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- 1. Universiteit van Amsterdam Master Program in International Finance Thesis Cointegration among Biotech StocksStudent: Peter ZobelSupervisor: Dr. Frank KleibergenAmsterdam, 5 September 2000
- 2. Table of Contents1 Introduction 12 Theoretical Framework 22.1 Unit Root Testing 22.2 Cointegration Testing 33 Stock Valuation and Biotech Companies 53.1 Valuing Stock 53.2 Biotech Stock Characteristics 53.3 Biotech Stock Selection 74 Data and Preliminary Results 84.1 Data 84.2 Unit Root Testing 84.3 Testing for Cointegration 95 Discussion of the Cointegration Results 116 Conclusion 12References 13Appendix 15
- 3. 1 IntroductionStock markets and their interdependence have been the subject of many studies in the last years. These stud-ies were motivated by an increasing flow of funds across national borders, potential gains from internationaldiversification and the existence of “home bias”. In the beginning, analyses were limited to the study of stockmarket returns. By differencing the non-stationary (log-) stock market returns were made stationary and sub-sequently analyzed. However, purging the non-stationarity by differencing and using only differenced vari-ables for estimation purposes means that valuable information from economic theory concerning the long-runproperties of the data is lost.The concept of cointegration, first introduced by Granger, implies that several non-stationary time seriesmove stochastically together over time. Within this framework common stochastic trends can be analyzed:“The idea behind cointegration is that sometimes the lack of stationarity of a multidimensional process iscaused by common stochastic trends, which can be eliminated by taking suitable linear combinations of theprocess, thereby making the linear combination stationary” (Johansen, 2000: 361).While there are quite some studies on cointegration of stock market indices to test whether national stockmarkets share a common stochastic trend (e.g. Corhay et al., 1993; Kasa, 1992; Sanchez Valle, 1998), little isknown about cointegration of individual stock prices. This comes not as a surprise as the efficient markethypothesis states that all the available information is fully reflected in stock prices (Fama, 1970: 383). Coin-tegration of individual stocks, however, would imply that not all this information is priced. Stengos andPanas (1992), for example, use the cointegration test to test the semi-strong form of market efficiency in thebanking sector of the Athens stock exchange. Recently, Krämer (1999) presented a paper, which comes to theconclusion that the stocks of BASF, Bayer, and Hoechst are fractionally cointegrated. Krämer argues thatthese companies share a common root (they originated in IG Farben) and are subject to similar market condi-tions (HB, 16/05/2000).The purpose of this paper is to address the issue of cointegration between different biotech stocks. Althoughit was initially planned to look at biotech companies quoted on Frankfurt’s Neuer Markt, the companies thereonly went public one or two years ago. To have sufficient observations for analysis, biotech stocks from theNASDAQ were selected as they have a longer history as listed companies. The research question to be an-swered is whether one common force keeps these companies together and causes them to be cointegrated.The remainder of this paper is organized as follows. Chapter 2 discusses the theoretical framework of unitroot and cointegration tests. Chapter 3 describes the valuation of stocks in general, characteristics of biotechstocks in particular, and the selection procedure. Chapter 4 presents the empirical results of the cointegrationtests on selected biotech stocks. Chapter 5 discusses the obtained results and their implications. The finalchapter contains concluding remarks. Page 1 of 17
- 4. 2 Theoretical FrameworkThe theoretical framework serves only as a quick introduction into the concepts, which are used in practicaltesting and focuses on problematic issues in the testing process.2.1 Unit Root TestingTests for cointegration can only be used if the series are non-stationary but can be made stationary by differ-encing. Therefore, we will first have to test whether each series contains a unit root. Only after we have es-tablished that each series is non-stationary (i.e. has a unit root), we can test for cointegration.A first intuitive method to identify the order of integration of each variable would be to test for ρ = 0 in theautoregressive equation: yt = ρ*yt-1 + εtIf εt represents a white noise process, this equation is a random walk with ρ = 1. If, on the other hand, |ρ| < 1,then the process generating yt is integrated of order zero and stationary. However, estimating ρ with ordinaryleast squares may lead to a substantially biased result especially where the variable yt is non-stationary andthe distribution not known.Dickey