Mean Return: Expected Value of Investment Returns

A comprehensive analysis of the mean return, its calculation in security analysis and capital budgeting, alongside historical context, examples, and related concepts.

The Mean Return is a critical metric in financial and investment analysis. It represents the expected value or the average of all possible returns an investment or a portfolio of investments might generate. This concept is fundamental in both security analysis and capital budgeting.

Definition in Security Analysis

In security analysis, the mean return is calculated by taking the average of all potential returns of the investments within a portfolio. This provides investors with a measure of the expected performance of their portfolio over a specified period.

Definition in Capital Budgeting

In capital budgeting, the mean return is defined as the mean value of the probability distribution of possible returns on an investment. This analysis helps in evaluating the feasibility and profitability of potential projects by considering all probable outcomes.

Calculating Mean Return

Formula

$$ \mu = \sum_{i=1}^{n} p_i \cdot r_i $$

• \( \mu \) is the mean return.
• \( p_i \) is the probability of the i-th return.
• \( r_i \) is the i-th return value.
• \( n \) is the total number of possible returns.

Example Calculation

Assume an investment has possible returns of 5%, 10%, and -3% with probabilities of 0.2, 0.5, and 0.3 respectively.

$$ \mu = (0.2 \cdot 0.05) + (0.5 \cdot 0.10) + (0.3 \cdot -0.03) = 0.01 + 0.05 - 0.009 = 0.051 \text{ or } 5.1\% $$

This means the expected mean return for this investment is 5.1%.

Historical Context

The concept of mean return has its roots in the broader field of statistics, which emerged as a formal discipline in the 18th century. Its application to finance grew significantly in the 20th century, particularly with the advent of Modern Portfolio Theory (MPT) by Harry Markowitz in 1952. MPT revolutionized the understanding of risk and return in investing.

Applications of Mean Return

Investment Decision-Making

Investors rely on mean return to assess and compare the expected performance of different investments or portfolios, aiding in informed decision-making.

Risk Management

Mean return is used in conjunction with other metrics such as standard deviation and beta to evaluate the risk-adjusted performance of investments.

Project Evaluation

In capital budgeting, the mean return plays a crucial role in the appraisal of the expected profitability and viability of projects, helping businesses allocate resources effectively.

Related Concepts

• Standard Deviation: A measure of the dispersion or variability of returns around the mean return.
• Expected Value: The weighted average of all possible outcomes.
• Variance: The expectation of the squared deviations from the mean, used to quantify risk.

FAQs

What is the difference between mean return and expected return?

There is no difference; mean return and expected return are often used interchangeably to denote the average outcome one can anticipate from an investment.

How does mean return differ from median return?

The mean return is the arithmetic average of all possible returns, while the median return is the middle value in a sorted list of possible returns, which may better represent the expected return when data is skewed.

References

1. Markowitz, H. (1952). “Portfolio Selection.” The Journal of Finance.
2. Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments. McGraw-Hill Education.

Summary

The mean return is a fundamental concept in both security analysis and capital budgeting. It provides investors and managers with a crucial measure of expected performance, aiding in various financial decision-making processes. Understanding how to calculate, interpret, and apply the mean return is essential for effective portfolio management and project evaluation.