Jump Days and Volumes of Trading

1. Jump Days and Volumes of Trading Pat Amatyakul Econ 201FS February 25, 2009

2. 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.

3. 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.

4. 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

5. Volume as a function of time(Boeing)

6. 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

7. Day detected as a jump with very large trading volume Volume= 25.1 million Boeing and Alliant Techsystems Entering Long-Term Contract to Build Rocket Components in Luka, Mississippi HUNTINGTON BEACH, Calif., July 07, 1998 -- The Boeing [BA: NYSE] Company has selected Alliant Techsystems to produce composite structures for its new Delta IV family of rockets now in development. The long term contract, which is under negotiation, is estimated, with options, to be worth nearly $1 billion dollars.

8. 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

9. 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)

10. 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

12. Volume as a function of time (American Express)

13. 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

14. 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

16. 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

17. Continuing research • Choose more stocks • Use other jump tests