# TWR vs. IRR: How Do They Differ?

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The time-weighted rate of return measures how your investments have performed in a vacuum. Basically, for the assets that you purchased, it determines how much have they gained or lost value. Internal rate of return measures how your portfolio has performed based on your contributions, transactions and withdrawals. Given your money management strategy, this strategy looks at how much your investment has gained or lost value. One measures the objective strength of an investment while the other measures the subjective strength of your portfolio. Here’s what you need to know.

Consider working with a financial advisor if you need help determining an investment strategy for your portfolio.

## What Is Rate of Return?

The rate of return measures how much a given portfolio or asset has changed in value over time. For example, if you invest \$1 and have \$1.10 a month later, your rate of return is 10%. Investors have a number of different ways that they can measure the rate of return based on what they’re trying to learn and based on the nature of the underlying assets.

The most common three are known as simple rate of return, time-weighted rate of return (TWR) and internal rate of return (IRR). Internal rate of return is also known as the dollar-weighted rate of return. Each measures a different aspect of a portfolio.

## What Is a Simple Rate of Return?

A simple rate of return is rarely used. With this approach, you compare nothing more than the end value of a portfolio with the starting value of the portfolio. For example, say that you invest \$1,000 in a stock. Three years later you have \$1,250. The simple rate of return would be:

• (Final – Beginning) / Beginning = Simple Return
• (\$1,250 – \$1,000) / \$1,000 = 0.25

This portfolio has grown by 25%. The problem with a simple rate of return is that it gives you no further information. You don’t know how the assets performed while you held them, nor do you know how your contributions and withdrawals affected that growth. This leaves you unable to evaluate how your investment compared against the market at large, and how your personal strategy affected the portfolio’s value. For this reason, investors relatively rarely use a simple rate of return.

## What Is the Time-Weighted Rate of Return?

Time-weighted rate of return (TWR) measures how the value of an investment or asset changed over time while correcting for the distorting effect of cash flow in your account. This allows you to see how your investment has performed objectively so that you can compare it against other investments and strategies on the market.

When you calculate the time-weighted rate of return, you do so by calculating periods known as “holding intervals.” These are any set of times in which the value of your portfolio has significantly changed. You then compare the results of each holding interval against each other to see how the investment’s value has changed over time. Using this method corrects for any contributions, distributions and transactions that you made during the holding period so that you can measure how the asset’s value changed over time.

The most common windows for a time-weighted rate of return are quarterly (every three months), biannually or annually. For example, say that you invest \$1,000 in ABC Co. stock. You would like to measure your time-weighted rate of return based on ABC Co.’s quarterly performance. You have the following information:

• Q1 Starting Value – \$1,000
• Q1 Final Value – \$1,200
• Q1 Return – 20%
• Q2 Starting Value – \$1,200
• Q2 Final Value – \$1,100
• Q2 Return – -8%
• Q3 Starting Value – \$1,100
• Q3 Final Value – \$1,400
• Q3 Return – 27%
• Q4 Starting Value – \$1,400
• Q3 Final Value – \$1,500
• Q4 Return – 6%

The basic formula for the weighted rate of return is:

• TWR = [(1 + R1) * (1 + R2) * … (1 + RN)] – 1, where R is a given period’s return and N is the last number in the set

Here, we are looking to measure four periods, so N goes to 4. Our result is:

• TWR = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)] – 1
• TWR = [(1 + 0.20) * (1 + -0.08) * (1 + 0.27) * (1 + 0.06)] – 1
• TWR = [1.2*0.92*1.27*1.06] – 1
• TWR = 1.48 – 1
• TWR = 48%

Time-weighted rate of return is used to figure out how an asset or strategy performed on its own merits. You can use this to compare an investment against other assets on the market or to compare the strategies of different brokers or systems.

## What Is the Internal Rate of Return?

The internal rate of return is, in some ways, the opposite of the time-weighted rate of return. With this approach, you evaluate the rate of return based on your cash flows and transactions over a period of time. The goal of IRR is to figure out how your specific strategy and money management performed.

The approach to IRR is similar to the time-weighted rate of return. You select a specific holding period and calculate the investment’s rate of return over that window of time, then repeat the analysis for the period that you want to analyze. However, in the case of IRR, you must use the same holding period for each interval, while with TWR you can define holding periods broadly.

For example, say that you invest in XYZ Co. stock. The stock starts at \$10 per share in January and then increases to \$15 per share in June. You invested \$1,000 in XYZ Co. in January, buying 100 shares of stock. After the stock price increases, you invest another \$750 in June, buying 50 shares of stock. You now have 150 shares of stock at \$15 per share, for a total value of \$2,250.

Your IRR for this investment would be approximately 33% (\$1,500 investment over time / \$2,250 investment value). Your investment has a lower rate of return than its simple or time-weighted rates would reflect because you invested more later when the price of the stock went up. Your initial \$1,000 investment had a 50% rate of return while your subsequent \$750 investment had none.

This is also a very back-of-envelope version of IRR. It works because we used one time period, but it’s primarily by way of example. The formula to calculate the internal rate of return is:

• 0 = C0 + C1 / [(1+IRR)] + C2 / [1+IRR)^2] … + CN / [(1 + IRR)]^N

Here, C is your period cash flow over the period in question. So C0 is your initial investment. Then, C1 would be your total contributions and withdrawals over the first period. C2 would be your total contributions and withdrawals over the second period, and so on. N is the number of periods you are measuring. Each period must be the same length, for example, quarters or months.

This will give you the rate of return based on cash flow over time. If you did not make any contributions or withdrawals, your internal rate of return and your time-weighted rate of return will be the same. Otherwise, you will get a rate of return that reflects how your money management affected your gains or losses.

## Bottom Line

Time-weighted rate of return tells you how an investment or asset performed over time, accounting for fluctuations. Internal rate of return tells you how your own investment performed over time, accounting for how you added and withdrew money. You may want to get some professional advice to help you find the right way to analyze your own investments so you can make the right decisions moving forward.

## Technical Analysis Tips

• We did not have space in this article to get into the weeds, but there’s much more to know about how the Time-Weighted Rate of Return can help you account for cash flows when trying to analyze your objective returns. Let’s take a look at how you can calculate your deposits, dividends and withdrawals.