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Semivariance Significance

Semivariance Significance. Baishi Wu, 4/16/08. Outline. Motivation Background Math Data Information Summary Statistics Correlation Summary Regression Summary. Introduction. Want to examine predictive regressions for realized variance by using realized semi-variance as a regressor

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Semivariance Significance

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  1. Semivariance Significance Baishi Wu, 4/16/08

  2. Outline • Motivation • Background Math • Data Information • Summary Statistics • Correlation Summary • Regression Summary

  3. Introduction • Want to examine predictive regressions for realized variance by using realized semi-variance as a regressor • Test significance of realized semi-variance and realized up-variance by correlation with daily open-close returns • Regressions are of the HAR-RV form from Corsi (2003) • Semi-variance from Barndorff-Nielsen, Kinnebrock, and Shephard (2008)

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

  5. Equations • Realized Semivariance (RS) • Realized upVariance (upRV) upRV = RV - RS • Bipower Downard Variance (BPDV)

  6. Equations • Daily open to close returns (ri) ri = log(priceclose) – log(priceopen) • The daily open to close returns are correlated with the RV, upRV, and RS to determine whether market volatility is dependent on direction • This statistic is also squared to determine if the size of the open to close price shift correlates with the magnitude of realized volatility

  7. Equations • Heterogenous Auto-Regressive Realized Volatility (HAR-RV) from Corsi, 2003: • Multi-period normalized realized variation is defined as the average of one-period measures. The model is using rough daily, weekly, monthly periods.

  8. Equations • Extensions of HAR-RV • Created different regressions using lagged RS and lagged upRV in predicting RV creating HAR-RS and HAR-upRV • Compared to original HAR-RV model • Created combined regressions of a combination of both RS and upRV to predict RV using HAR-RS-upRV

  9. Equations • Tri-Power Quarticity • Relative Jump

  10. Equations • Max Version z-Statistic (Tri-Power) • The max version Tri-Power z-Statistic is used to measure jumps in the data in this case • Take one sided significance at .999 level, or z = 3.09

  11. Data Preparation • Collected at five minute intervals S&P 500 Data Set: 2000 to late 2007 (1959 Observations) Exxon Mobile Corp: 2000 to 2008 (1967 Observations) Intel Corp: 2000 to 2008 (1720 Observations) Pfizer Inc: 2000 to 2008 (1968 Observations) Allegheny Technologies Inc: 2000 to 2008 (1964 Observations) • Chose different stocks to view consistency in previous conclusions as well as dissect any errors found this week

  12. Statistical Summary

  13. Statistical Summary • When looking at upRV vs. RS, notice that they are approximately same in terms of mean and std • Individual stocks are expectedly less volatile than the market as a whole • Daily returns are negative on average

  14. Correlations with Daily Returns • RS and upRV are much more highly correlated with daily returns than RV is upon average - positive daily returns tend to indicate greater positive returns as a whole • Anticipate positive correlations of realized up-variance with daily returns, negative correlations of semi-variance • Expected to see a higher correlation with semi-variance and daily squared returns in order to indicate higher volatility in a down market (not the case) – price movements do not coincide with volatility

  15. Correlations with Daily Returns • Semi-variance and realized up-variance are not better correlated with themselves (shown by earlier autocorrelations ran through correlograms) • Larger daily returns in magnitude do not correlate with higher market volatility (if measured through semi-variance)

  16. Correlations with Daily Returns • PFE is unique: • RV magnitude is higher than average • RS magnitude is lower than average • ATI is unique: • RV magnitude is higher than average • RS magnitude is higher than average

  17. Combined Regressors Summary • Highest R2 values were found for the HAR-RS-upRV regression combination of using both the semi-variances and the realized-upvariances • Much of this is due to the strength of the regression coefficient in the HAR-RS regression • In general, semi-variance is a better predictor of RV than realized up-variance and RV itself; this indicates that the down market predicts overall volatility best

  18. Regression Summary • PFE – seen as an exception in an earlier circumstance; unreliable low correlations? Boost in predictive power comes from upRV • XOM – HAR-RS is very comparable to HAR-RS-upRV; is this difference negligible?

  19. F-Test Summary • PFE does not seem to find either RS or upRV predictions significant • Generally, the predictive power arrives from the HAR-RS regression with upRV only stronger in a weak predictive case

  20. A Look into Pfizer

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