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
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.
PACS: 89.65.Gh – Economics; econophysics, financial markets, business and management / 02.50.-r – Probability theory, stochastic processes, and statistics / 05.45.Tp – Time series analysis
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009