Kolmogorov-Smirnov Tests For Distribution Function Similarity With Applications To Portfolios of Common Stock

Jack Meyer, Robert H. Rasche

NBER Technical Working Paper No. 76
Issued in March 1989
NBER Program(s):   ME

If the elements of the choice set in a decision model involving randomness are not arbitrary, but restricted appropriately, an expected utility ordering of them can be represented by a mean standard deviation ranking function. These restrictions can apply to the form of, or can specify relationships among, the distribution functions. A particularly useful restriction is one which requires that elements in the choice set, when normalized to have a zero mean and unit variance, be identically distributed. No restriction is placed on the form of any individual distribution function. This research empirically tests for this and other useful restrictions on the relationships among the elements of a set of random variables. Observations from the random variables are used to test whether or not they have distribution functions which are appropriately related to one another. The tests are applied to rate of return data for portfolios of common stock. The tests indicate that one cannot reject the hypothesis that the distribution functions of these portfolios are sufficiently similar to imply that the efficient set of portfolios for any risk averse expected utility maximizer is contained in the mean-standard deviation efficient set.

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Document Object Identifier (DOI): 10.3386/t0076

Published: Meyer, J., and Rasche, R. H., 1992, "Sufficient Conditions for Expected Utility to Imply Mean-Standard Deviation Rankings: Empirical Evidence Concerning the Location and Scale Condition," The Economic Journal 102 (410), 91–106. 1992

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