Mean-Variance versus Mean-VaR and Mean-Utility Spanning

In this chapter, we contrast the optimal spanning properties of portfolios built under the traditional mean-variance (VAR) or mean-modified value-at-risk (MVaR) approaches with those created with the linear-exponential (linex) utility function. Unlike asset allocation procedures that build on volatility or MVaR as a measure of risk and a single risk aversion parameter that characterizes investors, the use of linex utility introduces risk differentiation amongst investors and the risk-return relation of the optimal portfolio trades off between mean, variance, skewness and kurtosis. We identify efficient portfolios under the three competing frameworks and analyze their optimal allocations.