and Fuller propose a test which also tests the hypothesis that ρ = 1 (unit root test) but in a slightlychanged equation, which may also include a drift β0: ∆yt = β0 + δ*yt-1 + εtThis is equivalent to: yt = β0 + (1 + δ)*yt-1 + εtThe Dickey-Fuller test consists of testing the negativity of δ because then ρ becomes smaller than one. Rejec-tion of the null hypothesis that δ = 0 and accepting the alternative hypothesis that δ < 0 implies that ρ < 1 andthat yt is integrated of order zero.To account for both drift and deterministic trend the equation is modified to: ∆yt = β0 + β1*t + δ*yt-1 + εtThis test does not take into account possible autocorrelation in the error process εt. If εt is not white noisethen the ordinary least squares estimates will not be efficient. Therefore the equation was modified to the so-called Augmented Dickey-Fuller (ADF) test: n ∆yt = β0 + β1*t + δ*yt-1 + ∑ δ *∆y i=1 i t-1 + εtThe number of lags (n) for ∆yt-1 should be large enough to account for possible autocorrelation in the errorterm but as small as possible to prevent a loss of degrees of freedom. Determining the right number of lags isa critical issue for cointegration tests. Page 2 of 17
- 5. 2.2 Cointegration TestingNon-stationary economic series can wander widely through time. While economic theory is adequate to de-scribe long-run equilibrium, in the short run shocks may push variables away from their equilibrium value. Itthen takes some time to move back to the long-run state. Differencing these time series makes them station-ary but leads to the loss of long-run properties. Cointegration resolves this problem and can therefore be seenas the statistical notion corresponding to the theoretical concept of long-run equilibrium. The effect of coin-tegration can be described as the existence of “some adjustment process which prevents the errors in the longrun relationship becoming larger and larger” (Charemza and Deadman, 1992: 154).Formally, two time series are said to be cointegrated of order (d, d) if each series individually is integrated oforder d (i.e. stationary after differencing d times), but a linear combination of these series is integrated oforder d – d = 0 (i.e. it is stationary in level).While Engle and Granger (1991) propose estimating the cointegrating relations using regressions, Johansen(1991) derives maximum likelihood estimators of the cointegrating vectors for an autoregressive process withindependent Gaussian errors and a likelihood ratio test for the number of cointegrating vectors. This proce-dure has the advantage of taking into account the error structure of the underlying process. It provides rela-tively powerful tests where long-run properties and short-run dynamics can be analyzed jointly, when themodel is correctly specified.The maximum likelihood procedure of Johansen starts with the k-th order unrestricted vector autoregressive(VAR) model of an (n × 1) vector Xt of random variables: k Xt = ∑ i =1 AiXt-i + Εt,where Xt contains all n variables of the model, i = 1, …, k, and Εt is a vector of white noise errors, Εt ~ i.i.d.(0, Σ). For simplicity, we will assume that all variables in Xt are integrated of order one and exclude inter-cepts and deterministic trends in this theoretical section.The unrestricted VAR model can be re-parameterized in the vector error correction model (VECM) form as: k −1 ∆Xt = ∑ i =1 Γi∆Xt-i + ΠXt-k + Εt,where: Γi = – (I – A1 – … – Ai) (I is a unit matrix) Π = – (I – A1 – … – Ak)The rank of matrix Π can at most be equal to n as its dimension is n × n. The interesting cases arise when itsrank is equal to r < n, in which case there are n – r unit roots in the system. (i.e. there are n – r commontrends, or long-run components) and r cointegrating relationships. Then the long-run impact matrix Π can bewritten as αβ’, where both α and β are (n × r) matrices of full common rank. Matrix β is called the cointe- Page 3 of 17
- 6. grating matrix and has the property that β’Xt is integrated of rank zero (i.e. stationary) while Xt is integratedof rank one.The columns of β are the cointegrating vectors, while the elements of α are the weights of the cointegratingvectors in the different equations. While the cointegrating vectors after normalization can be interpreted aslong-run parameters, the matrix α is called the adjustment matrix as the elements of α measure the speed ofadjustment with respect to disturbances of the equilibrium (Charemza and Deadman, 1992: 200).The Johansen approach is a procedure to identify the number of cointegrating vectors. The general principlesof this approach can be found in for example Charemza and Deadman (1992) and Franses (1998). Testingstarts from the hypothesis that that there are no cointegrating vectors in a VAR model (i.e. r = 0). If this nullhypothesis is rejected, the next test would be that there is at most one cointegrating vector. This testing pro-cedure continues until the null