1. Semivariance Significance
Baishi Wu, 3/19/08

2. Outline Motivation Background Math Data Information
Summary Statistics and Graphs
Correlation
HAR-RV, HAR-RS, HAR-upRV
Correlogram
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 improved predictive ability

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
Separated into different return matrices, then found the realized variance with those new matrices
Bipower Downard Variance (BPDV)

6. ri = log(priceclose) – log(priceopen)
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
S&P500 Data Set from 1990 to late 2007

9. S&P500 - Prices
S&P500

10. Realized and Bipower Variance
Statistic
Value
mean(RV)
8.1299e-05
std(RV)
1.2352e-04
mean(BV)
7.6804e-05
std(BV)
1.1303e-04
S&P500

11. Z-Scores S&P500 Statistic Value days 4509 mean(z) 0.6342 std(z) 1.3569
jump days
166
Jump %
3.68%
S&P500

12. Semivariance, Realized upVariance
Statistic
Value
mean(RS)
4.0894e-05
std(RS)
7.1114e-05
mean(upRV)
4.0405e-05
std(upRV)
6.3970e-05
S&P500

13. Bipower Downward Variation
Statistic
Value
mean(BV)
7.6804e-05
std(BV)
1.1303e-04
mean(BPDV)
2.4916e-06
std(BPDV)
2.7787e-05
S&P500

14. Summary Information
Semivariance statistics correlate much better with daily open-close returns, consistent with BNKS
Significant or by design? BPDV is also highly significant!
S&P500

15. Realized Variance Regression Results
Coefficients are statistically significant in this case, with fairly low standard errors
S&P500

16. HAR-RV Plot
S&P500

17. Semivariance Regression Results
Coefficients are relatively similar to the results found for Realized Variance (not surprising), with none of the being any more significant
Fairly small contrast between RV and RS in this case.
S&P500

18. HAR-RS Plot
S&P500

19. upRV Regression Results
Coefficients in this case are smaller and also less significant, in that they have much lower t-values
Unique to the data set? There appears to be nothing indicative about these different statistics.
S&P500

20. HAR-upRV Plot
S&P500

21. Correlogram – Realized Variance
S&P500

22. Correlogram – Realized Semivariance
S&P500

23. Correlogram – Realized upVariance
S&P500

24. Correlogram Summary
upRV autocorrelation is a lot lower, as well as the signifiance of the coefficients of the regression. When we look back on the graph of the upward variance it seems that upRV has spiked the most relative to its averages
Theoretically, because of the reduction of spikes in a certain direction, both RS and upRV are meant to have a better autocorrelation than RV. This dataset along with data found in the previous presentation disproves this theory.

25. Future
Try to use semivariance as a component of factor analysis when attempting to see industry relationships – maybe downward movements have better correlations with each other? (current problem, matching days correctly)
Expand the HAR-RV to include more regression terms?
Attempt semivariance with other jump tests? Lee- Mykland?