# How to Calculate the Expected Payoff of an Investment

The future is uncertain and so are most expected payoffs.
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It's natural to want to know how much an investment will make before you plunk down your money. You know the exact payoff of some investments, such as U.S. Treasury debt issues that you hold until maturity. These instruments pay a known amount of interest and a fixed value at maturity, backed by the full faith and credit of the U.S. government. Other investments are riskier and calculating their expected payoffs requires you to make predictions.

## Scoping the Scenarios

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The central activity behind an expected payoff calculation is to assign probabilities to different outcomes and take their weighted average. For example, suppose you predict that there is a 10 percent chance that shares of XYZ Corp will decline 5 percent in one year. You also think that there is a 20 percent chance the shares will remain the same, a 40 percent chance that they'll rise 8 percent and a 30 percent chance that they'll gain 15 percent. Armed with this information, you can create a spreadsheet and figure your expected payoff on XYZ shares.

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The calculation of expected payoff requires you to multiply each outcome by your estimate of its probability and then sum the products. In our example, a 10 percent chance of a 5 percent decline produces a result of -0.5 percent. Similarly, the three other percentages are (.20 x 0), (.40 x 8) and (.10 x 15). The result is -0.5 + 0 + 3.2 + 4.5, or 7.2 percent. According to your predictions, the expected payoff in one year for a \$10,000 investment will be \$720 more than you invested.

## It's a Risky World

The accuracy of your expected payoff prediction depends entirely on your ability to peer into the future. However, you can make your guess more educated by noting the past volatility of the investment and the predictions of experts regarding the investment and the economic environment. You can also employ some useful rules of thumb: high-rated bonds are less risky than are lower-rated ones, small growth stocks are more volatile than are large blue chips and a diversified portfolio is less risky than one containing only a few investments. Despite your best predictions, companies can go bankrupt, defaulting on their bonds and making their stock worthless. Many other risks apply to investments, and your predictions encapsulate all of these into the probabilities you assign to specific outcomes.