Abstract
We investigate the recently introduced variety of a set of stock returns traded in a financial market. This investigation is done by considering daily and intraday time horizons in a 15-day time period centered at the August 31st, 1998 crash of the S&P500 index. All the stocks traded at the NYSE during that period are considered in the present analysis. We show that the statistical properties of the variety observed in analyses of daily returns also hold for intraday returns. In particular the largest changes of the variety of the return distribution turns out to be most localized at the opening or (to a less degree) at the closing of the market.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, P. W., Arrow, K. J., Pines, D., (eds) (1988) The Economy as an Evolving Complex System. Addison-Wesley, Redwood City
Bak, P., Chen, K., Scheinkman, J., Woodford, M. (1993) Aggregate Fluctuations from Independent Sectoral Shocks: Self-Organized Criticality in a Model of Production and Inventory Dynamics. Ricerche Economiche 47, 3–30
Bouchaud, J.-P., Sornette, D. (1994) The Black & Scholes Option Pricing Problem in Mathematical Finance: Generalization and Extensions for a Large Class of Stochastic Processes. J. Phys. I France 4, 863–881
Bouchaud J.-P., Potters, M. (2000) Theory of financial risk. Cambridge University Press, Cambridge, UK
Bouchaud, J.-P., Lauritsen, K., Alstrom, P., (eds) (2000b) Proceedings of the International Conference on Application of Physics in Financial Analysis. Int. J. Theor. Appl. Finance 3, 309–608
Campbell, J. Y., Lo, A. W., MacKinlay, A. C. (1997) The Econometrics of Financial Markets. Princeton University Press, Princeton.
Cizeau, P., M. Potters, M., Bouchaud, J.-P. (2001) Correlation structure of extreme stock returns. Quantitative Finance 1, 217–222
Elton, E. J., Gruber, M. J. (1995) Modern Portfolio Theory and Investment Analysis. J. Wiley & Sons, New York
Gopikrishnan, P., Meyer, M., Amaral, L. A. N., Stanley, H. E. (1998) Inverse cubic law for the distribution of stock price variations. Eur. Phys. J. B 3 139–140.
Laloux, L., Cizeau, P., Bouchaud, J.-P., Potters, M. (1999) Noise Dressing of Financial Correlation Matrices. Phys. Rev. Lett. 83, 1467–1470
Li, W., (1991) Absence of 1/f Spectra in Dow Jones Daily Average. Int’l J. Bifurcations and Chaos 1, 583–597
Lillo, F., Mantegna, R. N. (2000a) Statistical Properties of Statistical Ensembles of Stock Returns. Int. J. Theor. Appl. Finance 3, 405–408
Lillo, F., Mantegna, R. N. (2000b) Variety and Volatility in Financial Markets. Phys. Rev. E 62 6126–6134
Lillo, F., Mantegna, R. N. (2000c) Symmetry alteration of ensemble return distribution in crash and rally days of financial market. Eur. Phys. J. B 15 603–606.
Lillo, F., Mantegna, R. N. (2001) Empirical properties of the variety of a financial portfolio and the single-index model, Eur. Phys. J. B. in press
Lux, T. (1996) The stable Paretian hypothesis and the frequency of large returns: an examination of major German stocks, Applied Financial Economics 6 463–475.
Mantegna, R. N. (1991) Lévy Walks and Enhanced Diffusion in Milan Stock Exchange. Physica A 179, 232–242
Mantegna, R. N., Stanley, H. E. (1995) Scaling Behaviour in the Dynamics of an Economic Index. Nature 376, 46–49
Mantegna, R. N. (1999a) Hierarchical Structure in Financial Markets. Eur. Phys. J. B 11, 193–197
Mantegna, R. N., (ed) (1999b) Proceedings of the International Workshop on Econophysics and Statistical Finance. Physica A 269, 1–188
Mantegna, R. N., Stanley, H. E. (2000) An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge, UK
Müller, U. A., Dacorogna, M. M., Olsen, R. B., Pictet, O. V., Schwarz, M. (1995) Statistical Study of Foreign Exchange Rates, Empirical Evidence of a Price Change Scaling Law and Intraday Analysis. J. Banking and Finance 14 1189–1208.
Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral L. A. N., Stanley, H. E. (1999) Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series. Phys. Rev. Lett. 83, 1471–1474
Takayasu, H., Miura, H., Hirabayashi, T., Hamada, K. (1992) Statistical Properties of Deterministic Threshold Elements — The Case of Market Price. Physica A 184, 127–134
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Japan
About this paper
Cite this paper
Lillo, F., Bonanno, G., Mantegna, R.N. (2002). Variety of Stock Returns in Normal and Extreme Market Days: The August 1998 Crisis. In: Takayasu, H. (eds) Empirical Science of Financial Fluctuations. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66993-7_9
Download citation
DOI: https://doi.org/10.1007/978-4-431-66993-7_9
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-66995-1
Online ISBN: 978-4-431-66993-7
eBook Packages: Springer Book Archive