A Sharper Ratio
The Sharpe ratio is the dominant measure for ranking risky assets and funds. This paper derives a generalized ranking measure which, under a regularity condition, is valid in the presence of a much broader assumption (utility, probability) space yet still preserves wealth separation for the broad HARA utility class. Our ranking measure, therefore, can be used with
fat tails'' as well as multi-asset class portfolio optimization. We also explore the foundations of asset ranking, including proving a key impossibility theorem: any ranking measure that is valid at non-Normal higher moments'' cannot generically be free from investor preferences. Finally, we derive a closed-form approximate measure (that can be used without numerical analysis), which nests some previous attempts to include higher moments. Despite the added convenience, we demonstrate that approximation measures are unreliable even with an infinite number of higher moments.