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Analysis of Jump Detection in the Media Telecomm Industry

This presentation investigates jump detection and analysis in the media telecomm industry, focusing on companies such as Verizon, AT&T, and Walt Disney. The mathematical background, mergers and acquisitions, and investigation findings are discussed, along with the results of quartile realized variance tests. The potential problems with implementation and the conclusion of the research are also presented.

MikeCarlo
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Analysis of Jump Detection in the Media Telecomm Industry

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  1. Jump Detection and AnalysisInvestigation of Media/Telecomm Industry Prad Nadakuduty Presentation 3 3/5/08

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

  3. 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

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

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

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

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

  8. Verizon Communications (VZ)Z-tp Max Statistic Max: 7.3393 • 8/24/2004 Explanation? • Won civil case against text message spammer • Acquisition of MCI 6 months later

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

  10. Walt Disney Inc. (DIS)Z-tp Max Statistic Max: 5.4364 • 5/11/2005 Explanation? • Launch of 50 year celebration at theme parks • Released positive earning statements from film/DVD earnings

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

  12. AT&T (T)Z-tp Max Statistic Max: 7.6598 • 9/23/2003 Explanation? • Rumors of merger with BellSouth • Acquires assets from MCI-WorldCom bankruptcy

  13. S&P 5005 min Price Data High: 1443.7 • 12/15/2006 Low: 768 • 10/10/2002

  14. S&P 500Z-tp Max Statistic Max: 11.533 • 11/23/2006 Explanation? • Index reaches 6-year high • USD falls to 5-month low against Euro

  15. Summary Statistics Tri-power Quarticity and Max Statistic Significance Level .999  z = 3.09

  16. 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

  17. Investigation of Mergers & Acquisitions

  18. Results - Disney R = -0.0289 R = -0.0341 R = 0.0193

  19. Results - Verizon R = -0.0196 R = -0.0184 R = -0.0189

  20. 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

  21. 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

  22. Quantile-Based Realized Variance • 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 N = total obs in one day n bins of m obs

  23. QRV Problems • Possible problem with indexing over so many sub intervals • Scaling constant based on number of observations per subinterval Average Daily QRV for Disney = 467.99 “ “ RV for Disney = .00032665 “ “ BV for Disney = .00030651

  24. 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

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