Transformations  in
Business & Economics

MEASURING AND TESTING SKEWNESS OF FINANCIAL RETURN DISTRIBUTIONS
Krzysztof Piontek

ABSTRACT. The article concentrates on the issue of skewness testing for fat-tailed return distributions. Some characteristics of the rate of return time series (fat tails mainly) lead to the failure of certain widely used tests of symmetry. The aim of this paper is to investigate the possible skewness of the unconditional distribution of Polish stock or index returns using different types of tests. Four specific approaches are briefly reviewed and discussed for testing the skewness in the whole return distribution. Classical Jarque-Bera test, the adjusted Jarque-Bera test (taking fatter tails into consideration), the test based on the GARCH(1,1) model with the Pearson type IV conditional distribution and the test proposed by Peiro (2004) without any assumptions about the type of distribution (distribution free test for skewness for 2 subsamples) are used. In the empirical part of the paper, 282 Polish financial time series (stocks, indexes) are examined with the given tests. The results have proved that about 40% of the tested daily return distributions and about 18% of weekly return distributions are skewed, however, in many cases, the tests give different conclusions and the results are ambiguous  .

KEYWORDS: skewness, tests of symmetry, distribution of stock return, outliers, fat tails.

JEL classification: C46, C58, C12, G10.