Integration of VaR and expected utility under departures from normality

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AbstractThis article identifies the level of the expected utility (EU) risk aversion and Value‐at‐Risk (VaR) confidence level that yield the same choice from a given distribution of outcomes, and thus allow for consistent application of the two criteria. The result for a given distribution is an explicit mapping between risk aversion under EU and VaR, for both normal and nonnormal distributions. The Cornish–Fisher expansion is used to establish adjusted mean‐deviates for nonnormal outcome distributions and the investor's preference function is expanded to include elements for variance, skewness, and excess kurtosis. A farm‐level application with nonnormal revenue distribution illustrates these approaches.