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I did some more research on the topic of Utility Theory. There is a good discussion in "Investments" by Bodie, Kane, & Marcus.
When referring to a plot of "Annualized Return" vs. "Annualized Standard Deviation of Returns", the Utility function of an individual can be approximated by:
Utility = Return - 0.5 * A * StdDev^2
where A is some constant for that person.
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If Utiity, Return, and StdDev are in percent the equation becomes:
Utility = Return - 0.005 * A * StdDev^2)
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The Indifference Curves would be a curves of a constant values of Utility so rearranging:
Return = Utility + 0.5 * A * StdDev^2
So in my example, the curves for the Little Old Lady and the Young Engineer would turn out to be give by the following values:
A Utility
Little Old Lady 60.0 6.4%
Young Engineer 4.2 22.5%
These two curves are plotted on the attached Chart1a.
People with a positive value of A are called "risk-averse". Most people are risk-averse.
A person who decides to trade at Optimal_f would have a value of A = 0. Such people are called "risk-neutral".
Some people even have a negative value of A. They are called "risk-lovers". This would include people addicted to gambling. With casino gambling, the expected return would be slightly negative (to allow for the house's "take") but the negative A of those people would make the Utility of this activity positive for them.
I found this interesting. Thanks for all of the questions.
Bob Fulks
Attachment Converted: "f:\eudora\attach\Chart1a1.gif"
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