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Semivariance Significance

Semivariance Significance. Baishi Wu, 2/27/08. Outline. Motivation Background Math Data Preparation Basic Jump Data Semivariance Correlation Matrix Summary Correlograms Future. Introduction.

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Semivariance Significance

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  1. Semivariance Significance Baishi Wu, 2/27/08

  2. Outline • Motivation • Background Math • Data Preparation • Basic Jump Data • Semivariance • Correlation Matrix Summary • Correlograms • Future

  3. Introduction • Used Paper by Barndorff-Nielsen, Kinnebrock, and Shephard (2008) “Measuring downside risk – realized semivariance” as the model • Examine new realized semivariance and bipower downward variation statistics to test for jumps in this model as well as solely upward variation • Correlated the results against one another as well, regressed lagged results, created correlograms

  4. Equations • Realized Volatility (RV) • Bipower Variance (BV)

  5. Equations • Realized Semivariance (RS) • Running an “if” loop to only take values of the returns if they are less than zero • Separated into different return matrices, then found the realized variance with those new matrices • Bipower Downard Variance (BPDV)

  6. Equations • Tri-Power Quarticity • Relative Jump • Daily open to close returns (ri) ri = log(priceclose) – log(priceopen)

  7. Equations • Max Version z-Statistic (Tri-Power) • Take one sided significance at .999 level, or z = 3.09

  8. Data • Collected at five minute intervals • First data point collected is the fifth entry for that day while the last data point is the last entry of the day (as there are exactly 385) • Three stocks are analyzed because they are the 12th, 13th and 14th stocks in the S&P 500 • Two stocks have 2669 days, the last one started a little later and has 2665 days only

  9. Altria Group (Philip Morris) Altria Group

  10. Realized Volatility, Bipower Variance Altria Group

  11. Z-Scores Altria Group

  12. Intel Corp. Intel Corp.

  13. Realized Volatility, Bipower Variance Intel Corp.

  14. Z-Scores Intel Corp.

  15. Pfizer Pfizer

  16. Realized Volatility, Bipower Variance Pfizer

  17. Z-Scores Pfizer

  18. Semivariance, Upvariance Altria Group

  19. Bipower Downward Variation Altria Group

  20. Summary Information • Unlike the literature, there is no real sign that RS provides a significantly higher correlation to the daily open/close return than RV does. upRV is actually less than RV. Altria Group

  21. Semivariance, Upvariance Intel Corp

  22. Bipower Downward Variation Intel Corp

  23. Summary Information • In this case, the upRV and the RS have a much higher correlation to the returns than the RV does. This seems to imply that there is predictability through time with this statistic. Intel Corp.

  24. Semivariance, Upvariance Pfizer

  25. Bipower Downward Variation Pfizer

  26. Summary Information • Again, the correlation with upRV and RS is significantly higher than RV. Is there anything about the dataset that seems to confirm the stronger performance of semivariance? Pfizer

  27. Correlogram • Graph of autocorrelations versus time lags, where autocorrelations measure the strength of a relationship between observations as a function of time separation between them • In the paper, it is suggested the the realised semivariance has much more dependence in it than RV and RV-RS (which I’m assuming is upRV since you can’t correlate two variables… can only do it with time)

  28. Correlogram – Realized Variance Altria Group

  29. Correlogram – Realized Semivariance Altria Group

  30. Correlogram – Realized upVariance Altria Group

  31. Correlogram – Realized Variance Intel Corp

  32. Correlogram – Realized Semivariance Intel Corp

  33. Correlogram – Realized upVariance Intel Corp

  34. Correlogram – Realized Variance Pfizer

  35. Correlogram – Realized Semivariance Pfizer

  36. Correlogram – Realized upVariance Pfizer

  37. Future • None of the correlograms proved that RS had better autocorrelation statistics than RV or upRV… • Since two of the three stocks demonstrated impressive improvements in correlation of closing returns with the new semivariance statistics, should we extend this to further lagged models and GARCH analysis?

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