Expected Values (EV)

Expected values are widely used in decision making under uncertainty.

Definition

An expected value is a weighted average of all possible outcomes. It calculates the average return that will be made if a decision is repeated again and again.

In other words it is obtained by multiplying the value of each possible outcome (x) by the probability of that outcome (p), and summing the results.

The formula for the expected value is EV = Σpx

Illustration

Returns from a new restaurant venture depend on whether a competitor decides to open up in the same area. The following estimates are made :

Since the expected value shows the long-run average outcome of a decision which is repeated time and time again,it is a useful decision rule for a risk neutral  decision maker. This is because a risk neutral investor neither seeks risk or avoids it; he is happy to accept an average outcome.

Advantages and disadvantages of EVs

Advantages

• Takes uncertainty into account by considering the probability of each possible outcome and using this information to calculate an expected value.
• The information is reduced to a single number resulting in easier decisions.
• Calculations are relatively simple.

Disadvantages

• The probabilities used are usually very subjective.
• The EV is merely a weighted average and therefore has little meaning for a one­off project.
• The EV gives no indication of the dispersion of possible outcomes about the EV, i.e. the risk.
• The EV may not correspond to any of the actual possible outcomes.

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