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- Title
EMPIRICAL COMPARISONS OF DISTRIBUTIONAL MODELS FOR STOCK INDEX RETURNS.
- Authors
Gray, J. Brian; French, Dan W.
- Abstract
This article examines the ability of the normal distribution to model the log price returns from the S&P 500 Composite Index. There are three main contributions of this paper. First, a previously untested alternative distribution was examined, the logistic distribution, for describing stock returns. Secondly, four alternative models are simultaneously compared on a large base of stock index returns. Finally, we use a combination of numerical and graphical techniques to identify the alternative providing a superior fit instead of relying on a single numerical test such as the K-S test. An early infinite-variance alternative to the normal distribution for describing log share returns was the scaled-t distribution. The family of logistic distributions also exhibits the heavy tails and peakedness needed to better fit empirical return distributions. Several market studies have suggested that log stock return distributions do not follow the normal law as is often assumed, but instead have much longer tails and more peakedness than the normal family. In this article, the distribution of log stock index returns were considered and reached the same conclusion. Three alternative distributions, the scaled-f, logistic and exponential power distributions, demonstrate a greater ability to model log stock index returns from the S&P 500 Composite Index, of the three alternative models considered, the exponential power distributions appears to provide a superior fit.
- Publication
Journal of Business Finance & Accounting, 1990, Vol 17, Issue 3, p451
- ISSN
0306-686X
- Publication type
Academic Journal
- DOI
10.1111/j.1468-5957.1990.tb01197.x