Chapter 3 compared alternative mean-variance approximations to the geometric mean or, equivalently, the expected log. The present chapter compares the QE approximation of the preceding chapter with risk-return approximations to the expected log using four alternative measures of risk. Each of these alternative risk measures has active proponents. Ideally, such proponents should either explain why expected utility should not be the touchstone of rational decision making or demonstrate that their proposed risk measure is better able to approximate expected utility than variance is. Since this has not been forthcoming from such sources, we will do our best to objectively evaluate mean-variance approximations ...

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