What Is Expected Return?

A comprehensive guide to Expected Return, its calculation, importance in finance, and relationship with Mean Return.

Expected Return is a fundamental concept in finance that represents the anticipated profit or loss from an investment over a specified period, considering various possible outcomes and their probabilities. It is closely related to the Mean Return, thus sometimes referred interchangeably.

Formula

The Expected Return can be calculated using the formula:

$$ E(R) = \sum_{i=1}^{n} p_i \times R_i $$

where:

• \( E(R) \) is the Expected Return.
• \( p_i \) is the probability of each possible return.
• \( R_i \) is the return in each scenario.
• \( n \) represents the total number of different possible outcomes.

Importance in Finance

Expected Return serves as a crucial benchmark for investors when making decisions. It helps in:

• Portfolio Management: Balancing risk and return by evaluating expected performance of individual assets.
• Risk Assessment: Comparing investments with different risk levels.
• Capital Allocation: Optimal distribution of capital to maximize returns.

Calculating Expected Return

Step-by-Step Example

Consider an investment with the following possible outcomes:

• 20% probability of a 15% return.
• 50% probability of a 10% return.
• 30% probability of a 5% return.

Using the Expected Return formula:

$$ E(R) = (0.20 \times 15) + (0.50 \times 10) + (0.30 \times 5) $$

$$ E(R) = 3 + 5 + 1.5 $$

$$ E(R) = 9.5\% $$

The Expected Return is 9.5%.

Historical Context

The concept of Expected Return has long roots, dating back to the early theories of probability and risk. It aligns with Harry Markowitz’s Modern Portfolio Theory (1952), which formalized how investors could construct efficient portfolios that maximize return for a given level of risk.

Applicability

In Different Markets

• Stock Market: Estimating returns of individual stocks or portfolios.
• Bond Market: Assessing coupon payments and maturity values.
• Real Estate: Projecting rental income and property appreciation.
• Cryptocurrencies: Predicting volatile price movements.

Comparisons

• Expected Return vs. Variance: While Expected Return focuses on average outcomes, Variance measures the dispersion or volatility around the average.
• Expected Return vs. Actual Return: The Expected Return is predictive, while the Actual Return is what is realized over a period.

Related Terms

• Mean Return: The average return of a set of returns. Often used synonymously with Expected Return.
• Risk-Free Return: The return on an investment with zero risk, typically associated with government bonds.

FAQs

Q1: What is the difference between Expected Return and Mean Return?
A1: Mean Return is the average of historical returns, while Expected Return is the probability-weighted average of potential future returns.

Q2: Can the Expected Return be negative?
A2: Yes, if the probable losses outweigh the gains, the Expected Return can be negative.

Q3: How reliable is the Expected Return?
A3: It is as reliable as the model and assumptions used to calculate it. Unpredictable market conditions can affect actual returns.

References

1. Markowitz, Harry. “Portfolio Selection.” The Journal of Finance, vol. 7, no. 1, 1952, pp. 77-91.
2. Bodie, Zvi, et al. “Investments.” McGraw-Hill Education, 10th Edition, 2019.

Summary

Expected Return is a pivotal measure in finance, providing investors a glimpse into potential future gains or losses based on probabilities. Its application spans diverse markets, illuminating pathways to optimize portfolios and assess risks effectively. Understanding its calculation, historical significance, and related terms equips investors with deeper insights into enhancing investment strategies.

For more information, see [Mean Return].