Jump Days and Volumes of Trading

Pat AmatyakulEcon 201FS

February 25, 2009

Questions to be answered

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

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 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 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 The null hypothesis, , 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

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)

0H

2

22

1

21

21

n

s

n

s

YYt

Test results

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 for days in the bottom quartile in volume

11.91

2.46 .55

Jump percentage for days in the top quartile in volume

16.43

5.48 1.23

Volume as a function of time (American Express)

Statistics for American Express 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

t at 99.9% = 2.1782 p=.0150 t at 99% = 3.2412 p=.0007 t at 95% = 3.8712 p=.0001

Confidence Level

95 99 99.9

Jump percentage

15.4 6.57 1.68

Jump percentage for days in the bottom quartile in volume

13.83

6.02 1.37

Jump percentage for days in the top quartile in volume

20.53

9.72 3.42

Conclusion 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

Choose more stocks Use other jump tests