Transcript High Frequency Finance

Semivariance Significance
Baishi Wu, 2/13/08
Outline
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Motivation
Background Math
Data Preparation
Altria Group/Phillip Morris (MO) Plots
Apple (APPL) Plots
Summary Statistics
Future
Introduction
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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 zscores for the following as well
The separation of RS from RV is supposed to beat out
the prediction mechanism used solely on GARCH
memory
Equations
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Realized Volatility (RV)
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Bipower Variance (BV)
Equations
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Realized Semivariance (RS)
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Bipower Downard Variance (BPDV)
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Running an “if” loop to only take values of the returns if they are less
than zero in order to solely decreases
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
Equations
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Tri-Power Quarticity
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Relative Jump
Equations
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Max Version z-Statistic (Tri-Power)
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Take one sided significance at .999 level, or z = 3.09
Data
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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 1997-2008 (2669)
Apple is sampled between 1997-2000 (676)
Altria Group (Phillip Morris)
Realized Volatility, Bipower Variance
Realized Variance, Z-Scores
Semivariance, Bipower Downward Variance
Realized Semivariance, Z-Scores
Upward Variance, BPUV
Realized Upvariance, Z-Scores
Apple Computers
Realized Volatility, Bipower Variance
Realized Variance, Z-Scores
Semivariance, Bipower Downward Variance
Realized Semivariance, Z-Scores
Upward Variance, BPUV
Realized Upvariance, Z-Scores
Summary Statistics
MO
AAPL
Mean
Std
Mean
Std
RV
3.32E-04
0.0017
0.0012
0.0017
upRV
2.24E-04
0.0017
0.0007
0.0008
RS
1.74E-04
3.24E-04
0.0007
0.0017
BV
2.65E-04
4.37E-04
0.001
0.001
BPUV
1.39E-04
0.0016
0.0004
0.0004
BPDV
9.74E-05
1.90E-04
0.0004
0.0013
Jumps
0.37%
0.15%
Jumps Down
0.00%
52.66%
57.00%
0.59%
Jumps Up
Questions
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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…?
Additional Extensions
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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