Knowledge base",

What Is Expected Return?

Expected return represents the anticipated profit or loss an investor can foresee receiving on an investment over a specific period. It is a fundamental concept within portfolio theory, providing a probabilistic estimate of an investment's potential future performance⁴⁹. While the expected return offers a rational forecast, it is crucial to understand that it is not a guaranteed outcome. Instead, it serves as a long-term weighted average of potential results, considering various scenarios and their likelihoods. This metric is vital for investors aiming to align their asset allocation and manage investment risk effectively.

History and Origin

The concept of expected return gained prominence with the development of modern financial theories in the mid-20th century. A significant milestone was the introduction of the Capital Asset Pricing Model (CAPM) by William F. Sharpe in 1964⁴⁸. This model provided a structured way to determine the appropriate rate of return for a risky asset, linking its expected return to its systematic risk. The CAPM, and its underlying principles of diversification, simplified assumptions about financial markets, and the relationship between risk and expected return, became a cornerstone of modern finance⁴⁷. It offered a powerful framework for investors to evaluate the expected return of a security based on its beta, a measure of its volatility relative to the overall market⁴⁶.

Key Takeaways

Expected return is a probabilistic forecast of an investment's future profit or loss, not a guarantee.⁴⁵
It is calculated by weighting potential outcomes by their probabilities.⁴³, ⁴⁴
Expected return is a key input for financial models like the Modern Portfolio Theory and the Capital Asset Pricing Model (CAPM).⁴²
It should always be considered in conjunction with measures of risk, such as standard deviation.⁴¹
Past performance does not guarantee future results, and expected return relies on assumptions about future market conditions.³⁸, ³⁹, ⁴⁰

Formula and Calculation

The expected return can be calculated using different methods, depending on the available information.

One common approach, especially when considering discrete scenarios, is the probability-weighted average:

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

Where:

( E(R) ) = Expected Return
( R_i ) = Return in scenario ( i )
( P_i ) = Probability of scenario ( i ) occurring
( n ) = Number of scenarios

For individual securities, particularly within the framework of the Capital Asset Pricing Model (CAPM), the formula is:

$E(R_a) = R_f + \beta_a (E(R_m) - R_f)$

Where:

( E(R_a) ) = Expected return of asset ( a )
( R_f ) = Risk-free rate of return
( \beta_a ) = Beta of asset ( a )
( E(R_m) ) = Expected market return

Interpreting the Expected Return

Interpreting the expected return involves understanding it as a central tendency of potential investment outcomes. A higher expected return generally indicates a higher potential profit, but it typically also comes with higher risk³⁷. For example, if an asset has an expected return of 8%, it suggests that, on average, over many similar periods, an investor might anticipate an 8% gain. However, this average does not account for the short-term fluctuations or the potential for significant deviations from this expectation³⁶.

Investors use expected return to compare different investment opportunities and to assess whether a given investment provides adequate compensation for the associated risk³⁵. It helps in evaluating the attractiveness of an asset by comparing its potential profitability against other alternatives, including the risk-free rate. Furthermore, expected return is a crucial component in constructing a portfolio that aligns with an investor's risk tolerance and return objectives³⁴.

Hypothetical Example

Consider an investor evaluating a new tech stock, TechGrowth Inc. Based on market analysis, there are three potential scenarios for the stock's annual performance:

Boom Scenario: 30% probability of a 25% return.
Normal Growth Scenario: 50% probability of a 10% return.
Downturn Scenario: 20% probability of a -15% return (a loss).

To calculate the expected return for TechGrowth Inc.:

(0.30 * 0.25) = 0.075 (7.5%)
(0.50 * 0.10) = 0.050 (5.0%)
(0.20 * -0.15) = -0.030 (-3.0%)

Summing these weighted returns: 0.075 + 0.050 - 0.030 = 0.095.

Therefore, the expected return for TechGrowth Inc. is 9.5%. This calculation helps the investor understand the probable average return, factoring in various market conditions. This allows for a more informed decision when considering the stock's inclusion in a portfolio.

Practical Applications

Expected return is a cornerstone of quantitative finance and finds numerous practical applications across investment management, financial planning, and risk management.

