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# What is an Expected Monetary Value?

Expected monetary value is a value based on probability that factors in all possible monetary outcomes of a given situation. The value is reached by multiplying the percentage of each possibility occurring by the monetary loss or gain associated with that outcome. At that point all of those values, positive and negative, are combined to reach the expected monetary value. This calculation is a valuable tool for those tasked with making a decision involving several possible outcomes, as it represents the most statistically accurate estimation of the eventual result.

The ideal situation in making a decision would be to know the outcome before the decision is made, especially when it comes to ones involving money. Since that isn't the case, calculating the expected monetary value is a good way to come to the most informed monetary decision possible. It's an especially valuable tool for risk management assessments because of the way it takes into account all possible scenarios in a given decision.

For example, a company is faced with two possible alternatives. Choice A would give it a one in ten shot at $1,000 UD Dollars (USD), with no financial reward the other nine times out of ten. The $1,000 USD would be multiplied by the 10 percent chance of that outcome occurring for a total of $100 USD. Since the other nine possible outcomes come with no monetary gain or loss, that $100 USD would be the expected monetary value of choice A.

In choice B, there is a 50 percent chance of a $2,000 USD gain and a 50 percent chance of a $500 USD loss. To calculate the expected value here, $2,000 USD would be multiplied by 0.50 to get a gain of $1,000 USD, and negative-$500 USD is multiplied by 0.50 for a $250 loss. Adding the $1,000 USD to the negative-$250 yields an expected monetary value for choice B of $750 USD, making it the more preferable of the two choices by this standard.

If there is a cost attached to choices in a particular circumstance, they must be taken into account as well. In the example above, had there been a $700 attached to making choice B, then the expected monetary value would have dropped to just $50 USD, dropping it below the expected yield of choice A. In risk management, these calculations are often used in tandem with decision trees, which lay all of the choices and expected values next to each other in simple diagrams to clearly delineate the risks and opportunities associated with all possible choices.

## Discussion Comments

@everetra - That’s good to know, however I think you’re missing something. Expected monetary value uses probability and in your example there is no probability.

You don’t know the likelihood that a stock will swing up or down. I think a better expected monetary example is the online betting markets.

They pool together the wisdom of masses of investors who bet on different outcomes, and their bets create probabilities for those events. I don’t recommend betting of course, but I think it’s a better illustration.

I think expected monetary value analysis is standard operating procedure for anyone investing in stocks or other securities. Many people don’t realize you can determine maximum profit and maximum loss on a stock, by setting stop limit orders.

You could buy 100 shares of a stock at $10 per share, making your investment $1,000. Maybe you don’t want to lose more than 25% of that investment, however, so you set a stop limit sell order of $7.50.

If the stock drops below that value, it will sell automatically. You can also set an order on the upside as well. Maybe you want to automatically “cash in your chips” so to speak if the stock hits $20 a share; you can set a limit order on that as well.

In this way, you can calculate how much you can profit or lose on the transaction.

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