# Average Annual Return AAR Definition Calculation Example

## Average Annual Return (AAR) Definition

The Average Annual Return (AAR) is a financial metric used to measure the average rate of return on an investment over a specific period of time. It provides investors with an indication of the average profitability of an investment on an annual basis.

The AAR is calculated by taking the average of the annual returns of an investment over a given period. It is commonly used by investors to evaluate the performance of different investments and compare them to one another.

To calculate the AAR, the annual returns of an investment are added together and divided by the number of years in the investment period. The result is expressed as a percentage, representing the average annual return.

The AAR is a useful tool for investors as it allows them to assess the historical performance of an investment and make informed decisions about future investments. It provides a standardized measure that can be used to compare the returns of different investments, regardless of their initial investment amounts or time periods.

Year Annual Return
2016 10%
2017 8%
2018 12%
2019 6%

For example, let’s calculate the AAR for an investment that had annual returns of 10%, 8%, 12%, and 6% over a four-year period:

(10% + 8% + 12% + 6%) / 4 = 9%

Therefore, the AAR for this investment is 9%.

## What is Average Annual Return?

The Average Annual Return (AAR) is a financial metric used to measure the average rate of return on an investment over a specific period of time. It provides investors with a way to evaluate the performance of an investment and compare it to other investment opportunities.

The AAR is calculated by taking the average of the annual returns of an investment over a given period. It takes into account both the positive and negative returns, providing a more accurate representation of the investment’s performance.

Investors use the AAR to assess the profitability of an investment and make informed decisions about whether to buy, hold, or sell a particular asset. It is commonly used in the financial industry to evaluate the performance of mutual funds, stocks, bonds, and other investment vehicles.

The AAR is expressed as a percentage and can be calculated using the following formula:

Where:

• Ending Value is the value of the investment at the end of the period
• Beginning Value is the value of the investment at the beginning of the period
• Number of Years is the number of years the investment was held

For example, if an investment had an ending value of \$10,000, a beginning value of \$8,000, and was held for 5 years, the AAR would be calculated as:

This means that the investment had an average annual return of 4.71% over the 5-year period.

The AAR is a useful tool for investors to assess the performance of their investments and make informed decisions about their portfolios. It allows investors to compare the returns of different investments and determine which ones are the most profitable.

## Calculation of Average Annual Return

The average annual return (AAR) is a measure used in finance to calculate the average rate of return on an investment over a specified period of time. It is a useful tool for investors to assess the performance of their investments and compare them to other investment options.

Let’s break down the formula:

1. First, divide the ending value of the investment by the beginning value.
2. Next, raise the quotient to the power of 1 divided by the number of years.
3. Finally, subtract 1 from the result to get the average annual return.

For example, let’s say you invested \$10,000 in a stock and after 5 years, the value of your investment grew to \$15,000. To calculate the average annual return, you would use the following formula:

Simplifying the equation:

Calculating the result:

Therefore, the average annual return on your investment is 9.5%.

## Example of Average Annual Return

### Scenario:

Suppose you invested \$10,000 in a mutual fund on January 1, 2010. Over the next five years, the value of your investment grew to \$15,000. You decide to calculate the average annual return of your investment.

### Calculation:

Next, divide the total gain by the initial investment amount: \$5,000 / \$10,000 = 0.5.

Finally, divide the result by the time period in years: 0.5 / 5 = 0.1.

The average annual return of your investment is 0.1, or 10%.

This means that, on average, your investment grew by 10% per year over the five-year period.

By calculating the average annual return, investors can compare the performance of different investments and make informed decisions about their portfolios.