Integration of VaR and expected utility under departures from normality

This 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.