hypothesis cannot be rejected. The conclusion is then that there are r cointe-grating vectors, i.e. the rank of β is r.The Johansen test for cointegration is known to be sensitive to the choice of lag length (Cheung and Lai,1993). Some researchers deliberately over-specify the lag length as the random errors Εt have to be free fromautocorrelation. However, one has to be careful as these long lags may be inconsistent with economic inter-pretation. According to Charemza and Deadman (1992) “the lag length corresponds to the length of response(adjustment) to a deviation from a long run path, according to the interpretation of an error correction model”and these corrections are usually assumed to occur after a relatively short period of time (200). Furthermore,Bewley and Yang (1995) find that “there is a tendency for the Johansen test to over-reject the null hypothesisof no-cointegration in small samples, particularly when the lag length is too long” (254).Kasa (1991), for example, observes that tests with a small number of lags reveal little evidence for cointegra-tion, while larger number of lags provide much stronger evidence in favor of cointegration. Godbout and VanNorden (1997), however, demonstrate with Monte Carlo simulations that this phenomenon is most probablydue to size distortion and too few degrees of freedom (22).Cheung and Lai (1993) use Monte Carlo simulations to demonstrate that the Akaike and Schwartz lag selec-tion criteria are useful for choosing the right lag length. They find that, while the “AIC can pick the correctlag in more than 99.8 percent of all replications”, the “SIC seems to perform slightly better than the AIC”(Cheung and Lai, 1993: 322). In this paper, both Akaike and Schwartz Information Criteria will be taken intoconsideration when specifying the lag length. Page 4 of 17
- 7. 3 Stock Valuation and Biotech Companies3.1 Valuing StocksThe fundamentals of a stock are generally assumed to be the key driver of stock valuation. But what are theseeconomic variables affecting the value of a company and what other variables might have an influence? Oneof the most important macro-economic variables is the interest rate because it influences the discount rate –and the discounted cash flow (DCF) model is one of the important valuation methods used by stock analysts.Another important variable, which is more company specific, is company earnings, which generate the (laterdiscounted) cash flows. However, these earnings are future earnings and the further their realization in thefuture the more uncertainty is involved.Capital markets constantly re-assess the probability of forecasted earnings, which eventually leads to a cor-rection. Often, earnings announcements of one company serve as a trigger for re-evaluation of other compa-nies with similar characteristics. This is generally described in newspapers as the “market sentiment”, whichfavors certain sectors of the economy relative to others, or some companies, which share certain characteris-tics (e.g. growth versus value stocks).When markets are very optimistic concerning future developments affecting some companies, this results inhigh valuation ratios for these companies, i.e. high price/earnings (P/E) ratios or, in case that net earnings arestill negative, high enterprise value to earnings before interest and tax (EV/EBIT) ratios. To evaluate individ-ual stocks relative to others, stock analysts provide the following general selection criteria, on which inves-tors can base their investment decisions:• the relative appeal of the product and market segment,• the technological and competitive position of a company,• the quality of a company’s product(s),• the quality of the management,• the quality of a company’s business model,• the quality of a company’s investor relations and capital market reporting (transparency), and• the reliability of a company’s forecasts.3.2 Biotech Stock CharacteristicsBiotech stocks, however, make the investment decision difficult for investors because of some shared charac-teristics. Most of them are affected by macro-economic events like interest rate changes as they are not yetprofitable and rely on external funding. The political environment affects them, too, as the acceptance of bio-technology remains uncertain due to unresolved ethical issues. In addition, individual companies are gener- Page 5 of 17
