Download - Microsoft - Volatility modeling and analysis
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Microsoft Microsoft (MSFT)(MSFT)Augusto PucciAugusto Pucci
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OverviewOverview MSFT – Company OverviewMSFT – Company Overview MSFT – Return AnalysisMSFT – Return Analysis RT – AR(2) modelRT – AR(2) model RT – AR(2) – ARCH(1) modelRT – AR(2) – ARCH(1) model RT – AR(2) – ARCH(2) modelRT – AR(2) – ARCH(2) model RT – AR(2) – GARCH(1,1) modelRT – AR(2) – GARCH(1,1) model RT – AR(2) – TGARCH(1,1) modelRT – AR(2) – TGARCH(1,1) model Range model → Range2 modelRange model → Range2 model abs(RT) model → RT2 modelabs(RT) model → RT2 model RT – GARCH(1,1) model, Extended…RT – GARCH(1,1) model, Extended… RT – GARCH(1,1) model, Extended 2…RT – GARCH(1,1) model, Extended 2… RT – AR(2) – TGARCH(1,1) ShortFallRT – AR(2) – TGARCH(1,1) ShortFall Volatility Forecasting from TGARCH(1,1) modelVolatility Forecasting from TGARCH(1,1) model Volatility Forecasting from GARCH(1,1) eXt. modelVolatility Forecasting from GARCH(1,1) eXt. model Extra Stuff…Extra Stuff…
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Microsoft CampusMicrosoft Campus
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Microsoft: Company Microsoft: Company OverviewOverview
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Financial HighlightsFinancial Highlights Beta: Beta: 1.081.08 Fiscal Year Ends: Fiscal Year Ends: 30-June30-June Profitability Profit Margin: Profitability Profit Margin:
27.80%27.80% Operating Margin:Operating Margin:38.06%38.06% Return on Assets (ttm):Return on Assets (ttm):22.15%22.15% Return on Equity (ttm):Return on Equity (ttm):50.01%50.01%
Income StatementIncome Statement Revenue: Revenue: 61.98B61.98B Revenue Per Share: Revenue Per Share: 6.7816.781 Qtrly Revenue Growth:Qtrly Revenue Growth:1.60%1.60% Gross Profit:Gross Profit:48.82B48.82B EBITDA:EBITDA:25.94B25.94B Net Income Avl to Net Income Avl to
Common:Common:17.23B17.23B Diluted EPS:Diluted EPS:1.871.87 Qtrly Earnings Growth:Qtrly Earnings Growth:--
11.30%11.30%William Henry Gates III
(Seattle, 10/28/1955)
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Financial HighlightsFinancial Highlights
Balance SheetBalance Sheet Total Cash: Total Cash: 20.30B20.30B Total Cash Per Share:Total Cash Per Share:2.2832.283 Total Debt:Total Debt:2.00B2.00B Total Debt/Equity:Total Debt/Equity:N/AN/A Current Ratio:Current Ratio:1.5911.591 Book Value Per Share:Book Value Per Share:3.8793.879
Cash Flow StatementCash Flow Statement Operating Cash Operating Cash
Flow:Flow:20.32B20.32B Levered Free Cash Levered Free Cash
Flow:Flow:14.40B14.40B
Steven Anthony Ballmer (Detroit, 03/24/1956)
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Important DatesImportant Dates 1975 1975 Microsoft foundedMicrosoft founded Jan. 1, 1979Jan. 1, 1979 Microsoft moves from Albuquerque, New Mexico to Bellevue, Microsoft moves from Albuquerque, New Mexico to Bellevue,
WashingtonJuneWashingtonJune 25, 1981 Microsoft incorporates25, 1981 Microsoft incorporates Aug. 12, 1981Aug. 12, 1981 IBM introduces its personal computer with Microsoft's 16-bit IBM introduces its personal computer with Microsoft's 16-bit
operating system, MS-DOS 1.0operating system, MS-DOS 1.0 Feb. 26, 1986Feb. 26, 1986 Microsoft moves to corporate campus in Redmond, Washington Microsoft moves to corporate campus in Redmond, Washington March 13, 1986March 13, 1986 Microsoft stock goes public Microsoft stock goes public Aug. 1, 1989Aug. 1, 1989 Microsoft introduces earliest version of Office suite of productivity Microsoft introduces earliest version of Office suite of productivity
applicationsapplications May 22, 1990May 22, 1990 Microsoft launches Windows 3.0 Microsoft launches Windows 3.0 Aug. 24, 1995Aug. 24, 1995 Microsoft launches Windows 95Microsoft launches Windows 95 Dec. 7, 1995Dec. 7, 1995 Bill Gates outlines Microsoft's commitment to supporting and Bill Gates outlines Microsoft's commitment to supporting and
enhancing the Internetenhancing the Internet June 25, 1998June 25, 1998 Microsoft launches Windows 98Microsoft launches Windows 98 Jan. 13, 2000Jan. 13, 2000 Steve Ballmer named president and chief executive officer for Steve Ballmer named president and chief executive officer for
MicrosoftMicrosoft Feb. 17, 2000Feb. 17, 2000 Microsoft launches Windows 2000 Microsoft launches Windows 2000 Apr. 3, 2000Apr. 3, 2000 Microsoft accused of abusive monopolyMicrosoft accused of abusive monopoly June 22, 2000June 22, 2000 Bill Gates and Steve Ballmer outline Microsoft's .NET strategy for Bill Gates and Steve Ballmer outline Microsoft's .NET strategy for
Web servicesWeb services May 31, 2001May 31, 2001 Microsoft launches Office XP Microsoft launches Office XP
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Important Dates [2]Important Dates [2] Oct. 25, 2001Oct. 25, 2001 Microsoft launches Windows XP Microsoft launches Windows XP Jan. 15, 2002Jan. 15, 2002 Bill Gates outlines Microsoft's commitment to Trustworthy Bill Gates outlines Microsoft's commitment to Trustworthy
