Microsoft (MSFT) Augusto Pucci
Overview <ul><li>MSFT – Company Overview </li></ul><ul><li>MSFT – Return Analysis </li></ul><ul><li>RT – AR(2) model </li>...
Microsoft Campus
Microsoft: Company Overview
Financial Highlights <ul><li>Beta:  1.08 </li></ul><ul><li>Fiscal Year Ends:  30-June </li></ul><ul><li>Profitability Prof...
Financial Highlights <ul><li>Balance Sheet </li></ul><ul><li>Total Cash:  20.30B </li></ul><ul><li>Total Cash Per Share: 2...
Important Dates <ul><li>1975  Microsoft founded </li></ul><ul><li>Jan. 1, 1979  Microsoft moves from Albuquerque, New Mexi...
Important Dates [2] <ul><li>Oct. 25, 2001  Microsoft launches Windows XP </li></ul><ul><li>Jan. 15, 2002  Bill Gates outli...
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 ...
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 <ul><li>range = log(high/low)*sqr(252/(4*log(2)))*100 </li></ul><ul><li>Range model ->  Range 2  model </l...
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/...
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 - 02/0...
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/...
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 - 02/05/2...
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 ...
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 ...
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

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Microsoft - Volatility modeling and analysis

  1. 1. Microsoft (MSFT) Augusto Pucci
  2. 2. Overview <ul><li>MSFT – Company Overview </li></ul><ul><li>MSFT – Return Analysis </li></ul><ul><li>RT – AR(2) model </li></ul><ul><li>RT – AR(2) – ARCH(1) model </li></ul><ul><li>RT – AR(2) – ARCH(2) model </li></ul><ul><li>RT – AR(2) – GARCH(1,1) model </li></ul><ul><li>RT – AR(2) – TGARCH(1,1) model </li></ul><ul><li>Range model -> Range2 model </li></ul><ul><li>abs(RT) model -> RT2 model </li></ul><ul><li>RT – GARCH(1,1) model, Extended… </li></ul><ul><li>RT – GARCH(1,1) model, Extended 2… </li></ul><ul><li>RT – AR(2) – TGARCH(1,1) ShortFall </li></ul><ul><li>Volatility Forecasting from TGARCH(1,1) model </li></ul><ul><li>Volatility Forecasting from GARCH(1,1) eXt. model </li></ul><ul><li>Extra Stuff… </li></ul>
  3. 3. Microsoft Campus
  4. 4. Microsoft: Company Overview
  5. 5. Financial Highlights <ul><li>Beta: 1.08 </li></ul><ul><li>Fiscal Year Ends: 30-June </li></ul><ul><li>Profitability Profit Margin: 27.80% </li></ul><ul><li>Operating Margin: 38.06% </li></ul><ul><li>Return on Assets (ttm): 22.15% </li></ul><ul><li>Return on Equity (ttm): 50.01% </li></ul><ul><li>Income Statement </li></ul><ul><li>Revenue: 61.98B </li></ul><ul><li>Revenue Per Share: 6.781 </li></ul><ul><li>Qtrly Revenue Growth: 1.60% </li></ul><ul><li>Gross Profit: 48.82B </li></ul><ul><li>EBITDA: 25.94B </li></ul><ul><li>Net Income Avl to Common: 17.23B </li></ul><ul><li>Diluted EPS: 1.87 </li></ul><ul><li>Qtrly Earnings Growth: -11.30% </li></ul>William Henry Gates III (Seattle, 10/28/1955)
  6. 6. Financial Highlights <ul><li>Balance Sheet </li></ul><ul><li>Total Cash: 20.30B </li></ul><ul><li>Total Cash Per Share: 2.283 </li></ul><ul><li>Total Debt: 2.00B </li></ul><ul><li>Total Debt/Equity: N/A </li></ul><ul><li>Current Ratio: 1.591 </li></ul><ul><li>Book Value Per Share: 3.879 </li></ul><ul><li>Cash Flow Statement </li></ul><ul><li>Operating Cash Flow: 20.32B </li></ul><ul><li>Levered Free Cash Flow: 14.40B </li></ul>Steven Anthony Ballmer (Detroit, 03/24/1956)
