Microsoft - Volatility modeling and analysis
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Microsoft - Volatility modeling and analysis

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Microsoft - Volatility modeling and analysis Microsoft - Volatility modeling and analysis Presentation Transcript

  • 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 !!!