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

What’s the first metric that comes to mind when it comes to measuring your investment performance? If you’re like most investors, the answer is the growth rate. Investing is all about making your money work for you.

However, figuring out the growth rate of your investment portfolio probably seems a bit more complicated than it should. That’s because there are so many different ways to go about calculating it, each coming up with a different answer.

However, one method weeds out the noise and provides such an accurate assessment of your portfolio’s performance that it’s the default benchmark used by investment managers at the helm of exchange-traded funds (ETFs) and mutual funds.

It’s known as the time-weighted rate of return.

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But what exactly is the time-weighted rate of return, how do you calculate it, and why is it considered the gold standard when measuring a portfolio’s performance?

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

The time-weighted return of an investment is a relatively simple calculation to show investors what percentage returns their portfolio has experienced over a predetermined period of time. The fact that it ignores cash flows is what makes the rate of return such a compelling indicator of a portfolio’s performance.

The time-weighted rate of return is a calculation that would completely ignore the fact that 25% of the portfolio’s value was taken out of the portfolio. Instead you can see how the money you do have invested has performed over time. Here’s how it works:

## 3 Steps to Calculate the Time-Weighted Return

There are three broad steps to calculating the TWR of an investment portfolio:

### Step #1: Divide the Overall Time Into Sub-Periods

In order for the calculation to weed out the noise of cash inflows and outflows, you’ll need to divide the overall period of time into sub-periods based on when these deposits and withdrawals took place.

Every time you put money into or take money out of your portfolio, you’re ending the previous sub-period and starting a new one. If you haven’t made any contributions or taken any money out over the period of time you’re looking into, there will only be one sub-period.

### Step #2: Calculate Sub-Period Rates of Return (RoR)

Now, it’s time to calculate each sub-period return. To do so, divide the ending balance at the end of the sub-period by the beginning balance, and subtract 1. Here’s the equation:

Sub-Period Return = (Ending Value / Starting Value) – 1

Do this for each sub-period you have in your overall time period, resulting in a rate of return for each period.

### Step #3: Find the Geometric Mean

To find the geometric mean, you’ll add one to each period return, multiply them together, and subtract 1. The resulting percentage is the percentage gain or loss the portfolio has experienced on a time-weighted basis — your time-weighted rate of return.

## TWR Example Calculation

The steps above may seem like quite a bit to follow, so let’s break it down with a realistic example. For simplicity’s sake, let’s say John Doe invested 100% of his portfolio in the S&P 500, meaning we can use real-world data from the S&P 500 to form the example. To keep the calculations simple, we’ll assume Doe contributed the exact value of the S&P 500 each time he added funds, but you’ll use whatever dollar amount you contribute or withdraw to run these numbers yourself.

Mr. Doe wants to know his TWRR from January 28, 2021, to January 28, 2022. On January 28, 2021, he started with an initial investment of \$3,787.38. When stocks dipped in early March, he decided to add another \$3,768.47 to his portfolio on March 4. He then added another \$4,513.04 to his portfolio on December 1 when he got an end-of-the-year holiday bonus.

Here’s how Mr. Doe would do the return calculation:

#### Step #1: Find the Sub-Periods

The initial investment was made on January 28, 2021, with the next investment on March 4. Therefore, sub-period one ranges from January 28, 2021 through March 4, 2021.

He made his next contribution on December 1, 2021, meaning March 4, 2021 to December 1, 2021 is the second period.

Finally, December 1, 2021 to January 28, 2022 represents the third period.

#### Step #2: Calculate Period Returns

During the first period, John Doe’s portfolio fell from a value of \$3,787.38 to a value of \$3,768.47. Dividing \$3,768.47 by \$3,787.38 and subtracting 1 shows the rate of return in this period came to -0.005, or -0.5%.

Then Doe added a contribution, so in period 2 the starting balance was \$7,536.94. The ending balance was \$9,026.08. When you divide \$9,026.08 by \$7,536.94 and subtract 1, you come to 0.1976, or a 19.76% return for the period.

Finally, Doe made his last contribution. Period 3 had a starting balance of \$13,539.12 and an ending balance of \$13,109.61. Dividing the ending balance by the starting balance and subtracting 1 shows a loss of 0.0317, or -3.17% for this sub-period.

So, the overall returns for all three periods were:

1. Period 1: -0.005 (-0.5%)
2. Period 2: 0.1976 (+19.76%)
3. Period 3: -0.0317 (-3.17%)

#### Step #3: Find the TWR Using the Geometric Mean.

Start by adding 1 to all the values above, bringing you to the values of:

1. Period 1. 0.995
2. Period 2. 1.1976
3. Period 3. 0.9683

Now, John multiplies these three values together and gets 1.1538.

Now, by subtracting 1, Mr. Doe will find that his portfolio performance on a TWR basis was 0.1538 (15.38%) for the period ranging from January 28, 2021 to January 28, 2022.

## What Time-Weighted Return Measures

As the name of the metric suggests, time-weighted returns measure portfolio returns over a period of time. However, looking at the example above, you’ll find something interesting if you dig deep enough.

