The development of alternative investment has highlighted the limitations of standard performance measures like the Sharpe ratio, primarily because alternative strategies yield returns distributions which can be far from gaussian. In this paper, we propose a new framework in which trades, portfolios or strategies of various types can be analysed regardless of assumptions on payoff. The proposed class of measures is derived from natural and simple properties of the asset allocation. We establish representation results which allow us to describe our set of measures and involve the log-Laplace transform of the asset distribution. These measures include as particular cases the squared Sharpe ratio, Stutzer's rank ordering index and Hodges' Generalised Sharpe Ratio. Any measure is shown to be proportional to the squared Sharpe ratio for gaussian distributions. For non gaussian distributions, asymmetry and fat tails are taken into account. More precisely, the risk preferences are separated into gaussian and non-gaussian risk aversions.
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