## Scoping the Scenarios

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.

## Multiply and Add

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.

## Expecting a Call?

One risk specific to bonds, including some Treasury issues, is call risk. When an issuer calls a bond series, it redeems the bond before maturity -- on or after a specified call date -- for a set amount of cash. The call cancels the bond and you receive no further interest payments. Normally, bond investors account for call risk by figuring the yield-to-call, which is the percentage return the bond will pay up to the call date. Whether or not a bond is callable, bond investors must also account for reinvestment risk, which is the risk that you will not be able to reinvest interest payments -- or prematurely paid principal -- at the same rate as that of the original investment. You can incorporate these risks to refine your expected payoff calculation.