ComputingComputing Nov. 7, 2002Nov. 7, 2002 Microsoft and partners launch Tablet PC Microsoft and partners launch Tablet PC Jan. 16, 2003Jan. 16, 2003 Microsoft declares annual dividend Microsoft declares annual dividend April 24, 2003April 24, 2003 Microsoft launches Windows Server 2003 Microsoft launches Windows Server 2003 Oct. 21, 2003Oct. 21, 2003 Microsoft launches Microsoft Office System Microsoft launches Microsoft Office System March, 2004March, 2004 European antitrust legal action against MicrosoftEuropean antitrust legal action against Microsoft July 20, 2004July 20, 2004 Microsoft announces plans to return up to $75 billion to shareholders Microsoft announces plans to return up to $75 billion to shareholders
in dividends and stock buybacksin dividends and stock buybacks June 15, 2006June 15, 2006 Microsoft announces that Bill Gates will transition out of a day-to- Microsoft announces that Bill Gates will transition out of a day-to-
day role in the company in July 2008, Ray Ozzie is named chief software architect day role in the company in July 2008, Ray Ozzie is named chief software architect and Craig Mundie chief research and strategy officerand Craig Mundie chief research and strategy officer
July 20, 2006July 20, 2006 Microsoft announces a new $20 billion tender offer and authorizes an Microsoft announces a new $20 billion tender offer and authorizes an additional share-repurchase program of up to $20 billion over five yearsadditional share-repurchase program of up to $20 billion over five years
Jan. 30, 2007Jan. 30, 2007 Microsoft launches Windows Vista and the 2007 Microsoft Office Microsoft launches Windows Vista and the 2007 Microsoft Office System to consumers worldwideSystem to consumers worldwide
Feb. 27, 2008Feb. 27, 2008 Microsoft launches Windows Server 2008, SQL Server 2008 and Microsoft launches Windows Server 2008, SQL Server 2008 and Visual Studio 2008Visual Studio 2008
June 27, 2008June 27, 2008 Bill Gates transitions from his day-to-day role at Microsoft to spend Bill Gates transitions from his day-to-day role at Microsoft to spend more time on his work at The Bill & Melinda Gates Foundationmore time on his work at The Bill & Melinda Gates Foundation
Jan. 2009Jan. 2009 Microsoft announces layoffs of up to 5,000 employeesMicrosoft announces layoffs of up to 5,000 employees
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MSFT – Return MSFT – Return AnalysisAnalysis
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Adj_CloseAdj_Closefrom 03/13/1986 to from 03/13/1986 to
02/05/200902/05/2009
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RT from 03/13/1986 to RT from 03/13/1986 to 02/05/200902/05/2009
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Windows 95 & Windows Windows 95 & Windows 9898
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Windows 95 & Windows Windows 95 & Windows 9898
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Dot.Com Bubble & 9/11Dot.Com Bubble & 9/11
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European antitrust accuse & European antitrust accuse & massive layoffsmassive layoffs
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European antitrust accuse & European antitrust accuse & massive layoffsmassive layoffs
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RT - HistogramRT - Histogram
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Series: RTSample 3/13/1986 2/05/2009Observations 5776
Mean 1.503975Median 0.000000Maximum 283.3044Minimum -602.4211Std. Dev. 39.78974Skewness -0.619675Kurtosis 17.56243
Jarque-Bera 51406.45Probability 0.000000
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Windows 95 & Windows Windows 95 & Windows 9898
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Series: RTSample 1/03/1995 12/31/1999Observations 1263
Mean 3.425266Median 1.458384Maximum 149.6213Minimum -147.2664Std. Dev. 34.82695Skewness 0.096270Kurtosis 3.856238
Jarque-Bera 40.53260Probability 0.000000
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Series: RTSample 1/02/1998 12/31/2001Observations 1004
Mean 1.134653Median 0.960695Maximum 283.3044Minimum -269.1723Std. Dev. 44.87066Skewness -0.220573Kurtosis 7.322283
Jarque-Bera 789.6769Probability 0.000000
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RT Synth - HistogramRT Synth - Histogram
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Series: RT_SYNTHSample 3/13/1986 2/05/2009Observations 5777
Mean 1.418457Median 1.724196Maximum 143.1277Minimum -154.1308Std. Dev. 39.77694Skewness -0.064970Kurtosis 3.075513
Jarque-Bera 5.436769Probability 0.065981
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RT Vs. RT SynthRT Vs. RT SynthRT_SYNTH RT
Mean 1.410508 1.503975
Median 1.712924 0.000000
Maximum 143.1277 283.3044
Minimum -154.1308 -602.4211
Std. Dev. 39.77580 39.78974
Skewness -0.064653 -0.619675
Kurtosis 3.076041 17.56243
Jarque-Bera 5.415586 51406.45
Probability 0.066684 0.000000
Sum 8147.096 8686.960
Sum Sq. Dev. 9136709. 9143113.
