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Quantifying the behavior of stock correlations under market stress.

Preis T, Kenett DY, Stanley HE, Helbing D, Ben-Jacob E - Sci Rep (2012)

Bottom Line: Reliable estimates of correlations are absolutely necessary to protect a portfolio.Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed.Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios.

View Article: PubMed Central - PubMed

Affiliation: Warwick Business School, University of Warwick, Coventry, United Kingdom. mail@tobiaspreis.de

ABSTRACT
Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios.

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Related in: MedlinePlus

Quantification of state-dependent correlations among index components.(A) Graphs reflect the relationship between the average correlation coefficient C among stocks belonging to the Dow Jones Industrial Average and its normalized return in intervals of Δt trading days. The mean correlation coefficient shows a striking, non-constant behavior, with a minimum between 0 and +1 standard deviations reflecting typical market conditions. For the range of all Δt values analyzed, we find the data collapse onto a single line. Corresponding error bars are shown in Fig. 4A. The data collapse suggests that the striking increase of the mean correlation coefficient for positive and negative values of the normalized index return is independent of the time interval Δt. The largest mean correlation coefficients coincide with the most negative index returns. (B) Normalized DJIA returns, R(t, Δt), and mean correlation coefficients, C(t, Δt), shown for Δt = 10 days. For both time series, we reject the  hypothesis of non-stationarity on the basis of results from the Augmented Dickey-Fuller test. For R(t, Δt = 10), we obtain DF = −24.28, p < 0.01, while for C(t, Δt = 10) we obtain DF = −13.45, p < 0.01.
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f3: Quantification of state-dependent correlations among index components.(A) Graphs reflect the relationship between the average correlation coefficient C among stocks belonging to the Dow Jones Industrial Average and its normalized return in intervals of Δt trading days. The mean correlation coefficient shows a striking, non-constant behavior, with a minimum between 0 and +1 standard deviations reflecting typical market conditions. For the range of all Δt values analyzed, we find the data collapse onto a single line. Corresponding error bars are shown in Fig. 4A. The data collapse suggests that the striking increase of the mean correlation coefficient for positive and negative values of the normalized index return is independent of the time interval Δt. The largest mean correlation coefficients coincide with the most negative index returns. (B) Normalized DJIA returns, R(t, Δt), and mean correlation coefficients, C(t, Δt), shown for Δt = 10 days. For both time series, we reject the hypothesis of non-stationarity on the basis of results from the Augmented Dickey-Fuller test. For R(t, Δt = 10), we obtain DF = −24.28, p < 0.01, while for C(t, Δt = 10) we obtain DF = −13.45, p < 0.01.

Mentions: We relate mean correlation coefficients to corresponding market states, which we quantify by DJIA index returns for time intervals starting at trading day t and ending at trading day t + Δt, We normalize the time series of DJIA index returns, rDJIA(t, Δt), by its standard deviation, σDJIA(Δt), defined as The normalized time series of DJIA index returns, R(t, Δt), is given by In each time interval comprising Δt trading days, we calculate a local correlation matrix consisting of Pearson correlation coefficients49 capturing the dependencies among individual stock returns. Time-dependent returns of an individual stock i are given by In a Δt trading day interval, we calculate a correlation coefficient between return time series of stock i and return time series of stock j by with the standard deviation of return time series i determined in the same time interval comprising Δt trading days defined as The mean correlation coefficient of all DJIA components is given by the mean of all non-diagonal matrix elements of ci,jFigure 3A depicts the relationship between normalized DJIA index return and corresponding mean correlation coefficient capturing the dependency amoung its components. Figure 3B depicts both normalized DJIA index returns and mean correlation coefficients which are used in our analysis for Δt = 10 days. Negative index returns tend to come with stronger correlation coefficients than positive index returns (Fig. 3A). Results for different time intervals Δt collapse into one single curve, suggesting a universal relationship.


