factor analysis, har-rv regressions, and f-tests

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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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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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



P-Value = 0.0000P-Value = 0.0000

Conclusion: Strongly significantConclusion: Strongly significant

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Testing EMCTesting EMC



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


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



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



P-Value = 0.0000P-Value = 0.0000

Conclusion: Strongly significantConclusion: Strongly significant

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Testing MSFTTesting MSFT



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



P-Value = 0.0714P-Value = 0.0714

Conclusion: Almost significant, not quiteConclusion: Almost significant, not quite

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Testing TXNTesting TXN



P-Value = 0.9267P-Value = 0.9267

Conclusion: Completely insignificantConclusion: Completely insignificant

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Testing XRXTesting XRX



P-Value = 0.1194P-Value = 0.1194

Conclusion: InsignificantConclusion: Insignificant

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Testing S&P 500Testing S&P 500



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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factor analysis, har-rv regressions, and f-tests

Documents

day average lagsecon

day average testedfstatistic

day lagsecon

fstesting sp

fstesting ibmall

fstesting cscoall

fstesting intcall

fstesting orclall