Eur. Phys. J. B 76, 487-490 (2010)
https://doi.org/10.1140/epjb/e2009-00380-3

Common scaling behavior in finance and macroeconomics

¹ Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, 02215, USA
² Faculty of Civil Engineering, University of Rijeka, 51000 Rijeka, Croatia
³ Zagreb School of Economics and Management, 10000 Zagreb, Croatia
⁴ Department of Physics, University of Zagreb, 10000 Zagreb, Croatia
⁵ Assia Research Center, University of St. Gallen, 9000 St. Gallen, Switzerland

Corresponding authors: ^a bp@phy.hr - ^b davorh@phy.hr - ^c amp17@buphy.bu.edu - ^d njavro@gmail.com - ^e hes@bu.edu

Received: 15 July 2009
Revised: 21 September 2009
Published online: 7 November 2009

Abstract

In order to test whether scaling exists in finance at the world level, we test whether the average growth rates and volatility of market capitalization (MC) depend on the level of MC. We analyze the MC for 54 worldwide stock indices and 48 worldwide bond indices. We find that (i) the average growth rate 〈r〉 of the MC and (ii) the standard deviation σ(r) of growth rates r decrease both with MC as power laws, with exponents α_w = 0.28 ± 0.09 and β_w = 0.12 ± 0.04. We define a stochastic process in order to model the scaling results we find for worldwide stock and bond indices. We establish a power-law relationship between the MC of a country's financial market and the gross domestic product (GDP) of the same country.