Title
Date of Award
2013
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Applied Mathematics
First Advisor
Kent Smetters
Abstract
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.
Recommended Citation
Zhang, Xingtan, "A Sharper Ratio" (2013). Publicly Accessible Penn Dissertations. 951.
https://repository.upenn.edu/edissertations/951