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Quantitative relations between risk, return and firm size

Podobnik, Boris and Horvatic, Davor and Petersen, Alexander M. and Stanley, H. Eugene Quantitative relations between risk, return and firm size. EPL (Europhysics Letters), 85 (5). p. 50003. ISSN 0295-5075 (2009)

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We analyze —for a large set of stocks comprising four financial indices— the annual logarithmic growth rate R and the firm size, quantified by the market capitalization MC. For the Nasdaq Composite and the New York Stock Exchange Composite we find that the probability density functions of growth rates are Laplace ones in the broad central region, where the standard deviation σ(R), as a measure of risk, decreases with the MC as a power law σ(R)~(MC)- β. For both the Nasdaq Composite and the S&P 500, we find that the average growth rate langRrang decreases faster than σ(R) with MC, implying that the return-to-risk ratio langRrang/σ(R) also decreases with MC. For the S&P 500, langRrang and langRrang/σ(R) also follow power laws. For a 20-year time horizon, for the Nasdaq Composite we find that σ(R) vs. MC exhibits a functional form called a volatility smile, while for the NYSE Composite, we find power law stability between σ(r) and MC.

Item Type: Article
Identification Number: 10.1209/0295-5075/85/50003
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Q Science > QC Physics
Research Area: Economics and Institutional Change
Depositing User: Alexander Petersen
Date Deposited: 04 Jul 2011 09:21
Last Modified: 06 Apr 2016 08:02
URI: http://eprints.imtlucca.it/id/eprint/263

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