Optimal investment horizons for the main indices of the Warsaw Stock Exchange

Adam Szmagliński


The investment horizon is the smallest time interval when an asset crosses a fixed value of the return level. For a given return level, the investment horizon distribution is created by putting the investment horizons into a histogram. We fit probability distribution function to the histogram. The maximum of the function is called the optimal investment horizon. We performed the analysis of some indices of the Warsaw Stock Exchange for WIG, WIG20, mWIG40 and shares of KGHM and MBK. For these assets, we found the coefficients of linear proportion between the optimal investment horizons and the logarithm of their return levels.

Słowa kluczowe: econophysics, financial markets, inverse statistics

Bachelier L., Théorie de la Spéculation, Annales de l’Ecole normale superiure, 1900.

Samuelson P., Economics: The Original 1948 Edition, McGraw-Hill/Irwin.

Bouchaud J.P., Potters M., Theory of Financial Risks: From Statistical Physics to Risk Management, Cambridge University Press, Cambridge, 2000.

Mantegna R.N., Stanley H.E., An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press, Cambridge, 2000.

Hull J., Options, Futures and other Derivatives, Prentice-Hall, London 2000.

Mandelbrot B.B., J. Business, vol. 36 No. 4, 1963, 394-419.

Drożdż S., Kwapień J., Grümmer F., Ruf F., Speth J., Acta Phys. Pol. B, vol. 34, 2003, 4293-4306.

Rak R., Drożdż S., Kwapień J., Physica A, vol. 374, 2007, 315-324.

Drożdż S., Forczek M., Kwapień J., Oświęcimka P., Rak R., Physica A, vol. 383, 2007, 59-64.

Kwapień J., Drożdż S., Physics Reports, vol. 515, 2012, 115-226.

Jensen M.H., Phys. Rev. Lett., vol. 83, 1999, 76-79.

Mantegna R.N., Stanley H.E., Nature, vol. 383, 1996, 587-588.

Ghashghaie S., Breymann W., Peinke J., Talkner P., Dodge Y., Nature, vol. 381, 1996, 767-770.

Friedrich R., Peinke J., Renner Ch., Phys. Rev. Lett., vol. 84, 2000, 5224-5227.

Simonsen I., Jensen M.H., Johansen A., Eur. Phys. J. B, vol. 27, No. 4, 2002, 583-586.

Jensen M.H., Johansen A., Simonsen I., Physica A, vol. 234, 2003, 338-343.

Jensen M.H., Johansen A., Petroni F., Simonsen I., Physica A, vol. 340, 2004, 678-684.

Szmagliński A., Acta Phys. Pol. A, vol. 123, 2013, 621-623.

Redner S., A Guide to First Passage Process, Cambridge, New York 2001.

Ding M., Yang W., Phys. Rev. E, vol. 52, 1995, 207-213.

Rangarajan G., Ding M., Phys. Lett. A, vol. 273, 2000, 322-330.

Karpio K., Załuska-Kotur M., Orłowski A., Physica A, vol. 375, 2007, 599-604.

Załuska-Kotur M., Karpio K., Orłowski A., Acta Phys. Pol. B, vol. 37, 2006, 3187-3192.

Grudziecki M., Gnatowska E., Karpio K., Orłowski A., Załuska-Kotur M., Acta Phys. Pol. A, vol. 114, 2008, 569-574.

Czajkowski G., Eng. Th. Investment Horizon Distribution for Main Indices of Warsaw Stock Exchange, Kraków 2014.