Limits...
Quantifying Stock Return Distributions in Financial Markets.

Botta F, Moat HS, Stanley HE, Preis T - PLoS ONE (2015)

Bottom Line: Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide.Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales.Our findings may inform the development of models of market behavior across varying time scales.

View Article: PubMed Central - PubMed

Affiliation: Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, United Kingdom; Data Science Lab, Behavioural Science, Warwick Business School, University of Warwick, Coventry, CV4 7AL, United Kingdom.

ABSTRACT
Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide. Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales. Here, we analyze a dataset comprising the stocks forming the Dow Jones Industrial Average at a second by second resolution in the period from January 2008 to July 2010 in order to quantify the distribution of changes in market prices at a range of time scales. We find that the tails of the distributions of logarithmic price changes, or returns, exhibit power law decays for time scales ranging from 300 seconds to 3600 seconds. For larger time scales, we find that the distributions tails exhibit exponential decay. Our findings may inform the development of models of market behavior across varying time scales.

No MeSH data available.


Related in: MedlinePlus

Empirical distribution of normalised returns for American Express.We build returns distributions for the 25 stocks of the DJIA for different time lags across the full period of analysis. We standardize each distribution by subtracting the mean return from each observation and dividing by the standard deviation. We depict in blue the cumulative distribution function of the positive component of the return distributions for American Express for a time lag of 300 seconds. We depict in red the positive tail of a Gaussian distribution with mean zero and standard deviation one. We observe a strong deviation of the empirical distribution from the Gaussian distribution. Instead, visual inspection of the distribution tail reveals consistency with a linear relationship on a log-log scale. This provides initial evidence for possible power law behavior at this time scale.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4556674&req=5

pone.0135600.g002: Empirical distribution of normalised returns for American Express.We build returns distributions for the 25 stocks of the DJIA for different time lags across the full period of analysis. We standardize each distribution by subtracting the mean return from each observation and dividing by the standard deviation. We depict in blue the cumulative distribution function of the positive component of the return distributions for American Express for a time lag of 300 seconds. We depict in red the positive tail of a Gaussian distribution with mean zero and standard deviation one. We observe a strong deviation of the empirical distribution from the Gaussian distribution. Instead, visual inspection of the distribution tail reveals consistency with a linear relationship on a log-log scale. This provides initial evidence for possible power law behavior at this time scale.

Mentions: We compute the standardized distribution of the returns for the 25 components of the DJIA that we consider. We conduct separate analyses of the cumulative distribution function (CDF) of the positive and negative component of the distribution of returns. Fig 2 depicts the positive CDF for American Express for Δt = 300 seconds and compares this to a Gaussian distribution. Note that the empirical distribution strongly deviates from the Gaussian distribution and provides initial evidence for power law behavior. We perform a statistical analysis to check the consistency of the tails of the empirical distributions with power law behavior across different time scales, as proposed by Clauset, Shalizi and Newman [45] and detailed in the Methods section.


Quantifying Stock Return Distributions in Financial Markets.

Botta F, Moat HS, Stanley HE, Preis T - PLoS ONE (2015)

Empirical distribution of normalised returns for American Express.We build returns distributions for the 25 stocks of the DJIA for different time lags across the full period of analysis. We standardize each distribution by subtracting the mean return from each observation and dividing by the standard deviation. We depict in blue the cumulative distribution function of the positive component of the return distributions for American Express for a time lag of 300 seconds. We depict in red the positive tail of a Gaussian distribution with mean zero and standard deviation one. We observe a strong deviation of the empirical distribution from the Gaussian distribution. Instead, visual inspection of the distribution tail reveals consistency with a linear relationship on a log-log scale. This provides initial evidence for possible power law behavior at this time scale.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4556674&req=5

pone.0135600.g002: Empirical distribution of normalised returns for American Express.We build returns distributions for the 25 stocks of the DJIA for different time lags across the full period of analysis. We standardize each distribution by subtracting the mean return from each observation and dividing by the standard deviation. We depict in blue the cumulative distribution function of the positive component of the return distributions for American Express for a time lag of 300 seconds. We depict in red the positive tail of a Gaussian distribution with mean zero and standard deviation one. We observe a strong deviation of the empirical distribution from the Gaussian distribution. Instead, visual inspection of the distribution tail reveals consistency with a linear relationship on a log-log scale. This provides initial evidence for possible power law behavior at this time scale.
Mentions: We compute the standardized distribution of the returns for the 25 components of the DJIA that we consider. We conduct separate analyses of the cumulative distribution function (CDF) of the positive and negative component of the distribution of returns. Fig 2 depicts the positive CDF for American Express for Δt = 300 seconds and compares this to a Gaussian distribution. Note that the empirical distribution strongly deviates from the Gaussian distribution and provides initial evidence for power law behavior. We perform a statistical analysis to check the consistency of the tails of the empirical distributions with power law behavior across different time scales, as proposed by Clauset, Shalizi and Newman [45] and detailed in the Methods section.

Bottom Line: Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide.Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales.Our findings may inform the development of models of market behavior across varying time scales.

View Article: PubMed Central - PubMed

Affiliation: Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, United Kingdom; Data Science Lab, Behavioural Science, Warwick Business School, University of Warwick, Coventry, CV4 7AL, United Kingdom.

ABSTRACT
Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide. Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales. Here, we analyze a dataset comprising the stocks forming the Dow Jones Industrial Average at a second by second resolution in the period from January 2008 to July 2010 in order to quantify the distribution of changes in market prices at a range of time scales. We find that the tails of the distributions of logarithmic price changes, or returns, exhibit power law decays for time scales ranging from 300 seconds to 3600 seconds. For larger time scales, we find that the distributions tails exhibit exponential decay. Our findings may inform the development of models of market behavior across varying time scales.

No MeSH data available.


Related in: MedlinePlus