Kolmogorov-Smirnov Tests for Distribution Function Similarity with Applications to Portfolios of Common Stock

38 Pages Posted: 4 Feb 2001 Last revised: 26 Sep 2010

See all articles by Jack Meyer

Jack Meyer

Michigan State University

Robert Rasche

Michigan State University; National Bureau of Economic Research (NBER)

Date Written: March 1989

Abstract

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.

Suggested Citation

Meyer, Jack and Rasche, Robert, Kolmogorov-Smirnov Tests for Distribution Function Similarity with Applications to Portfolios of Common Stock (March 1989). NBER Working Paper No. t0076, Available at SSRN: https://ssrn.com/abstract=248585

Jack Meyer (Contact Author)

Michigan State University ( email )

201 Marshall Hall
East Lansing, MI 48824
United States
517-355-7749 (Phone)

Robert Rasche

Michigan State University ( email )

East Lansing, MI 48824
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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