During the period from January 28, 2021 to January 28, 2022, the overall return of the S&P 500 also came in at 15.38%. The example was written with the S&P 500 as the underlying asset to make exactly this point.

Although Doe made three total contributions to his portfolio, the returns of his portfolio were exactly that of the underlying assets, no more, no less, regardless of the contributions he added and when.

With the calculation’s ability to weed out cash flows, it provides a full view of exactly what investors are earning on their investments.

## TWR vs. Other Rates of Return

Determining the return of your investment portfolio is often a difficult task, largely because there are so many calculations you can use that each come to a different result. The key is choosing the right rate of return to use for the situation at hand.

### Money-Weighted Rate of Return (MWR)

Another commonly used calculation is known as the money-weighted, or dollar-weighted, return. This return rate focuses on both the returns of the underlying assets held by the portfolio and cash flows in and out of the portfolio.

Using the example of John Doe’s portfolio above, on January 28, 2021, he started with an initial investment of \$3,787.38 and had an ending balance on January 28, 2022 of \$13,109.61.

Calculating the MWR is best done in a spreadsheet like Microsoft Excel or Google Sheets by plotting the start date, followed by the date of each contribution, and the end date in column A. In column B, plot all contributions as positives and the ending balance as a negative (as though you were withdrawing the balance at the end).

Then, use the internal rate of return (XIRR) function in your spreadsheet to find the MWR for the column of values. When you’re done, your chart should look like this (based on the John Doe example above).

Based on the data we have, John Doe’s MWR comes to 13.25%, a pretty far cry from the TWR of 15.38%.

So, what makes the difference?

The money-weighted return tracks the contributions and deductions made in a portfolio, and the timing of these moves. Since John Doe’s biggest contribution was made right before a market correction led to significant declines, and the market hadn’t recovered by the end of the overall time period, his MWR was affected pretty significantly.

Here are the ways in which MWR and TWR differ:

### The Modified Dietz Model

The Dietz model was created by Peter Dietz in 1960 as a way to calculate your money-weighted return rate in a less computer-intensive way. Today, computers are far more powerful than anything in 1960, and the need for less intensive computing doesn’t exist anymore.

Today, the Dietz model provides an easier method for calculating your true money-weighted return. However, it’s important to mention that the modified Dietz model doesn’t always provide an accurate depiction of your MWR.

This return model requires the portfolio value on the start date and end date, but unlike the traditional TWRR, you won’t need to know your portfolio’s overall value on the date of each cash flow. You will need to know the date and amount of each cash flow event, and whether it’s an inflow or outflow. The Corporate Finance Institute offers an in-depth look at the Modified Dietz Model and the formula if you’re interested in learning how it works.

Here are the key differences between the TWR and the Dietz Model:

## TWR Pros and Cons

As with any metric used to gauge the performance of an investment portfolio, there are pros and cons to consider when using the time-weighted rate of return.

### TWR Pros

The time-weighted return is a widely used metric for determining the performance of a portfolio. Here’s why:

• Measures the Actual Return of Assets. This is the most accurate way to determine the performance of assets within your portfolio in terms of how they perform over time. By weeding out the noise of account contributions and deductions, the metric gives you the ability to see exactly how assets in your portfolio are performing.
• Simplicity. At first glance, the metric seems intimidating to calculate. When you break it down, you’ll find that it’s actually quite simple, offering a tool that all investors can use to assess their market performance.
• The Standard Measure Used by Portfolio Managers. The TWR is considered the gold standard of performance metrics among investment managers, suggesting it’s a metric you can trust.

### TWR Cons

Although there are plenty of reasons to incorporate time-weighted rate of return in your efforts to track your performance, there are also a few reasons you might skip the metric altogether. These include:

• An Inaccurate Judge of Hard Money Returns. While the metric does a great job of outlining the average returns of underlying assets, when contribution and deduction timing is kept out of the mix, you don’t get the real picture of what’s going on in your unique portfolio. After all, large contributions or deductions made right before big movements in the market can make significant differences in your actual overall return.
• Time Consuming for Active Investors. If you’re a passive, buy-and-hold investor who contributes new money infrequently, calculating your TWR will be simple and relatively quick. However, if you make regular contributions to your account — say on a weekly basis — this calculation will become time consuming, because sub-periods must be calculated each time a contribution or deduction takes place. Weekly contributions mean there will be 52 sub-periods to calculate to determine the time-weighted rate of return over the course of a year.

## Final Word

Because the time-weighted rate of return doesn’t take contributions or deductions into account, it has its limitations as a measure of your portfolio’s real return. However, it is a great metric for determining whether the underlying assets within your portfolio are beating benchmark averages.

For a total picture of your portfolio’s performance, it’s best to look into both time-weighted and money-weighted rates of return. By looking at both of these, you’ll be able to determine how the assets you’ve chosen are performing overall as well as how the timing and amount of your contributions and deductions have assisted in growth or otherwise.

These are great tools to have, especially when reassessing opportunities within your portfolio or during regular portfolio balancing.