https://doi.org/10.1007/s100510170229
Empirical properties of the variety of a financial portfolio and the single-index model
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
Corresponding author: a mantegna@unipa.it
Received:
30
August
2000
Published online: 15 April 2001
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.
PACS: 02.50.Ey – Stochastic processes / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.90.+n – Other topics in areas of applied and interdisciplinary physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
