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2/20/08 Brian Jansen Co-jumps in the Oil Industry

Motivational Mathematics (skip) Data Information (skip) Graphing prices

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Motivational Mathematics (skip) Data Information (skip) Graphing prices Motivation for my research Correlation in stock prices Correlation in returns Factor Analysis Z-stats RV RV-BV Extensions. - r t,j is log return, M is total # of observations per day. Realized Variance - PowerPoint PPT Presentation

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Page 1: Motivational Mathematics (skip) Data Information (skip) Graphing prices

2/20/08 Brian Jansen

Co-jumps in the Oil Industry

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• Motivational Mathematics (skip)• Data Information (skip)• Graphing prices • Motivation for my research

– Correlation in stock prices– Correlation in returns

• Factor Analysis– Z-stats– RV– RV-BV

• Extensions

Co-Jumps in Oil Brian Jansen

Outline

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-rt,j is log return, M is total # of observations per day

• Realized Variance

• Realized Bi-Power Variation

Motivational Maths Brian Jansen

Realized and Bi-Power Variation

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Motivational Maths Brian Jansen

Asymptotic Properties of RV and BV

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Motivational Maths Brian Jansen

Tri-power, Max Verison BN-S

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• Sampled at the 5-minute frequency• Sampled from 9/3/2002 to 12/31/07 for 1323 total

observed days• Oil futures data at the 5-min frequency, from 1987

– Changing number of observations per day– Different trading days than equity stocks

• Ticker Symbols– XOM—Exxon Mobile– CVX—Chevron Oil– COP—Conoco Phillips

Co-Jumps in Oil Brian Jansen

Data Used

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RV, Ztp Statistics Summary Brian Jansen

Statistics Summary

Variable Mean Min Max

COP

RV .2185(ann. vol.) 1.8591e-05 0.0015

Ztp .4849 -3.357 9.4655

XOM

RV .1935(ann. vol.) 1.409e-05 .0014

Ztp .4494 -2.7796 4.7739

CVX

RV .1982(ann. Vol.) 1.5489e-05 .0016

Ztp .4682 -3.001 9.9190

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Jump Analysis Brian Jansen

Z-test Graphs

XOM:29 CVX:41 COP:38

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Motivational Graphs Brian Jansen

XOM, CVX, COP

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Motivational Graphs Brian Jansen

XOM, CVX, COP (close up!)

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Motivation Brian Jansen

Stock Price/Jump Correlation

PtCOP PtXOM

PtXOM .9708 1PtCVX .9647 .9921

-Correlation between 5-minute prices

-CVX had 41 jumps out of 1343 days observed; 4 of which were shared by either XOM or COP

-XOM had 29 jumps out of 1343 days observed; 6 of which were shared by either CVX or COP

-COP had 38 jumps out of 1343 days observed; 6 of which were shared by either CVX or XOM

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Graphs Brian Jansen

Stock Returns

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Graphs Brian Jansen

Stock Returns (Zoom)

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Statistics Brian Jansen

Stock Returns

RtCOP RtCVX

RtCVX .974 1

RtXOM .857 .843

-High degree of correlation between the stock returns, especially between CVX and COP

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Graphs Brian Jansen

Oil Futures vs. XOM Prices

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Graphs Brian Jansen

Oil Futures vs. COP Returns

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Statistics Brian Jansen

Stock Returns

RtCOP RtCVX RtXOM RtOIL

RtCOP 1

RtCVX .974 1

RtXOM .857 .843 1

RtOIL .341 .322 .222 1

-Not great correlation between any of the stocks and oil returns

-Questionable return for oil given the nature of the data

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Factor Analysis Brian Jansen

Z-Statistic Analysis

z_oil 0.0473 0.1526 0.9745 z_xom 0.2443 0.1462 0.9190 z_cvx 0.9742 -0.0336 0.0498 z_cop 0.9751 -0.0105 0.0491 Variable Factor1 Factor2 Uniqueness

Factor loadings (pattern matrix) and unique variances

LR test: independent vs. saturated: chi2(6) = 3671.73 Prob>chi2 = 0.0000 Factor4 -0.04283 . -0.0222 1.0000 Factor3 -0.03276 0.01007 -0.0170 1.0222 Factor2 0.04590 0.07866 0.0238 1.0391 Factor1 1.96175 1.91585 1.0154 1.0154 Factor Eigenvalue Difference Proportion Cumulative

Rotation: (unrotated) Number of params = 6 Method: principal factors Retained factors = 2Factor analysis/correlation Number of obs = 1323

(obs=1323). factor z_cop z_cvx z_xom z_oil

-For both COP and CVX, Factor1 is loads positively and most variance is explained by common factors (high communality)

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Factor Analysis Brian Jansen

