Transcript Jump Days and Volumes of Trading

Jump Days and Volumes of
Trading
Pat Amatyakul
Econ 201FS
February 25, 2009
Questions to be answered
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When jump days are detected, does the
volume of trading in that day tend to be
higher or lower than those days where
jumps are not detected?
Is there any bias in the jump detection
test against days where relatively few
or many trades occur? And how to take
that into account.
Tests to be made
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Mean(volume) in jump days =?
Mean(volume) non-jump days
For days with volume for the bottom
quartile of all days, what is the
percentage of jump days compared to
normal and compared to days with
volume in the top quartile.
Background
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Use 5 minute intervals in order to construct
jump tests
Use BNS jump tests with Quadpower
Quarticity at 95, 99, and 99.9 percent
confidence levels
Since our volume data was not verified and
could be inaccurate, volume data from google
finance is used as a substitution
Volume as a function of
time(Boeing)
Day detected as a jump with
small trading volume
Volume traded on this day=1.1 million
•Boeing stock has high liquidity. The volume is almost always over 1
million shares traded per day
Day detected as a jump with
very
large
trading
volume
Volume= 25.1 million
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Basic statistics
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Mean Volume per day =4.627 million
Standard Deviation=2.497 million
Minimum value= 0.996 million
Maximum value=37.1 million
Correlation between volume and Realized Variance=.19
From last time, from a total of 2922 days from April 1997 to
January 2009, number of jump days are as follows: 402 at 95%,
110 at 99%, and 26 at 99.9% level
Mean volumes of jump days:
At 99.9%- 5.11 million
At 99% - 5.14 million
At 95% - 4.80 million
Test statistic
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The null hypothesis,H 0 , is that the mean volume of the jump
days are equal to the mean volume of the non-jump days
The alternative is that the volume will be greater for jump days
and this will be a one sided test
t
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Y1 Y 2
s12 s 22

n1 n2
Where 1 represents a detected jump day and 2 represents a
nonjump day. s represents the standard deviation of the sample
and n is the number of samples
The degrees of freedom =(n1-1)+(n2-1)
Test results
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t at 99.9%(jump days)=3.0049
p=.0014
t at 99%(jump days)=2.1663
p=.0155
t at 95%(jump days)=1.4617
p=.0724
Confidence Level 95
99
99.9
Jump percentage 13.75 3.76
.89
Jump percentage 11.91 2.46
for days in the
bottom quartile
in volume
Jump percentage 16.43 5.48
for days in the
top quartile in
volume
.55
1.23
Volume as a function of time
(American Express)
Statistics for American Express
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Mean Volume per day =7.053 million
Standard Deviation=5.2079 million
Minimum value= 1.553 million
Maximum value=56.354 million
From last time, from a total of 2922 days from April 1997 to
January 2009, number of jump days are as follows: 450 at 95%,
192 at 99%, and 49 at 99.9% level
Mean volumes of jump days:
At 95%- 8.05 million
At 99% - 8.59 million
At 99.9% - 8.86 million
Test results for american
express
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t at 99.9% = 2.1782
t at 99% = 3.2412
t at 95% = 3.8712
p=.0150
p=.0007
p=.0001
Confidence Level 95
99
99.9
Jump percentage 15.4
6.57
1.68
Jump percentage 13.83 6.02
for days in the
bottom quartile
in volume
Jump percentage 20.53 9.72
for days in the
top quartile in
volume
1.37
3.42
Conclusion
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Days with higher volume of trade tend to
have more jumps than days with lower
volume of trade.
Although volume correlates with the chance
of jump detection, it is probably not a causal
relationship. I would think that some other
underlying events cause both high volume of
trade and jumps in prices of stocks
Continuing research
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Choose more stocks
Use other jump tests