Expected Return: Formula, How It Works, Limitations, and Examples

Summary:

The concept of expected return is pivotal in investment analysis, aiding investors in estimating potential profits or losses. Calculated through a combination of probabilities and historical rates of return, it offers a predictive framework for assessing investments. Although not an absolute guarantee, expected return provides valuable insights for decision-making. This article delves into the intricacies of expected return, its computation, limitations, and its significance within the realm of financial choices.

Understanding expected return

The significance of expected return extends to financial theory and business strategies, including models such as Modern Portfolio Theory (MPT) and the Black-Scholes options pricing model. To illustrate, consider an investment with equal odds of gaining 20% or losing 10%, resulting in an expected return of 5%.

Expected return serves as a tool for assessing whether an investment’s net outcome tends towards positive or negative averages. Its calculation involves the expected value (EV) of an investment, factoring in potential returns across diverse scenarios:

Expected return = Σ (Returni x Probabilityi)

Here, “i” represents each known return along with its corresponding probability in the series.

Although the expected return is rooted in historical data, it does not guarantee future results. Instead, it establishes reasonable predictions, reflecting a prolonged weighted average of historical returns. However, it’s essential to acknowledge that intrinsic risks, like systematic and unsystematic risks, can influence the realization of expected returns. Systematic risk pertains to broader market risks, while unsystematic risk applies to specific companies or industries.

Calculating expected return

For individual investments or portfolios, a more structured equation for expected return in financial investments can be expressed as:

Expected return = risk-free premium + Beta (expected market return – risk-free premium)

Where:

• ra = expected return;
• rf = risk-free rate of return;
• β = investment’s beta; and
• rm = expected market return.

This formulation implies that expected return above the risk-free rate depends on the investment’s beta, signifying its relative volatility compared to the broader market.

Both expected return and standard deviation serve as statistical measures for portfolio analysis. Expected return represents the projected returns a portfolio could generate, whereas standard deviation gauges the extent of returns’ divergence from the mean, indicating risk. It’s important to note that expected return is predictive, not realized.

Limitations of the expected return

However, making investment decisions solely based on expected return calculations can be simplistic and perilous. It’s crucial to consider investment opportunities’ risk characteristics and their alignment with portfolio objectives. For instance, two investments with identical expected returns may significantly differ in risk. Therefore, assessing the likelihood of realizing the expected return is as vital as its magnitude.

Pros and cons

WEIGH THE RISKS AND BENEFITS

Here is a list of the advantages and drawbacks of employing the expected return:

Pros
• Gauges the performance of an asset
• Weighs different scenarios
Cons
• Doesn’t take risk into account
• Based largely on historic data

Expected return example

The concept of expected return extends beyond individual assets to portfolios encompassing multiple investments. For instance, consider an investor interested in the tech sector with a portfolio containing Alphabet Inc., Apple Inc., and Amazon.com Inc. If the expected return of each investment is known, the overall expected return of the portfolio becomes a weighted average of their individual expected returns.

Expected Portfolio Return = (WeightA x ReturnA) + (WeightB x ReturnB) + (WeightC x ReturnC)

This calculation allows investors to assess the potential return of a diversified portfolio.

Expected return in finance

Expected return calculations find utility in various financial models, such as Modern Portfolio Theory (MPT) and the Black-Scholes options pricing model. It assists in determining an investment’s average net outcome, offering reasonable expectations rooted in historical data. However, its predictive nature implies it’s not a guarantee, and investors should weigh it alongside other risk factors before making decisions.

What are historical returns?

Historical returns refer to past performance data of securities or indices. They offer insights by helping analysts predict future returns and estimate how an asset might respond to various economic scenarios. By examining the historical returns, investors can set benchmarks and gauge where future data points might fall, especially concerning standard deviations.

How does expected return differ from standard deviation?

Expected return and standard deviation serve distinct roles in the realm of investment analysis:

• Expected Return: It denotes the average returns a portfolio or asset is projected to earn. This measure gives an estimate of what investors might expect from an investment.
• Standard Deviation: This is a measure of the variability or volatility of returns. It indicates how much the returns of an asset or portfolio deviate from its mean return. A higher standard deviation implies more volatility and hence more risk.

Together, these metrics provide a comprehensive understanding of an investment’s potential return and associated risk.

Why can’t we solely rely on expected return?

While expected return offers a predictive insight into potential profits or losses, it’s based on historical data and probabilities, which are not guaranteed indicators of future performance. Various factors can influence the actual returns, including changes in the broader economic environment, company-specific events, or global market shifts. Therefore, while it’s a valuable tool, it shouldn’t be the only consideration when making investment decisions.

What is the role of Beta in the expected return equation?

Beta represents an investment’s sensitivity or responsiveness to market movements. A Beta greater than 1 indicates that the investment is more volatile than the market, whereas a Beta less than 1 suggests it’s less volatile. In the expected return equation, Beta measures the risk associated with an investment relative to the overall market. Hence, it plays a crucial role in gauging the risk-adjusted potential returns of an asset.

How does systematic risk differ from unsystematic risk?

Both systematic and unsystematic risks influence the realization of expected returns, but they originate from different sources:

• Systematic Risk: Often termed market risk, this pertains to risks that affect the broader market or entire sectors. Factors like geopolitical events, interest rate changes, or inflation are sources of systematic risk.
• Unsystematic Risk: Also known as company-specific or diversifiable risk, this pertains to risks specific to individual companies or industries. Issues like company management, sector disruptions, or product recalls are examples of unsystematic risks.

Investors can mitigate unsystematic risks through diversification, but systematic risks are inherent and cannot be diversified away.

What’s the relevance of the risk-free rate in calculating expected return?

The risk-free rate represents the return on an investment with zero risk, usually associated with government bonds. It serves as a baseline in the expected return equation, helping investors discern how much additional return they should expect for taking on extra risk with a particular investment.

Key takeaways

• Expected return is a predictive tool used to assess an investment’s potential profit or loss.
• Calculations involve weighing potential outcomes by their probabilities.
• Expected return isn’t guaranteed but provides reasonable expectations based on historical data.
• It’s crucial to consider both expected return and risk factors before making investment decisions.
View article sources
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2. Calculating rate of return – Consumer Financial Protection Bureau
3. Returns on Investment (finance) – SuperMoney
4. What is Return of Capital (ROC)? – SuperMoney