  7. 7. Important Dates <ul><li>1975 Microsoft founded </li></ul><ul><li>Jan. 1, 1979 Microsoft moves from Albuquerque, New Mexico to Bellevue, WashingtonJune </li></ul><ul><li>25, 1981 Microsoft incorporates </li></ul><ul><li>Aug. 12, 1981 IBM introduces its personal computer with Microsoft's 16-bit operating system, MS-DOS 1.0 </li></ul><ul><li>Feb. 26, 1986 Microsoft moves to corporate campus in Redmond, Washington </li></ul><ul><li>March 13, 1986 Microsoft stock goes public </li></ul><ul><li>Aug. 1, 1989 Microsoft introduces earliest version of Office suite of productivity applications </li></ul><ul><li>May 22, 1990 Microsoft launches Windows 3.0 </li></ul><ul><li>Aug. 24, 1995 Microsoft launches Windows 95 </li></ul><ul><li>Dec. 7, 1995 Bill Gates outlines Microsoft's commitment to supporting and enhancing the Internet </li></ul><ul><li>June 25, 1998 Microsoft launches Windows 98 </li></ul><ul><li>Jan. 13, 2000 Steve Ballmer named president and chief executive officer for Microsoft </li></ul><ul><li>Feb. 17, 2000 Microsoft launches Windows 2000 </li></ul><ul><li>Apr. 3, 2000 Microsoft accused of abusive monopoly </li></ul><ul><li>June 22, 2000 Bill Gates and Steve Ballmer outline Microsoft's .NET strategy for Web services </li></ul><ul><li>May 31, 2001 Microsoft launches Office XP </li></ul>
  8. 8. Important Dates [2] <ul><li>Oct. 25, 2001 Microsoft launches Windows XP </li></ul><ul><li>Jan. 15, 2002 Bill Gates outlines Microsoft's commitment to Trustworthy Computing </li></ul><ul><li>Nov. 7, 2002 Microsoft and partners launch Tablet PC </li></ul><ul><li>Jan. 16, 2003 Microsoft declares annual dividend </li></ul><ul><li>April 24, 2003 Microsoft launches Windows Server 2003 </li></ul><ul><li>Oct. 21, 2003 Microsoft launches Microsoft Office System </li></ul><ul><li>March, 2004 European antitrust legal action against Microsoft </li></ul><ul><li>July 20, 2004 Microsoft announces plans to return up to $75 billion to shareholders in dividends and stock buybacks </li></ul><ul><li>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 </li></ul><ul><li>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 </li></ul><ul><li>Jan. 30, 2007 Microsoft launches Windows Vista and the 2007 Microsoft Office System to consumers worldwide </li></ul><ul><li>Feb. 27, 2008 Microsoft launches Windows Server 2008, SQL Server 2008 and Visual Studio 2008 </li></ul><ul><li>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 </li></ul><ul><li>Jan. 2009 Microsoft announces layoffs of up to 5,000 employees </li></ul>
  9. 9. MSFT – Return Analysis
  10. 10. Adj_Close from 03/13/1986 to 02/05/2009 9/11 Win95 Win98 monopoly accuse European antitrust action 5,000 emp. layoffs
  11. 11. RT from 03/13/1986 to 02/05/2009 9/11 Win95 Win98 monopoly accuse European antitrust action 5,000 emp. layoffs
  12. 12. Windows 95 & Windows 98 Win95 Win98
  13. 13. Windows 95 & Windows 98 Win95 Win98
  14. 14. Dot.Com Bubble & 9/11 9/11 monopoly accuse
  15. 15. Dot.Com Bubble & 9/11 9/11 monopoly accuse
  16. 16. European antitrust accuse & massive layoffs European antitrust action 5,000 emp. layoffs
  17. 17. European antitrust accuse & massive layoffs European antitrust action 5,000 emp. layoffs
  18. 18. RT - Histogram
  19. 19. Windows 95 & Windows 98
  20. 20. Dot.Com Bubble & 9/11
  21. 21. RT Synth - Histogram
  22. 22. 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
