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What Is Expected Return?

Expected return represents the anticipated profit or loss on an investment portfolio or individual asset, projected over a specific time horizon. It is a cornerstone concept in portfolio theory and quantitative finance, providing a forward-looking estimate of an investment's potential performance. While the expected return is not a guarantee of future outcomes, it serves as a critical metric for investors and analysts to gauge the attractiveness of an investment, especially when balanced against its associated risk. The calculation of expected return considers various possible scenarios for an investment and assigns a probability to each.

History and Origin

The concept of expected return gained prominence with the advent of Modern Portfolio Theory (MPT), pioneered by Harry Markowitz in his seminal 1952 paper, "Portfolio Selection." Markowitz's work revolutionized investment management by introducing a quantitative framework for analyzing and constructing portfolios based on the principles of diversification and the risk-return tradeoff. Before MPT, investors often focused solely on maximizing returns, often leading to undiversified portfolios. Markowitz's contribution highlighted that investors should consider both the expected return of an asset and its variance (a measure of risk) when making investment decisions. His model demonstrated how combining assets could reduce overall portfolio risk for a given level of expected return, or increase expected return for a given level of risk⁶.

Key Takeaways

Expected return is a probabilistic estimate of an investment's future profit or loss, not a guaranteed outcome.
It is a fundamental input in various financial models, including Modern Portfolio Theory and the Capital Asset Pricing Model.
The calculation typically involves weighting potential outcomes by their probabilities.
Expected return should always be considered in conjunction with risk when evaluating an investment.
Historical data often forms the basis for estimating future expected returns, but past performance does not dictate future results.

Formula and Calculation

The expected return of an investment can be calculated as the sum of the products of each possible outcome's return and its probability of occurring. For a single asset, the formula is:

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

Where:

( E(R) ) = Expected return
( n ) = Number of possible outcomes
( P_i ) = Probability of outcome ( i ) occurring
( R_i ) = Return of outcome ( i )

For a portfolio, the expected return is the weighted average of the expected returns of its individual assets, based on their proportional weight in the total portfolio value:

E(R_p) = \sum_{i=1}^{n} (w_i \times E(R_i))

Where:

( E(R_p) ) = Expected return of the portfolio
( n ) = Number of assets in the portfolio
( w_i ) = Weight (proportion) of asset ( i ) in the portfolio
( E(R_i) ) = Expected return of asset ( i )

This formula underscores the impact of asset allocation on a portfolio's overall expected return.

Interpreting the Expected Return

Interpreting the expected return requires understanding that it is a statistical average derived from assumptions about future events. A higher expected return generally implies greater potential for profit, but it often comes with a higher degree of risk. For instance, a growth stock might have a higher expected return than a utility stock, reflecting its greater earnings volatility and market sensitivity. Investors use expected return alongside measures of risk, such as standard deviation, to assess the risk-adjusted return of an investment. This allows for a more comprehensive comparison between different investment opportunities, aligning them with an investor's risk tolerance and financial goals.

Hypothetical Example

Consider an investor evaluating a potential investment in a new technology startup. Based on market analysis and financial projections, the investor identifies three possible scenarios for the startup's annual return:

Best-case scenario: A 30% return, with a 20% probability.
Most likely scenario: A 10% return, with a 60% probability.
Worst-case scenario: A -15% return (a loss), with a 20% probability.

Using the expected return formula:

( E(R) = (0.20 \times 0.30) + (0.60 \times 0.10) + (0.20 \times -0.15) )
( E(R) = 0.06 + 0.06 + (-0.03) )
( E(R) = 0.09 )

The expected return for this startup investment is 9%. This means that, on average, if this scenario were to be repeated many times, the investor could anticipate an annual return of 9%. However, it's crucial to remember that the actual outcome in any given year will be one of the three discrete scenarios, not necessarily the 9% expected return itself. This calculation forms a part of overall investment analysis.

