Return characteristics

What Is Expected Return?

Expected Return is the anticipated profit or loss an investor projects on an investment over a specified period. It is a core concept within portfolio theory, representing the probabilistic average of possible returns, weighted by their likelihood of occurrence. Investors and analysts use expected return to make informed decisions about asset allocation and to compare potential investments. This metric considers various factors that could influence future performance, aiming to provide a forward-looking estimate rather than a historical observation. Expected return is a fundamental component of various financial models and is crucial for understanding the potential growth of an investment over time.

History and Origin

The concept of expected return has roots in classical probability theory but gained significant prominence in finance with the development of modern portfolio diversification theory in the mid-20th century. Harry Markowitz's groundbreaking work in 1952, which introduced the concept of efficient portfolios, formalized the role of expected return alongside risk (measured by standard deviation) in investment decision-making. His mean-variance optimization framework became a cornerstone of modern finance, emphasizing that investors should consider both the potential return and the associated risk when constructing a portfolio. The accurate estimation of the equity premium, a key component of expected return for stocks, has been a subject of extensive academic research and is central to many finance applications.⁴, ⁵, ⁶ Research from institutions like the Federal Reserve Bank of San Francisco has explored methodologies for estimating this premium, highlighting its importance in financial analysis.³

Key Takeaways

Expected Return is a forward-looking estimate of an investment's potential gain or loss.
It is calculated as the weighted average of all possible returns, with weights reflecting their probabilities.
Expected return is a critical input for asset allocation and various quantitative financial models.
It does not guarantee actual performance; rather, it is a projection based on available information and assumptions.
Understanding expected return is essential for effective risk management and investment planning.

Formula and Calculation

The formula for expected return involves multiplying each possible return by its probability and then summing these products.

Let ( E(R) ) be the expected return, ( R_i ) be the ( i )-th possible return, and ( P_i ) be the probability of the ( i )-th return occurring.

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

Where:

( E(R) ) = Expected Return
( R_i ) = The ( i )-th possible return (e.g., 5%, 10%, -2%)
( P_i ) = The probability of the ( i )-th return occurring (e.g., 0.30 for a 30% chance)
( n ) = The number of possible outcomes

Another common way to estimate the expected return for an asset like a stock, particularly in the context of the Capital Asset Pricing Model (CAPM), incorporates the risk-free rate and the equity risk premium:

E(R_i) = R_f + \beta_i \times (E(R_m) - R_f)

Where:

( E(R_i) ) = Expected return on investment ( i )
( R_f ) = Risk-free rate of return
( \beta_i ) = Beta of investment ( i ) (a measure of its systematic risk)
( E(R_m) ) = Expected return of the market portfolio
( (E(R_m) - R_f) ) = Market risk premium

Interpreting the Expected Return

Expected return provides a forecast, not a certainty. A higher expected return generally indicates a greater potential for profit, but it often comes with a higher degree of volatility or risk. Investors interpret expected return in conjunction with risk measures, such as standard deviation, to assess the risk-reward profile of an investment. For example, two investments might have the same expected return, but one could have significantly lower expected volatility, making it more attractive for a risk-averse investor. It helps in setting realistic expectations for future portfolio performance and plays a key role in financial planning, particularly when calculating concepts like future value or required returns to meet financial goals.

Hypothetical Example

Consider an investment in a new tech startup with three possible outcomes over the next year:

Best Case: A 40% return with a 30% probability.
Base Case: A 10% return with a 50% probability.
Worst Case: A -20% return (a loss) with a 20% probability.

To calculate the expected return:

(0.40 * 0.30) = 0.12 (or 12%)
(0.10 * 0.50) = 0.05 (or 5%)
(-0.20 * 0.20) = -0.04 (or -4%)

Summing these values:
Expected Return = 0.12 + 0.05 + (-0.04) = 0.13, or 13%.

This means that, based on the probabilities assigned to each scenario, the expected return for this investment is 13%. While the actual return could be 40%, 10%, or -20%, 13% represents the weighted average of these potential outcomes. This calculation helps an investor evaluate the potential profitability when considering their overall investment strategy.