Observations 5776 5776
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RT SynthRT Synth
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RT Vs. RT Synth [2]RT Vs. RT Synth [2]
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RT Vs. RT Synth [3]RT Vs. RT Synth [3]
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RT - CorrelogramRT - Correlogram
Sign. Level (5%) = ± 0.025
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RTRT22 - Correlogram - Correlogram
Sign. Level (5%) = ± 0.025
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abs(RT) - Correlogramabs(RT) - Correlogram
Sign. Level (5%) = ± 0.025
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RTRT22
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RTRT22 - Histogram - Histogram
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Series: RT2Sample 3/13/1986 2/05/2009Observations 5776
Mean 1585.211Median 326.5124Maximum 362911.2Minimum 0.000000Std. Dev. 6425.544Skewness 33.63031Kurtosis 1758.877
Jarque-Bera 7.43e+08Probability 0.000000
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abs(RT)abs(RT)
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abs(RT) - Histogramabs(RT) - Histogram
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Series: RT_ABSSample 3/13/1986 2/05/2009Observations 5776
Mean 26.22082Median 18.06964Maximum 602.4211Minimum 0.000000Std. Dev. 29.96389Skewness 3.571797Kurtosis 36.66024
Jarque-Bera 284959.5Probability 0.000000
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RT – AR(2) modelRT – AR(2) model
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RTF - AR(2) Static RTF - AR(2) Static ForecastForecast
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Forecast: RTFActual: RTForecast sample: 3/13/1986 2/05/2009Adjusted sample: 3/18/1986 2/05/2009Included observations: 5774
Root Mean Squared Error 39.65853Mean Absolute Error 26.44798Mean Abs. Percent Error 88.89025Theil Inequality Coefficient 0.935928 Bias Proportion 0.000000 Variance Proportion 0.896076 Covariance Proportion 0.103924
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RT Vs. RTF AR(2) Static RT Vs. RTF AR(2) Static ForecastForecast
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RTF - AR(2) Dynamic RTF - AR(2) Dynamic ForecastForecast
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Forecast: RTFActual: RTForecast sample: 3/13/1986 2/05/2009Adjusted sample: 3/18/1986 2/05/2009Included observations: 5774
Root Mean Squared Error 39.71565Mean Absolute Error 26.38541Mean Abs. Percent Error 87.99759Theil Inequality Coefficient 0.963430 Bias Proportion 0.000000 Variance Proportion 0.993422 Covariance Proportion 0.006578
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RT AR(2) – Residual PlotRT AR(2) – Residual Plot
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RT AR(2) – Residual Plot RT AR(2) – Residual Plot [2][2]
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RT AR(2) – Residual RT AR(2) – Residual HistogramHistogram
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Series: ResidualsSample 3/18/1986 2/05/2009Observations 5774
Mean -3.06e-10Median -1.577343Maximum 282.5983Minimum -606.2254Std. Dev. 39.66197Skewness -0.674704Kurtosis 17.79372
Jarque-Bera 53090.73Probability 0.000000
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RT AR(2) – Residual RT AR(2) – Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT AR(2) – Residual RT AR(2) – Residual ARCH TestARCH Test
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RT – AR(2) – ARCH(1) RT – AR(2) – ARCH(1) modelmodel
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RT – AR(2) – ARCH(1) RT – AR(2) – ARCH(1) modelmodel
σ2 = 1,618.1026σ = 40.225647
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RT – ARCH(1) Residual PlotRT – ARCH(1) Residual Plot
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RT – ARCH(1) Conditional RT – ARCH(1) Conditional Variance PlotVariance Plot
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RT – ARCH(1) Residual Vs. Conditional RT – ARCH(1) Residual Vs. Conditional Variance PlotVariance Plot
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RT – ARCH(1) Std. Residual RT – ARCH(1) Std. Residual PlotPlot
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RT – ARCH(1) Residuals Vs. Std. Residuals RT – ARCH(1) Residuals Vs. Std. Residuals PlotPlot
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RT – ARCH(1) Std. Residuals Vs. RT – ARCH(1) Std. Residuals Vs. ResidualsResiduals
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RT – ARCH(1) Conditional Variance Vs. Std. RT – ARCH(1) Conditional Variance Vs. Std. ResidualsResiduals
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RT – ARCH(1) Residual RT – ARCH(1) Residual HistogramHistogram
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Mean 0.002564Median -0.036891Maximum 7.251408Minimum -8.116231Std. Dev. 1.000086Skewness -0.098849Kurtosis 9.585103
Jarque-Bera 10441.96Probability 0.000000
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RT – ARCH(1) Std. Residual RT – ARCH(1) Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT – ARCH(1) Squared Std. Residual RT – ARCH(1) Squared Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT ARCH(1) – Residual RT ARCH(1) – Residual ARCH TestARCH Test
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RT – AR(2) – ARCH(2) RT – AR(2) – ARCH(2) modelmodel
