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Here is a generalized explanation of the Optimal f when used for buying
and selling stocks. Also managing portfolio's optimal factional investment
in equities to maximize returns.
http://www.portfolioinsight.com/optimalf.htm
Robert
At 12:25 PM 6/11/00 -0400, Bob Fulks wrote:
>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.
>
>----------
>If Utiity, Return, and StdDev are in percent the equation becomes:
>
> Utility = Return - 0.005 * A * StdDev^2)
>----------
>
>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 Chart1a (see next message for the chart).
>
>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
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