Portfolio Construction and Optimization: Investors use expected return as a key input when building diversified portfolios. In portfolio optimization, expected returns, alongside risk measures, are used to select assets that maximize return for a given level of risk or minimize risk for a target return. Academic models, such as those developed by Research Affiliates, rely on expected returns to forecast asset class performance and construct portfolios that aim to generate alpha over an investor's time horizon³², ³³.
Valuation Models: Expected return is integrated into various corporate valuation models and scenario analysis to quantify uncertainty and support strategic recommendations³¹.
Performance Benchmarking: While expected returns are forward-looking, they provide a basis for evaluating the performance of an investment or portfolio against initial expectations. This can inform future investment decisions and adjustments to an investment strategy.
Economic Analysis: Broader economic indicators, such as interest rates published by the Federal Reserve, can influence the expected returns of various asset classes²⁹, ³⁰. For instance, a rise in the risk-free rate can impact the expected return derived from models like the CAPM. Understanding these macroeconomic factors is crucial for refining expected return estimates.

Limitations and Criticisms

Despite its widespread use, the expected return has several important limitations. Primarily, it is a theoretical estimate and does not guarantee the actual return an investment will yield²⁷, ²⁸. Actual returns can deviate significantly due to unforeseen market volatility, economic shifts, or company-specific events²⁶.

One major criticism is its reliance on historical data to estimate probabilities or inputs like earnings per share (EPS) growth or changes in the price-to-earnings (P/E) ratio ²³, ²⁴, ²⁵. As the well-known disclaimer states, "past performance is not indicative of future results"²². Future market conditions may not resemble historical patterns, rendering historical data less reliable as a sole predictor²¹. For example, there have been extended periods where realized stock market returns were less than the risk-free rate, indicating that historical averages can be poor proxies for future expectations²⁰.

Another limitation is that expected return, when considered in isolation, does not explicitly factor in the full spectrum of investment risk ¹⁸, ¹⁹. Two investments might have the same expected return but vastly different levels of volatility or potential downside. Furthermore, expected return calculations often make simplifying assumptions, such as a normal distribution of returns, which may not hold true in reality, especially during extreme market events¹⁷. For instance, highly influential investor Jack Bogle's simple model for predicting future stock returns, while intuitive, highlights that while components like dividend yield are known, estimating earnings growth and valuation changes can be challenging and subject to significant forecast error¹⁵, ¹⁶.

Expected Return vs. Realized Return

The distinction between expected return and realized return is fundamental in finance. Expected return is a forward-looking concept, representing the anticipated profit or loss an investor expects to receive from an investment based on probabilities and assumptions about future outcomes¹², ¹³, ¹⁴. It is a theoretical construct used for decision-making before an investment is made.

In contrast, realized return is a backward-looking measure that represents the actual profit or loss an investor has earned on an investment over a specific period¹⁰, ¹¹. It is calculated based on historical performance, including capital gains or losses and any income received, such as dividends⁹. While expected return is a prediction, realized return is the concrete outcome. Investors often compare realized returns against their initial expected returns to evaluate the performance of their investment decisions⁸.

FAQs

Q: Is expected return a guarantee?
A: No, expected return is a projection based on probabilities and assumptions, not a guaranteed outcome. Actual returns can differ significantly due to market conditions and other factors.⁷

Q: How is expected return used in investing?
A: Expected return is used to estimate potential profits, compare different investment opportunities, and help in constructing portfolios that align with an investor's goals and risk appetite.⁵, ⁶

Q: Can I use historical returns to predict future expected returns?
A: While historical data can inform expected return calculations, past performance is not a reliable indicator or guarantee of future results. Market conditions and other factors change over time.³, ⁴

Q: What is the relationship between expected return and risk?
A: Generally, higher expected returns are associated with higher levels of risk. Investors typically demand greater potential compensation for taking on more risk. Expected return should always be evaluated alongside measures of risk.²

Q: What is the risk-free rate used in expected return calculations?
A: The risk-free rate is the theoretical return of an investment with zero risk. In practice, this is often approximated by the yield on short-term government securities, such as U.S. Treasury bills.¹