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RT – AR(2) – ARCH(2) RT – AR(2) – ARCH(2) modelmodel
σ2 = 1,635.1865σ = 40.437440
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RT – ARCH(2) Residual PlotRT – ARCH(2) Residual Plot
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RT – ARCH(2) Conditional RT – ARCH(2) Conditional Variance PlotVariance Plot
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RT – ARCH(2) Residual Vs. Conditional RT – ARCH(2) Residual Vs. Conditional Variance PlotVariance Plot
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RT – ARCH(2) Std. Residual RT – ARCH(2) Std. Residual PlotPlot
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RT – ARCH(2) Std. Residuals Vs. RT – ARCH(2) Std. Residuals Vs. ResidualsResiduals
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RT – ARCH(2) Conditional Variance Vs. Std. RT – ARCH(2) Conditional Variance Vs. Std. ResidualsResiduals
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RT – ARCH(2) Residual RT – ARCH(2) Residual HistogramHistogram
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Series: Standardized ResidualsSample 3/18/1986 2/05/2009Observations 5774
Mean -0.004841Median -0.047257Maximum 7.802617Minimum -9.038780Std. Dev. 1.000086Skewness -0.064868Kurtosis 10.17817
Jarque-Bera 12400.39Probability 0.000000
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RT – ARCH(2) Std. Residual RT – ARCH(2) Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT – ARCH(2) Squared Std. Residual RT – ARCH(2) Squared Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT ARCH(2) – Residual RT ARCH(2) – Residual ARCH TestARCH Test
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RT – AR(2) – GARCH(1,1) RT – AR(2) – GARCH(1,1) modelmodel
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RT – AR(2) – GARCH(1,1) RT – AR(2) – GARCH(1,1) modelmodel
σ2 = 2,391.1118σ = 48.898996
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RT – GARCH(1,1) Residual PlotRT – GARCH(1,1) Residual Plot
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RT – GARCH(1,1) Conditional RT – GARCH(1,1) Conditional Variance PlotVariance Plot
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RT – GARCH(1,1) Std. Residual RT – GARCH(1,1) Std. Residual PlotPlot
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RT – GARCH(1,1) Std. Residuals Vs. RT – GARCH(1,1) Std. Residuals Vs. ResidualsResiduals
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RT – GARCH(1,1) Conditional Variance Vs. RT – GARCH(1,1) Conditional Variance Vs. Std. ResidualsStd. Residuals
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RT – GARCH(1,1) Residual RT – GARCH(1,1) Residual HistogramHistogram
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Series: Standardized ResidualsSample 3/18/1986 2/05/2009Observations 5774
Mean -0.002391Median -0.030605Maximum 6.955800Minimum -11.64137Std. Dev. 0.999853Skewness -0.334206Kurtosis 9.932213
Jarque-Bera 11668.86Probability 0.000000
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RT – GARCH(1,1) Std. Residual RT – GARCH(1,1) Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT – GARCH(1,1) Squared Std. Residual RT – GARCH(1,1) Squared Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT GARCH(1,1) – Residual RT GARCH(1,1) – Residual ARCH TestARCH Test
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RT GARCH(1,1) - Sign RT GARCH(1,1) - Sign Bias TestBias Test
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RT GARCH(1,1) – Negative Size RT GARCH(1,1) – Negative Size Bias TestBias Test
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RT – AR(2) – TGARCH(1,1) RT – AR(2) – TGARCH(1,1) modelmodel
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RT – AR(2) – TGARCH(1,1) RT – AR(2) – TGARCH(1,1) modelmodel
σ2 = 2,656.5854σ = 51.542074
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RT – TGARCH(1,1) Residual RT – TGARCH(1,1) Residual PlotPlot
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RT – TGARCH(1,1) Conditional RT – TGARCH(1,1) Conditional Variance PlotVariance Plot
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RT – TGARCH(1,1) Std. RT – TGARCH(1,1) Std. Residual PlotResidual Plot
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RT – TGARCH(1,1) Std. Residuals Vs. RT – TGARCH(1,1) Std. Residuals Vs. ResidualsResiduals
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RT – TGARCH(1,1) Conditional Variance Vs. RT – TGARCH(1,1) Conditional Variance Vs. Std. ResidualsStd. Residuals
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Mean 0.004466Median -0.025805Maximum 6.494105Minimum -11.52324Std. Dev. 0.999918Skewness -0.334445Kurtosis 9.651680
Jarque-Bera 10752.21Probability 0.000000
RT – TGARCH(1,1) Residual RT – TGARCH(1,1) Residual HistogramHistogram
![Page 93: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/93.jpg)
RT – TGARCH(1,1) Std. Residual RT – TGARCH(1,1) Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT – TGARCH(1,1) Squared Std. Residual RT – TGARCH(1,1) Squared Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT TGARCH(1,1) – Residual ARCH RT TGARCH(1,1) – Residual ARCH TestTest
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Range & RangeRange & Range22
range = range = log(high/low)*sqr(252/(4*log(2)))*10log(high/low)*sqr(252/(4*log(2)))*10
00
Range model → Range model → RangeRange22 modelmodel
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RangeRange22 model model
