# Reordering a Decision Tree

To reflect any risk attitude other than risk neutrality when evaluating a decision tree, DPL needs a way to look at any lottery and convert it to the decision-maker's certain equivalent (the expected value is a risk-neutral decision-maker's certain equivalent). It needs a "utility function" specified as part of the model. You can use DPL's built-in utility function or specify one of your own.

To use the either the built-in exponential utility function or a custom utility function, select theRisk Tolerance tab of the Objective & Utility dialog. For more on the Objective & Utility dialog see Objective & Utility dialog.

Estimating the Coefficient for the Built-in Utility Function

DPL's built-in utility function is of the form

`-exp(-X / R)`
where exp(A) means e to the power of A, X is the objective function value and R is the risk tolerance coefficient. One suggestion for assessing the risk tolerance coefficient is to present the decision-maker with the following question: "If I offered you (or your company) a bet in which you had a 50% chance of making a certain amount of money and a 50% chance of losing half that amount, what is the maximum amount you (or your company) would wager?" The answer to this question is a reasonable estimate for the risk tolerance coefficient.

Impact of Risk Tolerance on the Model

The risk tolerance will be used when you run an analysis based on the model, but will not appear in the model itself. By default, all outputs will still be generated using expected values. You can view expected value or certain equivalent results for many of the outputs DPL generates. Click View | Results | CE to toggle back and forth between certain equivalent results and expected value results. If you create a Risk Profile Chart for optimal decision alternative only, DPL will create two sets of Risk Profile Data, titled "Certain Equivalent" and "Expected Value". (DPL creates a pair for each decision alternative if Initial decision alternatives is selected.)

Specifying Risk Tolerance on Individual Branches

Occasionally, a model requires that a different risk tolerance be specified for different parts of the decision tree. Models which require these specifications are extremely rare, so caution should be used when utilizing this feature. You can specify a risk tolerance on a particular branch or branches in the Risk Tolerance tab of the Branch Definition dialog. Note: this tab is available only if the Risk tolerance and utility functions by branch is turned on within under Advanced Settings within Model Setting | Decision Tree.

Versions: DPL Professional, DPL Enterprise, DPL Portfolio