Eur. Phys. J. B 73, 23-28 (2010)
https://doi.org/10.1140/epjb/e2009-00358-1

What distinguishes individual stocks from the index?

¹ Institute for Theoretical Physics, University of Kiel, Leibnizstr. 15, 24098 Kiel, Germany
² Department of Economics, University of Kiel, Olshausenstr. 40, 24118 Kiel, Germany
³ Department of Economics, Universitat Jaume I, Campus del Riu Sec, 12071 Castellòn, Spain

Corresponding author: milakovic@bwl.uni-kiel.de

Received: 24 February 2009
Revised: 13 August 2009
Published online: 22 October 2009

Abstract

Stochastic volatility models decompose the time series of financial returns into the product of a volatility factor and an iid noise factor. Assuming a slow dynamic for the volatility factor, we show via nonparametric tests that both the index as well as its individual stocks share a common volatility factor. While the noise component is Gaussian for the index, individual stock returns turn out to require a leptokurtic noise. Thus we propose a two-component model for stocks, given by the sum of Gaussian noise, which reflects market-wide fluctuations, and Laplacian noise, which incorporates firm-specific factors such as firm profitability or growth performance, both of which are known to be Laplacian distributed. In the case of purely Gaussian noise, the chi-squared probability for the density of individual stock returns is typically on the order of 10^-20, while it increases to values of O(1) by adding the Laplace component.