Companies continually face risks, and prudent companies set aside contingency reserves to cover any costs associated with those risks. Yet when a company isn't certain whether a given event is going to occur, it's impossible to come up with a precise dollar amount that will guarantee being able to cover any resulting costs. Instead, many companies use the expected value method to estimate what amount of reserves will be adequate.

A simple exercise in probability
In order to use the expected value method, you need to know two things: how much a given event will cost the company if it happens and the probability of that event actually happening. Once you have those two figures for every potential setback that the company could face, you can set up a contingency reserve by multiplying each event's probability of happening by the resulting cost if it happens and then adding up the results for all potential events.

For instance, say you run a medical business and perform surgical procedures. You have a high success rate of 99%, but 1% of the time a patient suffers complications for which you're responsible. The cost of fixing the situation when that happens is \$100,000. In order to set up an appropriate contingency reserve fund, you should set aside \$1,000 for every surgical procedure you do. Alternatively, if you obtain malpractice and professional liability insurance, you should expect to pay somewhere in the neighborhood of that amount in premiums.

One problem with the expected value method
One shortcoming of the expected value method is that it treats each potential adverse event as independent from the others. For instance, in the example above, the method assumes if one patient suffers complications, the next is no more likely to have the same problem. For many problems, that assumption is true. However, for situations such as product liability or quality control issues, multiple problems often arise all at once, and that can overwhelm a contingency reserve that doesn't allow for the possibility of correlated problems leading to concentrations of loss events.

Even with those shortcomings, calculating contingency reserves using expected values is a good first step in risk management. From there, you can look at the types of losses you face in order to come up with a more accurate figure to meet your company's needs.

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