One of the most important and most common methods investors use to measure their returns is the time weighted rate of return formula. That’s because the time-weighted rate of return measures a compound rate of growth.
The time-weighted rate of return incorporates the impact of transactions such as portfolios rebalancing, contributions, and withdrawals. That leaves investors with a clearer picture of their portfolio’s overall performance.
What Is the Time-Weighted Rate of Return?
Starting with the basics, a return on investment (ROI) is a measure of how much money investments earn, or how much they’ve grown in value. Returns can be positive or negative (if a stock loses value following its purchase, for example). But obviously, investors make decisions with the goal of earning positive returns.
A rate of return, then, is a measure of the pace at which investments are accruing value, expressed as a percentage. The higher the rate of return, the better. Essentially, it’s a measure of a portfolio’s or investment’s performance over time. Rates of return can be calculated for certain time periods, such as a month or a year, and can be helpful when comparing different types of investments.
But investment portfolios are rarely static. Many investors make contributions or withdrawals to their portfolios on a regular basis. Many people contribute to their 401(k) with each paycheck, for example, or rebalance when market moves throw their asset allocation out of whack.
During these transactions, investors are buying and selling investments at different prices and times based on their investing strategy. That can make it more difficult and complicated to calculate a portfolio’s overall rate of return.
That’s where the time-weighted rate of return formula becomes useful. In short, the time-weighted rate of return formula takes into account a portfolio’s cash flows, and bakes in their effect on the portfolio’s overall returns. That gives investors a better, more accurate assessment of their portfolio’s performance.
That’s why the time-weighted rate of return calculation is, for many in the financial industry, the standard formula for gauging performance, over both the short- and the long-term.
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The Time-Weighted Rate of Return Formula
The time-weighted rate of return formula can look intimidating for even seasoned investors, but it’s an important step in building and maintaining an investment portfolio. But like many other financial formulas, once the variables are identified, it’s a matter of plug-and-play to run through the calculation.
First, let’s take a look at the basic portfolio return calculation:
Basic portfolio return = (Current value of portfolio – initial value of portfolio) ÷ initial value
While this formula provides a value, it assumes that an investor made one investment and simply left their money in-place to grow. But again, investors tend to make numerous investments over several time periods, limiting this calculation’s ability to tell an investor much about their strategy’s effectiveness.
That’s where the time-weighted rate of return comes in. In essence, the time-weighted formula calculates returns for a number of different time periods — usually additional purchases, withdrawals, or sales of the investment.
It then “weights” each time period (assigns them all roughly equal importance, regardless of how much was invested or withdrawn during a given period). Then, the performance of each period is included in the formula to get an overall rate of return for a specified period.
Calculating the time-weighted rate of return over the course of a year, for instance, would include the performance from each individual month. And, yes, that’s a lot of math. Computers and software programs can help, but it’s also doable the old-fashioned way.
This is what the time-weighted rate of return formula looks like:
Time-weighted return = [(1 + RTP1)(1 + RTP2)(1 + RTPn)] – 1
There are variables needed to calculate the equation:
n = Number of time periods, or months
RTP = Return for time period (month) = (End value – initial value + cash flow) ÷ (initial value + cash flow)
RTPn = Return for the time period “n”, depending on how many time periods there are
Let’s break it down again, and assume we’re trying to calculate the time-weighted return over three months. That would involve calculating the return for each individual month, three in all. Then, multiplying those returns together — “weighting” them — to arrive at an overall, time-weighted return.
How to Calculate Time-Weighted Rate of Return
To run through an example, assume we want to calculate a three-month, time-weighted return. An investor invests $100 in their portfolio on January 31. On February 15, the portfolio has a value of $102, and the investor makes an additional deposit of $5. At the end of the three-month period on April 30, the portfolio contains $115.
For this calculation, we wouldn’t think of our time periods as merely months. Instead, the time periods would be split in two — one for when a new deposit was made. So, there was the initial $100 deposit that would constitute a time period that ends on February 15. Then a second time period, when the $5 deposit was made, which constitutes a second time period.
With this information, we can make the calculation. That includes calculating the return for each time period during our three-month stretch. So, for time period one, the basic formula looks like this:
Return for time period = (End value – initial value + cash flow) ÷ (initial value + cash flow)
Now, we plug in our variables and calculate. Remember, there was no additional cash flow during this first period, so that won’t be included in this first calculation.
Time period 1:
($102 – $100) ÷ $100 = 0.02, or 2%
Then, do the same to calculate time period two’s return:
Time period 2:
[$115 – ($102 + $5)] ÷ ($102 + $5) = 0.074, or 7.4%
Now, take the returns from these two time periods and use them in the time-weighted rate of return formula:
Time-weighted return = [(1 + RTP1)(1 + RTP2)(1 + RTPn) – 1
With the variables — remember to properly use percentages!
TWR = [(1 + 0.02) x (1 + 0.074)] – 1 = 0.95, or 9.5%
So, the time-weighted return over this three-month stretch (which included two time periods for our calculation), is 9.5%. If we had simply done a basic return calculation, we’d reach a different number:
Basic portfolio return = (Current value of portfolio – initial value of portfolio) ÷ initial value
$115 – $100 ÷ $100 = 0.15, or 15%
That 15% figure is too high, because it doesn’t account for cash flow. In this case, that was a $5 deposit made in mid-February. The basic return formula folds that into the overall return figure. The time-weighted calculation gives us a more accurate return percentage, and one that accounts for that mid-February deposit.
While the time-weighted rate of return is an important measurement, it’s not the only way to look at a portfolio’s returns. Some investors may also choose to evaluate a portfolio or investment based on its money-weighted rate of return. That calculation is similar to the time-weighted rate of return because it incorporates inflows and outflows, but it does not break the overall investment period into smaller intervals.
Another common measure is the compound annual growth rate, (CAGR), which measures an investment’s annual growth rate over time and does not include the impact of inflows and outflows.
Having an accurate, timely view of a portfolio’s performance is critical for understanding current investments, planning future investments, and considering changes to your asset allocation. While other rate of return calculations can be useful, it’s important to understand their limitations.
The time-weighted rate of return formula is helpful because it takes into account the numerous inflows and outflows of money over various time periods. Armed with that insight, investors can adjust their strategy to try to increase their rate of return. That may mean reallocating or rebalancing their portfolio to include more aggressive investments or less risky securities.
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