Understanding Expected Return: A Guide to Investment Profitability

What Is Expected Return?

The expected return is the profit or loss an investor expects from an investment based on past returns. Thus, the expected return is like a long-term average of past returns.

Understanding the Theory Behind Expected Return

Expected return calculations are crucial in business and financial theory, as seen in modern portfolio theory (MPT) and the Black-Scholes model.

The expected return helps determine whether an investment has a positive or negative average net outcome.

The expected return is calculated as the expected value (EV) of an investment's potential returns, shown by this formula:

Expected Return = Σ (Return_i x Probability_i)

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.

Calculating Expected Return: The Formula Explained

For individual investments or portfolios, a formal equation for expected return is:

Where:

• r_a = expected return;
• r_f = the risk-free rate of return;
• β = the investment's beta; and
• r_m =the expected market return

The expected return above the risk-free rate of return (RoR) 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 portfolio's expected return is the average of its possible returns. 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 of Expected Return

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.

Where:

xi =Value of the ith point in the data set

x =The mean value of the data set

n =The number of data points in the data set

Practical Examples of Expected Return Calculations

The expected return can apply to a single security or asset or be expanded to analyze a 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%

The Bottom Line

The expected return is the average return that an investment or portfolio should generate over a certain period. Riskier assets require a higher expected return to offset the added risk. Expected return is not a guarantee, but a prediction based on historical data and other relevant factors.