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E[ RangeE[ Range22t t | I| I(t-1) (t-1) ] (from Range ] (from Range
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RangeRange22tt Vs. E[ Range Vs. E[ Range22
t t | | II(t-1) (t-1) ]]
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![Page 100: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/100.jpg)
abs(RT) model → RTabs(RT) model → RT22 modelmodel
![Page 101: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/101.jpg)
RTRT22 model model
![Page 102: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/102.jpg)
E[ RTE[ RT22t t | I| I(t-1) (t-1) ] (from abs(RT) ] (from abs(RT)
MEM)MEM)
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RTRT22tt Vs. E[ RT Vs. E[ RT22
t t | I| I(t-1) (t-1) ]]
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RT – GARCH(1,1) modelRT – GARCH(1,1) modelExtended…Extended…
![Page 105: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/105.jpg)
RT – GARCH(1,1) eXt. RT – GARCH(1,1) eXt. modelmodel
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RT – GARCH(1,1) eXt.RT – GARCH(1,1) eXt. Residual Residual PlotPlot
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RT – GARCH(1,1) eXt. Conditional RT – GARCH(1,1) eXt. Conditional Variance PlotVariance Plot
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RT – GARCH(1,1) eXt. Std. RT – GARCH(1,1) eXt. Std. Residual PlotResidual Plot
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RT – GARCH(1,1) eXt. Std. Residuals Vs. RT – GARCH(1,1) eXt. Std. Residuals Vs. ResidualsResiduals
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RT – GARCH(1,1) eXt. Conditional Variance RT – GARCH(1,1) eXt. Conditional Variance Vs. Std. ResidualsVs. Std. Residuals
![Page 113: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/113.jpg)
RT – GARCH(1,1) eXt. Residual RT – GARCH(1,1) eXt. Residual HistogramHistogram
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Series: Standardized ResidualsSample 3/17/1986 2/05/2009Observations 5775
Mean 0.040886Median 0.000000Maximum 5.427238Minimum -9.489069Std. Dev. 0.999128Skewness -0.221303Kurtosis 7.435210
Jarque-Bera 4780.495Probability 0.000000
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RT – GARCH(1,1) eXt. Std. Residual RT – GARCH(1,1) eXt. Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT – GARCH(1,1) eXt. Squared Std. RT – GARCH(1,1) eXt. Squared Std. Residual CorrelogramResidual Correlogram
Sign. Level (5%) = ± 0.025
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RT - GARCH(1,1) eXt – Residual RT - GARCH(1,1) eXt – Residual ARCH TestARCH Test
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RT – GARCH(1,1) modelRT – GARCH(1,1) modelExtended 2…Extended 2…
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RT – GARCH(1,1) eXt.2 RT – GARCH(1,1) eXt.2 modelmodel
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RT – GARCH(1,1) eXt.2RT – GARCH(1,1) eXt.2 Residual PlotResidual Plot
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RT – GARCH(1,1) eXt.2 Conditional RT – GARCH(1,1) eXt.2 Conditional Variance PlotVariance Plot
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RT – GARCH(1,1) eXt.2 Residual Vs. Conditional RT – GARCH(1,1) eXt.2 Residual Vs. Conditional Variance PlotVariance Plot
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RT – GARCH(1,1) eXt.2 Std. RT – GARCH(1,1) eXt.2 Std. Residual PlotResidual Plot
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RT – GARCH(1,1) eXt.2 Residuals Vs. Std. RT – GARCH(1,1) eXt.2 Residuals Vs. Std. Residuals PlotResiduals Plot
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RT – GARCH(1,1) eXt.2 Std. Residuals RT – GARCH(1,1) eXt.2 Std. Residuals Vs. ResidualsVs. Residuals
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RT – GARCH(1,1) eXt.2 Conditional Variance RT – GARCH(1,1) eXt.2 Conditional Variance Vs. Std. ResidualsVs. Std. Residuals
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RT – GARCH(1,1) eXt.2 Residual RT – GARCH(1,1) eXt.2 Residual HistogramHistogram
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Series: Standardized ResidualsSample 3/14/1986 2/05/2009Observations 5776
Mean 0.041525Median 0.000000Maximum 5.839957Minimum -10.81130Std. Dev. 0.999256Skewness -0.272238Kurtosis 8.627599
Jarque-Bera 7693.228Probability 0.000000
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RT – GARCH(1,1) eXt.2 Std. Residual RT – GARCH(1,1) eXt.2 Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT – GARCH(1,1) eXt.2 Squared Std. Residual RT – GARCH(1,1) eXt.2 Squared Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RT - GARCH(1,1) eXt.2 – Residual RT - GARCH(1,1) eXt.2 – Residual ARCH TestARCH Test
![Page 130: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/130.jpg)
RT – AR(2) – TGARCH(1,1) RT – AR(2) – TGARCH(1,1) ShortFallShortFall
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RT Vs. Expected Loss [ -RT Vs. Expected Loss [ -1.000*sqr(GARCH) ]1.000*sqr(GARCH) ]
Zα = 1.000
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SHORTFALL
Shortfall [ min{rt-Shortfall [ min{rt-loss_hat,0}]loss_hat,0}]
Zα = 1.000
![Page 133: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/133.jpg)
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Series: SHORTFALLSample 3/13/1986 2/05/2009 IF SHORTFALL<0Observations 701
Mean -22.68773Median -13.04273Maximum -0.013943Minimum -538.5431Std. Dev. 34.00902Skewness -6.561950Kurtosis 81.88871
