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Jump Testing with Healthcare Stocks Haoming Wang Date: February 13 th, 2008

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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).

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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.

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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.

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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.

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Mathematical Equations Realized variation (where r t,j is the log-return): Realized bi-power variation :

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Mathematical Equations Tri-Power Quarticity: Quad-Power Quarticity:

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Mathematical Equations Both quarticities of the previous slide are estimators of Thus, we can construct test statistics of the form

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Max Version Test Statistics

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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.

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Summary Statistics (ABT and BMY) AvgStd devMinMax# of jump days (total = 2682) ABT rv (x10 -4 ) 2.84042.94950.1895746 bv (x10 -4 )2.6032.78620.1523445 jump (x10 -4 )0.28730.5298013 Ztp-max0.95881.017406.3778110 (4.09%) BMY rv (x10 -4 ) 3.34219.91320.17502479 bv (x10 -4 )2.99936.8340.13513305 jump (x10 -4 )0.33190.7122018 Ztp-max1.04551.082908.6625137 (5.11%)

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Summary Statistics (JNJ and MRK) AvgStd devMinMax# of jump days (Total=2682) JNJ rv (x10 -4 ) 1.82522.2750.080443.55 bv (x10 -4 )1.68012.1260.0731139.69 jump (x10 -4 )0.17720.3951011.76 Ztp-max0.9361.10109.1424114 (4.25%) MRK rv (x10 -4 ) 2.4292.93730.099647.63 bv (x10 -4 )2.2322.56090.093742.43 jump (x10 -4 )0.24440.9872033.65 Ztp-max0.87610.982909.985686 (3.20%)

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Summary Statistics (PFE) AvgStd devMinMax# of jump days (Total=2682) PFE rv (x10 -4 ) 2.80783.03580.188846.77 bv (x10 -4 )2.60352.84080.143751.94 jump (x10 -4 )0.265010.6953016.24 Ztp-max0.85730.996807.287395 (3.54%)

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Plots

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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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Analysis

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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.

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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?

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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?

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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.

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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?

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Regression

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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.

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Graph of z-test with previous day average

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Results PfeZCoef.Std. Err.tPr>|t|95% CI averageZ.16416.03540164.640.000.0947427.2335772 constant.7002682.037473818.690.000.6267878.7737486 R-squared0.0085 Adj R- squared 0.0081 Root MSE.99256

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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.

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Further Work

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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?

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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?

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