# Annualized Total Return Formula and Calculation

> **Definition**
>
> Annualized total return is the average return an investment has generated annually over a period of several years.

## What Is Annualized Total Return?

An annualized total return is the average annual return earned by an investment over several annual periods. The annualized return formula is calculated as a geometric average to show what an investor would earn over a specified period if the annual return were compounded.

An annualized total return provides only a snapshot of an investment's performance and does not give investors any indication of its [volatility](https://www.investopedia.com/terms/v/volatility.asp) or price fluctuations.

### Key Takeaways

*   An annualized total return is the [geometric average](https://www.investopedia.com/terms/g/geometricmean.asp) amount of money an investment earns each year over several annual periods.
*   The annualized return formula shows what an investor would earn over a specified period if the annual return were compounded.
*   Calculating the annualized rate of return needs only two variables: the returns for a given period and the time the investment was held.

![Annualized Total Return](https://www.investopedia.com/thmb/XkK7uD9FAi0K3WNAk8HL3_IaYC0=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Annualized-Total-Return-FINAL-69a0de5921b84ad88984ae90ff4e3733.jpg)

*— Investopedia / Jiaqi Zhou*

## Understanding Annualized Total Return

To understand what annualized total return is, it helps to compare the hypothetical performances of two mutual funds. Below is the annualized rate of return over five years for two funds:

*   Mutual Fund A Returns: 3%, 7%, 5%, 12%, and 1%
*   Mutual Fund B Returns: 4%, 6%, 5%, 6%, and 6.7%

Both mutual funds have an annualized rate of return of 5.5%. However, in this case, it's important to look beyond the annualized rate of return to how each fund performs. For instance, Mutual Fund A is much more volatile than Mutual Fund B. Its [standard deviation](https://www.investopedia.com/terms/s/standarddeviation.asp) is 4.2%, while Mutual Fund B's standard deviation is only 1%. The amount of volatility can make a significant difference, depending on how long you plan to hold an investment and your strategy and goals.

## Annualized Return Formula and Calculation

The formula to calculate the annualized rate of return requires only two variables: the returns for a given period and the time the investment was held. The formula is:

$\begin{aligned} \text{Annualized Return} = &\big ( (1 + r_1 ) \times (1 + r_2) \times (1 + r_3) \times \\ &\dots \times (1 + r_n) \big ) ^ \frac{1}{n} - 1 \\ \end{aligned}$

For example, take the annual rates of return of Mutual Fund A above. You'd substitute each _r_ variable with the appropriate return and _n_ with the number of years the investment was held. In this case, five years. The annualized return of Mutual Fund A is calculated as:

$\begin{aligned} \text{Annualized Return} &= \big ( (1 + .03) \times (1 + .07) \times (1 + .05) \times \\ &\quad \quad (1 + .12) \times (1 + .01) \big ) ^ \frac{1}{5} -1 \\ &= 1.309 ^ {0.20} - 1 \\ &= 1.0553 - 1 \\ &= .0553, \text{or } 5.53\% \\ \end{aligned}$

An annualized return does not have to be limited to yearly returns. If an investor has a [cumulative return](https://www.investopedia.com/terms/c/cumulativereturn.asp) for a given period, even if it is a specific number of days, an annualized performance figure can be calculated; however, the annual return formula must be slightly adjusted to:

$\begin{aligned} &\text{Annualized Return} = ( 1 + \text{Cumulative Return} ) ^ \frac {365}{ \text{Days Held} } - 1 \\ \end{aligned}$

For example, assume a mutual fund was held by an investor for 575 days and earned a cumulative return of 23.74%. The annualized rate of return would be:

$\begin{aligned} \text{Annualized Return} &= ( 1 + .2374) ^ \frac{365}{575} - 1 \\ &= 1.145 - 1 \\ &= .145, \text{or } 14.5\% \\ \end{aligned}$

## Difference Between Annualized Return and Average Return

Average returns differ from annualized returns in that they are calculated by summing the returns for each period and then dividing the result by the number of periods. For example, you would add the rate of return for each period and divide the result by the number of periods.

The annualized total return uses each period's rate of return (expressed as a percentage), which accounts for compounding. The result is generally less than the average return and more accurately reflects how the investment performed.

## Reporting Annualized Return

According to the [Global Investment Performance Standards (GIPS)](https://www.investopedia.com/terms/g/gips.asp)—a set of standardized, industry-wide principles that guide the ethics of performance reporting—any investment that does not have a track record of at least 365 days cannot "ratchet up" its performance to be annualized.

Thus, if a fund has been operating for only six months and has earned 5%, it is not allowed to say its annualized performance is approximately 10%, as that would predict future performance instead of stating facts from the past. In other words, calculating an annualized rate of return must be based on historical numbers.

## How Is Annualized Total Return Calculated?

The annualized total return is a metric that captures the average annual performance of an investment or portfolio of investments. It is calculated as a geometric average, meaning that it captures the effects of compounding over time. The annualized total return is sometimes called the [compound annual growth rate (CAGR)](https://www.investopedia.com/terms/c/cagr.asp).

## What Does 3-Year Annualized Return Mean?

A three-year annualized return is a calculation of an investment's rate of return for a period of three years.

## Is 10% Annualized Return Good?

A 10% annualized total return might be considered good by some investors, while others would prefer to see a higher rate. It depends on your investing goals, timeframe, and strategy.

## The Bottom Line

Annualized total return represents the geometric average amount that an investment has earned each year over a specific period. By calculating a geometric average, the annualized total return formula accounts for compounding when depicting the yearly earnings the investment would generate over the holding period. While the metric provides a useful snapshot of an investment's performance, it does not reveal volatility and price fluctuations.