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On Distributions for Stock Returns: A Survey of Empirical Investigations

  • József Varga
Part of the Applied Optimization book series (APOP, volume 19)

Abstract

In this paper we give a brief survey of the empirical investigations of the distributions for stock returns and some detailed discussion of German and Hungarian stock returns using refined methods. As a conclusion the stable law hypothesis for the stock returns is rejected and procedures requiring much weaker distributional assumptions are suggested instead of the more traditional techniques.

Keywords

Pareto-distribution Extremal value theory Tail index 

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References

  1. Akgiray, V. and Booth, G.G. (1988), “The Stable-Law Model of Stock Returns”, Journal of Business & Economics 6, 51–57.Google Scholar
  2. Akgiray, V., Booth, G.G. and Seifert, B. (1988), “Distribution Properties of Latin American Black Market Exchange Rates”, Journal of International Money & Finance 7, 37–48.CrossRefGoogle Scholar
  3. Akgiray, V., Booth, G.G. and Loistl, O. (1989), “Stable Laws Are Inappropriate for Describing German Stock Returns”, Allgemeines Statistisches Archiv 73, 115–21.Google Scholar
  4. Baumol, W. and Benhabib, J. (1989), “Chaos: Significance, Mechanism and Economic Applications”, Journal of Economic Perspectives 3, 77–105.CrossRefGoogle Scholar
  5. Boldrin, M. and Woodford, M. (1990), “Equilibrium Models Displaying Endogenous Fluctuations and Chaos”, Journal of Monetary Economics 25, 189–222.CrossRefGoogle Scholar
  6. Brock, W.A. (1988), “Nonlinearity and Complex Dynamics in Economics and Finance”, in: The Economy as an Evolving Complex System, SFI Studies in the Sciences of Complexity, Addison-Wesley Publishing Company.Google Scholar
  7. Cornew, R.W., Town, D.E. and Crowson, L.D. (1984), “Stable Distributions, Futures Prices, and the Measurement of Trading Performance”, Journal of Futures Markets 4, 531–57.CrossRefGoogle Scholar
  8. Dekkers, A.L.M. and de Haan, L. (1989), “On the Estimation of the Extreme-Value Index and Large Quantile Estimation”, Annals of Statistics 17, 1795–1832.CrossRefGoogle Scholar
  9. Dewachter, H. and Gielens, G. (1991), “A Note on the Sum-Stability of Exchange Rate Returns”, Catholic University of Leuven: mimeo.Google Scholar
  10. DuMouchel, W. (1971), Stable Distributions in Statistical Inference, Ph. D. Thesis: Yale University.Google Scholar
  11. DuMouchel, W. (1983), “Estimating the Stable Index a in order to Measure Tail Thickness: A critique”, Annals of Statistics 11, 1019–1031.Google Scholar
  12. Engle, R.F. (1982), “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation”, Econometrica 50, 987–1008.CrossRefGoogle Scholar
  13. Fama, E.F. (1965), “The Behavior of Stock Market Prices”, Journal of Business 38, 34–105.CrossRefGoogle Scholar
  14. Friedman, D. and Bandersteel, S. (1982), “Short-Run Fluctuations in Foreign Exchange Rates”, Journal of International Economics 13, 171–186.CrossRefGoogle Scholar
  15. Hall, J.A., Brorsen, B.W. and Irwin, S.H. (1989), “The Distribution of Futures Prices: A Test of the Stable Paretian and Mixture of Normal Hypotheses”, Journal of Financial & Quantitative Analysis 24, 105–116.CrossRefGoogle Scholar
  16. Hanoch, G. and Levy, H. (1970), “Efficient Portfolio Selection with Quadratic and Cubic Utility”, Journal of Business 43, 181–189.CrossRefGoogle Scholar
  17. Hill, B.M. (1975), “A Simple General Approach to Interference about the Tail of a Distribution”, Annals of Statistics 3, 1163–1173.CrossRefGoogle Scholar
  18. Hols, M.C.A.B. and de Vries, CG. (1991), “The Limiting Distribution of External Exchange Rate Returns”, Journal of Applied Econometrics 6, 287–302.CrossRefGoogle Scholar
  19. Hsu, D.A., Miller, R.B. and Wiehern, D.W. (1974), “On the Stable Paretian Behavior of Stock Market Prices”, Journal of the American Statistical Association 69, 1008–1013.CrossRefGoogle Scholar