  23. 23. RT Synth
  24. 24. RT Vs. RT Synth [2]
  25. 25. RT Vs. RT Synth [3]
  26. 26. RT - Correlogram Sign. Level (5%) = ± 0.025
  27. 27. RT 2 - Correlogram Sign. Level (5%) = ± 0.025
  28. 28. abs(RT) - Correlogram Sign. Level (5%) = ± 0.025
  29. 29. RT 2
  30. 30. RT 2 - Histogram
  31. 31. abs(RT)
  32. 32. abs(RT) - Histogram
  33. 33. RT – AR(2) model
  34. 34. RTF - AR(2) Static Forecast
  35. 35. RT Vs. RTF AR(2) Static Forecast
  36. 36. RTF - AR(2) Dynamic Forecast
  37. 37. RT AR(2) – Residual Plot
  38. 38. RT AR(2) – Residual Plot [2]
  39. 39. RT AR(2) – Residual Histogram
  40. 40. RT AR(2) – Residual Correlogram Sign. Level (5%) = ± 0.025
  41. 41. RT AR(2) – Residual ARCH Test
  42. 42. RT – AR(2) – ARCH(1) model
  43. 43. RT – AR(2) – ARCH(1) model σ 2 = 1,618.1026 σ = 40.225647
  44. 44. RT – ARCH(1) Residual Plot
  45. 45. RT – ARCH(1) Conditional Variance Plot
  46. 46. RT – ARCH(1) Residual Vs. Conditional Variance Plot
  47. 47. RT – ARCH(1) Std. Residual Plot
  48. 48. RT – ARCH(1) Residuals Vs. Std. Residuals Plot
  49. 49. RT – ARCH(1) Std. Residuals Vs. Residuals
  50. 50. RT – ARCH(1) Conditional Variance Vs. Std. Residuals
  51. 51. RT – ARCH(1) Residual Histogram
  52. 52. RT – ARCH(1) Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  53. 53. RT – ARCH(1) Squared Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  54. 54. RT ARCH(1) – Residual ARCH Test
  55. 55. RT – AR(2) – ARCH(2) model
  56. 56. RT – AR(2) – ARCH(2) model σ 2 = 1,635.1865 σ = 40.437440
  57. 57. RT – ARCH(2) Residual Plot
  58. 58. RT – ARCH(2) Conditional Variance Plot
  59. 59. RT – ARCH(2) Residual Vs. Conditional Variance Plot
  60. 60. RT – ARCH(2) Std. Residual Plot
  61. 61. RT – ARCH(2) Residuals Vs. Std. Residuals Plot
  62. 62. RT – ARCH(2) Std. Residuals Vs. Residuals
  63. 63. RT – ARCH(2) Conditional Variance Vs. Std. Residuals
  64. 64. RT – ARCH(2) Residual Histogram
  65. 65. RT – ARCH(2) Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  66. 66. RT – ARCH(2) Squared Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  67. 67. RT ARCH(2) – Residual ARCH Test
  68. 68. RT – AR(2) – GARCH(1,1) model
  69. 69. RT – AR(2) – GARCH(1,1) model σ 2 = 2,391.1118 σ = 48.898996
  70. 70. RT – GARCH(1,1) Residual Plot
  71. 71. RT – GARCH(1,1) Conditional Variance Plot
  72. 72. RT – GARCH(1,1) Residual Vs. Conditional Variance Plot
  73. 73. RT – GARCH(1,1) Std. Residual Plot
  74. 74. RT – GARCH(1,1) Residuals Vs. Std. Residuals Plot
  75. 75. RT – GARCH(1,1) Std. Residuals Vs. Residuals
  76. 76. RT – GARCH(1,1) Conditional Variance Vs. Std. Residuals
  77. 77. RT – GARCH(1,1) Residual Histogram
  78. 78. RT – GARCH(1,1) Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  79. 79. RT – GARCH(1,1) Squared Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  80. 80. RT GARCH(1,1) – Residual ARCH Test
  81. 81. RT GARCH(1,1) - Sign Bias Test
  82. 82. RT GARCH(1,1) – Negative Size Bias Test
  83. 83. RT – AR(2) – TGARCH(1,1) model
  84. 84. RT – AR(2) – TGARCH(1,1) model σ 2 = 2,656.5854 σ = 51.542074
  85. 85. RT – TGARCH(1,1) Residual Plot
  86. 86. RT – TGARCH(1,1) Conditional Variance Plot
  87. 87. RT – TGARCH(1,1) Residual Vs. Conditional Variance Plot
  88. 88. RT – TGARCH(1,1) Std. Residual Plot
  89. 89. RT – TGARCH(1,1) Residuals Vs. Std. Residuals Plot
  90. 90. RT – TGARCH(1,1) Std. Residuals Vs. Residuals
