Jump Detection and Analysis Investigation of Media/Telecomm Industry

1. Jump Detection and AnalysisInvestigation of Media/Telecomm Industry Prad Nadakuduty 4/9/08

2. Outline • Introduction • Mathematical Background • Data Preparation and Graphs • Summary Statistics • Correlation • HAR Regressions • Conclusion • Appendix • Jump Statistics

3. Motivation • Investigate regressions of realized variance using semi-variance • Analyze correlation of variance of M&T industry with S&P 500 • Semi-variance from Barndorff-Nielsen, Kinnebrock, and Shephard (2008) • HAR-RV regressions from Corsi (2003)

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

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

6. Mathematical Background • Realized Semi-Variance (RS) • Realized Upward Semi-Variance (upRV) upRV = RV - RS

7. Mathematical Background • Realized semi-variance converges to half the BPV plus negative squared jumps: • Deviation above/below half implies increased/decreased volatility during down-ward market

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

9. Mathematical Background • Heterogeneous autoregressive realized variance (HAR-RV) Model with daily, weekly, and monthly periods: • Daily open-close log returns (ri)

10. Data Preparation • Investigate Media/Telecomm Industry • Verizon Telecommunications (VZ) • AT&T Inc. (T) • Walt Disney Inc. (DIS) • Include S&P 500 for comparison • Data taken from 1/2/2001 to 12/29/2006 • 5 min interval (78 observations per day) to reduce microstructure noise • Over ~100K total observations • Incomplete trading days removed

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

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

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

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

15. Data Trends • Downward market from 2001 thru mid 2002 followed by upward market until end of 2006 to nearly same levels • Industry-wide shock from Sept 11, especially Disney • Expect semi-variance and up-variance to have similar but opposite correlations with daily squared returns

16. Summary Statistics

17. Summary Statistics • M&T Industry has nearly 3x more RV than S&P 500 • Slightly more upward-RS for given time range than downward-RS (exception for Verizon) • Suggests more volatility during downward market?

18. Correlation – S&P 500 • Nearly equal (but opposite) correlation of RS and upRS with returns, as expected • upRS more correlated with daily squared returns than RS; more volatility during upward market

19. Correlation - Verizon • upRS highest correlation with daily returns amongst all coefficients for all firms

20. Correlation - AT&T • Squared returns weakly negatively correlated with daily returns • RS and upRS have similar correlation with squared returns; contradicts intuition of higher volatility during downward market

21. Correlation - Disney • Largest correlation magnitude discrepancy between returns and RS, upRS

22. Correlation - Summary • Upward semi-variance largest correlation with daily returns (except for S&P 500, RS slightly bigger in magnitude) • Both semi-variances are more correlated with daily returns than realized variance • M&T firms share similar results and trends with each other and S&P

23. Regression • Regression with Newey-West standard errors • 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 RV_ATT l1.RV_ATT l5RV_ATT l22RV_ATT, lag(60)

24. HAR-RV Regression – S&P 500 • R2 = .6631 • Monthly lag not significant

25. HAR-RV Regression - Verizon • R2 = .7441 • Monthly and (especially) daily lags not significant

26. HAR-RV Regression - AT&T • R2 = .5606 • Monthly and daily lags not significant

27. HAR-RV Regression - Disney • R2 = .6637 • Monthly and (less so) daily lags not significant

28. HAR-RV Regression Summary • Monthly lags insignificant across M&T industry and S&P 500 • Comparable R2 values • Varying results in daily lag suggests that significance function of particular data set and not industry-wide trend

29. Combined Regression • Regress realized variance against HAR semi-variances for each firm • Possible extension: Regress realized variance of S&P 500 against HAR semi-variances for each firm to identify possible predictive measures of market with M&T industry

30. Combined Regression – S&P 500

31. Combined Regression – Verizon

32. Combined Regression – AT&T

33. Combined Regression - Disney

34. Combined Regression Summary • S&P: daily, monthly lag upRS significant • Verizon: daily lag RS significant • AT&T: weekly lag RV significant • Disney: daily lag RS and monthly lag upRS

35. Combined Regression Summary • Collinearity results in upRS statistics being dropped from regression (except for S&P) • No overarching pattern in statistic significance • Extension: Investigate regression of one firm’s lagged semi-variances against market