How do you annualize multiple year returns?

The simple return on equity refers to the total income divided by the total shareholders' equity over any specified period of time. For example, you use the simple return on equity to find the overall growth rate during the time you held a stock, but because of compounding, you can't simply divide the total return on equity by the number of years you held the investment. Compounding refers to the fact that as returns are added to an account, those returns then begin to generate additional returns, increasing the growth.

Step 1

Divide the simple return by 100 to convert it to a decimal. For example, if your return on equity over the five-year life of the investment is 35 percent, divide 35 by 100 to get 0.35.

Add 1 to the result. In this example, add 1 to 0.35 to get 1.35.

Divide 1 by the number of years you held the investment. For example, if you held the investment for five years, divide 1 by 5 to get 0.2.

Raise the Step 2 result to the power of the Step 3 result. In this example, raise 1.35 to the 0.2 power to get 1.0619.

Subtract 1 from the result to calculate the annualized return as a decimal. In this example, subtract 1 from 1.0619 to get 0.0619.

Multiple the result by 100 to calculate the annualized return expressed as a percentage. Completing the example, multiply 0.0619 by 100 to get 6.19 percent.

Tips

• A calculator is significantly helpful when calculating powers. Usually, the power function on a calculator is shown as "^" or "x^y."

Writer Bio

Based in the Kansas City area, Mike specializes in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."

As an investor, you want to make smart choices with your money. One way to do that is by figuring an investment's annualized total return. The annualized total return tells you the average return (or loss) of an investment over a 12-month period. It's often given as a percentage.

You can find annualized total return for many types of investments, including stocks, bonds, mutual funds, real estate, and more. By doing so, you can compare two distinct types of investments, such as a stock purchase vs. a real estate investment. You can do it even if these investments are held during different periods of time.

Learn more about annualized total return and how to find it.

What Is Annualized Total Return?

Annualized total return calculates the average amount of money earned by an investment on an annual basis. This may be over the course of a calendar year, or it may be for an alternative 12-month period. 

Note

Annualized total return is different from average annual return. Annualized total return accounts for compounding over an investment period, while average annual return does not.

Knowing annualized total return is helpful when the return of an investment in dollar terms is known, but the actual percentage rate is not. It also allows you to compare the investments' returns over different periods of time.

For instance, suppose you've held a stock for a certain number of years and a real estate investment for a different number of years. Using the annualized total return, you can directly compare how well these two investments have performed.

You could compare two mutual funds with a change in value over a different number of years. Annualized total return is a good way to compare the success of your investments.

How Annualized Total Return Works

Let’s say you want to compare the performance of two mutual funds. To do so, you need to know two variables: the return for a given period of time, and how long the investment was held.

Here's the equation:

In the above equation, “R” is the return, and “N” is the number of years the investment was held.

Let’s say you own a mutual fund, and it has had these annual returns over a period of four years: 7%, 10%, 8%, and 12%. When plugged in, the equation would be:

Annualized Total Return = {(1 + .07) x (1 + .10) x (1 + .08) x (1 + .12)1 / 4 - 1 or 1.09232 - 1 = .09232 x 100 (to express as a percent) = 9.23%.

So, the annualized total return of the mutual fund is 9.23%. Suppose you then wanted to compare the return of this mutual fund with another, and it gives different annual returns across a two-year period. You would then repeat the equation, putting in the new percentages for R, and two for N, instead of four. 

Annualized Total Return vs. Average Annual Return

Often, an investment is assessed in terms of average annual return rather than annualized total return. Be aware that these two metrics are not the same.

Average annual return is simply the total return over a time period, divided by the number of periods that have taken place. It ignores compounding, which annualized total return takes into account.

Average return is often used to assess the performance of a mutual fund or compare two or more. If a fund returned 12% one year, lost 20% the next year, and gained 15% in the third year, the three-year average annual return would be:

Average Return = (12% + -20% + 15%) / 3 years = 2.33%

The annualized total return for that same three years would be much different. Plugging the same numbers into the formula for finding annualized total return looks like this:

Annualized Total Return = {(1.12) (.80) (1.15)}1/3 – 1 = 0.0100 x 100 ≈ 1.00%

In the year the investment lost 20%, you have 80% of the balance from the end of the first year. This is why you multiply by .80. You can see the impact that second year’s loss has on the annualized total return vs. the average annual return.

Annualized total return accounts for compounding; the loss of 20% in year two drags on the positive impact.

The Benefit of Annualized Total Return

The annualized total return, compared to the average return, is often a clearer snapshot of the worth of the investment.

Annualized total return gives you a preview of the performance of investments, but keep in mind that it does not give any indication of price fluctuations or volatility. When looking at metrics, investors tend to put a higher value net earnings, or the amount of money an investment has made or lost over a period of time, after subtracting fees.

Key Takeaways

• Annualized total return allows you to compare two different investments over varying periods of time. 
• It often provides a clearer snapshot of the worth of the investment, as it accounts for compounding.
• While the metric provides a preview of an investment’s success, it does not give any indication of price fluctuations. 

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