  20. Jensen, D.W. and de Vries, C.G. (1991), “On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective”, Review ofEconomics & Statistics 73, 18–24.CrossRefGoogle Scholar
  21. Jean, W. (1971), “The Extension of Portfolio Analysis to Three or More Parameters”, Journal of Financial and Quantitative Analysis 6, 505–515.CrossRefGoogle Scholar
  22. Jean, W. (1973), “More on Multidimensional Portfolio Analysis”, Journal of Financial and Quantitative Analysis 8, 475–490.CrossRefGoogle Scholar
  23. Kähler, J. (1993), “On the Modelling of Speculative Prices by Stable Paretian Distributions and Regularly Varying Tails”, ZEW University of Mannheinrmimeo.Google Scholar
  24. Koedijk, KG. and Kool, C.J.M. (1983), “Tail Estimates of East-European Exchange Rates”, Journal of Business & Economic Statistics 10, 83–96.Google Scholar
  25. Koedijk, K.G., Stork, P.A. and de Vries, C.G. (1992), “Differences between Foreign Exchange Rate Regimes: The View from the Tails”, Journal of International Money & Finance 11, 462–73.CrossRefGoogle Scholar
  26. Kraus, A. and Litzenberger, R.H. (1976), “Skewness Preference and the Valuation of Risk Assets”, Journal of Finance 31, 1085–1100.Google Scholar
  27. Leadbetter, R., Lindgren, G. and Rootzen, H. (1983), Extremes and Related Properties of Random Sequences and Processes, Springer Verlag, Berlin.CrossRefGoogle Scholar
  28. Levy, H. and Sarnat, M. (1972), Investment and Portfolio Analysis, Wiley, New York.Google Scholar
  29. Lux, T., and Varga, J. (1996), “The Stable Paretian Hypothesis for Stock Returns : An Empirical Investigation”, SZIGMA, 1996–4, 157–179 (In Hungarian).Google Scholar
  30. Lux, T. (1995), The Stable Paretian Hypothesis and the Frequency of Large Returns: An examination of major German stocks, University of Bamberg: mimeo.Google Scholar
  31. Mandelbrot, B. (1963), “The Variation of Certain Speculative Prices”, Journal of Business 35, 394–419.Google Scholar
  32. Markowitz, H. (1991), “Foundations of Portfolio Theory”, Journal of Finance 8, 77–91.Google Scholar
  33. McCulloch, J.H. (1986), “Simple Consistent Estimators of Stable Distribution Parameters”, Communications in Statistics: Simulation 15, 1109–32.CrossRefGoogle Scholar
  34. McFarland, J.W., Pettit, R.R. and Sung, S.K. (1980), “The Distribution of Foreign Exchange Price Changes: Trading day effects and risk measurement”, Journal of Finance 37, 693–715.CrossRefGoogle Scholar
  35. Peccati, L. and Tibiletti, L. (1993), “On the Asymmetry of Stock Return Distribution”, Presented at the EWGFM, Mantova.Google Scholar
  36. Rubinstein, M. (1973), “The Fundamental Theorem of Parameter Preference Security Valuation”, Journal of Financial and Quantitative Analysis 8, 61–69.CrossRefGoogle Scholar
  37. Samuelson, P. (1970), “The Fundamental Approximation of Theorem of Portfolio Analysis in Terms of Means, Variances and Higher Moments”, Review of Economic Studies 37, 537–542.CrossRefGoogle Scholar
  38. Simkowitz, M.A. and Beedles, W. L. (1980), “Asymmetric Stable Distributed Security Returns”, Journal of the American Statistical Association 75, 306–312.CrossRefGoogle Scholar
  39. So, J.C. (1987a), “The Distribution of Foreign Exchange Price Changes: Trading Day Effects and Risk Measurement — A comment”, Journal of Finance 42, 181–188.Google Scholar
  40. So, J.C. (1987b), “The Sub-Gaussian Distribution of Currency Futures: Stable Paretian or Nonstationary?” Review of Economics & Statistics 69, 100–107.CrossRefGoogle Scholar
  41. Teichmoeller, J. (1971), “A Note on the Distribution of Stock Price Changes”, Journal of the American Statistical Association 66, 282–284.CrossRefGoogle Scholar
  42. Upton, D.E. and Shannon, D.S. (1979), “The Stable Paretian Distribution, Subordinated Stochastic Processes and Asymptotic Lognormality: An Empirical Investigation”, Journal of Finance 34, 131–139.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • József Varga
    • 1
  1. 1.Faculty of Business & EconomicsJanus Pannonius UniversityPécsHungary

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