Quantifying the behavior of stock correlations under market stress.

Preis T, Kenett DY, Stanley HE, Helbing D, Ben-Jacob E - Sci Rep (2012)

Quantification of state-dependent correlations among index components.(A) Graphs reflect the relationship between the average correlation coefficient C among stocks belonging to the Dow Jones Industrial Average and its normalized return in intervals of Δt trading days. The mean correlation coefficient shows a striking, non-constant behavior, with a minimum between 0 and +1 standard deviations reflecting typical market conditions. For the range of all Δt values analyzed, we find the data collapse onto a single line. Corresponding error bars are shown in Fig. 4A. The data collapse suggests that the striking increase of the mean correlation coefficient for positive and negative values of the normalized index return is independent of the time interval Δt. The largest mean correlation coefficients coincide with the most negative index returns. (B) Normalized DJIA returns, R(t, Δt), and mean correlation coefficients, C(t, Δt), shown for Δt = 10 days. For both time series, we reject the  hypothesis of non-stationarity on the basis of results from the Augmented Dickey-Fuller test. For R(t, Δt = 10), we obtain DF = −24.28, p < 0.01, while for C(t, Δt = 10) we obtain DF = −13.45, p < 0.01.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3475344&req=5

f3: Quantification of state-dependent correlations among index components.(A) Graphs reflect the relationship between the average correlation coefficient C among stocks belonging to the Dow Jones Industrial Average and its normalized return in intervals of Δt trading days. The mean correlation coefficient shows a striking, non-constant behavior, with a minimum between 0 and +1 standard deviations reflecting typical market conditions. For the range of all Δt values analyzed, we find the data collapse onto a single line. Corresponding error bars are shown in Fig. 4A. The data collapse suggests that the striking increase of the mean correlation coefficient for positive and negative values of the normalized index return is independent of the time interval Δt. The largest mean correlation coefficients coincide with the most negative index returns. (B) Normalized DJIA returns, R(t, Δt), and mean correlation coefficients, C(t, Δt), shown for Δt = 10 days. For both time series, we reject the hypothesis of non-stationarity on the basis of results from the Augmented Dickey-Fuller test. For R(t, Δt = 10), we obtain DF = −24.28, p < 0.01, while for C(t, Δt = 10) we obtain DF = −13.45, p < 0.01.
Mentions: We relate mean correlation coefficients to corresponding market states, which we quantify by DJIA index returns for time intervals starting at trading day t and ending at trading day t + Δt, We normalize the time series of DJIA index returns, rDJIA(t, Δt), by its standard deviation, σDJIA(Δt), defined as The normalized time series of DJIA index returns, R(t, Δt), is given by In each time interval comprising Δt trading days, we calculate a local correlation matrix consisting of Pearson correlation coefficients49 capturing the dependencies among individual stock returns. Time-dependent returns of an individual stock i are given by In a Δt trading day interval, we calculate a correlation coefficient between return time series of stock i and return time series of stock j by with the standard deviation of return time series i determined in the same time interval comprising Δt trading days defined as The mean correlation coefficient of all DJIA components is given by the mean of all non-diagonal matrix elements of ci,jFigure 3A depicts the relationship between normalized DJIA index return and corresponding mean correlation coefficient capturing the dependency amoung its components. Figure 3B depicts both normalized DJIA index returns and mean correlation coefficients which are used in our analysis for Δt = 10 days. Negative index returns tend to come with stronger correlation coefficients than positive index returns (Fig. 3A). Results for different time intervals Δt collapse into one single curve, suggesting a universal relationship.

Bottom Line: Reliable estimates of correlations are absolutely necessary to protect a portfolio.Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed.Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios.

View Article: PubMed Central - PubMed

Affiliation: Warwick Business School, University of Warwick, Coventry, United Kingdom. mail@tobiaspreis.de

ABSTRACT
Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios.

Show MeSH
Related in: MedlinePlus