How to Calculate the Arithmetic Average Return

When evaluating investment performance, understanding how to measure returns is a fundamental step for any investor. A simple and widely used method for assessing average performance over multiple periods is the arithmetic average return. This straightforward calculation provides a clear picture of an investment’s historical performance, helping individuals make informed decisions about their financial assets.

Understanding Arithmetic Average Return

The arithmetic average return represents the sum of returns over various periods, divided by the total number of periods. This calculation provides a direct, unweighted average of historical performance data. It helps understand an investment’s typical return during a specific timeframe.

Investors commonly utilize the arithmetic average return for short-term analyses or when individual period returns are considered independent of one another. This measure is useful for comparing the average performance of different assets over the same short duration. While it summarizes individual period returns, this calculation does not account for the compounding effect of returns over time.

Identifying Necessary Data

To calculate the arithmetic average return, specific data points are needed. The individual return for each period (months, quarters, or years) is the most important input. These period returns must be accurately determined.

The total count of the periods being analyzed is also required. If individual period returns are not readily available, they can be calculated using a basic formula. This involves taking the ending value of the investment, subtracting its beginning value, adding any dividends or distributions received during the period, and then dividing the result by the beginning value. All data points must be gathered.

Performing the Calculation

Once individual period returns and the total number of periods are known, calculating the arithmetic average return is a two-step process. The first step involves summing all individual returns from each period. For example, if an investment had annual returns of 10%, 5%, and 15% over three years, these percentages would be added together.

The second step requires dividing this sum by the total number of periods. Using the previous example, the sum of 10%, 5%, and 15% equals 30%. Since there are three periods, this sum is then divided by three, resulting in an arithmetic average return of 10%. The formula can be expressed as: Arithmetic Average Return = (Sum of All Individual Period Returns) / (Number of Periods).

Consider another example to illustrate the process further. Suppose an investment yielded returns of 8% in year one, -3% in year two, 12% in year three, and 7% in year four. First, sum these returns: 8% + (-3%) + 12% + 7% = 24%. Next, divide this sum by the number of periods, which is four. Therefore, 24% divided by 4 yields an arithmetic average return of 6%.

Practical Application and Context

The calculated arithmetic average return helps investors understand an investment’s typical performance over a historical period. This average is useful for making quick comparisons between different investment options over similar short-term horizons. For instance, an investor might use this measure to compare the average yearly performance of two different mutual funds over the past five years.

The result shows the average rate at which an investment grew or declined during each period, without accounting for the effect of reinvesting returns. It offers a clear figure that helps assess an asset’s general trend. This measure is effective for quick analyses.