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Microsoft (MSFT) Augusto Pucci
Overview MSFT – Company Overview MSFT – Return Analysis RT – AR(2) model RT – AR(2) – ARCH(1) model RT – AR(2) – ARCH(2) model RT – AR(2) – GARCH(1,1) model RT – AR(2) – TGARCH(1,1) model Range model -> Range2 model abs(RT) model -> RT2 model RT – GARCH(1,1) model, Extended… RT – GARCH(1,1) model, Extended 2… RT – AR(2) – TGARCH(1,1) ShortFall Volatility Forecasting from TGARCH(1,1) model Volatility Forecasting from GARCH(1,1) eXt.  model Extra Stuff…
Microsoft Campus
Microsoft: Company Overview
Financial Highlights Beta:  1.08 Fiscal Year Ends:  30-June Profitability Profit Margin:  27.80% Operating Margin: 38.06% Return on Assets (ttm): 22.15% Return on Equity (ttm): 50.01% Income Statement Revenue:  61.98B Revenue Per Share:  6.781 Qtrly Revenue Growth: 1.60% Gross Profit: 48.82B EBITDA: 25.94B Net Income Avl to Common: 17.23B Diluted EPS: 1.87 Qtrly Earnings Growth: -11.30% William Henry Gates III   (Seattle, 10/28/1955)
Financial Highlights Balance Sheet Total Cash:  20.30B Total Cash Per Share: 2.283 Total Debt: 2.00B Total Debt/Equity: N/A Current Ratio: 1.591 Book Value Per Share: 3.879 Cash Flow Statement Operating Cash Flow: 20.32B Levered Free Cash Flow: 14.40B Steven Anthony Ballmer   (Detroit, 03/24/1956)
Important Dates 1975  Microsoft founded Jan. 1, 1979  Microsoft moves from Albuquerque, New Mexico to Bellevue, WashingtonJune 25, 1981 Microsoft incorporates Aug. 12, 1981  IBM introduces its personal computer with Microsoft's 16-bit operating system, MS-DOS 1.0 Feb. 26, 1986  Microsoft moves to corporate campus in Redmond, Washington March 13, 1986  Microsoft stock goes public Aug. 1, 1989  Microsoft introduces earliest version of Office suite of productivity applications May 22, 1990  Microsoft launches Windows 3.0 Aug. 24, 1995   Microsoft launches Windows 95 Dec. 7, 1995  Bill Gates outlines Microsoft's commitment to supporting and enhancing the Internet June 25, 1998   Microsoft launches Windows 98 Jan. 13, 2000  Steve Ballmer named president and chief executive officer for Microsoft Feb. 17, 2000  Microsoft launches Windows 2000 Apr. 3, 2000   Microsoft accused of abusive monopoly June 22, 2000  Bill Gates and Steve Ballmer outline Microsoft's .NET strategy for Web services May 31, 2001  Microsoft launches Office XP
Important Dates [2] Oct. 25, 2001  Microsoft launches Windows XP Jan. 15, 2002  Bill Gates outlines Microsoft's commitment to Trustworthy Computing Nov. 7, 2002  Microsoft and partners launch Tablet PC Jan. 16, 2003  Microsoft declares annual dividend April 24, 2003  Microsoft launches Windows Server 2003 Oct. 21, 2003  Microsoft launches Microsoft Office System March, 2004   European antitrust legal action against Microsoft July 20, 2004  Microsoft announces plans to return up to $75 billion to shareholders in dividends and stock buybacks June 15, 2006  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 and Craig Mundie chief research and strategy officer July 20, 2006  Microsoft announces a new $20 billion tender offer and authorizes an additional share-repurchase program of up to $20 billion over five years Jan. 30, 2007  Microsoft launches Windows Vista and the 2007 Microsoft Office System to consumers worldwide Feb. 27, 2008  Microsoft launches Windows Server 2008, SQL Server 2008 and Visual Studio 2008 June 27, 2008  Bill Gates transitions from his day-to-day role at Microsoft to spend more time on his work at The Bill & Melinda Gates Foundation Jan. 2009   Microsoft announces layoffs of up to 5,000 employees