  91. 91. RT – TGARCH(1,1) Conditional Variance Vs. Std. Residuals
  92. 92. RT – TGARCH(1,1) Residual Histogram
  93. 93. RT – TGARCH(1,1) Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  94. 94. RT – TGARCH(1,1) Squared Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  95. 95. RT TGARCH(1,1) – Residual ARCH Test
  96. 96. Range & Range 2 <ul><li>range = log(high/low)*sqr(252/(4*log(2)))*100 </li></ul><ul><li>Range model -> Range 2 model </li></ul>
  97. 97. Range 2 model
  98. 98. E[ Range 2 t | I (t-1) ] (from Range MEM)
  99. 99. Range 2 t Vs. E[ Range 2 t | I (t-1) ]
  100. 100. abs(RT) model -> RT 2 model
  101. 101. RT 2 model
  102. 102. E[ RT 2 t | I (t-1) ] (from abs(RT) MEM)
  103. 103. RT 2 t Vs. E[ RT 2 t | I (t-1) ]
  104. 104. RT – GARCH(1,1) model Extended…
  105. 105. RT – GARCH(1,1) eXt. model
  106. 106. RT – GARCH(1,1) eXt. Residual Plot
  107. 107. RT – GARCH(1,1) eXt. Conditional Variance Plot
  108. 108. RT – GARCH(1,1) eXt. Residual Vs. Conditional Variance Plot
  109. 109. RT – GARCH(1,1) eXt. Std. Residual Plot
  110. 110. RT – GARCH(1,1) eXt. Residuals Vs. Std. Residuals Plot
  111. 111. RT – GARCH(1,1) eXt. Std. Residuals Vs. Residuals
  112. 112. RT – GARCH(1,1) eXt. Conditional Variance Vs. Std. Residuals
  113. 113. RT – GARCH(1,1) eXt. Residual Histogram
  114. 114. RT – GARCH(1,1) eXt. Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  115. 115. RT – GARCH(1,1) eXt. Squared Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  116. 116. RT - GARCH(1,1) eXt – Residual ARCH Test
  117. 117. RT – GARCH(1,1) model Extended 2…
  118. 118. RT – GARCH(1,1) eXt.2 model
  119. 119. RT – GARCH(1,1) eXt.2 Residual Plot
  120. 120. RT – GARCH(1,1) eXt.2 Conditional Variance Plot
  121. 121. RT – GARCH(1,1) eXt.2 Residual Vs. Conditional Variance Plot
  122. 122. RT – GARCH(1,1) eXt.2 Std. Residual Plot
  123. 123. RT – GARCH(1,1) eXt.2 Residuals Vs. Std. Residuals Plot
  124. 124. RT – GARCH(1,1) eXt.2 Std. Residuals Vs. Residuals
  125. 125. RT – GARCH(1,1) eXt.2 Conditional Variance Vs. Std. Residuals
  126. 126. RT – GARCH(1,1) eXt.2 Residual Histogram
  127. 127. RT – GARCH(1,1) eXt.2 Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  128. 128. RT – GARCH(1,1) eXt.2 Squared Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  129. 129. RT - GARCH(1,1) eXt.2 – Residual ARCH Test
  130. 130. RT – AR(2) – TGARCH(1,1) ShortFall
  131. 131. RT Vs. Expected Loss [ -1.000*sqr(GARCH) ] Z α = 1.000
  132. 132. Shortfall [ min{rt-loss_hat,0}] Z α = 1.000
  133. 133. Shortfall Histogram [12.1406 %] Z α = 1.000 [12.1406 %]
  134. 134. RT Vs. Expected Loss [ -2.000*sqr(GARCH) ] Z α = 2.000
  135. 135. Shortfall [ min{rt-loss_hat,0}] Z α = 2.000
  136. 136. Shortfall Histogram [1.9050 %] Z α = 2.000 [1.9050 %]
  137. 137. RT Vs. Expected Loss [ -2.250*sqr(GARCH) ] Z α = 2.250
  138. 138. Shortfall [ min{rt-loss_hat,0}] Z α = 2.250
  139. 139. Shortfall Histogram [1.3508 %] Z α = 2.250 [1.3508 %]
  140. 140. RT Vs. Expected Loss [ -2.250*sqr(GARCH) ] Z α = 2.426
  141. 141. Shortfall [ min{rt-loss_hat,0}] Z α = 2.426
  142. 142. Shortfall Histogram [1.0737 %] Z α = 2.426 [1.0737 %]
  143. 143. RT Vs. Expected Loss [ -3.000*sqr(GARCH) ] Z α = 3.000
  144. 144. Shortfall [ min{rt-loss_hat,0}] Z α = 3.000
  145. 145. Shortfall Histogram [0.5542 %] Z α = 3.000 0.5542 %]
  146. 146. RT Vs. Expected Loss [ -4.000*sqr(GARCH) ] Z α = 4.000
  147. 147. Shortfall [ min{rt-loss_hat,0}] Z α = 4.000
