Certainty Equivalents

One problem with using utility rather than monetary value is that it is difficult to understand what the numbers mean and almost impossible to explain them to someone else. However, DecisionPro allows you to apply utility while still viewing your results in terms of dollar equivalents.

Consider the following example:

What value for Option 2 would make you indifferent between these two options?  Let’s say that if Option 2 were to receive a certain $40,000, you would be indifferent. In other words, a 50% chance of receiving $100,000 is the same as a certain receipt of $40,000. If this were the case, you would want the decision tree to show the value of Option 1 to be $40,000 rather than $50,000. $40,000 is the risk-adjusted expected monetary value. This value is often called a certainty equivalent. It is a certain amount of money that is equivalent to the uncertain payout.

Certainty equivalents and utility are closely related. In fact, it is quite easy to translate values between certainty equivalents and utility. DecisionPro converts dollar quantities to utility values before performing EMV calculations; then it converts the result back to dollars. In this way you can use the concept of utility to model risk aversion while still working with monetary values.

Applying a high level of risk aversion to the example creates a decision tree that looks like this:

Note that a 50% chance of earning $100,002 combined with a 50% chance of losing $100,000 is now worth negative $35,375 rather than $1 as before. You can control what this value will be by setting the level of risk aversion. DecisionPro then consistently applies that level of aversion to all parts of the tree.

Earlier in this chapter we stated that EMV is calculated using the equation

with utility, the actual equation is

where U(x) is the utility function. This calculation is carried out by the emv primitive.