What Is Expected Value?

Expected value (EV) is a for❀mula investors use to estimate the likely average return they might earn from an investment over time. They use expected value to estimate the worth of investments, often relative to their risk.

By calculating EVs, investors can choose the scenario most likely to produce the outcome they seek. In statistics and probability analysis, the EV is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.

Understanding Expected Value

Expected value refers to the anticipated value of an asset in 𒐪the future. The EV of a random variable gives a measure of the center of the distribution of the variable. The EV is essentially the long-term average value of the variable.

Because of the 澳洲幸运5开奖号码历史查询:law of large numbers, the average value of the variable converges to the EV as the number of rep🎉etitions approaches infinity. EV is also known as expectation, the mean, or the first moment.

EV can be calculated for single discrete variables, single continuous v🍸ariables, multiple discrete variables, and multiple continuous variables. For continuous variable situations, integrals must be used.

澳洲幸运5开奖号码历史查询:Scenario analysis is one technique for calculating the EV of an investment opportunity. It uses estimated probabilities with 澳洲幸运5开奖号码历史查询:multivariate models to examine possible outcomes for a proposed investment. Scenario analysis also helps investors determine whether they are taking on an appr🌳opriate level of risk given the likely outcome of the investment.

Formula for Expected Value

澳洲幸运5开奖号码历史查询: The formula for expected value is:

$\begin{aligned} EV=\sum P(X_i)\times X_i\end{aligned}$EV=∑P(Xi​)×Xi​​

澳洲幸运5开奖号码历史查询:where:

• X is a random variable
• Xi are specific values of X
• P(Xi) is the probability of Xi occurring

Thus, the EV of a random variable X is taken as each value of the random variable multiplied by its probability, and each of those products is summe💖d.

Expected Value in Portfolio Construction

Investors need to understand several key factors when they want to construct their investment or 澳洲幸运5开奖号码历史查询:financial portfolios. These include how assets work and their associated risks. Investors should also have a firm grasp on their financial situation, investment goals, and investmꦅent time horizon.

Once they thoroughly understand these factors, investors and their financial advisors can employ EV to build a portfolio that maximizes their retu𒀰rns while minimizing th🌺eir risks.

Example of an Investor Using EV

You ♕can use EV to determine the potential return of an investment🤪 and therefore, which assets to add to your portfolio based on your preference for return.

So, to calculate expected value, first multiply the probability of a positive outcome by the potential return. Say, an investment has a 60% chance of increasing in value by $10,000. The calculation would be: 0.6 x $10,000 = $6,000.

Then, multiply the probability of a negative outcome by the potential loss. For instance, the investment also has a 40% chance of decreasing in value by $5,000. The calculation would be: 0.4 x $5,000 = $2,000.

Finally, subtract the second result from the first: $6,000 - $2,000 = $4,000. That's the EV for this investment.

Next, you may wish to compare two or more investments in which you're interested. Follow the same steps and compare the expected returns. This can help you make selections as you build your portfolio.

Compare EVs for Different Assets

Also, bear in mind that different assets have different EVs. That is, a stock comes with a different expected value (and risk profile) than a bond or an 澳洲幸运5开奖号码历史查询:exchange-traded fund (ETF). It's useful to calculate EVs for the various assets that youᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚ're interested i𒊎n and compare those results.

You can also use EV to adjust your portfolio once it's built. For instance, compare EVs to determine whether selling an underperforming asset with no expectation of a rise in value and replacing it with another with a higher EV makes sense.

Example of Expected Value

To calculate the EV for a single discrete random variable, yo🐽u must multiply each value of t🐲he variable by the probability of that value occurring.

Take, for example, a normal six-sidedꩲ die. Once you roll the die, it has an equal one-sixth probability of landing on the values of either one, two, three, four, five, or six. Given this information, the calculation is:

$\begin{aligned}\left(\frac{1}{6}\times1\right)&+\left(\frac{1}{6}\times2\right)+\left(\frac{1}{6}\times3\right)\\&+\left(\frac{1}{6}\times4\right)+\left(\frac{1}{6}\times5\right)+\left(\frac{1}{6}\times6\right)=3.5\end{aligned}$(61​×1)​+(61​×2)+(61​×3)+(61​×4)+(61​×5)+(61​×6)=3.5​

If you were to💟 roll a six-sided die an infinite number of times, you would find that the average value equal😼s 3.5.

The Bottom Line

Understanding the con🐠cept of expected value is important for investors. It can aid them in determining the level of return that they might expect from an investment. Expected value and scenario analysis can provide insight into the risk of an investment versus its return and help an investor decide whether or not to include it in their portfolio.