1 / 35

Jump Detection and Analysis Investigation of Media/Telecomm Industry

This investigation focuses on the analysis of jumps in the Media/Telecomm Industry using mathematical models and regression analysis. The study includes data preparation, summary statistics, correlation analysis and HAR regressions. The aim is to analyze the correlation of variance of M&T industry with S&P 500 and identify possible predictive measures of the market.

ivyc
Download Presentation

Jump Detection and Analysis Investigation of Media/Telecomm Industry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related