Z-Statistic Analysis w/ PCF

z_oil 0.0953 0.9544 0.0801 z_xom 0.4321 0.2697 0.7406 z_cvx 0.9689 -0.1111 0.0489 z_cop 0.9703 -0.1029 0.0479 Variable Factor1 Factor2 Uniqueness

Factor loadings (pattern matrix) and unique variances

LR test: independent vs. saturated: chi2(6) = 3671.73 Prob>chi2 = 0.0000 Factor4 0.03359 . 0.0084 1.0000 Factor3 0.88397 0.85038 0.2210 0.9916 Factor2 1.00645 0.12248 0.2516 0.7706 Factor1 2.07598 1.06953 0.5190 0.5190 Factor Eigenvalue Difference Proportion Cumulative

Rotation: (unrotated) Number of params = 6 Method: principal-component factors Retained factors = 2Factor analysis/correlation Number of obs = 1323

(obs=1323). factor z_cop z_cvx z_xom z_oil, pcf

-Principle-Component Factors: treating the communalities (1-uniqueness) as 1, thus allowing for no unique factors

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• Interesting: With RV, we see Factor1 explaining COP and XOM, with a high degree of communality

Factor Analysis Brian Jansen

RV Analysis

rv_oil -0.0293 0.1001 0.9891 rv_xom 0.8959 0.0071 0.1973 rv_cvx -0.0146 0.0957 0.9906 rv_cop 0.8962 -0.0023 0.1967 Variable Factor1 Factor2 Uniqueness

Factor loadings (pattern matrix) and unique variances

LR test: independent vs. saturated: chi2(6) = 1799.69 Prob>chi2 = 0.0000 Factor4 -0.11968 . -0.0803 1.0000 Factor3 -0.01667 0.10301 -0.0112 1.0803 Factor2 0.01923 0.03590 0.0129 1.0915 Factor1 1.60696 1.58773 1.0786 1.0786 Factor Eigenvalue Difference Proportion Cumulative

Rotation: (unrotated) Number of params = 6 Method: principal factors Retained factors = 2Factor analysis/correlation Number of obs = 1323

(obs=1323). factor rv_cop rv_cvx rv_xom rv_oil

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rv_oil -0.0589 0.7013 0.5047 rv_xom 0.9641 0.0377 0.0691 rv_cvx -0.0298 0.7231 0.4762 rv_cop 0.9646 0.0275 0.0688 Variable Factor1 Factor2 Uniqueness

Factor loadings (pattern matrix) and unique variances

LR test: independent vs. saturated: chi2(6) = 1799.69 Prob>chi2 = 0.0000 Factor4 0.13763 . 0.0344 1.0000 Factor3 0.98128 0.84365 0.2453 0.9656 Factor2 1.01688 0.03561 0.2542 0.7203 Factor1 1.86421 0.84733 0.4661 0.4661 Factor Eigenvalue Difference Proportion Cumulative

Rotation: (unrotated) Number of params = 6 Method: principal-component factors Retained factors = 2Factor analysis/correlation Number of obs = 1323

(obs=1323). factor rv_cop rv_cvx rv_xom rv_oil, pcf

Factor Analysis Brian Jansen

RV Analysis w/ PCF

-When communality is forced to be 1, Factor1 explains COP and XOM while Factor 2 explains CVX and OIL

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• Pretty terrible results for RV-BV

Factor Analysis Brian Jansen

RV-BV Analysis

rvbv_oil 0.0866 -0.0829 0.9856 rvbv_xom 0.3702 0.0135 0.8628 rvbv_cvx -0.0239 0.0971 0.9900 rvbv_cop 0.3697 0.0122 0.8632 Variable Factor1 Factor2 Uniqueness

Factor loadings (pattern matrix) and unique variances

LR test: independent vs. saturated: chi2(6) = 70.49 Prob>chi2 = 0.0000 Factor4 -0.17293 . -1.6677 1.0000 Factor3 -0.02180 0.15113 -0.2103 2.6677 Factor2 0.01663 0.03843 0.1604 2.8779 Factor1 0.28180 0.26518 2.7176 2.7176 Factor Eigenvalue Difference Proportion Cumulative

Rotation: (unrotated) Number of params = 6 Method: principal factors Retained factors = 2Factor analysis/correlation Number of obs = 1323

(obs=1323). factor rvbv_cop rvbv_cvx rvbv_xom rvbv_oil

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• More familiarity with the practices of the oil industry, especially their trading desk operation to determine how they deal with oil price volatility

• Introducing a new jump test that can detect multiple jumps per day and time of jump. Lee-Mykland (2008)? Dobrev et. al (2007)

• Auto correlation with small lag times• Can we use the implied volatility of same industry

companies and oil futures to forecast volatility using the HAR-RV-CJ model?

Conclusion Brian Jansen

Extensions