Applies to: PrecisionTree 5.x and Up

What is a Utility Function in PrecisionTree and Why Use One

 

A utility function is a way to translate monetary or other branch values in a decision tree into a measure of personal or organizational value, called utility. Unlike raw dollar amounts, utility accounts for your risk preferences—how much you value gains versus losses.

Why Use a Utility Function

• Standard decision trees assume all dollars are equal: gaining $100 is as valuable as avoiding losing $100.

• For larger stakes relative to wealth, or if you are risk-averse, this assumption may not hold.

• A utility function allows you to adjust branch values to reflect your true preferences. For example:

  • Losing $200,000 is much worse than gaining $200,000 is good.

  • You may prefer safer decisions with smaller gains/losses over risky ones with larger potential outcomes.

How it Works in PrecisionTree

1. Go to the Utility Function tab in Model Settings.

2. Select Use Utility Function.

3. You can display:

   • Expected Value – original branch values.

   • Expected Utility – computed using your utility function.

   • Certainty Equivalent – a single equivalent value reflecting risk preferences.

4. PrecisionTree uses the utility-adjusted values to choose paths that maximize expected utility, not just raw returns.

Examples

• Tree #1 – no utility function; decisions are based purely on expected dollar value.

• Tree #2 – uses a predefined Exponential utility function; riskier options may be avoided even if their expected dollar value is higher.

• Tree #3 – uses a custom utility function (e.g., (U = \sqrt{R + $})) to reflect your specific risk profile.

Using a utility function is essential when decisions involve large stakes, personal or organizational risk preferences, or asymmetric consequences. It ensures that the decision tree reflects true preferences, not just raw dollar calculations.

 

Attachments:
KB1378 Utility Functions (Expected Utility).xlsm
KB1378 Utility Functions (Expected Value).xlsm