Expected return

What Is Expected Return?

Expected return is the anticipated profit or loss an investor can expect to receive on an investment. It is a key concept within portfolio theory, providing a forward-looking estimate of an asset's or portfolio's performance. While the expected return is not a guarantee of future outcomes, it serves as a central input for financial decision-making and investment analysis. It helps investors assess the potential average outcome of an investment given various possible scenarios.

The calculation of expected return takes into account the potential returns of an investment across different market conditions or outcomes, weighted by the probability of each outcome occurring. This probabilistic approach makes expected return a foundational element in quantitative finance, particularly in models like the Modern Portfolio Theory (MPT) which aims to maximize portfolio returns for a given level of risk tolerance.

History and Origin

The concept of expected return, particularly in the context of investment portfolios, gained significant academic prominence with the advent of Modern Portfolio Theory (MPT). Pioneered by economist Harry Markowitz, MPT was introduced in his seminal 1952 paper, "Portfolio Selection," published in The Journal of Finance.¹⁴, ¹⁵ This groundbreaking work provided a mathematical framework for assembling a portfolio of assets to maximize expected return for a given level of risk, or equivalently, to minimize risk for a desired expected return.

Before MPT, investors often had a more intuitive understanding of portfolio diversification. Markowitz's work formalized this idea, demonstrating how the overall risk and return of a portfolio are not simply the sum of individual asset risks and returns, but also depend on their co-movements.¹³ The emphasis on expected return as a quantifiable metric for future performance, alongside risk, became a cornerstone of modern financial economics, leading to further developments like the Capital Asset Pricing Model (CAPM).¹²

Key Takeaways

• Expected return is a probabilistic estimate of an investment's future performance, not a guaranteed outcome.
• It is calculated by weighting potential returns in different scenarios by their respective probabilities.
• A higher expected return often corresponds with a higher level of risk.
• Expected return is a fundamental component of various financial models, including Modern Portfolio Theory and the Capital Asset Pricing Model.
• While useful for planning, actual returns may deviate significantly from the expected return due to market volatility and unforeseen events.

Formula and Calculation

The expected return of a single asset can be calculated using the following formula, which involves multiplying each possible outcome by its probability and summing the results:

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

Where:

• (E(R)) = Expected Return
• (P_i) = Probability of outcome (i)
• (R_i) = Return in outcome (i)
• (n) = Total number of possible outcomes

For a portfolio consisting of multiple assets, the expected return of the portfolio is the weighted average of the expected returns of its individual assets:

$E(R_p) = \sum_{j=1}^{m} (w_j \times E(R_j))$

Where:

• (E(R_p)) = Expected Return of the portfolio
• (w_j) = Weight (proportion) of asset (j) in the portfolio
• (E(R_j)) = Expected Return of asset (j)
• (m) = Total number of assets in the portfolio

Understanding the probability distribution of potential returns is crucial for accurately estimating the expected return.

Interpreting the Expected Return

Interpreting the expected return requires understanding that it is a statistical average, not a precise forecast. An expected return of 8%, for example, does not mean the investment will yield exactly 8%; rather, it suggests that, over a large number of similar trials or a long period, the average return would converge around 8%.

Investors use expected return to compare different investment opportunities. All else being equal, an investment with a higher expected return is generally preferred. However, expected return must always be considered in conjunction with risk, which is often quantified by metrics like standard deviation. A higher expected return often comes with a higher level of risk. Therefore, an investor's asset allocation decisions are typically made by balancing the expected return with their individual risk tolerance.

Hypothetical Example

Consider an investor evaluating a hypothetical stock, "GrowthTech Inc." They identify three possible future scenarios for the stock over the next year:

1. Boom Market (25% probability): GrowthTech's stock price increases, resulting in a 30% return.
2. Normal Market (50% probability): GrowthTech's stock price experiences moderate growth, resulting in a 10% return.
3. Bear Market (25% probability): GrowthTech's stock price declines, resulting in a -15% return.

To calculate the expected return for GrowthTech Inc.:

$E(R_{GrowthTech}) = (0.25 \times 0.30) + (0.50 \times 0.10) + (0.25 \times -0.15)$
$E(R_{GrowthTech}) = 0.075 + 0.050 - 0.0375$
$E(R_{GrowthTech}) = 0.0875 \text{ or } 8.75\%$

Based on this analysis, the expected return for GrowthTech Inc. is 8.75%. This figure provides a quantitative basis for the investor to consider GrowthTech as part of their broader investment strategy.

