eprintid: 263
rev_number: 14
eprint_status: archive
userid: 27
dir: disk0/00/00/02/63
datestamp: 2011-07-04 09:21:46
lastmod: 2016-04-06 08:02:07
status_changed: 2011-07-04 09:21:46
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Podobnik, Boris
creators_name: Horvatic, Davor
creators_name: Petersen, Alexander M.
creators_name: Stanley, H. Eugene
creators_id: 
creators_id: 
creators_id: alexander.petersen@imtlucca.it
creators_id: 
title: Quantitative relations between risk, return and firm size
ispublished: pub
subjects: HA
subjects: HG
subjects: QC
divisions: EIC
full_text_status: none
abstract: 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.
date: 2009
date_type: published
publication: EPL (Europhysics Letters)
volume: 85
number: 5
publisher: IOPscience
pagerange: 50003
id_number: 10.1209/0295-5075/85/50003 
refereed: TRUE
issn: 0295-5075      
official_url: http://stacks.iop.org/0295-5075/85/i=5/a=50003
citation:   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)