Jarque-Bera 186806.7Probability 0.000000
Shortfall Histogram Shortfall Histogram [12.1406 %]
Zα = 1.000
[12.1406 %]
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LOSS_HAT RT
RT Vs. Expected Loss [ -RT Vs. Expected Loss [ -2.000*sqr(GARCH) ]2.000*sqr(GARCH) ]
Zα = 2.000
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Shortfall [ min{rt-Shortfall [ min{rt-loss_hat,0}]loss_hat,0}]
Zα = 2.000
![Page 136: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/136.jpg)
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Series: SHORTFALLSample 3/13/1986 2/05/2009 IF SHORTFALL<0Observations 110
Mean -34.69664Median -21.39431Maximum -0.045751Minimum -474.6651Std. Dev. 54.15019Skewness -5.307540Kurtosis 41.24680
Jarque-Bera 7221.030Probability 0.000000
Shortfall Histogram Shortfall Histogram [1.9050 %]
Zα = 2.000
[1.9050 %]
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LOSS_HAT RT
RT Vs. Expected Loss [ -RT Vs. Expected Loss [ -2.250*sqr(GARCH) ]2.250*sqr(GARCH) ]
Zα = 2.250
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Shortfall [ min{rt-Shortfall [ min{rt-loss_hat,0}]loss_hat,0}]
Zα = 2.250
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Series: SHORTFALLSample 3/13/1986 2/05/2009 IF SHORTFALL<0Observations 78
Mean -37.84129Median -21.40151Maximum -0.397317Minimum -458.6956Std. Dev. 58.78183Skewness -5.043842Kurtosis 35.14740
Jarque-Bera 3689.453Probability 0.000000
Shortfall Histogram Shortfall Histogram [1.3508 %]
Zα = 2.250
[1.3508 %]
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RT Vs. Expected Loss [ -RT Vs. Expected Loss [ -2.250*sqr(GARCH) ]2.250*sqr(GARCH) ]
Zα = 2.426
![Page 141: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/141.jpg)
Shortfall [ min{rt-Shortfall [ min{rt-loss_hat,0}]loss_hat,0}]
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SHORTFALL Zα = 2.426
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Series: SHORTFALLSample 3/13/1986 2/05/2009 IF SHORTFALL<0Observations 62
Mean -39.82862Median -22.99443Maximum -0.788588Minimum -447.4530Std. Dev. 62.32909Skewness -4.809761Kurtosis 30.90806
Jarque-Bera 2251.104Probability 0.000000
Shortfall Histogram Shortfall Histogram [1.0737 %]
Zα = 2.426
[1.0737 %]
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RT Vs. Expected Loss [ -RT Vs. Expected Loss [ -3.000*sqr(GARCH) ]3.000*sqr(GARCH) ]
Zα = 3.000
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Shortfall [ min{rt-Shortfall [ min{rt-loss_hat,0}]loss_hat,0}]
Zα = 3.000
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Series: SHORTFALLSample 3/13/1986 2/05/2009 IF SHORTFALL<0Observations 32
Mean -44.26316Median -27.63546Maximum -0.542937Minimum -410.7870Std. Dev. 75.18691Skewness -3.863235Kurtosis 18.99085
Jarque-Bera 420.5407Probability 0.000000
Shortfall Histogram Shortfall Histogram [0.5542 %]
Zα = 3.000
0.5542 %]
![Page 146: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/146.jpg)
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RT Vs. Expected Loss [ -RT Vs. Expected Loss [ -4.000*sqr(GARCH) ]4.000*sqr(GARCH) ]
Zα = 4.000
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Shortfall [ min{rt-Shortfall [ min{rt-loss_hat,0}]loss_hat,0}]
Zα = 4.000
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Series: SHORTFALLSample 3/13/1986 2/05/2009 IF SHORTFALL<0Observations 8
Mean -84.82702Median -31.48301Maximum -1.965430Minimum -346.9090Std. Dev. 113.7577Skewness -1.734299Kurtosis 4.692967
Jarque-Bera 4.965769Probability 0.083502
Shortfall Histogram Shortfall Histogram [0.1383 %]
Zα = 4.000
[0.1383 %]
![Page 149: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/149.jpg)
Volatility ForecastingVolatility Forecasting
from: TGARCH(1,1) modelfrom: TGARCH(1,1) model
![Page 150: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/150.jpg)
TGARCH(1,1) - Plot RT TGARCH(1,1) - Plot RT ±±2 2 σσ
![Page 151: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/151.jpg)
TGARCH(1,1) – Variance Dynamic TGARCH(1,1) – Variance Dynamic ForecastForecast
(out of the sample)(out of the sample)02/06/2009 - 02/06/201002/06/2009 - 02/06/2010
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Forecast of Variance
![Page 152: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/152.jpg)
TGARCH(1,1) - Plot RT TGARCH(1,1) - Plot RT ±±2 2 σσ
Variance Dynamic Forecast (out of the Variance Dynamic Forecast (out of the sample)sample)
![Page 153: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/153.jpg)
TGARCH(1,1) – Variance Dynamic TGARCH(1,1) – Variance Dynamic ForecastForecast
(in the sample)(in the sample)
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Forecast: RTFActual: RTForecast sample: 1/02/2008 2/05/2009Included observations: 277
Root Mean Squared Error 49.70124Mean Absolute Error 35.52234Mean Abs. Percent Error 103.4389Theil Inequality Coefficient 0.974449 Bias Proportion 0.009734 Variance Proportion 0.988903 Covariance Proportion 0.001363
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Forecast of Variance
Training Set: 03/13/1986 - 12/31/2007
Test Set: 01/01/2008 - 02/05/2009
![Page 154: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/154.jpg)
TGARCH(1,1) - Plot RT TGARCH(1,1) - Plot RT ±±2 2 σσ
Variance Dynamic Forecast (in the Variance Dynamic Forecast (in the sample)sample)
![Page 155: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/155.jpg)
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RTF
