Expected rate of return

What Is Expected Rate of Return?

The expected rate of return is the profit or loss an investor anticipates receiving on an investment over a specific future period. It is a forward-looking estimate, representing the weighted average of all possible returns, with the weights corresponding to the probability of each return occurring. This concept is fundamental to portfolio theory, as it helps investors gauge the potential profitability of an asset or portfolio. Understanding the expected rate of return is crucial for making informed investment decisions, evaluating risk tolerance, and constructing a diversified portfolio. The expected rate of return is a central element in financial modeling, guiding strategic asset allocation and assessing the attractiveness of various financial instruments.

History and Origin

The conceptualization of the expected rate of return as a core component of investment analysis gained prominence with the advent of Modern Portfolio Theory (MPT). This groundbreaking framework was introduced by economist Harry Markowitz in his seminal 1952 paper, "Portfolio Selection." Markowitz's work revolutionized investment thinking by formally integrating the concepts of expected return and risk (measured by volatility) into a mathematical model for portfolio optimization. His contributions laid the foundation for modern financial economics and earned him a share of the Nobel Memorial Prize in Economic Sciences in 1990. MPT demonstrated that investors should not only consider the expected return of individual assets but also how they interact within a portfolio to achieve optimal diversification.⁴

Key Takeaways

• The expected rate of return is a probabilistic forecast of an investment's future performance.
• It is a critical component in financial modeling, guiding investment decisions and portfolio construction.
• Calculating the expected rate of return involves assigning probabilities to various possible outcomes.
• The expected rate of return is distinct from the historical returns an investment has achieved.
• It is used in conjunction with risk measures to evaluate investment opportunities and inform asset allocation.

Formula and Calculation

The expected rate of return for an asset or portfolio is calculated as the sum of the products of each possible return scenario and its corresponding probability.

The formula is expressed as:

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

Where:

• (E(R)) = Expected rate of return
• (R_i) = Return in scenario i
• (P_i) = Probability of return in scenario i
• (n) = Number of possible scenarios

For example, if an investment has three possible outcomes: a 20% return with a 30% probability, a 10% return with a 50% probability, and a -5% return with a 20% probability, the calculation would apply this formula. This method allows for a quantitative assessment of potential outcomes based on anticipated conditions.

Interpreting the Expected Rate of Return

The expected rate of return provides a forward-looking estimate that can guide investment decisions. A higher expected rate of return generally indicates a more attractive investment, assuming all other factors, especially risk, remain constant. However, it is essential to understand that this is an expectation, not a guarantee. Investors use the expected rate of return in conjunction with measures of risk, such as standard deviation or beta, to evaluate the risk-adjusted return of an asset. For instance, an asset with a high expected rate of return but also high risk might not be suitable for an investor with a low risk tolerance. It is a key input in sophisticated financial models that aim to optimize portfolio performance based on an investor's objectives and constraints. Understanding how to interpret this metric is crucial for effective asset allocation.

Hypothetical Example

Consider a hypothetical investment in a new energy startup. An investor assigns the following probabilities and potential returns for the next year:

• Scenario 1: High Success
  • Probability ((P_1)): 30%
  • Return ((R_1)): 40%
• Scenario 2: Moderate Growth
  • Probability ((P_2)): 50%
  • Return ((R_2)): 15%
• Scenario 3: Poor Performance
  • Probability ((P_3)): 20%
  • Return ((R_3)): -10%

Using the formula for expected rate of return:

$E(R) = (0.40 \times 0.30) + (0.15 \times 0.50) + (-0.10 \times 0.20)$
$E(R) = 0.12 + 0.075 - 0.02$
$E(R) = 0.175$

The expected rate of return for this startup investment is 17.5%. This calculated value helps the investor weigh the potential gain against the inherent risks before committing capital. It's a foundational step in determining the future value of such an investment.

Practical Applications

The expected rate of return is a ubiquitous concept across various facets of finance. In corporate finance, businesses use it to evaluate potential projects through capital budgeting techniques, comparing a project's expected return to its cost of capital. For investors, it informs decisions on purchasing stocks, bonds, or other securities, often weighed against a target risk premium or the risk-free rate.

In portfolio management, the expected rate of return is central to constructing diversified portfolios that align with an investor's objectives. Analysts also use it in valuation models, where future cash flows are discounted by a rate often derived from expected returns. Moreover, macroeconomic indicators, such as inflation expectations, influence the expected rate of return for various asset classes.³ These expectations, monitored by institutions like the Federal Reserve Bank of Cleveland, can shift investor perceptions of future profitability and influence market behavior.

Limitations and Criticisms

While the expected rate of return is a powerful analytical tool, it is subject to several limitations. First and foremost, it is an estimate based on assumptions and probabilities, which may not accurately reflect future outcomes. Events like economic downturns, regulatory changes, or unforeseen market shocks can significantly alter actual returns from what was expected. The accuracy of the expected rate of return relies heavily on the quality and objectivity of the input probabilities and potential returns, which can be difficult to assess, especially for novel investments.

Furthermore, relying solely on an expected rate of return without considering risk can lead to suboptimal decisions. An investment with a high expected return might also carry a disproportionately high level of risk, making it unsuitable for many investors. Academic research, such as that highlighted by John H. Cochrane, indicates that while stock return predictability exists to some extent, it does not guarantee specific outcomes.² Financial disclosures often include "forward-looking statements" that come with caveats, reminding investors that projections are not guarantees and actual results may differ materially.¹ This acknowledges the inherent uncertainty in forecasting future financial performance and the need for investors to understand the speculative nature of such projections.

Expected Rate of Return vs. Realized Rate of Return

The expected rate of return and the realized rate of return are two distinct but related concepts in finance. The key difference lies in their temporal orientation:

• Expected Rate of Return: This is a forward-looking projection or forecast of what an investment is anticipated to yield over a future period. It is based on a probabilistic assessment of various potential outcomes and is used for decision-making before an investment is made.
• Realized Rate of Return: This is the historical or actual return achieved on an investment over a past period. It is a verifiable outcome, calculated after the investment period has concluded, reflecting the actual profit or loss.

The expected rate of return is a theoretical construct used to guide investment choices, while the realized rate of return is a factual measurement of past performance. Investors aim for their realized returns to align with their expected returns, but market dynamics, unforeseen events, and inherent uncertainty mean these two figures rarely match perfectly.

FAQs

What factors influence the expected rate of return?

The expected rate of return is influenced by various factors, including the perceived risk of the investment, prevailing interest rates (such as the discount rate), economic outlook, industry trends, company-specific performance, and market sentiment. Higher perceived risk typically demands a higher expected return to compensate investors.

Is the expected rate of return guaranteed?

No, the expected rate of return is never guaranteed. It is a probabilistic estimate based on available information and assumptions about future events. Actual returns can, and often do, differ from expected returns due to unforeseen market fluctuations, economic changes, and other unpredictable factors.

How is expected rate of return used in investment decisions?

Investors use the expected rate of return as a key input to compare potential investments. They often consider it alongside risk measures to assess the risk-adjusted potential of an asset. For example, an investor performing present value calculations might use the expected return as a discount rate for future cash flows. It helps in constructing portfolios that balance potential gains with acceptable levels of risk, aligning with an individual's financial goals.

Can historical performance be used to determine the expected rate of return?

While historical returns can provide a basis for analysis and insights into an asset's past behavior, they are not a direct indicator of future expected returns. Past performance does not guarantee future results. However, historical data can be used to model potential scenarios and probabilities, which then inform the calculation of the forward-looking expected rate of return.