Asymmetric Stable Distributed Security Returns

Abstract

Included in the canon of applied statistics and finance is the conclusion that the symmetric stable paradigm better characterizes security return distributions than the Gaussian. The focus of the present effort is on the symmetry of the distributions. Evidence is provided that indicates that securities tend to display substantial positive skewness, motivating a reexamination of past attempts to measure the parameters of the stable distribution, particularly the characteristic exponent.

Volume and skewness in international equity markets

“…With regard to the third moment of equity market returns, however, there is less agreement about the nature, extent and implications of skewness. Simkowitz and Beedles (1980) found evidence that the returns on individual securities are positively skewed. Subsequent work by Singleton and Wingender (1986), Aggarwal et al (1989), Alles and Kling (1994), Peiró (1999Peiró ( , 2002, Aggarwal and Schatzberg (1997), Cont (2001), Jondeau and Rockinger (2003) and Kearney and Lynch (2007) have found varying degrees of skewness in equity securities and markets.…”

The stable Paretian hypothesis and the frequency of large returns: an examination of major German stocks

“…a S < 2, as evidence in favour of the non-Gaussian stable 0960Ð 3107 Ó 1996 Routledge distributions without further testing of ® t. Examples in the literature include Teichmoeller (1971) and Simkowitz and Beedles (1980) examining stock returns, McFarland et al (1980) and So (1987a) who investigate exchange rate changes, as well as the studies of futures returns by Cornew et al (1984) and So (1987b), to name only a few. On the other hand, some indication of violation of the stabilityunder-addition property, expressing itself as non-constancy of the exponent a S over daily, weekly, etc., observations made others question the stable law hypothesis (e.g.…”

Asymmetry in Australian Equity Returns

“…This metric was selected to reflect asymmetry because it is amenable to significance testing. See Simkowitz and Beedles (1980) for discussion of measurement issues and D' Agostino and Pearson (1973) for a transformation that is used when dealing with small (T < 20) samples. distributions that were positively asymmetric.…”