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Semivariance Significance

Explore downside risk measurement using realized semivariance model on Altria Group and Apple stocks. Compare results, analyze z-scores, address code issues, and suggest improvements.

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Semivariance Significance

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  1. Semivariance Significance Baishi Wu, 2/13/08

  2. Outline • Motivation • Background Math • Data Preparation • Altria Group/Phillip Morris (MO) Plots • Apple (APPL) Plots • Summary Statistics • 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, ought to focus on squared negative jumps • Also did a focus on only positive jumps and computed z-scores for the following as well • The separation of RS from RV is supposed to beat out the prediction mechanism used solely on GARCH memory

  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 in order to solely decreases • Bipower Downard Variance (BPDV) • BPDV = RS – (1/2)BV • if r(i,j) <= 0 • RS(1, j) = sum(r(:,j).^2); • BPDV(1,j) = RS(1,j) -.5*BV(1,j); • else • RS(1, j) = 0; • BPDV(1, j) = 0; • end

  6. Equations • Tri-Power Quarticity • Relative Jump

  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 • Rewrote code so that the 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) • Two stocks are being analyzed, notably for their differences for the results in the analysis as they respond uniquely to the downward variance analysis • Altria Group is sampled between 1997-2008 (2669) • Apple is sampled between 1997-2000 (676)

  9. Altria Group (Phillip Morris)

  10. Realized Volatility, Bipower Variance

  11. Realized Variance, Z-Scores

  12. Semivariance, Bipower Downward Variance

  13. Realized Semivariance, Z-Scores

  14. Upward Variance, BPUV

  15. Realized Upvariance, Z-Scores

  16. Apple Computers

  17. Realized Volatility, Bipower Variance

  18. Realized Variance, Z-Scores

  19. Semivariance, Bipower Downward Variance

  20. Realized Semivariance, Z-Scores

  21. Upward Variance, BPUV

  22. Realized Upvariance, Z-Scores

  23. Summary Statistics

  24. Questions • Problems with the code? Is there something that I’m not doing correctly with measuring downside risk • Why the difference in the two stocks’ characteristics? • Improvements in the Tri-Power or Max z-statistic that explain the drastic differences in z-scores that you see? • Verified decreases in mean and standard deviation for the one-directional jumping (is this just because values have been replaced by zeros?) • Extend to GARCH model analysis…?

  25. Additional Extensions • Determining Tri-Power Quarticity for only semivariance • Using a larger sample of stocks to view effects of trimming the data • Effect of noise on data

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