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) Bipower Downard Variance (BPDV)
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 (2669)
Apple is sampled between (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 MO AAPL Mean Std RV 3.32E-04 0.0017 0.0012 upRV
0.0007
0.0008 RS
1.74E-04
3.24E-04 BV
2.65E-04
4.37E-04
0.001
BPUV
1.39E-04
0.0016
0.0004
BPDV
9.74E-05
1.90E-04
0.0013
Jumps
0.37%
0.15%
Jumps Down
0.00%
52.66%
Jumps Up
57.00%
0.59%

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