MSFT – Return Analysis
Adj_Close from 03/13/1986 to 02/05/2009 9/11 Win95 Win98 monopoly accuse European antitrust action 5,000 emp. layoffs
RT from 03/13/1986 to 02/05/2009 9/11 Win95 Win98 monopoly accuse European antitrust action 5,000 emp. layoffs
Windows 95 & Windows 98 Win95 Win98
Windows 95 & Windows 98 Win95 Win98
Dot.Com Bubble & 9/11 9/11 monopoly accuse
Dot.Com Bubble & 9/11 9/11 monopoly accuse
European antitrust accuse & massive layoffs European antitrust action 5,000 emp. layoffs
European antitrust accuse & massive layoffs European antitrust action 5,000 emp. layoffs
RT - Histogram
Windows 95 & Windows 98
Dot.Com Bubble & 9/11
RT Synth - Histogram
RT Vs. RT Synth 5776 5776 Observations 9143113. 9136709. Sum Sq. Dev. 8686.960 8147.096 Sum 0.000000 0.066684 Probability 51406.45 5.415586 Jarque-Bera 17.56243   3.076041 Kurtosis -0.619675 -0.064653 Skewness   39.78974   39.77580 Std. Dev. -602.4211 -154.1308 Minimum 283.3044    143.1277 Maximum   0.000000   1.712924 Median   1.503975   1.410508 Mean RT RT_SYNTH
RT Synth
RT Vs. RT Synth [2]
RT Vs. RT Synth [3]
RT - Correlogram Sign. Level (5%) =  ± 0.025
RT 2  - Correlogram Sign. Level (5%) =  ± 0.025
abs(RT) - Correlogram Sign. Level (5%) =  ± 0.025
RT 2
RT 2  - Histogram
abs(RT)
abs(RT) - Histogram
RT – AR(2) model
RTF - AR(2) Static Forecast
RT Vs. RTF AR(2) Static Forecast
RTF - AR(2) Dynamic Forecast
RT AR(2) – Residual Plot
RT AR(2) – Residual Plot [2]
RT AR(2) – Residual Histogram
RT AR(2) – Residual Correlogram Sign. Level (5%) =  ± 0.025
RT AR(2) – Residual ARCH Test
RT – AR(2) – ARCH(1) model
RT – AR(2) – ARCH(1) model σ 2  = 1,618.1026 σ   =  40.225647
RT – ARCH(1) Residual Plot
RT – ARCH(1) Conditional Variance Plot
RT – ARCH(1) Residual Vs. Conditional Variance Plot
RT – ARCH(1) Std. Residual Plot
RT – ARCH(1) Residuals Vs. Std. Residuals Plot
RT – ARCH(1) Std. Residuals Vs. Residuals
RT – ARCH(1) Conditional Variance Vs. Std. Residuals
RT – ARCH(1) Residual Histogram
RT – ARCH(1) Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT – ARCH(1) Squared Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT ARCH(1) – Residual ARCH Test
RT – AR(2) – ARCH(2) model
RT – AR(2) – ARCH(2) model σ 2  = 1,635.1865 σ   =  40.437440
RT – ARCH(2) Residual Plot
RT – ARCH(2) Conditional Variance Plot
RT – ARCH(2) Residual Vs. Conditional Variance Plot
RT – ARCH(2) Std. Residual Plot
RT – ARCH(2) Residuals Vs. Std. Residuals Plot
RT – ARCH(2) Std. Residuals Vs. Residuals
RT – ARCH(2) Conditional Variance Vs. Std. Residuals
RT – ARCH(2) Residual Histogram
RT – ARCH(2) Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT – ARCH(2) Squared Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT ARCH(2) – Residual ARCH Test
RT – AR(2) – GARCH(1,1) model
RT – AR(2) – GARCH(1,1) model σ 2  = 2,391.1118 σ   =  48.898996
RT – GARCH(1,1) Residual Plot
RT – GARCH(1,1) Conditional Variance Plot
RT – GARCH(1,1) Residual Vs. Conditional Variance Plot
RT – GARCH(1,1) Std. Residual Plot
RT – GARCH(1,1) Residuals Vs. Std. Residuals Plot
RT – GARCH(1,1) Std. Residuals Vs. Residuals
