Average Return: Definition, Calculations, and Practical Examples

Comprehensive overview of average return including definition, how to calculate it, and practical examples along with its significance in fields like finance and investments.

Average return is the simple mathematical average of a series of returns generated over a specified period of time. It provides insight into the overall performance of an investment by summarizing its periodic returns into a single figure.

Calculation of Average Return

To calculate the average return, you add up all the periodic returns and then divide by the number of periods. The formula for average return \( R_{\text{avg}} \) over \( n \) periods is:

$$ R_{\text{avg}} = \frac{R_1 + R_2 + \cdots + R_n}{n} $$

Where:

• \( R_1, R_2, \ldots, R_n \) are the periodic returns.
• \( n \) is the number of periods.

Example Calculation

Suppose an investment generates returns of 5%, 10%, and 15% over three periods. The average return can be calculated as:

$$ R_{\text{avg}} = \frac{5\% + 10\% + 15\%}{3} = \frac{30\%}{3} = 10\% $$

Types of Average Return

Arithmetic Average Return

The arithmetic average return is the simple average of a series of returns. It does not take into account the compounding effects over time, making it less accurate for long-term performance analysis.

Geometric Average Return

The geometric average return accounts for compounding and is calculated by multiplying all the returns and then taking the nth root, where \( n \) is the number of periods. It provides a more accurate reflection of investment performance over time.

$$ R_{\text{geom}} = \left( \prod_{i=1}^{n} (1 + R_i) \right)^{\frac{1}{n}} - 1 $$

Annualized Average Return

Annualized return standardizes the return over a year, allowing for comparisons across different time periods and investments.

Historical Context

The concept of average return has been used in finance and investments for decades to evaluate the performance of various instruments. It offers a straightforward method for comparing the profitability of different investments.

Applicability

Average return is extensively used in:

• Finance: To assess investment performance and portfolio returns.
• Economic Analysis: For evaluating economic indicators over time.
• Business Management: In performance metrics evaluation.

Comparisons

Average Return vs. Total Return

Average Return:

• Focuses on the mean performance over periods.
• Can be misleading if there are extreme variations in returns.

Total Return:

• Considers all returns, including dividends and capital gains.
• Provides a holistic view of investment performance.

Average Return vs. Compounded Return

Average Return:

• Simple average.
• May not reflect the true growth of investment value over time.

Compounded Return:

• Reflects the value growth due to compounding.
• More accurate for long-term investment performance.

Related Terms

• Mean Return: Synonymous with average return, particularly in statistical analysis.
• Expected Return: The anticipated return on an investment based on probability.

FAQs

How is the average return useful in investment analysis?

It provides a quick summary of periodic performance, aiding in comparisons and decision-making.

Can the average return be negative?

Yes, if the sum of negative returns outweighs the positive ones, the average return can be negative.

Why is geometric average return preferred over arithmetic average return for long-term analysis?

Because it accounts for compounding, providing a more accurate measure of true investment growth.

References

1. Malkiel, B. G. (A Random Walk Down Wall Street).
2. Damodaran, A. (Investment Valuation: Tools and Techniques).

Summary

The average return is a fundamental concept in finance that captures the mean performance of an investment or series of returns over specified periods. It aids in quick performance assessment, though it comes with limitations that can be addressed by using geometric average return or total return measures. Understanding how to calculate and interpret average return is essential for investors and financial analysts to gauge investment performance more effectively.