Jump Detection and Analysis Investigation of Media/Telecomm Industry Prad Nadakuduty Presentation 3 3/5/08

Outline Introduction Mathematical Background Price and Z-max Statistics Graphs Summary Correlation of Jumps Data taken from 1/2/2001 to 12/29/2006 5 min interval (78 observations per day) Over ~100K total observations Qualitative findings linking clusters of jumps to industry events / macroeconomic shocks

Introduction Investigate Media/Telecomm Industry Verizon Telecommunications (VZ) AT&T Inc. (T) Walt Disney Inc. (DIS) Data taken from 1/2/2001 to 12/29/2006 5 min interval (78 observations per day) Over ~100K total observations Qualitative findings linking clusters of jumps to industry events / macroeconomic shocks

Mathematical Background Realized Variation (IV with jump contribution) Bipower Variation (robust to jumps)

Mathematical Background Tri-Power Quarticity Z Tri-Power Max Statistic Significance Value .999  z > 3.09

Mathematical Background Previous equations used to estimate integrated quarticity Relative Jump (measure of jump contribution to total price variance)

Verizon Communications (VZ) 5 min Price Data High: 57.40 7/19/2001 Low: 26.16 7/24/2002

Verizon Communications (VZ) Z-tp Max Statistic 8/24/2004 Explanation? Won civil case against text message spammer Acquisition of MCI 6 months later

Walt Disney Inc. (DIS) 5 min Price Data High: 34.88 12/19/2006 Low: 13.15 8/8/2002

Walt Disney Inc. (DIS) Z-tp Max Statistic 5/11/2005 Explanation? Launch of 50 year celebration at theme parks Released positive earning statements from film/DVD earnings

AT&T (T) 5 min Price Data High: 43.95 7/12/2001 Low: 13.50 4/16/2003

AT&T (T) Z-tp Max Statistic 9/23/2003 Explanation? Rumors of merger with BellSouth Acquires assets from MCI-WorldCom bankruptcy

S&P 500 5 min Price Data High: 1443.7 12/15/2006 Low: 768 10/10/2002

S&P 500 Z-tp Max Statistic Max: 11.533 11/23/2006 Explanation? Rumors of merger with BellSouth Acquires assets from MCI-WorldCom bankruptcy

Summary Statistics Tri-power Quarticity and Max Statistic Mean Std. Dev. Max Min Num of jumps Jump Day %tage Verizon (VZ) .5623 1.3690 7.3393 -3.3541 55 N = 1491 (3.68%) Disney (DIS) .5832 1.3185 5.4364 -2.9944 61 N = 1492 (4.09%) AT&T (T) 0.6523 1.4104 7.6598 -2.8460 70 N= 1486 (4.71%) S&P 500 0.7099 1.4007 11.533 -3.051 57 N = 1514 (3.76%) Tri-power Quarticity and Max Statistic Significance Level .999  z = 3.09

Correlation of Jumps A Visual Exercise Count Frequency No Jumps 1267 85.26% Only 1 Jump 200 13.46% Only 2 Jumps 17 1.14% Only 3 Jumps 2 0.13% 4 Jumps 0.00% Triple Jump Dates Jan 3, 2001 Investors jumping on New Year of trading AT&T announce price increase Jun 4, 2004 AT&T announces VoIP Verizon enters Yellow Pages business

Regression Regress tri-power Z max statistic of each firm with that of S&P 500 one week forward Look for predictive power of any firm Newey-West  heteroskedasticity robust standard errors Will provide consistent estimators even if error term is correlated with its own past Newey command in STATA newey SPztp l5.ATTztp, lag(5)

Regression Statistics M&T Firms with S&P 500 SPztp Coef. Newey-West Std. Err. t P>|t| 95% Conf Interval Verizon L5.VZztp -.0447 .0277 -1.62 0.106 [-0.9902 .00957] Disney L5.DISztp .01154 .0286 0.40 0.686 [-.04447 .06754] AT&T L5.ATTztp -.0357 .025507 -1.40 0.162 [-.08574 .01432] SPztp = β1 * L5.VZztp + β0 No coefficients statistically significant  None of these three firms have significant predictive power of S&P 500

Regression Statistics Inter-industry Analysis VZztp DISztp ATTztp Coef Std. Err t Verizon L5.VZztp .0236 .0264 0.90 .0169 .0267 .063 .0718 .0261 2.75 Disney L5.DISztp -.0466 .0277 -1.68 .0048 .0252 0.19 -0.246 .0299 -0.82 AT&T L5.ATTztp .0166 .0250 0.66 .0031 .0249 0.13 .0325 1.25 No statisitically significant coefficients, so these firms are poor indicators of the jump statistic, even of themselves.

Further Exploration Determine HAR-RV-CJ Forecasts Include more companies for wider view Consider investigating industry with more readily available data  Technology, Financial Services Investigate effect of mergers & acquisitions Correlate “size” of acquisition with size of test statistic