Practical Applications

Expected return is widely applied across various facets of finance and investing. In portfolio management, it helps guide asset allocation decisions, allowing managers to construct portfolios that aim to achieve specific return objectives while managing risk. It is a key input in asset pricing models like the Capital Asset Pricing Model (CAPM), which uses expected return to determine the appropriate discount rate for valuing securities. For corporate finance, businesses use expected return to evaluate potential capital projects and determine the viability of new ventures through techniques such as discounted cash flow analysis.

Furthermore, regulatory bodies like the U.S. Securities and Exchange Commission (SEC) provide guidance on the use of forward-looking statements by companies. These guidelines emphasize that any projections or statements about future financial performance, which inherently involve an expected return, must be made in good faith and with a reasonable basis, often accompanied by cautionary language to inform investors of the inherent uncertainties⁵,⁴. The SEC's "Safe Harbor" provisions aim to protect companies from liability for such statements if they meet certain criteria, acknowledging the speculative nature of future projections³.

Limitations and Criticisms

Despite its widespread use, the concept of expected return has several limitations. Chief among them is its reliance on historical data and probabilistic assumptions, which may not accurately predict future market conditions. Unexpected events, shifts in economic cycles, or unforeseen company-specific developments can significantly deviate actual returns from the expected return². For instance, a study found that investor expectations of future stock market returns can be positively correlated with past stock returns, yet negatively correlated with model-based expected returns, suggesting a behavioral bias towards extrapolating past performance¹.

Another criticism is that expected return models often struggle to account for qualitative factors, such as management quality, geopolitical events, or sudden technological disruptions, which can profoundly impact an investment's actual performance. Additionally, some models assume a normal distribution of returns, which may not hold true in reality, especially during periods of extreme market volatility or "tail events." While expected return is a valuable tool for financial modeling and comparison, investors should use it with caution, understanding that it provides an estimate rather than a guarantee of actual investment outcomes. It's essential to integrate expected return analysis with thorough qualitative research and a robust understanding of market volatility.

Expected Return vs. Required Rate of Return

Expected return and required rate of return are two distinct but related concepts in finance, often a source of confusion. Expected return is what an investor anticipates earning on an investment, based on analysis of potential future outcomes and their probabilities. It is a forward-looking forecast. In contrast, the required rate of return is the minimum rate of return an investor or company demands from an investment to justify the associated risk. It represents the compensation needed for holding a risky asset over a risk-free one. If an investment's expected return is lower than its required rate of return, the investment would generally be considered unattractive, as it doesn't meet the investor's minimum compensation threshold for the risk taken. Conversely, if the expected return exceeds the required rate of return, the investment may be seen as a worthwhile opportunity.

FAQs

How accurate is expected return?

Expected return is an estimate and not a guarantee. Its accuracy depends heavily on the quality of the data used, the assumptions made about future probabilities, and the stability of market conditions. It provides a useful benchmark but rarely matches actual realized returns precisely.

Can expected return be negative?

Yes, expected return can be negative. A negative expected return indicates that, based on the probabilities and potential outcomes, the investment is anticipated to result in a loss on average. While investors typically seek positive returns, sometimes a negative expected return might be accepted if the investment serves other strategic purposes, such as hedging or extreme diversification within a broader portfolio.

How does risk relate to expected return?

In finance, there is generally a positive correlation between risk and expected return. Higher expected returns typically come with higher levels of risk. This is known as the risk-return tradeoff. Investors demand greater compensation (higher expected return) for taking on more uncertainty or volatility in their investments. Understanding this relationship is crucial for effective investment decision-making.

Is expected return the same as historical return?

No, expected return and historical returns are not the same. Historical return refers to the actual returns an investment has generated in the past. While historical data is often used as a basis to calculate or inform the expected return, the expected return is a forward-looking projection. Past performance is not indicative of future results, and an investment's expected return can differ significantly from its historical performance due to changing market dynamics, economic conditions, or company-specific factors.