What Is Expected Return?

The expected return is the profit or loss that an investor anticipates on an investment based on historical 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:historical returns.

Expected Return Theory

Expected return calculations are a key piece of business operations and financial theory, and are described in the 澳洲幸运5官方开奖结果体彩网:modern portfolio theory (MPT) or the 澳洲幸运5官方开奖结果体彩网:Black-Scholes options pricing model. The expected return helps determine whether an investment𝔍 has a positive or negative average net outꦯcome.

The sum is calculated as the 澳洲幸运5官方开奖结果体彩网:expected value (EV) of an inve🍨stment given its potential returns in different scenarios, a🦩s illustrated by the following 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 澳洲幸运5官方开奖结果体彩网:systematic and 澳洲幸运5官方开奖结果体彩网:unsystematic risks.

Formula

When considering individual investmen𝐆ts orไ portfolios, a more formal equation for the expected return of a financial investment is:

澳洲幸运5官方开奖结果体彩网: 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 depends on the investment's beta, or relative volatility compared to the broader market. The expected return and 澳洲幸运5官方开奖结果体彩网:standard deviation are two statistical measures that can be used to analyze a po🌃rtfolio.

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 澳洲幸运5官方开奖结果体彩网:review the risk characteristics of opportunities to determine if the investments align with their portfolio goals. Assume two hypothetical investments exist. Their a🍸nnual 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 retu𒅌rns 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

Example

The expected return can apply to a single security or asset or be expanded to analyze a port🔯folio 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 areဣ 50%, 20%, and 30%, respectively. The expected retur༺n of the total portfolio is:

(50% x 15%) + (20% x 6%) + (30% x 9%) = 11.4%

The Bottom Line

The expect🎃ed 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.