Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Applied Mathematics

First Advisor

Kent Smetters


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.