following formula, which is a part of the total TWR formula:

HP1 = (100,850 - 100,000) / 100,000 = 0.8%

Now suppose that during the second month, you make an additional contribution of $1,000. By the end of the period, your portfolio balance is $102,870. The formula would look like this:

HP2 = (102,870 - (100,850 + 1,000)) / (100,850 + 1,000) = 1%

Finally, in the third month, you make the same contribution of $1,000. By the end of the month, your portfolio balance is $109,100. The formula looks like this:

HP3 = (103,390 - (102,870 + 1,000)) / (102,870 + 1,000) = -0.4%

Once you’ve done the calculations for each separate sub-period, you can run the full TWR formula. Here’s what that would look like, using the numbers above:

TWR = [(1+.008) x (1+0.01) x (1+ -.004)] – 1 = 1.4%

In the example above, you can see that your time-weighted rate of return is 1.4% over a three-month period. 

Time-Weighted Rate of Return vs. Rate of Return

Rate of return (RoR) is another method for calculating the profit or loss on an investment over a specific period of time. Unlike TWR, this calculation doesn’t eliminate the effects of incoming and outgoing cash flows.

Rate of return, expressed as a percentage, calculates the return on a particular investment using the initial investment and the total profit or loss from the investment. The formula to calculate RoR is:

RoR = (Net profit or loss / initial investment) x 100

Instead of accounting for incoming and outgoing cash flows, it simply counts the total investment as one large sum. When the ROR is positive, it is considered an investment gain and when the ROR is negative, it reflects a loss. The rate of return can be valuable for an individual investor to determine their return on a specific investment. However, it’s not as helpful in comparing the returns of multiple portfolios.

What TWR Means for Individual Investors

It’s important for investors to understand the returns on investments in their portfolios or investments they’re considering adding to their portfolios. 

If you’re simply looking for the return on a particular investment, the rate of return may be a more useful calculation. You can find return information by visiting either your online brokerage account or the brokerage’s website to track a particular asset.