Forecast: RTFActual: RTForecast sample: 1/02/2008 2/05/2009Included observations: 277
Root Mean Squared Error 49.46354Mean Absolute Error 35.39842Mean Abs. Percent Error 103.4706Theil Inequality Coefficient 0.959512 Bias Proportion 0.010551 Variance Proportion 0.953923 Covariance Proportion 0.035525
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Forecast of Variance
TGARCH(1,1) – Variance Static TGARCH(1,1) – Variance Static ForecastForecast
(in the sample)(in the sample)
Training Set: 03/13/1986 - 12/31/2007
Test Set: 01/01/2008 - 02/05/2009
![Page 156: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/156.jpg)
TGARCH(1,1) - Plot RT TGARCH(1,1) - Plot RT ±±2 2 σσ
Variance Static Forecast (in the Variance Static Forecast (in the sample)sample)
![Page 157: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/157.jpg)
Volatility ForecastingVolatility Forecasting
from: Rangefrom: Range22 model model
![Page 158: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/158.jpg)
RangeRange22 - Plot RT - Plot RT ±±2 2 σσ
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RANGEF
Forecast: RANGEFActual: RANGEForecast sample: 1/02/2008 2/05/2009Included observations: 277
Root Mean Squared Error 39.61914Mean Absolute Error 33.85970Mean Abs. Percent Error 100.0000Theil Inequality Coefficient 1.000000 Bias Proportion 0.730392 Variance Proportion 0.269608 Covariance Proportion 0.000000
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Forecast of Variance
RangeRange22 – Variance Dynamic – Variance Dynamic ForecastForecast
(in the sample)(in the sample)
Training Set: 03/13/1986 - 12/31/2007
Test Set: 01/01/2008 - 02/05/2009
![Page 160: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/160.jpg)
RangeRange22 - Plot RT - Plot RT ±±2 2 σσ Variance Dynamic Forecast (in the Variance Dynamic Forecast (in the
sample)sample)
![Page 161: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/161.jpg)
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RANGEF
Forecast: RANGEFActual: RANGEForecast sample: 1/02/2008 2/05/2009Included observations: 277
Root Mean Squared Error 39.61914Mean Absolute Error 33.85970Mean Abs. Percent Error 100.0000Theil Inequality Coefficient 1.000000 Bias Proportion 0.730392 Variance Proportion 0.269608 Covariance Proportion 0.000000
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Forecast of Variance
RangeRange22 – Variance Static Forecast – Variance Static Forecast(in the sample)(in the sample)
Training Set: 03/13/1986 - 12/31/2007
Test Set: 01/01/2008 - 02/05/2009
![Page 162: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/162.jpg)
RangeRange22 - Plot RT - Plot RT ±±2 2 σσ Variance Static Forecast (in the Variance Static Forecast (in the
sample)sample)
![Page 163: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/163.jpg)
Volatility ForecastingVolatility Forecasting
from: GARCH(1,1) eXt. from: GARCH(1,1) eXt. modelmodel
![Page 164: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/164.jpg)
GARCH(1,1) eXt.2GARCH(1,1) eXt.2 - Plot - Plot RT RT ±±2 2 σσ
![Page 165: Microsoft - Volatility modeling and analysis](https://reader036.vdocuments.us/reader036/viewer/2022062405/5562d3a7d8b42a49398b4dd0/html5/thumbnails/165.jpg)
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Forecast: RTFActual: RTForecast sample: 1/02/2008 2/05/2009Included observations: 277
Root Mean Squared Error 49.58125Mean Absolute Error 35.33305Mean Abs. Percent Error 99.27798Theil Inequality Coefficient 1.000000 Bias Proportion 0.004929 Variance Proportion 0.995071 Covariance Proportion 0.000000
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GARCH(1,1) eXt.2 – Variance Dynamic GARCH(1,1) eXt.2 – Variance Dynamic ForecastForecast
(in the sample)(in the sample)
Training Set: 03/13/1986 - 12/31/2007
Test Set: 01/01/2008 - 02/05/2009
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GARCH(1,1) eXt.2 - Plot RT GARCH(1,1) eXt.2 - Plot RT ±±2 2 σσ
Variance Dynamic Forecast (in the Variance Dynamic Forecast (in the sample)sample)
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GARCH(1,1) eXt.2 –GARCH(1,1) eXt.2 – Variance Static Variance Static ForecastForecast
(in the sample)(in the sample)
Training Set: 03/13/1986 - 12/31/2007
Test Set: 01/01/2008 - 02/05/2009
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Forecast: RTFActual: RTForecast sample: 1/02/2008 2/05/2009Included observations: 277
Root Mean Squared Error 49.58125Mean Absolute Error 35.33305Mean Abs. Percent Error 99.27798Theil Inequality Coefficient 1.000000 Bias Proportion 0.004929 Variance Proportion 0.995071 Covariance Proportion 0.000000
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GARCH(1,1) eXt.2 - Plot RT GARCH(1,1) eXt.2 - Plot RT ±±2 2 σσ
Variance Static Forecast (in the Variance Static Forecast (in the sample)sample)
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Conditional Variance Conditional Variance ComparisonsComparisons
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Extra Stuff…Extra Stuff…
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S&P 500S&P 500
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RT MSFT Vs. RM S&P500RT MSFT Vs. RM S&P500
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RT MSFT
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RX = RT - RMRX = RT - RM
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RX = RT - RM
9/11Win95Win98monopoly
accuse
European antitrust
action
5,000 emp.
