Jump Testing with Healthcare Stocks

Haoming WangDate: 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 Std dev Min Max # of jump days

(total = 2682)ABT rv (x10-4) 2.8404 2.9495 0.18957 46 bv (x10-4) 2.603 2.7862 0.15234 45 jump (x10-4) 0.2873 0.5298 0 13 Ztp-max 0.9588 1.0174 0 6.3778 110 (4.09%)

BMY rv (x10-4) 3.3421 9.9132 0.17502 479 bv (x10-4) 2.9993 6.834 0.13513 305 jump (x10-4) 0.3319 0.7122 0 18 Ztp-max 1.0455 1.0829 0 8.6625 137 (5.11%)

Summary Statistics (JNJ and MRK)Avg Std dev Min Max # of jump days

(Total=2682)JNJ rv (x10-4) 1.8252 2.275 0.0804 43.55

bv (x10-4) 1.6801 2.126 0.07311 39.69

jump (x10-4) 0.1772 0.3951 0 11.76

Ztp-max 0.936 1.101 0 9.1424 114 (4.25%)

MRK rv (x10-4) 2.429 2.9373 0.0996 47.63

bv (x10-4) 2.232 2.5609 0.0937 42.43

jump (x10-4) 0.2444 0.9872 0 33.65

Ztp-max 0.8761 0.9829 0 9.9856 86 (3.20%)

Summary Statistics (PFE)Avg Std dev Min Max # of jump days

(Total=2682)PFE rv (x10-4) 2.8078 3.0358 0.1888 46.77

bv (x10-4) 2.6035 2.8408 0.1437 51.94

jump (x10-4) 0.26501 0.6953 0 16.24

Ztp-max 0.8573 0.9968 0 7.2873 95 (3.54%)

Plots

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ABT Ztp-Max Test Stats

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9BMY Ztp-Max Test Statistics

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10JNJ Ztp-Max Test Statistics

• 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.

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10MRK Ztp-Max Test Statistics

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8PFE Ztp-Max test statistic

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

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pfeztest

averageztest

ResultsPfeZ 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 R-squared

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?