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.


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