Multifactor analysis of multiscaling in volatility return intervals

Fengzhong Wang, Kazuko Yamasaki, Shlomo Havlin, H. Eugene Stanley

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40 Scopus citations


We study the volatility time series of 1137 most traded stocks in the U.S. stock markets for the two-year period 2001-2002 and analyze their return intervals τ, which are time intervals between volatilities above a given threshold q. We explore the probability density function of τ, Pq (τ), assuming a stretched exponential function, Pq (τ) ∼ e- τγ. We find that the exponent γ depends on the threshold in the range between q=1 and 6 standard deviations of the volatility. This finding supports the multiscaling nature of the return interval distribution. To better understand the multiscaling origin, we study how γ depends on four essential factors, capitalization, risk, number of trades, and return. We show that γ depends on the capitalization, risk, and return but almost does not depend on the number of trades. This suggests that γ relates to the portfolio selection but not on the market activity. To further characterize the multiscaling of individual stocks, we fit the moments of τ, μm (τ/ τ) m 1/m, in the range of 10< τ ≤100 by a power law, μm ∼ τδ. The exponent δ is found also to depend on the capitalization, risk, and return but not on the number of trades, and its tendency is opposite to that of γ. Moreover, we show that δ decreases with increasing γ approximately by a linear relation. The return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization.

Original languageEnglish
Article number016103
JournalPhysical Review E
Issue number1
StatePublished - 5 Jan 2009


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