# Arithmetic Return

Last Updated :

21 Aug, 2024

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Dheeraj Vaidya

Table Of Contents

## What Is Arithmetic Return?

Arithmetic return is a basic measure of average investment performance, calculated by summing periodic returns and dividing it by the number of periods. It provides a simple overview of returns, suitable for quick comparisons and analysis, particularly in shorter time frames.

Its importance extends across various fields, such as finance, economics, statistics, and business. In finance, it's fundamental for assessing investment performance and portfolio management, and in economics, it aids in analyzing economic indicators and growth rates. In statistics, it's used for measuring central tendency. Furthermore, in business, it informs decision-making regarding profitability and resource allocation.

##### Table of Contents

- Arithmetic return is the average return on investment calculated by summing periodic returns and dividing by the number of periods, providing a basic measure of performance.
- It provides a basic measure of investment performance, aiding in quick comparisons and assessments. It's valuable for evaluating historical returns, guiding investment decisions, and assessing portfolio performance, especially in shorter time frames.
- The metric calculates the average return by summing periodic returns and dividing by the number of periods. Geometric return reflects the compounded growth rate of an investment over time, providing a more accurate representation of growth.

### Arithmetic Return Explained

Arithmetic return is a foundational concept in finance used to evaluate investment performance over a specified period. It involves calculating the average return by summing the individual returns for each sub-period and then dividing by the total number of periods. The arithmetic return calculation provides a basic average without accounting for compounding. This simplicity makes it a convenient tool for quick assessments, especially in shorter time frames or when the impact of compounding is minimal.

Despite its simplicity, this method is widely utilized across various financial domains, including portfolio management, performance evaluation, and risk assessment. Investors often rely on this type of average calculation to gauge their investment strategies' effectiveness and compare the performance of different assets or portfolios. Financial analysts also use this average method to assess the historical performance of securities, analyze market trends, and forecast future returns. While this type of average return may not capture the full complexities of investment returns, its accessibility, and ease of calculation make it an indispensable metric for decision-making in finance.

### Arithmetic Return Calculation

The arithmetic return is determined by summing the rate of returns for "n" sub-periods and then dividing the total by "n". This involves adding the returns of "n" sub-periods and dividing by "n" to ascertain the average return value. Referred to as the "Arithmetic Average Return" due to its method resembling the calculation of the average of a numerical series, the formula for its calculation is:

*Arithmetic Return = (Total Value of the Returns) / (Total Number of Returns)*

Investors and market analysts commonly employ the arithmetic average return to assess a stock's historical performance. This metric is also instrumental in evaluating a company's portfolio.

### Examples

Let us look at a few arithmetic return examples to understand the concept better -

#### Example #1

Suppose John invests $10,000 in a stock. Over one year, the stock experiences the following monthly returns:

- In January, the stock gains 2%.

- February sees a 3% increase.

- March records a decrease of 1%.

- April shows a 4% gain.

- May sees another 2% increase.

- June's return is a modest 1%.

- July experiences a 3% increase.

- August sees a 2% rise.

- September records a decline of 1%.

- October sees a 3% increase.

- November gains 2%.

- December ends the year with a 4% increase.

To calculate the average return for John's investment over the year, we sum up all the monthly returns:

2% + 3% - 1% + 4% + 2% + 1% + 3% + 2% - 1% + 3% + 2% + 4%

= 24%.

Then, we divide the total return by the number of periods (which is 12 months):

= 24% / 12 = 2%.

In this example, John's investment yields an arithmetic return of 2% over one year.

#### Example #2

Imagine Sarah creating a diversified portfolio of stocks, bonds, and real estate. Over a year, the portfolio experiences fluctuations in value due to market conditions, economic scenarios, and other factors. During the year, some months show positive returns, reflecting growth in the value of the investments, while other months might show negative returns due to market downturns or other factors affecting asset prices.

At the end of the year, Sarah evaluates the overall performance of her portfolio by calculating the arithmetic return. This calculation involves summing up the returns of all the individual investments within her portfolio and dividing by the total number of investments.

The resulting arithmetic return provides Sarah with a general measure of the average performance of her portfolio over the one year, helping her assess whether her investment strategy was successful and guiding her future investment decisions.

### Arithmetic Return vs Geometric Return

The differences between arithmetic and geometric return us as follows:

- Arithmetic return represents the average return over a series of periods, while geometric return, also known as compound annual growth rate (CAGR), reflects the compounded growth rate of an investment over time.
- Arithmetic return calculates the average return over a series of periods without considering the compounding effect, while geometric return accounts for compounding by reflecting the cumulative growth rate of an investment over time.

### Frequently Asked Questions (FAQs)

**What is the importance of arithmetic return?**

Arithmetic return is an important concept in various fields, such as finance, economics, statistics, and business. Its application is a simple process and serves as a fundamental measure for assessing investment performance, aiding in decision-making processes related to portfolio management, economic analysis, statistical measurements, and business profitability.

**What is the difference between arithmetic return and logarithmic return?**

Arithmetic return calculates the average return over a series of periods by adding periodic returns and dividing by the number of periods. On the other hand, logarithmic return or log return, calculates the return on investment as the natural logarithm of the ratio of final to initial asset value.

**What are the limitations of arithmetic return?**

The arithmetic return has its limitations. It doesn't consider the timing or magnitude of cash flows. The calculation method assumes constant returns over time, which may not accurately represent real-world investment scenarios characterized by fluctuating market conditions and changing risk profiles. This method may not fully capture the complexities of investment returns.

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