layoffs
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RX - HistogramRX - Histogram
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Series: RXSample 3/13/1986 2/05/2009Observations 5776
Mean 1.149853Median 0.045307Maximum 229.0877Minimum -263.9850Std. Dev. 32.61286Skewness -0.192156Kurtosis 11.08033
Jarque-Bera 15749.09Probability 0.000000
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RX - CorrelogramRX - Correlogram
Sign. Level (5%) = ± 0.025
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RXRX22 - Correlogram - Correlogram
Sign. Level (5%) = ± 0.025
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RX – AR(2) modelRX – AR(2) model
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RXF - AR(2) Static RXF - AR(2) Static ForecastForecast
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RXF
Forecast: RXFActual: RXForecast sample: 3/13/1986 2/05/2009Adjusted sample: 3/18/1986 2/05/2009Included observations: 5774
Root Mean Squared Error 32.49066Mean Absolute Error 21.72832Mean Abs. Percent Error 146.6416Theil Inequality Coefficient 0.952797 Bias Proportion 0.000000 Variance Proportion 0.934372 Covariance Proportion 0.065628
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RX Vs. RXF AR(2) Static RX Vs. RXF AR(2) Static ForecastForecast
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RXF - AR(2) Dynamic RXF - AR(2) Dynamic ForecastForecast
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RXF
Forecast: RXFActual: RXForecast sample: 3/13/1986 2/05/2009Adjusted sample: 3/18/1986 2/05/2009Included observations: 5774
Root Mean Squared Error 32.50845Mean Absolute Error 21.74181Mean Abs. Percent Error 141.7840Theil Inequality Coefficient 0.966035 Bias Proportion 0.000000 Variance Proportion 0.994750 Covariance Proportion 0.005250
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RX AR(2) – Residual PlotRX AR(2) – Residual Plot
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Residual Actual Fitted
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RX AR(2) – Residual Plot RX AR(2) – Residual Plot [2][2]
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RX Residuals
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RX AR(2) – Residual RX AR(2) – Residual HistogramHistogram
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Series: ResidualsSample 3/18/1986 2/05/2009Observations 5774
Mean -1.34e-10Median -1.075838Maximum 229.3795Minimum -265.8949Std. Dev. 32.49348Skewness -0.222536Kurtosis 10.99945
Jarque-Bera 15442.88Probability 0.000000
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RX AR(2) – Residual RX AR(2) – Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RX AR(2) – Squared RX AR(2) – Squared Residual CorrelogramResidual Correlogram
Sign. Level (5%) = ± 0.025
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RX AR(2) – Residual RX AR(2) – Residual ARCH TestARCH Test
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RX – AR(2) – GARCH(1,1) RX – AR(2) – GARCH(1,1) modelmodel
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RX – AR(2) – GARCH(1,1) RX – AR(2) – GARCH(1,1) modelmodel
σ2 = 1,055.5790σ = 32.489675
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RX – AR(2) - GARCH(1,1) RX – AR(2) - GARCH(1,1) Residual PlotResidual Plot
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RX – AR(2) - GARCH(1,1) RX – AR(2) - GARCH(1,1) Conditional Variance PlotConditional Variance Plot
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RX – AR(2) – GARCH(1,1) Residual Vs. Conditional RX – AR(2) – GARCH(1,1) Residual Vs. Conditional Variance PlotVariance Plot
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RX – AR(2) -GARCH(1,1) Std. RX – AR(2) -GARCH(1,1) Std. Residual PlotResidual Plot
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STD_RESID
RX – AR(2) - GARCH(1,1) Residuals Vs. Std. RX – AR(2) - GARCH(1,1) Residuals Vs. Std. Residuals PlotResiduals Plot
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RX – AR(2) - GARCH(1,1) Std. Residuals Vs. RX – AR(2) - GARCH(1,1) Std. Residuals Vs. ResidualsResiduals
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RX – AR(2) - GARCH(1,1) Conditional Variance Vs. Std. RX – AR(2) - GARCH(1,1) Conditional Variance Vs. Std. ResidualsResiduals
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RX – AR(2) - GARCH(1,1) Residual RX – AR(2) - GARCH(1,1) Residual HistogramHistogram
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Series: Standardized ResidualsSample 3/18/1986 2/05/2009Observations 5774
Mean 0.010620Median -0.019988Maximum 6.570933Minimum -13.00676Std. Dev. 0.999150Skewness -0.432622Kurtosis 11.72297
Jarque-Bera 18486.16Probability 0.000000
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RX – AR(2) - GARCH(1,1) Std. Residual RX – AR(2) - GARCH(1,1) Std. Residual CorrelogramCorrelogram
Sign. Level (5%) = ± 0.025
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RX – AR(2) - GARCH(1,1) Squared Std. RX – AR(2) - GARCH(1,1) Squared Std. Residual CorrelogramResidual Correlogram
Sign. Level (5%) = ± 0.025
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RX - AR(2) - GARCH(1,1) – Residual RX - AR(2) - GARCH(1,1) – Residual ARCH TestARCH Test
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RX - AR(2) - GARCH(1,1) – RX - AR(2) - GARCH(1,1) – Variance Dynamic ForecastVariance Dynamic Forecast
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Grazie dell’Attenzione !!!Grazie dell’Attenzione !!!