Transcript Jump testing for GE and BAC

Jump Testing with Healthcare
Stocks
Haoming Wang
Date: February 13th, 2008
Introduction
• Want to investigate how jumps for a company
in a specific sector affect jump likelihood for
another company in the same sector.
• Chose the healthcare industry because as a
whole the industry is relatively decoupled
from the broader markets.
• The healthcare SPDR (sector ETF) has low beta
of 0.63 (second lowest of all sectors).
Introduction
• Healthcare companies are seem to be more
information dependent: success and failures of
drug testing can cause wild price fluctuations.
• Healthcare products are mostly very inelastic, if
you need the medication, economic cycles that
hit other industries most likely wouldn’t cause
you to stop taking your medicine.
• Thus, most jumps should be unique to the
industry/company.
Introduction
• Companies are in competition with each other
for drug research, information about one drug
trial might have an affect on other companies.
• Would hope to find some kind of jump day
clustering.
• In other words, a jump in one of the
healthcare stocks affects the jump statistic of
the other healthcare stocks.
Introduction
• Examine price data for Abbott Labs (ABT),
Bristol Meyers Squibb (BMY), Johnson &
Johnson (JNJ), Merck (MRK), and Pfizer (PFE).
• All data is from 4/11/1997 to 1/24/2008.
• Data is from the S&P 100 set that Prof.
Tauchen posted.
• 5-minute intervals are used to minimize
microstructure noise.
Mathematical Equations
• Realized variation (where rt,j is the log-return):
• Realized bi-power variation :
Mathematical Equations
• Tri-Power Quarticity:
• Quad-Power Quarticity:
Mathematical Equations
• Both quarticities of the previous slide are
estimators of
• Thus, we can construct test statistics of the
form
Max Version Test Statistics
Test Statistics
• We will looked at results at the 0.999
significance level.
• Thus, we are looking for test-statistics greater
than 3.09 since we are using the one-sided
significance test.
Summary Statistics (ABT and BMY)
Avg
ABT
BMY
Std dev
Min
Max
rv (x10-4)
-4
bv (x10 )
-4
jump (x10 )
2.8404
2.603
0.2873
2.9495
2.7862
0.5298
0.18957 46
0.15234 45
0
13
Ztp-max
0.9588
1.0174
0
rv (x10-4)
-4
bv (x10 )
-4
jump (x10 )
3.3421
2.9993
0.3319
9.9132
6.834
0.7122
0.17502 479
0.13513 305
0
18
Ztp-max
1.0455
1.0829
0
6.3778
8.6625
# of jump days
(total = 2682)
110 (4.09%)
137 (5.11%)
Summary Statistics (JNJ and MRK)
Avg
JNJ
Min
Max
# of jump days
(Total=2682)
1.8252
2.275
0.0804
43.55
1.6801
2.126
0.07311
39.69
jump (x10 )
0.1772
0.3951
0
11.76
Ztp-max
0.936
1.101
0
9.1424 114 (4.25%)
rv (x10-4)
-4
bv (x10 )
2.429
2.9373
0.0996
47.63
2.232
2.5609
0.0937
42.43
jump (x10 )
0.2444
0.9872
0
33.65
Ztp-max
0.8761
0.9829
0
9.9856 86 (3.20%)
rv (x10-4)
-4
bv (x10 )
-4
MRK
Std dev
-4
Summary Statistics (PFE)
Avg
PFE
Std dev
Min
Max
# of jump days
(Total=2682)
2.8078
3.0358
0.1888
46.77
2.6035
2.8408
0.1437
51.94
jump (x10 )
0.26501
0.6953
0
16.24
Ztp-max
0.8573
0.9968
0
7.2873 95 (3.54%)
rv (x10-4)
-4
bv (x10 )
-4
Plots
ABT Ztp-Max Test Stats
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BMY Ztp-Max Test Statistics
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JNJ Ztp-Max Test Statistics
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1000
1500
2000
• The spike at around day 2000 is caused by a data error.
• No pricing data for most points in the date range.
• Data assumes that price stays constant so there’s always the
presence of jumps once the correct data appears.
2500
MRK Ztp-Max Test Statistics
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PFE Ztp-Max test statistic
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Analysis
Qualitative Analysis
• Possible data error with BMY?
– No! The spike in realized variation occurred on
02/19/2000, when Bristol Meyers withdrew its
application for a new drug from FDA
consideration. The stock fell 23% that day and
trading was actually suspended for an hour.
Qualitative Analysis
• Jump Clustering : Investigated data from 2007,
looked for shared jump days and then used
Factiva to check for any news stories that day.
• First cluster: Jan 29 – Jan 31
– Statistically significant jumps for ABT (1/29), MRK
(1/31), and PFE (1/31)
– Jan 29: Thai government announces plans to sell
special generic versions of drugs made by ABT and
BMY
– Jan 31: Merck releases earnings, PFE released
earnings a week ago, perhaps some effect?
Qualitative Analysis
• Second Cluster: Feb 14
– 2/14: Sanofi-Aventis (European pharmaceuticals
company) announces earnings, does not comment
on rumors of BMY acquisition
– BMY and PFE both have significant jumps.
– No significant PFE news, indirect impact from
takeover rumors?
Qualitative Analysis
• Third Cluster: Oct 16-Oct 17
– Jumps for BMY (10/16, 10/17) and JNJ (10/17)
– Oct 16: BMY receives approval for new drug
– Oct 17: JNJ releases earnings
– No direct effects, both jumps can be attributed to
company specific news.
Qualitative Analysis
• Jump clustering seems to be to strict to find
true effects.
• It’s possible for jumps in one company to
impact another without there being a
statistically significant jump.
• Cut-off of a statistically significant jump might
be too high to observe this effect.
• Regression?
Regression
Regression
• Regressed the Ztp-Max test statistic of PFE on
the average of the previous day Ztp-Max
statistics of ABT, BMY, JNJ, and MRK.
• Want to see if there’s any predictive power of
previous day industry jumps.
• Used regress command in STATA with
heteroskedasticity robust errors.
Graph of z-test with previous day
average
8
pfeztest
averageztest
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Results
PfeZ
Coef.
Std. Err.
t
Pr>|t|
95% CI
averageZ
.16416
.0354016
4.64
0.000
.0947427
.2335772
constant
.7002682 .0374738
18.69
0.000
.6267878
.7737486
R-squared
0.0085
Adj Rsquared
0.0081
Root MSE
.99256
Analysis
• Statistically significant coefficient on previous
day’s average Ztp-Max stat.
• However, effect is not actually significant. If on
average there’s a statistically significant jump in
the previous day, regression only predicts the PFE
test stat to be 1.21.
• Low R-squared, very little of the variation in PFE
test stat can be explained by variation in the
previous day average test stat.
• High root MSE, estimator not very accurate.
Further Work
Extensions
• Study how the effect of industry wide jump
days changes for different industries.
• Different regressors? Different methods?
• Should we be using an average? How should it
be weighted? Any other suggestions for
regressors?
• Different models? Different regressions?
Extensions
• RV regression more telling? See previous day’s
industry RV’s affect on next day RV?
• Compare HAR-RV-J regression from Andersen,
Bollerslev, Diebold 2006? Implied volatility
work that Andrey did?
• Adapt HAR-RV-J regression to intra-sector
stocks?