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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

Consistency of empirical returns distributions with power law and exponential decay.(a) For Δt > 60 minutes, we note a decrease in the number of tails consistent with power law decay. We investigate whether the tails of the returns distributions are consistent with power law behavior or exponential decay using the Kolmogorov-Smirnov statistic, as described in the methods section. We first consider all trading days present in our dataset. At short time scales, we observe that the tails of most empirical distributions are consistent with power law behavior. As we increase the time lag, the number of tails consistent with power law behavior decreases and we see an increase in the number of tails of returns distributions that are consistent with exponential decay. We depict here the overall number of tails, both for the positive and negative returns distributions, for the 25 components of the DJIA. (b) We consider transaction days on which the prices of stocks have changed by more than 1%. We refer to this as a stress level of 1%. In this scenario, the number of tails consistent with power law decreases more sharply. Consistency with exponential decay appears when Δt is roughly 2 hours. (c) In a similar fashion, when we consider a stress level of 2%, we again observe a sharp decrease in the number of distributions consistent with power law behavior. We also find an increase in the number of tails consistent with exponential decay again when Δt is roughly 2 hours. (d) Under a stress level of 3%, the number of empirical distributions consistent with power law behavior decreases more quickly than in the other scenarios. The number of tails consistent with exponential decay peaks at a lower number than in other scenarios, but is again highest when Δt is roughly two hours, similar to other scenarios.
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pone.0135600.g004: Consistency of empirical returns distributions with power law and exponential decay.(a) For Δt > 60 minutes, we note a decrease in the number of tails consistent with power law decay. We investigate whether the tails of the returns distributions are consistent with power law behavior or exponential decay using the Kolmogorov-Smirnov statistic, as described in the methods section. We first consider all trading days present in our dataset. At short time scales, we observe that the tails of most empirical distributions are consistent with power law behavior. As we increase the time lag, the number of tails consistent with power law behavior decreases and we see an increase in the number of tails of returns distributions that are consistent with exponential decay. We depict here the overall number of tails, both for the positive and negative returns distributions, for the 25 components of the DJIA. (b) We consider transaction days on which the prices of stocks have changed by more than 1%. We refer to this as a stress level of 1%. In this scenario, the number of tails consistent with power law decreases more sharply. Consistency with exponential decay appears when Δt is roughly 2 hours. (c) In a similar fashion, when we consider a stress level of 2%, we again observe a sharp decrease in the number of distributions consistent with power law behavior. We also find an increase in the number of tails consistent with exponential decay again when Δt is roughly 2 hours. (d) Under a stress level of 3%, the number of empirical distributions consistent with power law behavior decreases more quickly than in the other scenarios. The number of tails consistent with exponential decay peaks at a lower number than in other scenarios, but is again highest when Δt is roughly two hours, similar to other scenarios.

Mentions: We observe that for Δt > 60 minutes the number of tails consistent with power law behavior decreases (Fig 4a). We investigate this change in behavior at a range of time scales and analyze whether we start to observe consistency with exponential decay. Exponential decay has already been observed in daily returns of stocks from the National Stock Exchange in the Indian stock market [48].


Quantifying Stock Return Distributions in Financial Markets.

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

Consistency of empirical returns distributions with power law and exponential decay.(a) For Δt > 60 minutes, we note a decrease in the number of tails consistent with power law decay. We investigate whether the tails of the returns distributions are consistent with power law behavior or exponential decay using the Kolmogorov-Smirnov statistic, as described in the methods section. We first consider all trading days present in our dataset. At short time scales, we observe that the tails of most empirical distributions are consistent with power law behavior. As we increase the time lag, the number of tails consistent with power law behavior decreases and we see an increase in the number of tails of returns distributions that are consistent with exponential decay. We depict here the overall number of tails, both for the positive and negative returns distributions, for the 25 components of the DJIA. (b) We consider transaction days on which the prices of stocks have changed by more than 1%. We refer to this as a stress level of 1%. In this scenario, the number of tails consistent with power law decreases more sharply. Consistency with exponential decay appears when Δt is roughly 2 hours. (c) In a similar fashion, when we consider a stress level of 2%, we again observe a sharp decrease in the number of distributions consistent with power law behavior. We also find an increase in the number of tails consistent with exponential decay again when Δt is roughly 2 hours. (d) Under a stress level of 3%, the number of empirical distributions consistent with power law behavior decreases more quickly than in the other scenarios. The number of tails consistent with exponential decay peaks at a lower number than in other scenarios, but is again highest when Δt is roughly two hours, similar to other scenarios.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4556674&req=5

pone.0135600.g004: Consistency of empirical returns distributions with power law and exponential decay.(a) For Δt > 60 minutes, we note a decrease in the number of tails consistent with power law decay. We investigate whether the tails of the returns distributions are consistent with power law behavior or exponential decay using the Kolmogorov-Smirnov statistic, as described in the methods section. We first consider all trading days present in our dataset. At short time scales, we observe that the tails of most empirical distributions are consistent with power law behavior. As we increase the time lag, the number of tails consistent with power law behavior decreases and we see an increase in the number of tails of returns distributions that are consistent with exponential decay. We depict here the overall number of tails, both for the positive and negative returns distributions, for the 25 components of the DJIA. (b) We consider transaction days on which the prices of stocks have changed by more than 1%. We refer to this as a stress level of 1%. In this scenario, the number of tails consistent with power law decreases more sharply. Consistency with exponential decay appears when Δt is roughly 2 hours. (c) In a similar fashion, when we consider a stress level of 2%, we again observe a sharp decrease in the number of distributions consistent with power law behavior. We also find an increase in the number of tails consistent with exponential decay again when Δt is roughly 2 hours. (d) Under a stress level of 3%, the number of empirical distributions consistent with power law behavior decreases more quickly than in the other scenarios. The number of tails consistent with exponential decay peaks at a lower number than in other scenarios, but is again highest when Δt is roughly two hours, similar to other scenarios.
Mentions: We observe that for Δt > 60 minutes the number of tails consistent with power law behavior decreases (Fig 4a). We investigate this change in behavior at a range of time scales and analyze whether we start to observe consistency with exponential decay. Exponential decay has already been observed in daily returns of stocks from the National Stock Exchange in the Indian stock market [48].

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