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

Outline Introduction Mathematical Background –RV and BV Graphs Summary Statistics Mergers & Acquisitions Investigation –Findings –Results Quartile-Realized Variance Test –Background –Problems with implementation Conclusion

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: /19/2001 Low: /24/2002

Verizon Communications (VZ) Z-tp Max Statistic Max: /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: /19/2006 Low: /8/2002

Walt Disney Inc. (DIS) Z-tp Max Statistic Max: /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: /12/2001 Low: /16/2003

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

S&P min Price Data High: /15/2006 Low: /10/2002

S&P 500 Z-tp Max Statistic Max: /23/2006 Explanation? Index reaches 6-year high USD falls to 5-month low against Euro

Summary Statistics Tri-power Quarticity and Max Statistic Significance Level.999  z = 3.09 MeanStd. Dev. MaxMinNum of jumps Jump Day %tage Verizon (VZ) N = 1491 (3.68%) Disney (DIS) N = 1492 (4.09%) AT&T (T) N= 1486 (4.71%) S&P N = 1514 (3.76%)

Investigation of Mergers & Acquisitions Created binary variable for days marking announced merger or acquisition Data taken from Factiva, corporate Annual Reports Only consider M&A deals within data range 1/2/2001 to 12/29/2006 when first announced by company Does not include divestures, sale of assets, or strategic alliances not involving trade of common stock

Investigation of Mergers & Acquisitions VerizonAT&TWalt Disney # of M&A deals 36 (includes MCI deals before merger) N/A (unreliable data) 43 Notable deals Verizon+MCI (Oct 2005) Price Comm (Aug 2002) Dobson Comm (Dec 2001) SBC + AT&T merger (June 2005) Fox Family Worldwide (Feb 2001) Pixar (May 2006)

Results - Disney R = R = R =

Results - Verizon R = R = R =

Results No statistically significant relationship between announcement of acquisition and realized variance Intuition: Deals within the M&T industry are so large and predictable, that variance may be smoothened by expectations Caveat: Diverse classification of deals makes comparisons between deals and across companies difficult Additional caveat: Unlike announcements on overall economic data from centralized source, rumors of mergers spread amongst business forums and communities, therefore the “initial” date of information release is difficult to determine

Quantile-Based Realized Variance Introduced in Christensen, Oomen, Podolskij (2008) Simultaneously robust to noise and jumps –Effectively ignores fraction of largest/smallest return observations Like RV and BV, consistent estimator of IV

Quantile-Based Realized Variance n bins of m obs N = total obs in one day Divides set of observations into subintervals, and truncates λ quantile –Levels of m, λ optimized to maximize efficiency of estimator –If constructed with multiple quartiles, can be more efficient than BPV and close to RV while maintaining robustness to jumps Calculate squared λ-quantile, sum for whole day, and scale to find QRV Performs well in “clean” and “noisy” high frequency data over short horizons compared to RV

QRV Problems Average Daily QRV for Disney = “ “ RV for Disney = “ “ BV for Disney = Possible problem with indexing over so many sub intervals Scaling constant based on number of observations per subinterval

Conclusion Research track investigating effect of mergers and acquisitions within M&T market interesting, but too many confounding variables for accurate research Implement QRV test on M&T and other stocks and compare with RV, BV