Average Annual Return (AAR) is a financial metric that calculates the average annual rate of return on an investment over a specified period. It is a measure used to assess the historical performance of an investment, portfolio, or financial instrument.

The formula for calculating the Average Annual Return is:

\[ \text{AAR} = \left( \frac{\text{Total Cumulative Return}}{\text{Number of Years}} \right) \times 100 \]

Here, the components are:

– **Total Cumulative Return:** The total return earned on the investment over the entire period. It is calculated as the ending value minus the beginning value, including any income generated, dividends, or interest.

– **Number of Years:** The total number of years over which the return is measured.

The result is then multiplied by 100 to express the return as a percentage.

The Average Annual Return provides a smoothed representation of the investment’s performance over time, allowing investors to gauge the average annual growth or decline in the investment’s value.

Here’s a step-by-step example of how to calculate AAR:

1. Determine the ending value of the investment.
2. Determine the beginning value of the investment.
3. Calculate the total cumulative return by subtracting the beginning value from the ending value.
4. Determine the number of years over which the return is being measured.
5. Apply the formula to calculate AAR.

For example, if an investment had an initial value of $10,000 and grew to $15,000 over a period of 5 years, the total cumulative return would be $5,000. The AAR would be calculated as follows:

\[ \text{AAR} = \left( \frac{\$5,000}{5} \right) \times 100 \]

The result would be the average annual return over the 5-year period, expressed as a percentage.

Average Annual Return is a useful metric for investors to evaluate the historical performance of their investments and compare different investment opportunities. However, it’s important to note that past performance does not guarantee future results, and other factors, such as risk and market conditions, should also be considered when making investment decisions.