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A random Matrix Approach to collective Trends of falling and rising Stock Markets
Norwegian University of Science and Technology, Faculty of Natural Sciences and Technology, Department of Physics.
2011 (English)MasteroppgaveStudent thesis
Abstract [en]

An inverse statistics analysis of one minute stock quotes from 492 large European companies has revealed the existence of a gain-loss asymmetry in the following index. The gain-loss asymmetry differs from that observed for daily closure prices of the Dow Jones Industrial Average [38], as the probability of the optimal investment horizon for a gain is higher than that of a loss. For individual stocks, the gain-loss asymmetry was observed to only appear for significantly larger return-levels. To the best of our knowledge, this is the first time such an analysis has been performed on high-frequency data. A principal component analysis was done by performing an eigenvalue decomposition of the correlation matrix from a sliding time-window. The first principal component was observed to describe the market excellently. Its corresponding eigenvalue was observed to be significantly larger than theoretical predictions from random matrix theory, implying that the eigenvalue carries information common to all stocks. Using this eigenvalue as an index measuring the collectivity in the market has revealed the existence of collective trends that appear to be stronger during falling than rising markets. This has been observed for two different datasets, the above described one minute stock quotes and daily closure prices from 29 stocks composing the DJIA late February 2008. The observation is in accordance with results of Balogh et al. [40], and provides further support to the speculation of Johansen et al. [37] that a difference in collective trends is the reason behind the gain-loss asymmetry observed in indexes and not for individual stocks for the same return-level. The key idea behind the fear factor model of Donangelo et al. [42] has been strongly supported by the observation that collective trends appear to be stronger during sharp index drops. As the collectivity increment has been observed to be dependent on the size of the index drop, it is suggested that the model should incorporate also individual fear factors for economic sectors, in addition to the global fear factor governing the market as a whole. Periods exhibiting a rising index positively correlated to the strength of collectivity has indicated the presence of an optimism factor that also should be incorporated in the fear factor model [42], forcing stocks to rise synchronously.

Place, publisher, year, edition, pages
Institutt for fysikk , 2011. , 137 p.
Keyword [no]
ntnudaim:6623, MTFYMA fysikk og matematikk, Teknisk fysikk
URN: urn:nbn:no:ntnu:diva-16328Local ID: ntnudaim:6623OAI: diva2:517088
Available from: 2012-04-20 Created: 2012-04-20

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