Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-08T06:49:09.838Z Has data issue: false hasContentIssue false
  • English
  • Français

Further Results on Asymmetric Stable Distributions of Stock Price Chances

Published online by Cambridge University Press:  19 October 2009

Bruce D. Fielitz
Get access Rights & Permissions [Opens in a new window]

Extract

In a previous paper in the Journal of the American Statistical Association, Fielitz and Smith [16] present evidence in favor of asymmetric members of the stable family of distributions for describing stock price changes. Support for this contention is derived from an empirical examination of the daily closing prices of 200 stocks from the New York Stock Exchange from December 23, 1963, to November 29, 1968. In particular, the empirical examination of these securities indicates that outliers (especially in the short-tail (left-hand tail) of the distributions), kurtosis, and skewness are present in the distributions. These characteristics are consistent with the hypothesis that stock price changes belong to the asymmetric class of members of the stable family of distributions.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 11 , Issue 1 , March 1976 , pp. 39 - 55
Copyright
Copyright © School of Business Administration, University of Washington 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Georgia State University. The author wishes to express appreciation to Jay Light, Harvard University, and to an unidentified referee for helpful comments. Also, Charles Backer of the Georgia State University Computer Center provided computational assistance.

References

REFERENCES

[1] Barnea, A., and Downes, D. H.. “A Reexamination of the Empirical Distribution of Stock Price Changes.” Journal of the American Statistical Association, Vol. 68 (June 1973), pp. 348–350.CrossRefGoogle Scholar
[2] Bendat, J. S., and Piersol, A. G.. Measurement and Analysis of Random Data (New York: John Wiley and Sons, Inc., c. 1966), p. 147.Google Scholar
[3] Blattberg, R., and Sargent, T.. “Regression with Non-Gaussian Stable Disturbances: Some Sampling Results.” Econometrica, Vol. 39 (May 1971), pp. 501–510.CrossRefGoogle Scholar
[4] Blum, M. E. “Portfolio Theory: A Step toward Its Practical Application.” Journal of Business, Vol. 43 (April 1970), pp. 152–173.CrossRefGoogle Scholar
[5] Bradley, J. V. Distribution-Free Statistical Tests. Englewood Cliffs, N.J.: Prentice-Hall, Inc., c. 1968, pp. 296–303.Google Scholar
[6] Brenner, M. “On the Stability of the Distribution of the Market Component in Stock Price Changes.” Journal of Financial and Quantitative Analysis, Vol. 9 (December 1974), pp. 945–961.CrossRefGoogle Scholar
[7] DuMouchel, W. H. Stable Distributions in Statistical Inference. Unpublished Ph.D. dissertation, Yale University (1971).Google Scholar
[8] Fama, E. “The Behavior of Stock Market Prices.” Journal of Business, Vol. 38 (January 1965), pp. 34–105.CrossRefGoogle Scholar
[9] Fama, E. “Portfolio Analysis in a Stable Paretian Market.” Management Science, Vol. 11 (January 1965), pp. 404–419.CrossRefGoogle Scholar
[10] Fama, E. “Risk, Return, and Equilibrium.” Journal of Political Economy, Vol. 79 (January–February 1971), pp. 30–55.CrossRefGoogle Scholar
[11] Fama, E., and Babiak, H.. “Dividend Policy: An Empirical Analysis.” Journal of the American Statistical Association, Vol. 63 (December 1968), pp. 1132–1161.CrossRefGoogle Scholar
[12] Fama, E., and MacBeth, J.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, Vol. 81 (May–June 1973), pp. 607–636.CrossRefGoogle Scholar
[13] Fama, E., and Roll, R.. “Parameter Estimates for Symmetric Stable Distributions.” Journal of the American Statistical Association, Vol. 66 (June 1971), pp. 331–338.CrossRefGoogle Scholar
[14] Fama, E., and Roll, R.. “Some Properties of Symmetric-Stable Distributions.” Journal of the American Statistical Association, Vol. 63 (September 1968), pp. 817–836.Google Scholar
[15] Fama, E. et al. “The Adjustment of Stock Prices to New Information.” International Economic Review, Vol. 10 (February 1969), pp. 1–21.CrossRefGoogle Scholar
[16] Fielitz, B. D., and Smith, E. W.. “Asymmetric Stable Distributions of Stock Price Changes.” Journal of the American Statistical Association, Vol. 67 (December 1972), pp. 813–814.CrossRefGoogle Scholar
[17] Gibbons, J. D. Nonparametric Statistical Inference. New York: McGraw-Hill Book Company, c. 1971, pp. 86–87.Google Scholar
[18] Granger, C. W. J., and Orr, D.. “Infinite Variance and Research Strategy in Time Series Analysis.” Journal of the American Statistical Association, Vol. 67 (June 1972), pp. 275–285.Google Scholar
[19] Hsu, D., Miller, R., and Wichern, D.. “On the Stable Paretian Behavior of Stock-Market Prices.” Journal of the American Statistical Association, Vol. 69 (March 1974), pp. 108–113.CrossRefGoogle Scholar
[20] Kadiyala, K. R. “Regression with Non-Gaussian Stable Disturbances: Some Sampling Results.” Econometrica, Vol. 40 (July 1972), pp. 719–722.CrossRefGoogle Scholar
[21] Kaplan, R. S., and Roll, R.. “Investor Evaluation of Accounting Information: Some Empirical Evidence.” Journal of Business, Vol. 45 (April 1972), pp. 225–257.CrossRefGoogle Scholar
[22] King, B. “Market and Industry Factors in Stock Price Behavior.” Journal of Business, Vol. 39 (Supplement, January 1966), pp. 139–190.CrossRefGoogle Scholar
[23] Lilliefors, H. W. “On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown.” Journal of the American Statistical Association, Vol. 62 (June 1967), pp. 399–402.CrossRefGoogle Scholar
[24] Lilliefors, H. W. “On the Kolmogorov-Smirnov Test for the Exponential Distribution with Mean Unknown.” Journal of the American Statistical Association, Vol. 64 (March 1969), pp. 387–389.CrossRefGoogle Scholar
[25] Officer, R. R. “The Distribution of Stock Returns.” Journal of the American Statistical Association, Vol. 67 (December 1972), pp. 807–812.CrossRefGoogle Scholar
[26] Press, S. J. Applied Multivariate Analysis. New York: Holt, Rinehart and Winston, Inc., 1972, pp. 140–144, 360–364.Google Scholar
[27] Roll, R. The Behavior of Interest Rates. New York: Basic Books, Inc., c. 1970.Google Scholar
[28] Shapiro, S. S. et al. “A Comparative Study of Various Tests for Normality.” Journal of the American Statistical Association, Vol. 63 (December 1968), pp. 1343–1372.CrossRefGoogle Scholar
[29] Teichmoeller, J. “A Note on the Distribution of Stock Price Changes.” Journal of the American Statistical Association, Vol. 66 (June 1971), pp. 282–284.CrossRefGoogle Scholar
[30] Williams, C. A. Jr. “On the Choice of the Number and Width of Classes for Chi-square Test of Goodness of Fit.” Journal of the American Statistical Association, Vol. 45 (March 1950), pp. 77–86.Google Scholar
[31] Wise, J. “Linear Estimators for Linear Regression Systems Having Infinite Residual Variances.” Paper presented at the Berkeley-Stanford Mathematical Seminar (October 1973).Google Scholar