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Wealthy People and Fat Tails: An Explanation for the Lévy Distribution of Stock Returns

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Author Info
Shiki Levy (Anderson School of Management)
Abstract

Although the Levy (stable-Paretian) distribution of stock returns was first observed by Mandelbrot 35 years ago, an explanation for this phenomenon has not yet been found. Several extensive studies have recently shown that short-term rates of return on stock indices and on single stocks are distributed according to the truncated Levy distribution. An apparently unrelated but well-documented fact is that wealth is distributed according to the Pareto-law distribution at high wealth levels. In this paper we suggest that the Levy distribution of rates of return originates from the Pareto-law wealth distribution among investors. We present a model which assumes i) a Pareto distribution of wealth and ii) that the effect an investor has on the price of a stock is proportional (in a ctochastic sense) to the investor's wealth. This model generates a truncated Levy distribution of stock returns. This result is robust to many variations of the basic model. The model leads to the prediction that the parameter Al of the Levy rate of return distribution should be equal to the Pareto constant Aw of the Pareto wealth distribution. Empirical evidence from the U.S., the U.K. and France reveals a striking agreement between these a-priori unrelated parameters (U.S.: Al=1.39, Aw=1.35; U.K. Al=1.12, ax=1.06; France: al=1.82, Aw=1.83).

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Paper provided by Anderson Graduate School of Management, UCLA in its series University of California at Los Angeles, Anderson Graduate School of Management with number 1118.

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Date of creation: 01 Nov 1998
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Handle: RePEc:cdl:anderf:1118

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  1. Akgiray, Vedat & Booth, G Geoffrey, 1988. "The Stable-Law Model of Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 51-57, January.
  2. Persky, Joseph, 1992. "Retrospectives: Pareto's Law," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 181-92, Spring. [Downloadable!] (restricted)
  3. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-17, June.
  4. N. Gregory Mankiw & Stephen P. Zeldes, 1991. "The Consumption of Stockholders and Non-Stockholders," NBER Working Papers 3402, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, A. Craig, 1992. "An ordered probit analysis of transaction stock prices," Journal of Financial Economics, Elsevier, vol. 31(3), pages 319-379, June. [Downloadable!] (restricted)
    Other versions:
  6. Hall, Joyce A. & Brorsen, B. Wade & Irwin, Scott H., 1989. "The Distribution of Futures Prices: A Test of the Stable Paretian and Mixture of Normals Hypotheses," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(01), pages 105-116, March. [Downloadable!]
  7. Haliassos, Michael & Bertaut, Carol C, 1995. "Why Do So Few Hold Stocks?," Economic Journal, Royal Economic Society, vol. 105(432), pages 1110-29, September. [Downloadable!] (restricted)
  8. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December. [Downloadable!] (restricted)
  9. Abhyankar, A & Copeland, L S & Wong, W, 1995. "Nonlinear Dynamics in Real-Time Equity Market Indices: Evidence from the United Kingdom," Economic Journal, Royal Economic Society, vol. 105(431), pages 864-80, July. [Downloadable!] (restricted)
  10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
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