Safety Third: Roy's Criterion and Higher Order Moments

Abstract

Roy's `Safety First' criterion for selecting one risky asset from many is adapted to the case of non-normal returns, via Cornish Fisher expansion. The resulting investment objective is consistent with first order stochastic dominance, and is equal to the Sharpe ratio for the case of normal returns. An investor selecting assets via this objective is not universally attracted to positive skew, rather the preference for skew depends on term, the expected return and the disastrous rate of return.