Note_04M.44-47

Note_04M.44-47 - 44 Appendix Normal Distribution Moment...

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44 Appendix Normal Distribution: , Moment Generating Function (MGF): Constant Absolute Risk Aversion utility function Maximization of is equivalent to the minimization of , which is equivalent to the maximization of
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45 Log-Normal distribution: Y is distributed as a lognormal with parameters : and F if is distributed as a . , Remark: Let (i) (ii) Constant Relative Risk Aversion utility function Both expressions are used, but the first one is more common. ( >1 is the Arrow-Pratt relative risk aversion coefficient. Most evidence suggests that ( is low, between 1 and 3, and at most 10.
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46 Notice that this expected utility is written as a function of the mean and variance of , not in terms of the mean and variance of Y . That is the reason why the expected utility appears to be an increasing function the variance. As shown above, the variance of Y depends on both : and of . To use this expression of the expected utility in portfolio analysis, one has to first transform Y to , estimate the mean and variance
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This note was uploaded on 04/05/2012 for the course ECON 445 taught by Professor Staff during the Fall '08 term at Texas A&M.

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Note_04M.44-47 - 44 Appendix Normal Distribution Moment...

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