GIPHY / istock / getty

# What Is the Time-Weighted Return?

The time-weighted return (TWR) measures a portfolio’s compound growth rate while accounting for cash flow in and out. The calculation breaks down a portfolio or fund’s returns into “sub-periods” to represent its rate of return more accurately.

## Time-weighted return, explained

The time-weighted return measures a portfolio’s growth rate by breaking returns into intervals (sub-periods) based on when deposits or withdrawals occur. Also called the geometric mean return, it multiplies the return for each sub-period by each other to show the effects of compounding.

The purpose of the time-weighted return calculation is to eliminate distortions caused by frequent deposits and withdrawals. In doing so, it presents a more accurate reflection of your returns compared to other metrics.

### Calculating the time-weighted return

The formula for time-weighted rate of return is:

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

In this formula:

• HP = [end value – (beginning value + cash flow)] / (beginning value + cash flow)
• HPn = the return period for “n”
• N = the number of sub-periods (you can add as many as you need)

While the formula looks complex – and can take a while – the math is fairly straightforward.

You start by adding together your starting balance and the return period’s cash flow. Then, you subtract the sum from the ending balance for the period.

Next, you divide the difference by the starting balance (plus cash flow) for the same time frame.

You repeat this process for each sub-period where cash moves in or out via deposits or withdrawals to get multiple rates of return. Then, you add 1 to each rate of return. (This makes calculating negative returns easier.)

Finally, you multiply all of the rates of return together and subtract 1 to yield your time-weighted return.

## How does the time-weighted return affect you?

Determining your portfolio’s real rate of return becomes difficult if you’re constantly making deposits or withdrawals. The time-weighted return solves that problem by calculating the rate of return between each instance of cash flow.

By isolating return periods and multiplying returns together, you generate a more accurate result that also accounts for compound interest.

However, individual investors rarely use the TWR formula, as it gets more complex the more deposits and withdrawals you make. (If you’re just looking for a simple return rate, the basic rate of return (ROR) formula should suffice.)

Generally, TWR calculations are used by analysts and fund managers who want to analyze and compare asset or fund performance.

## What this means for you

The time-weighted return is a valuable tool to measure or compare the performance of a mutual fund or fund(s). But for most investors, the calculation is too cumbersome to bother with – ROR is often a more suitable formula.

Fortunately, with Q.ai, you can have your cake and eat it too. We provide the TWR of all your investments right in your reporting dashboard – and you don’t have to use a calculator once.

### A quick example of TWR

Suppose you want to use TWR to calculate a mutual fund’s performance. For simplicity’s sake, say that you only contribute on the first day of each month and calculate your sub-periods on the last day.

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

You initially invest a contribution of \$100,000. At the end of the first month, your portfolio is valued at \$100,500.

For the first month’s subperiod, your calculation would be:

HP1 = (100,500 – 100,000) / 100,000 = .005, or 0.5%

During the second month, you make an additional contribution of \$1,000. By the end of the second month, your portfolio balance is \$102,950.

For the second month’s subperiod, your calculation would be:

HP2 = (102,950 – (100,500 + 1,000)) / (100,500 + 1,000) = 0.014, or 1.4%

Finally, in the third month, you make another \$1,000 contribution. By the end of the month, your balance is \$104,550.

For the third month’s subperiod, your calculation would be:

HP3 = (105,750 – (102,950 + 1,000)) / (102,950 + 1,000) = 0.017, or 1.7%

Now, we can calculate our TWR by adding 1 to each sub-period, multiplying these numbers together, and subtracting 1:

TWR = (1+0.005) x (1+0.014) x (1+0.017) – 1 = 0.036, or 3.6% total time-weighted return.

## Disclosures

Q.ai is the trade name of Quantalytics Holdings, LLC. Q.ai, LLC is a wholly-owned subsidiary of Quantalytics Holdings, LLC ("Quantalytics"). Quantalytics offers automated financial advice tools through Quantalytics Investment Advisors, LLC ("QAI"), an SEC-registered investment advisor. QIA’s investment advisory services are ONLY available only to residents of the United States. Disclosures concerning QIA’s investment advisory services are available on its Form ADV filed with the SEC. The content in this newsletter is for informational purposes only and does not constitute a comprehensive description of Q.ai's investment advisory services.