Jump Correlation within an Industry – A Beginning By: Zed Lamba ECON 201FS

Background + Mathematics All data is for a 10 year period All data is for a 10 year period 5-minute returns examined to minimize microstructure noise 5-minute returns examined to minimize microstructure noise Use log returns and daily realized variation Use log returns and daily realized variation Tri-power and quad-power quarticity Tri-power and quad-power quarticity Test Statistics (jump if exceeds critical value of 3.09, a.001 significance level): Test Statistics (jump if exceeds critical value of 3.09, a.001 significance level): ECON 201FS

MSFT Prices – Line Graph ECON 201FS

MSFT Prices – Scatter Plot ECON 201FS

MSFT – Max Test Statistics I ECON 201FS

MSFT – Max Test Statistics II ECON 201FS

IBM Prices – Line Graph ECON 201FS

IBM Prices – Scatter Plot ECON 201FS

IBM – Max Test Statistics I ECON 201FS

IBM – Max Test Statistics II ECON 201FS

HPQ Prices – Line Graph ECON 201FS

HPQ Prices – Scatter Plot ECON 201FS

HPQ – Max Test Statistics I ECON 201FS

HPQ – Max Test Statistics II ECON 201FS

Summary Statistics ECON 201FS MeanStDevMinMaxJumps MSFT ztpmax zqpmax IBM ztpmax zqpmax HPQ ztpmax zqpmax

Correlation Calculation If both companies are being compared over 10 days, and If both companies are being compared over 10 days, and the 1 st has jumps on days 1, 4, and 6 the 1 st has jumps on days 1, 4, and 6 the 2 nd has jumps on days 2, 5, and 9 the 2 nd has jumps on days 2, 5, and 9 Then simply create two arrays of size 3, one with 1, 4, and 6; and the other with 2, 5, and 9 Then simply create two arrays of size 3, one with 1, 4, and 6; and the other with 2, 5, and 9 Then calculate the correlation between the two arrays Then calculate the correlation between the two arrays ECON 201FS

High Positive Correlation Using technique previously described, and the good fortune that according to Tri- Power Quarticity Max Statistics, MSFT and IBM had the same number of jumps (76) from 1997 – 2008, the correlation coefficient is an astounding ! Using technique previously described, and the good fortune that according to Tri- Power Quarticity Max Statistics, MSFT and IBM had the same number of jumps (76) from 1997 – 2008, the correlation coefficient is an astounding ! ECON 201FS

Size inequalities will occur However, for the most part, the number of jumps will differ over the same range However, for the most part, the number of jumps will differ over the same range Correlation calculation requires arrays of the same size Correlation calculation requires arrays of the same size Possible solutions: Possible solutions: Fill up smaller array with average of other data points (days on which jump occurred) Fill up smaller array with average of other data points (days on which jump occurred) Prune down bigger array by only looking at biggest jumps (problem – what if a “small” jump correlates with a “big” jump in another company?) Prune down bigger array by only looking at biggest jumps (problem – what if a “small” jump correlates with a “big” jump in another company?) Other ideas? Other ideas? ECON 201FS

Questions for discussion with audience For comparing with limited data (ex: GOOG), should jumps over the same range be examined for comparison and correlation calculation (ex: 2004 – 2008 for both MSFT and GOOG)? For comparing with limited data (ex: GOOG), should jumps over the same range be examined for comparison and correlation calculation (ex: 2004 – 2008 for both MSFT and GOOG)? Possible regression to explain jumps: Possible regression to explain jumps: JumpsMSFT = B1(JumpsIBM) + B2(JumpsHPQ) + … + all other technology firms JumpsMSFT = B1(JumpsIBM) + B2(JumpsHPQ) + … + all other technology firms Will all arrays have to be over same range as that of the smallest array (so if GOOG were included in calculation, would we have to restrict all the firms’ data being considered to the range 2004 – 2008? Will all arrays have to be over same range as that of the smallest array (so if GOOG were included in calculation, would we have to restrict all the firms’ data being considered to the range 2004 – 2008? ECON 201FS