When a tree is rolled back, expected value, utility or certainty equivalent is calculated. While this is useful, it does not give a complete picture of the risk involved. The risk profile tool allows for the creation of probability plots and payoff tables.
A risk profile can be created for the following conditions:
- The optimal path through the tree from the base node.
- The optimal path for all branches of the base node.
A base node can be any decision node. This allows you to create risk profiles from intermediate decision nodes in the tree as well as the root node.
The probability mass plot will display each payoff possibility on the x-axis and the payoff’s associated probability on the y-axis. The cumulative probability chart will display payoffs on the x-axis and the cumulative probability (probability that x<=X) on the y-axis. A payoff table lists the payoff and probability for each end node on the optimal path.
The risk profile tool is not for decision trees containing random variables for Monte Carlo simulation. Trees of this nature are simulated, and the simulation output is the risk profile.
Example Decision Tree
The decision tree we'll use is shown below.
Optimal Path Through Tree
First, we'll create a risk profile for the optimal path through the tree.
The tree must be rolled back prior to creating a risk profile.
Activate the worksheet containing the decision tree and click the Risk Profile button on the DTace ribbon.
The Risk Profile form will appear. When the form is opened, all decision nodes will be included in the drop-down box. Only decision nodes can be a base node.
For our example, we will select the root node, 0.1. Since we want the optimal path through the tree, select Optimal path in the plot frame. We want to maximize return, so the decision rule is choose max.
We will also include both charts and the payoff table.
After clicking the Create button, the risk profile report will be created. The report is shown below. The charts will only show probabilities for end nodes located on the optimal path.
All Base Node Branches
Now we'll create a risk profile report for all base node branches. This report creates a risk profile and payoff table for each decision emanating from the base node.
Open the Risk Profile form and select node 0.1 as the base node. This time, select All base node branches.
The report is shown below. This report contains risk profiles and payoff tables of the optimal path for each decision of the base node.