RT – GARCH(1,1) Conditional Variance Vs. Std. Residuals
RT – GARCH(1,1) Residual Histogram
RT – GARCH(1,1) Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT – GARCH(1,1) Squared Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT GARCH(1,1) – Residual ARCH Test
RT GARCH(1,1) - Sign Bias Test
RT GARCH(1,1) – Negative Size Bias Test
RT – AR(2) – TGARCH(1,1) model
RT – AR(2) – TGARCH(1,1) model σ 2  = 2,656.5854 σ   =  51.542074
RT – TGARCH(1,1) Residual Plot
RT – TGARCH(1,1) Conditional Variance Plot
RT – TGARCH(1,1) Residual Vs. Conditional Variance Plot
RT – TGARCH(1,1) Std. Residual Plot
RT – TGARCH(1,1) Residuals Vs. Std. Residuals Plot
RT – TGARCH(1,1) Std. Residuals Vs. Residuals
RT – TGARCH(1,1) Conditional Variance Vs. Std. Residuals
RT – TGARCH(1,1) Residual Histogram
RT – TGARCH(1,1) Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT – TGARCH(1,1) Squared Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT TGARCH(1,1) – Residual ARCH Test
Range & Range 2 range = log(high/low)*sqr(252/(4*log(2)))*100 Range model ->  Range 2  model
Range 2  model
E[ Range 2 t  | I (t-1)  ] (from Range MEM)
Range 2 t   Vs. E[ Range 2 t  | I (t-1)  ]
abs(RT) model -> RT 2  model
RT 2  model
E[ RT 2 t  | I (t-1)  ] (from abs(RT) MEM)
RT 2 t   Vs. E[ RT 2 t  | I (t-1)  ]
RT – GARCH(1,1) model Extended…
RT – GARCH(1,1) eXt. model
RT – GARCH(1,1) eXt.   Residual Plot
RT – GARCH(1,1) eXt. Conditional Variance Plot
RT – GARCH(1,1) eXt. Residual Vs. Conditional Variance Plot
RT – GARCH(1,1) eXt. Std. Residual Plot
RT – GARCH(1,1) eXt. Residuals Vs. Std. Residuals Plot
RT – GARCH(1,1) eXt. Std. Residuals Vs. Residuals
RT – GARCH(1,1) eXt. Conditional Variance Vs. Std. Residuals
RT – GARCH(1,1) eXt. Residual Histogram
RT – GARCH(1,1) eXt. Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT – GARCH(1,1) eXt. Squared Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT - GARCH(1,1) eXt – Residual ARCH Test
RT – GARCH(1,1) model Extended 2…
RT – GARCH(1,1) eXt.2 model
RT – GARCH(1,1) eXt.2   Residual Plot
RT – GARCH(1,1) eXt.2 Conditional Variance Plot
RT – GARCH(1,1) eXt.2 Residual Vs. Conditional Variance Plot
RT – GARCH(1,1) eXt.2 Std. Residual Plot
RT – GARCH(1,1) eXt.2 Residuals Vs. Std. Residuals Plot
RT – GARCH(1,1) eXt.2 Std. Residuals Vs. Residuals
RT – GARCH(1,1) eXt.2 Conditional Variance Vs. Std. Residuals
RT – GARCH(1,1) eXt.2 Residual Histogram
RT – GARCH(1,1) eXt.2 Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT – GARCH(1,1) eXt.2 Squared Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RT - GARCH(1,1) eXt.2 – Residual ARCH Test
RT – AR(2) – TGARCH(1,1) ShortFall
RT Vs. Expected Loss [ -1.000*sqr(GARCH) ] Z α  = 1.000
Shortfall  [ min{rt-loss_hat,0}] Z α  = 1.000
Shortfall Histogram  [12.1406 %] Z α  = 1.000 [12.1406 %]
RT Vs. Expected Loss [ -2.000*sqr(GARCH) ] Z α  = 2.000
Shortfall  [ min{rt-loss_hat,0}] Z α  = 2.000
Shortfall Histogram  [1.9050 %] Z α  = 2.000 [1.9050 %]
RT Vs. Expected Loss [ -2.250*sqr(GARCH) ] Z α  = 2.250
Shortfall  [ min{rt-loss_hat,0}] Z α  = 2.250
Shortfall Histogram  [1.3508 %] Z α  = 2.250 [1.3508 %]
RT Vs. Expected Loss [ -2.250*sqr(GARCH) ] Z α  = 2.426
Shortfall  [ min{rt-loss_hat,0}] Z α  = 2.426
Shortfall Histogram  [1.0737 %] Z α  = 2.426 [1.0737 %]
RT Vs. Expected Loss [ -3.000*sqr(GARCH) ] Z α  = 3.000
Shortfall  [ min{rt-loss_hat,0}] Z α  = 3.000
