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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 the aggregated correlation.(A) Utilizing the data collapse reported in Fig. 3, we aggregate in each bin of the graph the mean correlation coefficients for 10 days ≤ Δt ≤ 60 days. Error bars are plotted depicting −1 and +1 standard deviations around the mean of the mean correlation values included in each bin. The increase of the aggregated correlation C* for positive and negative index returns is consistent with two linear relationships: C* = a+R + b+ with a+ = 0.064 ± 0.002 and b+ = 0.188 ± 0.004 (p – value < 0.001) quantifies the right part. C* = a−R + b− with a− = −0.085 ± 0.002 and b− = 0.267 ± 0.005 (p – value < 0.001). The red colored regions are used to obtain the coefficients. In order to reduce noise, the range of normalized DJIA returns is restricted to bin values occurring, on average, more than 10 times for individual Δt intervals. (B) By randomly shuffling time series of daily returns for each stock individually, we test the robustness of the relationship and find that the linear relationships reported in (A) disappear, supporting our findings. (C) We use non-shuffled time series of underlying stock returns for an additional parallel analysis with randomly shuffled DJIA returns. The above linear relationships also vanish in this test scenario underlining the robustness of our findings.
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f4: Quantification of the aggregated correlation.(A) Utilizing the data collapse reported in Fig. 3, we aggregate in each bin of the graph the mean correlation coefficients for 10 days ≤ Δt ≤ 60 days. Error bars are plotted depicting −1 and +1 standard deviations around the mean of the mean correlation values included in each bin. The increase of the aggregated correlation C* for positive and negative index returns is consistent with two linear relationships: C* = a+R + b+ with a+ = 0.064 ± 0.002 and b+ = 0.188 ± 0.004 (p – value < 0.001) quantifies the right part. C* = a−R + b− with a− = −0.085 ± 0.002 and b− = 0.267 ± 0.005 (p – value < 0.001). The red colored regions are used to obtain the coefficients. In order to reduce noise, the range of normalized DJIA returns is restricted to bin values occurring, on average, more than 10 times for individual Δt intervals. (B) By randomly shuffling time series of daily returns for each stock individually, we test the robustness of the relationship and find that the linear relationships reported in (A) disappear, supporting our findings. (C) We use non-shuffled time series of underlying stock returns for an additional parallel analysis with randomly shuffled DJIA returns. The above linear relationships also vanish in this test scenario underlining the robustness of our findings.

Mentions: To quantify the relationship between normalized index return and average correlation, we aggregate mean correlation coefficients for different values of Δt ranging from 10 trading days to 60 trading days (Fig. 4), We find consistency with two linear relationships quantifying the increase of the aggregated correlation C+ for positive index return R and the aggregated correlation C− for negative index return R, with a+ = 0.064 ± 0.002 and b+ = 0.188 ± 0.004 (p-value < 0.001) quantifies the right part in Fig. 4A. The aggregatated correlations, with a− = −0.085 ± 0.002 and b− = 0.267 ± 0.005 (p–value < 0.001) quantifies the left part in Fig. 4A. The larger is a negative or positive DJIA return the larger is the corresponding mean correlation. In contrast, a reference scenario of randomly shuffled stock returns leads to a constant relationship (Fig. 4B), supporting our findings in Fig. 4A. However, this method destroys all correlations of this complex financial system and not only the link between aggregated correlation C* and normalized index returns R. As an additional test, we use non-shuffled time series of underlying stock returns for our analysis and randomly shuffle the DJIA return time series only (Fig. 4C). We find that the linear relationships reported in Fig. 4A also vanishes in this scenario highlighting the robustness of our findings.


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 the aggregated correlation.(A) Utilizing the data collapse reported in Fig. 3, we aggregate in each bin of the graph the mean correlation coefficients for 10 days ≤ Δt ≤ 60 days. Error bars are plotted depicting −1 and +1 standard deviations around the mean of the mean correlation values included in each bin. The increase of the aggregated correlation C* for positive and negative index returns is consistent with two linear relationships: C* = a+R + b+ with a+ = 0.064 ± 0.002 and b+ = 0.188 ± 0.004 (p – value < 0.001) quantifies the right part. C* = a−R + b− with a− = −0.085 ± 0.002 and b− = 0.267 ± 0.005 (p – value < 0.001). The red colored regions are used to obtain the coefficients. In order to reduce noise, the range of normalized DJIA returns is restricted to bin values occurring, on average, more than 10 times for individual Δt intervals. (B) By randomly shuffling time series of daily returns for each stock individually, we test the robustness of the relationship and find that the linear relationships reported in (A) disappear, supporting our findings. (C) We use non-shuffled time series of underlying stock returns for an additional parallel analysis with randomly shuffled DJIA returns. The above linear relationships also vanish in this test scenario underlining the robustness of our findings.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Quantification of the aggregated correlation.(A) Utilizing the data collapse reported in Fig. 3, we aggregate in each bin of the graph the mean correlation coefficients for 10 days ≤ Δt ≤ 60 days. Error bars are plotted depicting −1 and +1 standard deviations around the mean of the mean correlation values included in each bin. The increase of the aggregated correlation C* for positive and negative index returns is consistent with two linear relationships: C* = a+R + b+ with a+ = 0.064 ± 0.002 and b+ = 0.188 ± 0.004 (p – value < 0.001) quantifies the right part. C* = a−R + b− with a− = −0.085 ± 0.002 and b− = 0.267 ± 0.005 (p – value < 0.001). The red colored regions are used to obtain the coefficients. In order to reduce noise, the range of normalized DJIA returns is restricted to bin values occurring, on average, more than 10 times for individual Δt intervals. (B) By randomly shuffling time series of daily returns for each stock individually, we test the robustness of the relationship and find that the linear relationships reported in (A) disappear, supporting our findings. (C) We use non-shuffled time series of underlying stock returns for an additional parallel analysis with randomly shuffled DJIA returns. The above linear relationships also vanish in this test scenario underlining the robustness of our findings.
Mentions: To quantify the relationship between normalized index return and average correlation, we aggregate mean correlation coefficients for different values of Δt ranging from 10 trading days to 60 trading days (Fig. 4), We find consistency with two linear relationships quantifying the increase of the aggregated correlation C+ for positive index return R and the aggregated correlation C− for negative index return R, with a+ = 0.064 ± 0.002 and b+ = 0.188 ± 0.004 (p-value < 0.001) quantifies the right part in Fig. 4A. The aggregatated correlations, with a− = −0.085 ± 0.002 and b− = 0.267 ± 0.005 (p–value < 0.001) quantifies the left part in Fig. 4A. The larger is a negative or positive DJIA return the larger is the corresponding mean correlation. In contrast, a reference scenario of randomly shuffled stock returns leads to a constant relationship (Fig. 4B), supporting our findings in Fig. 4A. However, this method destroys all correlations of this complex financial system and not only the link between aggregated correlation C* and normalized index returns R. As an additional test, we use non-shuffled time series of underlying stock returns for our analysis and randomly shuffle the DJIA return time series only (Fig. 4C). We find that the linear relationships reported in Fig. 4A also vanishes in this scenario highlighting the robustness of our findings.

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