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Empirical properties of the variety of a financial portfolio and the single-index model

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  • F. Lillo

    (Max-Planck Institut für Physik komplexer Systeme, Nöthnizer Str. 38, 01187 Dresden, Germany and Istituto Nazionale per la Fisica della Materia, Unità di Palermo, Viale delle Scienze, 90128 Palermo, Italy)

  • R.N. Mantegna

    (Max-Planck Institut für Physik komplexer Systeme, Nöthnizer Str. 38, 01187 Dresden, Germany and Istituto Nazionale per la Fisica della Materia, Unità di Palermo, Viale delle Scienze, 90128 Palermo, Italy)

Abstract

We investigate the variety of a portfolio of stocks in normal and extreme days of market activity. We show that the variety carries information about the market activity which is not present in the single-index model and we observe that the variety time evolution is not time reversal around the crash days. We obtain the theoretical relation between the square variety and the mean return of the ensemble return distribution predicted by the single-index model. The single-index model is able to mimic the average behavior of the square variety but fails in describing quantitatively the relation between the square variety and the mean return of the ensemble distribution. The difference between empirical data and theoretical description is more pronounced for large positive values of the mean return of the ensemble distribution. Other significant deviations are also observed for extreme negative values of the mean return.

Suggested Citation

  • F. Lillo & R.N. Mantegna, 2001. "Empirical properties of the variety of a financial portfolio and the single-index model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 503-509, April.
    • Handle: RePEc:spr:eurphb:v:20:y:2001:i:4:d:10.1007_s100510170229
    DOI: 10.1007/s100510170229
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    Cited by:

    1. Fabrizio Lillo & Giovanni Bonanno & Rosario N. Mantegna, 2001. "Variety of Stock Returns in Normal and Extreme Market Days: The August 1998 Crisis," Papers cond-mat/0104362, arXiv.org.
    2. Gu, Gao-Feng & Zhou, Wei-Xing, 2007. "Statistical properties of daily ensemble variables in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 497-506.
    3. Indranil Mukherjee & Amitava Sarkar, 2011. "Complexity, Financial Markets and their Scaling Laws," DEGIT Conference Papers c016_008, DEGIT, Dynamics, Economic Growth, and International Trade.
    4. Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N., 2001. "Levels of complexity in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 16-27.

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