Shortfall Histogram  [0.5542 %] Z α  = 3.000 0.5542 %]
RT Vs. Expected Loss [ -4.000*sqr(GARCH) ] Z α  = 4.000
Shortfall  [ min{rt-loss_hat,0}] Z α  = 4.000
Shortfall Histogram  [0.1383 %] Z α  = 4.000 [0.1383 %]
Volatility Forecasting from: TGARCH(1,1) model
TGARCH(1,1) - Plot RT  ± 2  σ
TGARCH(1,1) – Variance Dynamic Forecast (out of the sample) 02/06/2009  - 02/06/2010
TGARCH(1,1) - Plot RT  ± 2  σ   Variance Dynamic Forecast (out of the sample)
TGARCH(1,1) – Variance Dynamic Forecast (in the sample) Training Set:  03/13/1986 - 12/31/2007 Test Set:  01/01/2008 - 02/05/2009
TGARCH(1,1) - Plot RT  ± 2  σ   Variance Dynamic Forecast (in the sample)
TGARCH(1,1) – Variance Static Forecast (in the sample) Training Set:  03/13/1986 - 12/31/2007 Test Set:  01/01/2008 - 02/05/2009
TGARCH(1,1) - Plot RT  ± 2  σ   Variance Static Forecast (in the sample)
Volatility Forecasting from: Range 2  model
Range 2  - Plot RT  ± 2  σ
Range 2  – Variance Dynamic Forecast (in the sample) Training Set:  03/13/1986 - 12/31/2007 Test Set:  01/01/2008 - 02/05/2009
Range 2  - Plot RT  ± 2  σ   Variance Dynamic Forecast (in the sample)
Range 2  – Variance Static Forecast (in the sample) Training Set:  03/13/1986 - 12/31/2007 Test Set:  01/01/2008 - 02/05/2009
Range 2  - Plot RT  ± 2  σ   Variance Static Forecast (in the sample)
Volatility Forecasting from: GARCH(1,1) eXt. model
GARCH(1,1) eXt.2   - Plot RT  ± 2  σ
GARCH(1,1) eXt.2 – Variance Dynamic Forecast (in the sample) Training Set:  03/13/1986 - 12/31/2007 Test Set:  01/01/2008 - 02/05/2009
GARCH(1,1) eXt.2 - Plot RT  ± 2  σ   Variance Dynamic Forecast (in the sample)
GARCH(1,1) eXt.2 –  Variance Static Forecast (in the sample) Training Set:  03/13/1986 - 12/31/2007 Test Set:  01/01/2008 - 02/05/2009
GARCH(1,1) eXt.2 - Plot RT  ± 2  σ   Variance Static Forecast (in the sample)
Conditional Variance Comparisons
Extra Stuff…
S&P 500
RT MSFT Vs. RM S&P500
RX = RT - RM 9/11 Win95 Win98 monopoly accuse European antitrust action 5,000 emp. layoffs
RX - Histogram
RX - Correlogram Sign. Level (5%) =  ± 0.025
RX 2  - Correlogram Sign. Level (5%) =  ± 0.025
RX – AR(2) model
RXF - AR(2) Static Forecast
RX Vs. RXF AR(2) Static Forecast
RXF - AR(2) Dynamic Forecast
RX AR(2) – Residual Plot
RX AR(2) – Residual Plot [2]
RX AR(2) – Residual Histogram
RX AR(2) – Residual Correlogram Sign. Level (5%) =  ± 0.025
RX AR(2) – Squared Residual Correlogram Sign. Level (5%) =  ± 0.025
RX AR(2) – Residual ARCH Test
RX – AR(2) – GARCH(1,1) model
RX – AR(2) – GARCH(1,1) model σ 2  = 1,055.5790 σ   =  32.489675
RX – AR(2) - GARCH(1,1) Residual Plot
RX – AR(2) - GARCH(1,1) Conditional Variance Plot
RX – AR(2) – GARCH(1,1) Residual Vs. Conditional Variance Plot
RX – AR(2) -GARCH(1,1) Std. Residual Plot
RX – AR(2) - GARCH(1,1) Residuals Vs. Std. Residuals Plot
RX – AR(2) - GARCH(1,1) Std. Residuals Vs. Residuals
RX – AR(2) - GARCH(1,1) Conditional Variance Vs. Std. Residuals
RX – AR(2) - GARCH(1,1) Residual Histogram
RX – AR(2) - GARCH(1,1) Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RX – AR(2) - GARCH(1,1) Squared Std. Residual Correlogram Sign. Level (5%) =  ± 0.025
RX - AR(2) - GARCH(1,1) – Residual ARCH Test
RX - AR(2) - GARCH(1,1) – Variance Dynamic Forecast
Grazie dell’Attenzione !!!

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Microsoft - Volatility modeling and analysis