1. Factor Analysis, HAR-RV Regressions, and F-Tests
Zed Lamba
4/9/08

2. ECON 201FS
Recap from Monday
Established through Factor Analysis that Realized Variation amongst 10 tech stocks in S&P 100 had high communality.
Average Uniqueness was only , when analysis was done on ln(RV)
Question to be settled: how does introducing the market into the mix affect things? Can we establish whether the communality results from an industry effect or a market effect?

3. S&P 500 Log Levels 04/97 – 10/07 Critical to note scale on Y-axis
ECON 201FS
S&P 500 Log Levels 04/97 – 10/07
Critical to note scale on Y-axis

4. Factor Analysis on ln(RV)
ECON 201FS
Factor Analysis on ln(RV)
As before, there is 1 significant common factor
Goes against expectation that introducing the market would result in 2 common factors

5. ECON 201FS
Factor Analysis contd.
Average Uniqueness (ignoring S&P): (slightly lower than before)
Average Uniqueness (including S&P):

6. Factor Analysis Analysis
ECON 201FS
Factor Analysis Analysis
S&P 500 Realized Variation (Uniqueness = ) essentially not well-explained by common factor (0.6 is considered threshold)
Possible explanations:
Communality amongst stocks results from industry effect
S&P 500 contains numerous tech stocks that have not been examined here, so results are biased

7. ECON 201FS
HAR-RV Regressions
MSFT RV regressed against all stocks (including MSFT) and S&P
All regressors are lagged by 1 day, 5-day lag average, and 22-day lag average
Regressors’ Explanatory Power (Adjusted R2) = (was without S&P)

8. Testing 1-day lags Regressors Tested F-Statistic P-Value
ECON 201FS
Testing 1-day lags
Regressors Tested
F-Statistic
P-Value
All stocks’ 1-day lag other than MSFT
5.97
0.0000
S&P day lag added to above
6.29
MSFT 1-day lag added to above
9.28

9. Testing 5-day average lags
ECON 201FS
Testing 5-day average lags
Regressors Tested
F-Statistic
P-Value
All stocks’ 5-day average lags other than MSFT
9.18
0.0000
S&P day average lag added to above
9.33 (reduction in significance?)
MSFT 5-day average lag added to above
14.93

10. Testing 22-day average lags
ECON 201FS
Testing 22-day average lags
Regressors Tested
F-Statistic
P-Value
All stocks’ 22-day average lags other than MSFT
1.62
0.1034
S&P day average lag added to above
1.46
0.1483
MSFT 22-day average lag added to above
1.47
0.1368

11. ECON 201FS
Testing CSCO
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 4.03
P-Value =
Conclusion: Mildly significant

12. ECON 201FS
Testing DELL
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 13.56
P-Value =
Conclusion: Strongly significant

13. ECON 201FS
Testing EMC
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 0.13
P-Value =
Conclusion: Completely insignificant

14. ECON 201FS
Testing HPQ
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 0.86
P-Value =
Conclusion: Completely insignificant; surprising given DELL result. Perhaps Compaq merger can explain some unrelated RV?

15. ECON 201FS
Testing IBM
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 1.05
P-Value =
Conclusion: Insignificant, goes with EMC result

16. ECON 201FS
Testing INTC
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 7.63
P-Value =
Conclusion: Strongly significant

17. ECON 201FS
Testing MSFT
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 13.1
P-Value =
Conclusion: Very strongly significant, as expected

18. ECON 201FS
Testing ORCL
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 2.34
P-Value =
Conclusion: Almost significant, not quite

19. ECON 201FS
Testing TXN
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 0.15
P-Value =
Conclusion: Completely insignificant

20. ECON 201FS
Testing XRX
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 1.95
P-Value =
Conclusion: Insignificant

21. ECON 201FS
Testing S&P 500
All 3 lags (1-day, 5-day average, and 22-day average) tested
F-Statistic = 1.90
P-Value =
Conclusion: Insignificant (recall Possible Explanations from Factor Analysis section)

22. Testing Significant Stocks Together

23. Regressing against Significant Stocks
ECON 201FS
Regressing against Significant Stocks
Originally, 33 regressors combined for R2 of
12 regressors here have combined R2 of
Thus, 12 regressors account for 99.13% of R2
Should have reduced this to 9 regressors by removing 22-day average lags

24. Extensions for Final Presentation
ECON 201FS
Extensions for Final Presentation
Check S&P 500 handling
Now that long-term industry trends have been established, see where GOOG fits in
Extract common factor indicated in Factor Analysis and use as regressor, as per Prof. Bollerslev’s suggestion