## What is 'Expected Return'

Expected return is the profit or loss an investor anticipates on an investment that has known or expected rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring and then summing these results. For example, if an investment has a 50% chance of gaining 20% and a 50% change of losing 10%, the expected return is (50% * 20% + 50% * -10%), or 5%.

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## BREAKING DOWN 'Expected Return'

Expected return is a tool used to determine whether an investment has a positive or negative average net outcome. It's calculated as the expected value of an investment given its potential returns in different scenarios, as illustrated by the following formula:

Expected Return = SUM (Returni * Probabilityi), where i indicates each known return and its respective probability in the series.

Expected return is usually based on historical data and is therefore not guaranteed; it is merely a long-term weighted average of historical returns. In the example above, for instance, the 5% expected return may never be realized in the future, as the investment is inherently subject to systematic and unsystematic risks.

In addition to expected returns, wise investors should also consider the probability of return in order to better assess risk. After all, one can find instances in which certain lotteries offer a positive expected return despite the very low probability of realizing that return.

## Expected Return of a Portfolio

The expected return doesn't just apply to single investments. It can also 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 the following portfolio of stocks:

• Stock A: \$500,000 invested and an expected return of 15%
• Stock B: \$200,000 invested and an expected return of 6%
• Stock C: \$300,000 invested and an expected return of 9%

With a total portfolio value of \$1,000,000, the weights of Stock A, B and C are 50%, 20% and 30%, respectively. Thus, the expected return of the total portfolio is:

Expected return of portfolio = (50% x 15%) + (20% x 6%) + (30% x 9%) = 7.5% + 1.2% + 2.7% = 11.4%

## Limitations of the Expected Return

It is quite dangerous to make investment decisions based on expected returns alone. Before making any buying decisions, investors should always review the risk characteristics of investment opportunities to determine if the investments align with their portfolio goals. For example, assume two hypothetical investments exist. Their annual performance results for the last five years are:

• Investment A: 12%, 2%, 25%, -9%, 10%
• Investment B: 7%, 6%, 9%, 12%, 6%

Both of these investments have expected returns of exactly 8%. However, when analyzing the risk of each, as defined by the standard deviation, Investment A is approximately five times more risky than Investment B (Investment A has a standard deviation of 12.6% and Investment B has a standard deviation of 2.6%).

See Expected Return, Variance and Standard Deviation of aPortfolio for more on calculating and analyzing these statistical measures.

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