Semivariance Significance Baishi Wu, 3/19/08
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 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
Equations Realized Volatility (RV)
Bipower Variance (BV)
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)
Equations Tri-Power Quarticity
Relative Jump
Daily open to close returns (ri)
ri = log(priceclose) – log(priceopen)
Equations Max Version z-Statistic (Tri-Power)
Take one sided significance at .999 level, or z = 3.09
Data Collected at five minute intervals S&P500 Data Set from 1990 to late 2007
S&P500 - Prices
S&P500
Realized and Bipower Variance
S&P500
Statistic
Value
mean(RV) 8.1299e-05
std(RV) 1.2352e-04
mean(BV) 7.6804e-05
std(BV) 1.1303e-04
Z-Scores
S&P500
Statistic
Value
days 4509
mean(z) 0.6342
std(z) 1.3569
jump days 166
Jump % 3.68%
Semivariance, Realized upVariance
S&P500
Statistic
Value
mean(RS) 4.0894e-05
std(RS) 7.1114e-05
mean(upRV)
4.0405e-05
std(upRV) 6.3970e-05
Bipower Downward Variation
S&P500
Statistic
Value
mean(BV) 7.6804e-05
std(BV) 1.1303e-04
mean(BPDV)
2.4916e-06
std(BPDV) 2.7787e-05
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
Realized Variance Regression Results
Coefficients are statistically significant in this case, with fairly low standard errors
S&P500
HAR-RV Plot
S&P500
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
HAR-RS Plot
S&P500
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
HAR-upRV Plot
S&P500
Correlogram – Realized Variance
S&P500
Correlogram – Realized Semivariance
S&P500
Correlogram – Realized upVariance
S&P500
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.
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?