Safety Third: Roy's Criterion and Higher Order Moments

TL;DR

This paper extends Roy's Safety First criterion to non-normal returns using Cornish Fisher expansion, aligning with stochastic dominance and revealing nuanced investor preferences for skewness based on various factors.

Contribution

It introduces a novel adaptation of Roy's criterion for non-normal returns, incorporating higher moments and analyzing its implications for asset selection.

Findings

The adapted criterion aligns with the Sharpe ratio under normal returns.

Investor skew preferences depend on term, expected return, and disaster rate.

The approach is consistent with first order stochastic dominance.

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.