  148. 148. Shortfall Histogram [0.1383 %] Z α = 4.000 [0.1383 %]
  149. 149. Volatility Forecasting from: TGARCH(1,1) model
  150. 150. TGARCH(1,1) - Plot RT ± 2 σ
  151. 151. TGARCH(1,1) – Variance Dynamic Forecast (out of the sample) 02/06/2009 - 02/06/2010
  152. 152. TGARCH(1,1) - Plot RT ± 2 σ Variance Dynamic Forecast (out of the sample)
  153. 153. 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
  154. 154. TGARCH(1,1) - Plot RT ± 2 σ Variance Dynamic Forecast (in the sample)
  155. 155. 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
  156. 156. TGARCH(1,1) - Plot RT ± 2 σ Variance Static Forecast (in the sample)
  157. 157. Volatility Forecasting from: Range 2 model
  158. 158. Range 2 - Plot RT ± 2 σ
  159. 159. Range 2 – Variance Dynamic Forecast (in the sample) Training Set: 03/13/1986 - 12/31/2007 Test Set: 01/01/2008 - 02/05/2009
  160. 160. Range 2 - Plot RT ± 2 σ Variance Dynamic Forecast (in the sample)
  161. 161. Range 2 – Variance Static Forecast (in the sample) Training Set: 03/13/1986 - 12/31/2007 Test Set: 01/01/2008 - 02/05/2009
  162. 162. Range 2 - Plot RT ± 2 σ Variance Static Forecast (in the sample)
  163. 163. Volatility Forecasting from: GARCH(1,1) eXt. model
  164. 164. GARCH(1,1) eXt.2 - Plot RT ± 2 σ
  165. 165. 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
  166. 166. GARCH(1,1) eXt.2 - Plot RT ± 2 σ Variance Dynamic Forecast (in the sample)
  167. 167. 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
  168. 168. GARCH(1,1) eXt.2 - Plot RT ± 2 σ Variance Static Forecast (in the sample)
  169. 169. Conditional Variance Comparisons
  170. 170. Extra Stuff…
  171. 171. S&P 500
  172. 172. RT MSFT Vs. RM S&P500
  173. 173. RX = RT - RM 9/11 Win95 Win98 monopoly accuse European antitrust action 5,000 emp. layoffs
  174. 174. RX - Histogram
  175. 175. RX - Correlogram Sign. Level (5%) = ± 0.025
  176. 176. RX 2 - Correlogram Sign. Level (5%) = ± 0.025
  177. 177. RX – AR(2) model
  178. 178. RXF - AR(2) Static Forecast
  179. 179. RX Vs. RXF AR(2) Static Forecast
  180. 180. RXF - AR(2) Dynamic Forecast
  181. 181. RX AR(2) – Residual Plot
  182. 182. RX AR(2) – Residual Plot [2]
  183. 183. RX AR(2) – Residual Histogram
  184. 184. RX AR(2) – Residual Correlogram Sign. Level (5%) = ± 0.025
  185. 185. RX AR(2) – Squared Residual Correlogram Sign. Level (5%) = ± 0.025
  186. 186. RX AR(2) – Residual ARCH Test
  187. 187. RX – AR(2) – GARCH(1,1) model
  188. 188. RX – AR(2) – GARCH(1,1) model σ 2 = 1,055.5790 σ = 32.489675
  189. 189. RX – AR(2) - GARCH(1,1) Residual Plot
  190. 190. RX – AR(2) - GARCH(1,1) Conditional Variance Plot
  191. 191. RX – AR(2) – GARCH(1,1) Residual Vs. Conditional Variance Plot
  192. 192. RX – AR(2) -GARCH(1,1) Std. Residual Plot
  193. 193. RX – AR(2) - GARCH(1,1) Residuals Vs. Std. Residuals Plot
  194. 194. RX – AR(2) - GARCH(1,1) Std. Residuals Vs. Residuals
  195. 195. RX – AR(2) - GARCH(1,1) Conditional Variance Vs. Std. Residuals
  196. 196. RX – AR(2) - GARCH(1,1) Residual Histogram
  197. 197. RX – AR(2) - GARCH(1,1) Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  198. 198. RX – AR(2) - GARCH(1,1) Squared Std. Residual Correlogram Sign. Level (5%) = ± 0.025
  199. 199. RX - AR(2) - GARCH(1,1) – Residual ARCH Test
  200. 200. RX - AR(2) - GARCH(1,1) – Variance Dynamic Forecast
  201. 201. Grazie dell’Attenzione !!!
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