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: 57.40• 7/19/2001

Low: 26.16• 7/24/2002

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

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

Max: 5.4364• 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

Max: 7.6598• 9/23/2003

Explanation?• Rumors of

merger with BellSouth

• Acquires assets from MCI-WorldCom bankruptcy

S&P 5005 min Price Data

High: 1443.7• 12/15/2006

Low: 768• 10/10/2002

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

Summary Statistics

Tri-power Quarticity and Max Statistic

Significance Level .999 z = 3.09

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%)

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

Verizon AT&T Walt 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

_cons .000203 4.83e-06 42.03 0.000 .0001936 .0002125 is_disAcq -.0000554 .000032 -1.73 0.084 -.0001182 7.39e-06 RV_dis Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.0837 F( 1, 1490) = 2.99Robust regression Number of obs = 1492

_cons .0001926 4.56e-06 42.25 0.000 .0001836 .0002015 is_disAcq -.0000522 .0000302 -1.73 0.084 -.0001115 7.00e-06 BV_dis Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.0839 F( 1, 1490) = 2.99Robust regression Number of obs = 1492

_cons .5316541 .0349207 15.22 0.000 .4631551 .6001531 is_disAcq .2013258 .2313281 0.87 0.384 -.2524375 .6550891 zTP_dis Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.3843 F( 1, 1490) = 0.76Robust regression Number of obs = 1492

R = -0.0289

R = -0.0341

R = 0.0193

Results - Verizon

_cons .0001421 3.03e-06 46.97 0.000 .0001362 .0001481 is_vzAcq 7.23e-06 .0000197 0.37 0.714 -.0000315 .000046 RV_vz Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.7144 F( 1, 1489) = 0.13Robust regression Number of obs = 1491

_cons .0001353 2.85e-06 47.39 0.000 .0001297 .0001408 is_vzAcq 5.69e-06 .0000186 0.31 0.760 -.0000309 .0000422 BV_vz Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.7602 F( 1, 1489) = 0.09Robust regression Number of obs = 1491

_cons .5153637 .035811 14.39 0.000 .4451182 .5856091 is_vzAcq -.1493592 .2337339 -0.64 0.523 -.6078419 .3091236 zTP_vz Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.5229 F( 1, 1489) = 0.41Robust regression Number of obs = 1491

R = -0.0196

R = -0.0184

R = -0.0189

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 = 467.99

“ “ RV for Disney = .00032665

“ “ BV for Disney = .00030651

• 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