The PortScenPowUtilA.xlsx Model

Power Utility Measure for Portfolio Selection

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The Power utility function provides a flexible way of specifying your risk tolerance. If wealth( s) is your wealth outcome under scenario s, the Power utility function is: Utility( wealth(s)) = (wealth(s)^gamma -1)/gamma. where 0 <= gamma gamma = 1 means risk neutral, i.e. utility is linear in end of period wealth. gamma < 1 means risk averse, and gamma > 1 means risk preferring. Using L'hopital's rule, you can show that as gamma approaches 0, the power utility function value approaches log( w), where log( ) is the natural logarithm. Log Utility The Log utility function is a special case of the Power utility, corresponding to the case gamma = 0. utility( wealth(s)) = log( wealth( s)). In this case, rather than using the power utility with gamma = 0, one should use the Log utility explicitly.

Keywords:

Portfolio | Utility Function | Scenario | Risk Management | Power Utility |