Expected Value

What Is an Expected Value?

Expected value is the average outcome of an uncertain situation, with each possible outcome weighted by its probability. In investing, it gives a single figure summarizing what a decision might be worth on average if the same bet could be repeated many times. It does not predict what will happen in any single case.

How Expected Value Is Calculated

To calculate it, list every possible outcome, multiply each outcome's value by its probability, and add the results together. The probabilities must cover all possible outcomes and add up to 100 percent.

E(X) = (p1 × x1) + (p2 × x2) + ... + (pn × xn)

Here, x stands for each outcome's value and p stands for its probability. Investors often apply this method to expected return estimates, where the outcomes are percentage gains or losses rather than dollar amounts.

An Example

Suppose a hypothetical trade has a 60 percent chance of earning 10 percent and a 40 percent chance of losing 5 percent. The expected value is (0.60 × 10) + (0.40 × −5) = 6 − 2 = 4 percent. This is an average, so the actual result of any single trade could be a gain of 10 percent or a loss of 5 percent.

Advantages and Limitations

Expected value offers a simple way to compare uncertain choices on one scale. However, it is only as reliable as its inputs, and probabilities and outcome values are often estimates. It also says nothing about risk or how widely the possible results are spread. Two investments with the same expected value can have very different volatility and standard deviation, which is why investors often examine these measures alongside it.