On the quality of Taylor approximations to expected utility
This article presents evidence on the quality of Taylor series approximations to expected utility. To provide a transparent assessment in a broader setting, we assume that log portfolio returns follow a Gram--Charlier distribution that incorporates skewness and excess kurtosis and consider an investor with Constant Relative Risk Aversion (CRRA) preferences. In this framework, we obtain closed-form approximations to expected utility based on Taylor expansions with respect to gross and log portfolio return. We illustrate the quality of the two approximations across a wide range of scenarios in terms of distribution parameters and levels of risk aversion. The Taylor expansion with respect to log portfolio return is shown to produce reliable approximations.
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Volume (Year): 22 (2012)
Issue (Month): 11 (June)
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