### What Is Expected Return?

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

#### Expected Return

### How Expected Return Works

The expected return is a tool used to 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 its potential returns in different scenarios, as illustrated by the following formula:

**Expected Return = SUM (Return _{i} x Probability_{i})**

where: "i" indicates each known return and its respective probability in the series

The expected return is usually based on historical data and is therefore not guaranteed. This figure 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. Systematic risk the danger to a market sector or the entire market whereas unsystematic risk applies to a specific company or industry.

### Key Takeaways

- The expected return is the amount of profit or loss an investor can anticipate receiving on an investment.
- An expected return is calculated by multiplying potential outcomes by the odds of them occurring and then totaling these results.
- Essentially a long-term weighted average of historical results, expected returns are not guaranteed.

### Limitations of 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%, and 10%
- Investment B: 7%, 6%, 9%, 12%, and 6%

Both of these investments have expected returns of exactly 8%. However, when analyzing the risk of each, as defined by the standard deviation, Analyst use standard deviation to reveal historical volatility in investments. Investment A is approximately five times riskier than Investment B. That is, Investment A has a standard deviation of 12.6% and Investment B has a standard deviation of 2.6%.

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

#### Pros

Gages the performance of an asset

Weighs different scenarios

#### Cons

Doesn't take risk into account

Based largely on historic data

### Real World Example of Expected Return

The expected return doesn't just apply to a single security or asset. 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, let's assume we have an investor interested in the tech sector. His portfolio contains the following stocks:

With a total portfolio value of $1 million the weights of Alphabet, Apple, and Amazon in the portfolio are 50%, 20%, and 30%, respectively.

Thus, the expected return of the total portfolio is 11.4%:

- (50% x 15% = 7.5%) + (20% x 6% = 1.2%) + (30% x 9% = 2.7%)
- (7.5% + 1.2% + 2.7% = 11.4%)