TY - JOUR
AU - Smetters,Kent
AU - Zhang,Xingtan
TI - A Sharper Ratio: A General Measure for Correctly Ranking Non-Normal Investment Risks
JF - National Bureau of Economic Research Working Paper Series
VL - No. 19500
PY - 2013
Y2 - October 2013
DO - 10.3386/w19500
UR - http://www.nber.org/papers/w19500
L1 - http://www.nber.org/papers/w19500.pdf
N1 - Author contact info:
Kent Smetters
University of Pennsylvania
SH-DH 1358
3620 Locust Walk
Philadelphia, PA 19104
Tel: 215/898-9811
Fax: 215/898-0310
E-Mail: smetters@wharton.upenn.edu
Xingtan Zhang
3620 Locust Walk
SH-DH 3000
Philadelphia, PA 19104
E-Mail: xingtan@wharton.upenn.edu
AB - While the Sharpe ratio is still the dominant measure for ranking risky assets, a substantial effort has been made over the past three decades to find a way to account for non-Normally distributed risks. This paper derives a generalized ranking measure which, under a regularity condition, correctly ranks risks relative to the original investor problem for a broad probability space. Moreover, like the Sharpe ratio, the generalized measure maintains wealth separation for the broad HARA utility class. Besides being effective in the presence of "fat tails," the generalized measure is also a foundation for multi-asset class portfolio optimization due to its ability to pairwise rank two risks following two different probability distributions. This paper also explores the theoretical foundations of risk ranking, including proving a key impossibility theorem: any ranking measure that is valid for non-Normal distributions cannot generically be free from investor preferences. Finally, this paper shows that the generalized ratio provides substantially more ranking power than simpler approximation measures that have sometimes been used in the past to account for non-Normal higher moments, even if those approximations are extended to include an infinite number of higher moments.
ER -