Using The Following Returns Calculate The Arithmetic Average Returns

Calculating the arithmetic average of investment returns is a fundamental statistical technique used to determine the mean performance of a portfolio or individual investment over a specific period. This guide explains the formula, provides a step-by-step calculation method, and includes a practical example to help you understand how to apply this concept in your financial analysis.

What Is Arithmetic Average Returns?

The arithmetic average returns, also known as the arithmetic mean, is a measure of central tendency that represents the average performance of an investment or portfolio. It's calculated by summing all the individual returns and dividing by the number of periods. This simple average provides a straightforward way to assess overall performance.

The arithmetic average is sensitive to extreme values, meaning it can be skewed by unusually high or low returns. For this reason, it's often used alongside other measures like geometric mean returns for a more comprehensive analysis.

Key Characteristics

Simple to calculate and interpret
Provides a clear picture of average performance
Sensitive to extreme values
Useful for comparing different investment periods

How to Calculate Arithmetic Average Returns

Calculating the arithmetic average returns involves these straightforward steps:

List all the individual returns for the period you're analyzing
Sum all the returns together
Divide the total by the number of periods

Formula: Arithmetic Average Returns = (Sum of Individual Returns) / (Number of Periods)

Step-by-Step Calculation

Identify the returns for each period in your analysis
Add all the returns together to get the total
Count the number of periods included in your analysis
Divide the total sum by the number of periods
The result is your arithmetic average returns

Remember that returns should be expressed in the same units (e.g., percentages) for accurate calculations. If your returns are in different units, convert them first.

Example Calculation

Let's walk through a practical example to demonstrate how to calculate arithmetic average returns.

Scenario

You have tracked the monthly returns of an investment over 12 months. Here are the returns for each month:

Month	Return (%)
January	5.2
February	3.8
March	6.1
April	4.5
May	5.7
June	4.9
July	5.3
August	4.2
September	5.6
October	4.8
November	5.1
December	4.4

Calculation Steps

Sum all the returns: 5.2 + 3.8 + 6.1 + 4.5 + 5.7 + 4.9 + 5.3 + 4.2 + 5.6 + 4.8 + 5.1 + 4.4 = 58.9%
Count the number of periods: 12 months
Divide the total by the number of periods: 58.9 / 12 = 4.908%

Result

The arithmetic average return for this investment over the 12-month period is 4.91%.

When to Use Arithmetic Average

The arithmetic average is particularly useful in the following situations:

Comparing the performance of different investments over the same period
Assessing the overall performance of a portfolio
Identifying trends in investment performance
Making quick decisions about investment strategies

While the arithmetic average provides a clear picture of average performance, it's important to consider other factors like volatility and risk when making investment decisions.

FAQ

What is the difference between arithmetic and geometric average returns?: The arithmetic average is a simple mean that treats each return equally. The geometric average, on the other hand, accounts for compounding effects, making it more appropriate for calculating overall growth over time.
Can I use the arithmetic average for all types of investments?: Yes, the arithmetic average can be used for any type of investment, but it's most useful for comparing performance over the same time period.
Is the arithmetic average affected by extreme values?: Yes, the arithmetic average can be skewed by unusually high or low returns. For this reason, it's often used alongside other measures like the geometric average.
How do I interpret the arithmetic average returns?: The arithmetic average provides a simple measure of central tendency. A higher average indicates better overall performance, while a lower average suggests poorer performance.
Can I use this calculator for annual returns?: Yes, you can use this calculator for any time period by entering the returns for each period and calculating the average.