Practical Applications

Expected return is a cornerstone of various aspects of finance and investing:

• Portfolio Management: Fund managers and individual investors use expected returns, alongside risk metrics, to construct diversified portfolios. The goal is often to create a portfolio that offers the highest possible expected return for a given level of risk or the lowest risk for a desired expected return.
• Valuation: In financial modeling, expected returns are used as discount rates in valuation models, such as discounted cash flow (DCF) analysis, to determine the present value of future cash flows from an investment.
• Capital Budgeting: Corporations use expected returns to evaluate potential projects and investments. Projects with an expected return exceeding the company's cost of capital are generally considered viable.
• Risk-Adjusted Performance Measurement: Expected return is a component in calculating various risk-adjusted performance measures, helping investors understand how much return they are getting per unit of risk taken.
• Strategic Planning: Long-term financial planning, including retirement planning and college savings, often relies on assumptions about the expected return of various asset classes. Historically, the S&P 500, a broad market index, has delivered an average annual return of approximately 10% over the long term before inflation.¹¹ However, year-to-year returns can vary significantly.¹⁰

Limitations and Criticisms

Despite its widespread use, expected return has several significant limitations:

• Reliance on Assumptions: The calculation of expected return depends heavily on assumptions about future probabilities and outcomes, which are inherently uncertain. Future market conditions may not align with historical data or probabilistic forecasts, making the expected return an imperfect predictor of actual return on investment.⁸, ⁹
• Sensitivity to Inputs: Small changes in the assumed probabilities or potential returns can lead to substantial differences in the calculated expected return, highlighting its sensitivity to subjective inputs.
• Ignoring Tail Risks: Expected return, being an average, may not adequately capture extreme, low-probability events (often referred to as "tail risks") that can have a disproportionately large impact on actual returns. It assumes returns follow a normal distribution, which may not accurately reflect real-world financial markets that exhibit "fat tails" or extreme fluctuations.⁶, ⁷
• Does Not Account for Behavioral Factors: Expected return models typically assume rational investor behavior. In reality, investor sentiment and psychological biases can influence market movements and actual returns in ways not captured by these quantitative models.⁵ Academic research has shown that investor expectations of returns can be negatively correlated with model-based expected returns, suggesting a disconnect between perceived and calculated expectations.⁴
• Static Nature: Many expected return models, such as the basic Capital Asset Pricing Model, use static parameters (like beta) that may not hold constant over time in dynamic market conditions.³

Expected Return vs. Required Rate of Return

While often confused, expected return and required rate of return represent distinct concepts in finance.

In essence, expected return is what an investor hopes to get, while the required rate of return is what an investor needs to get to justify the investment. An investment is generally considered attractive if its expected return exceeds its required rate of return.

FAQs

Is expected return guaranteed?

No, the expected return is not guaranteed. It is a probabilistic estimate based on assumptions about future outcomes and their likelihoods. Actual returns can, and often do, differ significantly from the expected return due to market volatility, economic changes, and unforeseen events.

How does risk relate to expected return?

Generally, there is a positive relationship between risk and expected return. Investors typically demand a higher expected return for taking on greater levels of risk. This is a fundamental principle in finance, suggesting that investments with higher potential rewards also carry higher potential for losses. Understanding both the expected return and the associated risk (e.g., measured by systematic risk or unsystematic risk) is crucial for making informed investment decisions.

Can expected return be negative?

Yes, the expected return can be negative. If the weighted average of all possible outcomes for an investment results in a loss, then the expected return will be negative. This indicates that, on average, the investment is projected to lose money over time based on the probabilities assigned to various scenarios. Investors typically avoid investments with negative expected returns unless there are non-financial benefits or strategic reasons.

What is the difference between expected return and average historical return?

Average historical return is the mean return an investment has generated over a past period. Expected return, conversely, is a forward-looking estimate of what an investment might yield in the future. While historical returns often inform the calculation of expected returns, they are not the same; expected return incorporates current market views and probabilistic analysis. The risk-free rate and market risk premium are often components in models used to estimate expected returns, such as the Capital Asset Pricing Model.¹, ²