A Non-Random Walk down Wall Street by Lo Andrew W.; MacKinlay A. Craig; Lo Andrew W. W

Author:Lo, Andrew W.; MacKinlay, A. Craig; Lo, Andrew W. W.
Language: eng
Format: epub
Publisher: Princeton University Press

where Fx(·) is the marginal cumulative distribution function of Xi.

Proof See Yang (1977).

This result gives the large-sample joint distribution of a finite subset of induced order statistics whose identities are determined solely by their relative rankings (as ranked according to the order statistics Xi:N). From (8.1.4) it is evident that the 's are mutually independent in large samples. If Xi were the market value of equity of the ith company, Theorem 8.1.1 shows that the of the security with size at, for example, the 27th percentile is asymptotically independent of the of the security with size at the 45th percentile.9 If the characteristics {Xi} and {} are statistically independent, the joint distribution of the latter clearly cannot be influenced by ordering according to the former. It is tempting to conclude that as long as the correlation between Xi and is economically small, induced ordering cannot greatly affect inferences. Using Yang's result we show the fallacy of this argument in Sections 8.1.2 and 8.1.3.

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