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Semivariance Significance

Semivariance Significance. Baishi Wu, 3/19/08. Outline. Motivation Background Math Data Information Summary Statistics and Graphs Correlation HAR-RV, HAR-RS, HAR-upRV Correlogram Future. Introduction.

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Semivariance Significance

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  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) • 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 • S&P500 Data Set from 1990 to late 2007

  9. S&P500 - Prices S&P500

  10. Realized and Bipower Variance S&P500

  11. Z-Scores S&P500

  12. Semivariance, Realized upVariance S&P500

  13. Bipower Downward Variation 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?

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