Expectile Order and Asset Allocation

Quantile preferences applied to portfolio selection lead to tailoring asset allocation through the probability level τ. For high τ interpreted as risk-tolerance parameter no diversification is found and any risk-prone investor hold only one risky asset. We introduce expectile order in an asset allocation framework, analyzing its properties in connection with usual stochastic ordering rules among individual asset return distributions. Using alternatively expectile order yields diversification also for high values of τ which is in line with some recent trend in portfolio management, and is compatible with interval-based stochastic dominance rules and eventually a special form of positive comonotonicity for expectiles.