factor analysis, har-rv regressions, and f-tests
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Factor Analysis, HAR-RV Regressions, and F-Tests. Zed Lamba 4/9/08. 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 0.2374, when analysis was done on ln(RV) - PowerPoint PPT PresentationTRANSCRIPT
Factor Analysis, HAR-RV Factor Analysis, HAR-RV Regressions, and F-TestsRegressions, and F-Tests
Zed LambaZed Lamba
4/9/084/9/08
Recap from MondayRecap from Monday
Established through Factor Analysis that Established through Factor Analysis that Realized Variation amongst 10 tech stocks in Realized Variation amongst 10 tech stocks in S&P 100 had high communality.S&P 100 had high communality.
Average Uniqueness was only 0.2374, when Average Uniqueness was only 0.2374, when analysis was done on ln(RV)analysis was done on ln(RV)
Question to be settled: how does introducing the Question to be settled: how does introducing the market into the mix affect things? Can we market into the mix affect things? Can we establish whether the communality results from establish whether the communality results from an industry effect or a market effect?an industry effect or a market effect?
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S&P 500 Log Levels 04/97 – 10/07S&P 500 Log Levels 04/97 – 10/07
Critical to note scale on Y-axisCritical to note scale on Y-axis
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Factor Analysis on ln(RV)Factor Analysis on ln(RV)
As before, there is 1 significant common factorAs before, there is 1 significant common factor Goes against expectation that introducing the Goes against expectation that introducing the
market would result in 2 common factorsmarket would result in 2 common factors
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Factor Analysis contd.Factor Analysis contd.
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Average Uniqueness (ignoring S&P): 0.2356 Average Uniqueness (ignoring S&P): 0.2356 (slightly lower than before)(slightly lower than before)
Average Uniqueness (including S&P): 0.2678Average Uniqueness (including S&P): 0.2678
Factor Analysis AnalysisFactor Analysis Analysis
S&P 500 Realized Variation (Uniqueness S&P 500 Realized Variation (Uniqueness = 0.5893) essentially not well-explained by = 0.5893) essentially not well-explained by common factor (0.6 is considered common factor (0.6 is considered threshold)threshold)
Possible explanations:Possible explanations:Communality amongst stocks results from Communality amongst stocks results from
industry effectindustry effectS&P 500 contains numerous tech stocks that S&P 500 contains numerous tech stocks that
have not been examined here, so results are have not been examined here, so results are biasedbiased
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HAR-RV RegressionsHAR-RV Regressions
MSFT RV regressed against all stocks (including MSFT RV regressed against all stocks (including MSFT) and S&PMSFT) and S&P
All regressors are lagged by 1 day, 5-day lag All regressors are lagged by 1 day, 5-day lag average, and 22-day lag averageaverage, and 22-day lag average
Regressors’ Explanatory Power (Adjusted RRegressors’ Explanatory Power (Adjusted R22) = ) = 0.6546 (was 0.6542 without S&P)0.6546 (was 0.6542 without S&P)
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Testing 1-day lagsTesting 1-day lags
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Regressors TestedRegressors Tested F-StatisticF-Statistic P-ValueP-Value
All stocks’ 1-day lag All stocks’ 1-day lag other than MSFTother than MSFT
5.975.97 0.00000.0000
S&P 500 1-day lag S&P 500 1-day lag added to aboveadded to above
6.296.29 0.00000.0000
MSFT 1-day lag added MSFT 1-day lag added to aboveto above
9.289.28 0.00000.0000
Testing 5-day average lagsTesting 5-day average lags
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Regressors TestedRegressors Tested F-StatisticF-Statistic P-ValueP-Value
All stocks’ 5-day All stocks’ 5-day average lags other average lags other
than MSFTthan MSFT
9.189.18 0.00000.0000
S&P 500 5-day S&P 500 5-day average lag added to average lag added to
aboveabove
9.33 9.33 (reduction in (reduction in
significance?)significance?)
