What Is Expected Return?
The expected return is the profit or loss that an investor anticipates on an investment based on historical rates of return (RoR). The expected return is not guaranteed, but historical data sets reasonable expectations. Therefore, the expected return figure can be considered a long-term weighted average of historical returns.
Key Takeaways
- The expected return is the profit or loss an investor can anticipate receiving on an investment.
- Expected returns cannot be guaranteed.
- The expected return for a portfolio with multiple investments is the weighted average of the expected return of each investment.
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Expected Return Theory
Expected return calculations are a key piece of business operations and financial theory, and are described in the modern portfolio theory (MPT) or the Black-Scholes options pricing model. The expected return helps determine whether an investment has a positive or negative average net outcome.
The sum is calculated as the expected value (EV)of an investment given itspotential returns in different scenarios, as illustrated bythe following formula:
Expected Return = Σ (Returni x Probabilityi)
Where "i" indicates each known return and its respective probability in the series
For example, if an investment has a 50% chance of gaining 20% and a 50% chance of losing 10%, the expected return would be 5% = (50% x 20% + 50% x -10% = 5%). The 5% expected return may never be realized, as the investment is inherently subject to systematic and unsystematic risks.
Systematic risk affects a market sector or the entire market, whereas unsystematic risk applies to a specific company or industry.
Formula
When considering individual investments or portfolios, a more formal equation for the expected return of a financial investment is:
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Where:
- ra = expected return;
- rf = the risk-free rate of return;
- β = the investment's beta; and
- rm =the expected market return
The expected return above the risk-free rate of return depends on the investment's beta, or relative volatility compared to the broader market. The expected return and standard deviation are two statistical measures that can be used to analyze a portfolio.
The expected return of a portfolio is the anticipated amount of returns that it may generate, making it the average of the portfolio's possible return distribution. The standard deviation of a portfolio measures the amount that the returns deviate from its mean, making it a proxy for the portfolio's risk.
Limitations
Before making any investment decisions, investors review the risk characteristics of opportunities to determine if the investments align with their portfolio goals. Assume two hypothetical investments exist. Their annual performance results for the last five years are:
- Investment A: 12%, 2%, 25%, -9%, and 10%
- Investment B: 7%, 6%, 9%, 12%, and 6%
Both of these investments have expected returns of 8%.However,when analyzing the risk of each, as defined by the standard deviation, investment A is approximately five times riskier than investment B.
Investment A has a standard deviation of 11.26% and investment B has a standard deviation of 2.28%. Standard deviation is a common statistical metric to measure an investment's historical volatility or risk.
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Where:
xi =Valueoftheith pointinthedataset
x =Themeanvalueofthedataset
n =Thenumberofdatapointsinthedataset
Example
The expected return can apply to a single security or asset or be expanded to analyzea portfolio containing many investments. If the expected return for each investment is known, the portfolio's overall expected return is a weighted average of the expected returns of its components.
For example, assume an investor has the following portfolio:
- Alphabet Inc., (GOOG): $500,000 invested and an expected return of 15%
- Apple Inc. (AAPL): $200,000 invested and an expected return of 6%
- Amazon.com Inc. (AMZN): $300,000 invested and an expected return of 9%
With a total portfolio value of $1 million, the weights of Alphabet, Apple, and Amazon in the portfolio are 50%, 20%, and 30%, respectively. The expected return of the total portfolio is:
(50% x 15%) + (20% x 6%) + (30% x 9%) = 11.4%
How Is Expected Return Used in Finance?
Expected return calculations determine whether an investment has a positive or negative average net outcome.The equation is usually based on historical data and therefore cannot be guaranteed for future results, however, it can set reasonable expectations.
What Are Historical Returns?
Historical returns are the past performance of a security or index, such as the . Analysts review historical return data to predict future returns or to estimate how a security might react to a particular economic situation, such as a drop in consumer spending.
How Does Expected Return Differ From Standard Deviation?
Expected return and standard deviation are two statistical measures used to analyze a portfolio. The expected return of a portfolio is the anticipated returns a portfolio may generate, making it the average distribution. The standard deviation of a portfolio measures the amount that the returns deviate from its mean, making it a proxy for the portfolio's risk.
The Bottom Line
The expected return is the average return that an investment or portfolio should generate over a certain period. Riskier assets or securities demand a higher expected return to compensate for the additional risk. Expected return is not a guarantee, but a prediction based on historical data and other relevant factors.