Practical Applications

Expected return is a cornerstone in various aspects of finance. It is extensively used in constructing diversified portfolios, where investors combine assets with different expected returns and risk profiles to achieve an optimal blend. Financial planners use expected return to help clients project the growth of their retirement savings or other long-term investment goals, often accounting for factors like inflation. It is also a critical input for valuation models, such as discounted cash flow (DCF) analysis, where the expected return serves as a discount rate to calculate the present value of future cash flows. Institutional investors, such as pension funds and endowments, rely on expected return assumptions for their long-term strategic planning. Financial institutions are also required to provide clear disclosures regarding the nature of return projections. The U.S. Securities and Exchange Commission (SEC) provides guidance to investors on understanding investment performance, particularly emphasizing that hypothetical or projected returns are not guarantees of future results.² Furthermore, financial research firms, like Morningstar, develop sophisticated methodologies for forecasting capital market assumptions, which are essentially expected returns across different asset classes, to guide investment decisions.¹ Historical data on returns from various asset classes also plays a vital role in informing these expectations, with long-term studies providing insights into typical performance over extended periods.

Limitations and Criticisms

While a crucial metric, expected return has notable limitations. It is inherently a forward-looking estimate based on assumptions, which may not materialize. These assumptions can be influenced by historical data, market conditions, economic forecasts, and even behavioral biases. Critics point out that past performance, while often used to inform expected return, is not necessarily indicative of future results. Unexpected market events, economic shocks, or changes in regulatory environments can significantly deviate actual returns from expected returns. Moreover, the calculation of expected return relies on assigning probabilities to various outcomes, which can be subjective, particularly for less liquid or more speculative investments. Over-reliance on a single expected return figure without considering the range of possible outcomes and their associated risks can lead to poor decision-making. Investors should consider expected return within a broader risk management framework and understand that achieving the expected return is not guaranteed.

Expected Return vs. Realized Return

Expected Return and Realized Return are distinct but related concepts in finance.

Expected Return is the anticipated or projected return an investment is believed to yield over a future period. It is a theoretical calculation based on probabilities and assumptions about future events, market conditions, and economic performance. It serves as a planning tool for investors and analysts to make forward-looking decisions regarding portfolio construction and investment strategy.

Realized Return, conversely, is the actual profit or loss an investment generated over a specific past period. It is a historical fact, calculated based on the investment's actual performance, including any income (like dividends or interest) and capital appreciation or depreciation. Realized return reflects what genuinely happened, often differing from the initial expected return due to unforeseen market movements, economic shifts, or company-specific events.

The key difference lies in their temporal orientation and certainty: Expected Return looks to the future and is an estimate, while Realized Return looks to the past and is a definitive outcome. Investors typically use expected return to make decisions and then compare these expectations against realized returns to evaluate the effectiveness of their initial assessments and strategies.

FAQs

How accurate is expected return?

Expected return is a forecast and, as such, is not guaranteed to be accurate. Its accuracy depends heavily on the quality of the underlying assumptions and probabilities used in its calculation. Actual returns can, and often do, deviate significantly from expected returns due to unforeseen market conditions or economic events.

Can expected return be negative?

Yes, expected return can be negative. This indicates that, based on the probabilities and potential outcomes, the investment is expected to result in a loss over the specified period. Investments with negative expected returns are generally avoided unless they offer significant portfolio diversification benefits or act as a hedge against other risks.

What factors influence expected return?

Several factors influence expected return, including prevailing interest rates (like the risk-free rate), economic growth forecasts, inflation expectations, corporate earnings projections, and the specific risk characteristics (such as Beta and volatility) of the asset or security in question. Market sentiment and geopolitical events can also play a role in short-term expectations.

Is expected return the same as average return?

No, expected return is not strictly the same as average return, although historical average returns are often used as an input or proxy for expected return. Average return is a historical calculation of past performance, whereas expected return is a forward-looking probabilistic estimate of future performance. While historical averages can inform expectations, they do not account for changes in current market conditions or future outlooks.