0.00000.0000
MSFT 5-day average MSFT 5-day average lag added to abovelag added to above
14.9314.93 0.00000.0000
Testing 22-day average lagsTesting 22-day average lags
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Regressors TestedRegressors Tested F-StatisticF-Statistic P-ValueP-Value
All stocks’ 22-day All stocks’ 22-day average lags other average lags other
than MSFTthan MSFT
1.621.62 0.10340.1034
S&P 500 22-day S&P 500 22-day average lag added to average lag added to
aboveabove
1.461.46 0.14830.1483
MSFT 22-day average MSFT 22-day average lag added to abovelag added to above
1.471.47 0.13680.1368
Testing CSCOTesting CSCO
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 4.03F-Statistic = 4.03
P-Value = 0.0072P-Value = 0.0072
Conclusion: Mildly significantConclusion: Mildly significant
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Testing DELLTesting DELL
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 13.56F-Statistic = 13.56
P-Value = 0.0000P-Value = 0.0000
Conclusion: Strongly significantConclusion: Strongly significant
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Testing EMCTesting EMC
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 0.13F-Statistic = 0.13
P-Value = 0.9394P-Value = 0.9394
Conclusion: Completely insignificantConclusion: Completely insignificant
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Testing HPQTesting HPQ
All 3 lags (1-day, 5-day average, and 22-day All 3 lags (1-day, 5-day average, and 22-day average) testedaverage) tested
F-Statistic = 0.86F-Statistic = 0.86
P-Value = 0.4636P-Value = 0.4636
Conclusion: Completely insignificant; surprising Conclusion: Completely insignificant; surprising given DELL result. Perhaps Compaq merger can given DELL result. Perhaps Compaq merger can explain some unrelated RV?explain some unrelated RV?
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Testing IBMTesting IBM
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 1.05F-Statistic = 1.05
P-Value = 0.3681P-Value = 0.3681
Conclusion: Insignificant, goes with EMC Conclusion: Insignificant, goes with EMC resultresult
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Testing INTCTesting INTC
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 7.63F-Statistic = 7.63
P-Value = 0.0000P-Value = 0.0000
Conclusion: Strongly significantConclusion: Strongly significant
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Testing MSFTTesting MSFT
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 13.1F-Statistic = 13.1
P-Value = 0.0000P-Value = 0.0000
Conclusion: Very strongly significant, as Conclusion: Very strongly significant, as expectedexpected
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Testing ORCLTesting ORCL
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 2.34F-Statistic = 2.34
P-Value = 0.0714P-Value = 0.0714
Conclusion: Almost significant, not quiteConclusion: Almost significant, not quite
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Testing TXNTesting TXN
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 0.15F-Statistic = 0.15
P-Value = 0.9267P-Value = 0.9267
Conclusion: Completely insignificantConclusion: Completely insignificant
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Testing XRXTesting XRX
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 1.95F-Statistic = 1.95
P-Value = 0.1194P-Value = 0.1194
Conclusion: InsignificantConclusion: Insignificant
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Testing S&P 500Testing S&P 500
All 3 lags (1-day, 5-day average, and 22-All 3 lags (1-day, 5-day average, and 22-day average) testedday average) tested
F-Statistic = 1.90F-Statistic = 1.90
P-Value = 0.1274P-Value = 0.1274
Conclusion: Insignificant (recall Possible Conclusion: Insignificant (recall Possible Explanations from Factor Analysis section)Explanations from Factor Analysis section)
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Testing Significant Stocks TogetherTesting Significant Stocks Together
Regressing against Significant StocksRegressing against Significant Stocks
Originally, 33 regressors combined for ROriginally, 33 regressors combined for R22 of 0.6546 of 0.6546 12 regressors here have combined R12 regressors here have combined R22 of 0.6489 of 0.6489 Thus, 12 regressors account for 99.13% of RThus, 12 regressors account for 99.13% of R22
Should have reduced this to 9 regressors by Should have reduced this to 9 regressors by removing 22-day average lagsremoving 22-day average lags
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Extensions for Final PresentationExtensions for Final Presentation
Check S&P 500 handlingCheck S&P 500 handling
Now that long-term industry trends have Now that long-term industry trends have been established, see where GOOG fits inbeen established, see where GOOG fits in
Extract common factor indicated in Factor Extract common factor indicated in Factor Analysis and use as regressor, as per Analysis and use as regressor, as per Prof. Bollerslev’s suggestionProf. Bollerslev’s suggestion
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