Glossary term
Arithmetic Average Return
Arithmetic average return is the simple average of periodic returns, calculated by adding returns and dividing by the number of periods.
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What Is Arithmetic Average Return?
Arithmetic average return is the simple average of periodic investment returns. It is calculated by adding the returns for each period and dividing by the number of periods.
The measure is useful for summarizing a set of individual period returns, but it does not show the compounded return an investor actually earned over multiple linked periods.
Key Takeaways
- Arithmetic average return is a simple average of periodic returns.
- It adds returns and divides by the number of periods.
- It is often higher than geometric average return when returns vary.
- It can be useful for expected one-period return assumptions.
- It should not be confused with compounded performance over time.
Arithmetic Average Return Formula
In this formula, R1, R2, and the later Rn terms are the returns for each period. n is the number of periods being averaged.
Arithmetic vs. Geometric Average Return
Measure | What it answers | Best use |
|---|---|---|
Arithmetic average return | What was the simple average period return? | Summarizing independent period returns. |
Geometric average return | What steady return produced the same ending value? | Measuring compounded performance. |
Annualized return | What is the return expressed on a yearly basis? | Comparing different holding periods. |
Example
Suppose an investment gains 20% in year one and loses 10% in year two. The arithmetic average return is 5% because 20% plus negative 10% equals 10%, and 10% divided by two years equals 5%.
That does not mean the investor compounded at 5% per year. A $100 investment would grow to $120 after the first year and then fall to $108 after the second year. The compounded result is different.
Where It Shows Up
Arithmetic average return appears in performance summaries, risk models, capital market assumptions, and simple return comparisons. It is most useful when each period is treated as a separate observation rather than part of one continuous investment path.
That distinction matters. A model estimating next year's expected return may use an arithmetic average. A report explaining what an investor earned over several years usually needs a compounded measure.
When It Helps and When It Misleads
Arithmetic average return can help estimate an expected return for a single future period, especially in statistical models. It can mislead when used to describe actual multi-period investor experience because it ignores compounding.
The gap between arithmetic and geometric average return grows as volatility rises. The more uneven the returns, the more important the compounding difference becomes.
Forecasting Context
Arithmetic average return can be appropriate when estimating the expected return for one future period. If a model treats next year as one draw from a distribution of possible annual returns, the arithmetic mean can summarize that one-period expectation.
The problem begins when the same number is used to describe a multi-year wealth path. Compounding links each period to the next, so losses reduce the base on which later gains are earned. The arithmetic average can therefore overstate the return an investor actually compounded through a volatile sequence.
Investor Takeaway
When reviewing performance, ask what question the average is answering. If the question is the typical period return, arithmetic average return may be fine. If the question is how wealth grew over time, geometric average return, annualized return, or internal rate of return usually gives a more relevant answer.
The measure can also be distorted by outlier periods. One unusually high return can lift the arithmetic average even if the broader sequence was mediocre. Looking at the full return path, dispersion, and ending wealth keeps the simple average from carrying more meaning than it deserves.
The Bottom Line
Arithmetic average return is the simple average of periodic returns. It is easy to calculate and useful in some models, but geometric average return is usually better for describing compounded investment performance.