What Is Expected Return?
Let me explain what expected return means in investing. It's the profit or loss you, as an investor, can anticipate from an investment, based on historical rates of return. Remember, this isn't a guarantee—it's just setting reasonable expectations from past data. Think of it as a long-term weighted average of those historical returns.
Key Takeaways
You should know that expected return represents the anticipated profit or loss on your investment. It can't be guaranteed, no matter what. For a portfolio with multiple investments, it's simply the weighted average of each one's expected return.
Expected Return Theory
Expected return is central to business operations and financial theory, including modern portfolio theory (MPT) and the Black-Scholes model for options pricing. It helps you determine if an investment will have a positive or negative average net outcome on balance.
You calculate it as the expected value (EV) of the investment across different scenarios. The formula is straightforward: Expected Return = Σ (Return_i x Probability_i), where 'i' covers each known return and its probability.
For instance, if there's a 50% chance of gaining 20% and a 50% chance of losing 10%, your expected return is 5%—that's (50% x 20%) + (50% x -10%). But don't count on realizing exactly 5%; investments face systematic risks affecting markets and unsystematic risks tied to specific companies or industries.
The Formula
For individual investments or portfolios, the more formal equation is: Expected return = risk-free premium + Beta (expected market return - risk-free premium). Here, ra is the expected return, rf is the risk-free rate, β is the beta measuring volatility against the market, and rm is the expected market return.
The return above the risk-free rate hinges on the investment's beta. You can use expected return and standard deviation together to analyze a portfolio—the former shows anticipated returns as the average of possible distributions, while the latter measures deviation from the mean, indicating risk.
Limitations
Before deciding on investments, you need to review their risk characteristics to see if they fit your portfolio goals. Consider two hypothetical investments with annual returns over five years: Investment A at 12%, 2%, 25%, -9%, 10%; Investment B at 7%, 6%, 9%, 12%, 6%. Both have an expected return of 8%, but Investment A is about five times riskier with a standard deviation of 11.26% versus 2.28% for B.
Standard deviation is your go-to metric for historical volatility or risk. The formula is the square root of [(Sum(Each data point - Mean)^2) / (Number of data points - 1)], where xi is each value, x is the mean, and n is the number of points.
Example
Expected return applies to single assets or entire portfolios. If you know each investment's expected return, the portfolio's is a weighted average. Say you have $500,000 in Alphabet (GOOG) with 15% expected return, $200,000 in Apple (AAPL) at 6%, and $300,000 in Amazon (AMZN) at 9%. With a $1 million total, weights are 50%, 20%, 30%. The portfolio expected return is (50% x 15%) + (20% x 6%) + (30% x 9%) = 11.4%.
How Is Expected Return Used in Finance?
In finance, expected return helps you assess if an investment's average outcome is positive or negative. It's based on historical data, so future results aren't guaranteed, but it sets reasonable expectations.
What Are Historical Returns?
Historical returns are past performances of securities or indices like the S&P 500. You review them to predict future returns or gauge reactions to events, such as drops in consumer spending.
How Does Expected Return Differ From Standard Deviation?
Both are statistical tools for portfolio analysis. Expected return is the anticipated average return, while standard deviation shows how much returns vary from that average, serving as a risk proxy.
The Bottom Line
Expected return is the average return you can predict for an investment or portfolio over time. Riskier assets require higher expected returns to offset the risk. It's a prediction from historical data and factors, not a guarantee.