- 8. ally characterized by a lack of physical products, considerable uncertainty about future developments, and thedifficulty (at least for a layman) to understand their business (HB, 17/08/2000).This is not true for all the companies. Pioneers on the U.S. market like Amgen or Biogen are profitable andtransform themselves into integrated pharmaceutical companies that develop and market their own products(FTD, 03/08/2000). This forward integration is one of the key drivers for consolidation in this industry at themoment (HB, 02/08/2000a). But for the smaller companies in the sector this has yet to happen.For an investor in these smaller companies, which share the above characteristics, it is difficult to decidewhether a specific company will live up to the expectations. These companies are less visible in the news andnot broadly covered by analysts. In fact, stock analysts advise investors to choose profitable biotech enter-prises (DG Bank in Welt, 11/07/2000) or industry leaders (Goldman Sachs in HB, 02/08/2000b) to invest in.The hypothesis underlying this paper is that individual investors are not able to distinguish between compa-nies that are relatively small and make losses. These stocks are therefore driven by a general sentiment ofinvestors about the sector as a whole, but individually the stocks remain indistinguishable in the investor’sperspective. This might cause these stocks to be cointegrated. Cointegration, however, would link them in along-run relationship, which would imply that returns demonstrate significant predictability and would vio-late the efficient market hypothesis. Richards (1995) notes that at the individual company firm level thiswould “rule out the possibility that any decisions by corporate management could ever have a permanenteffect on a company’s return index relative to its competitors” (636). In the case of biotech stocks this is notlikely to happen as the shared characteristics are transitory. As soon as a company does show the above char-acteristics any more, it will be perceived to be different and no longer be affected by similar investor senti-ments. This implies that, even if small biotech stocks are cointegrated in their initial phase, this is not likelyto be a persistent (i.e. long-run) relationship.This contradicts cointegration theory as it is almost always interpreted in the way that “the regression equa-tion yt = βxt + ut makes sense because yt and xt do not drift too far apart from each other over time. Thus,there exists a long-run equilibrium relationship between them” (Maddala and Kim, 1998: 26; emphasisadded). “The cointegrating combination is interpreted as an equilibrium relationship, since it can be shownthat variables in the error-correction term in an ECM must be cointegrated, and vice versa, that cointegratedvariables must have an ECM representation. This is why economists have shown such interest in the conceptof cointegration – it provides a formal framework for testing for and estimating long-run (equilibrium) rela-tionships among economic variables” (Kennedy, 1998: 270; emphasis added). One way to test whether thiscointegrating relationship is transitory is to test for cointegration in an “industry leaders” group. This posesthe interesting, more general question of whether larger firms that are more closely followed by market par-ticipants are subject to the same (cointegrating) forces. This should not be the case if our way of argumenta-tion was correct. La Porta et al. (1997) provide two arguments for larger companies to behave different: ei-ther “the pricing of larger firms is more efficient” or “since these firms are followed more extensively byanalysts and get much more coverage in the financial press, it may just be that a greater fraction of funda-mental news about the larger firms is impounded into prices outside of quarterly earnings announcements”(869). Our argumentation would add that there might be fundamental differences, i.e. cointegration or theabsence of cointegration, between smaller and larger companies that make a distinction between the two. Page 6 of 17
- 9. 3.3 Biotech Stock SelectionThe goal behind the selection of biotech stocks to test for cointegration was to identify a first group of com-panies that are relatively small and still produce negative earnings (the so-called “indistinguishable compa-nies”). These were then to be compared with the second group of “industry leaders”, which have positiveearnings. As the NASDAQ biotechnology index consists of more than 200 companies, the first criterion forchoosing a company was a prototypical company name. Only companies that had the word ‘gene’ (or parts ofit) in their company name were selected as they are clearly identified as biotech companies. This reduced theshort list of companies to 36. The next criteria were market capitalization of at least US$ 250m and publiclisting for at least four years. Subsequently, the three companies with a market capitalization of more thanUS$ 2.5bn and positive earnings were picked as the “industry leaders” and the three companies with a marketcapitalization between US$ 0.5bn and 1.0bn and negative earnings were chosen as the “indistinguishablecompanies”. The following table shows these companies in an overview.Table 1: Biotech companies (market capitalization as of 28 July 2000)Company Symbol Market capitali- EPS P/E zation in US$m“Industry leaders”Amgen Inc. AMGN 69,665 1,07 63Biogen, Inc. BGEN 9,998 2,07 33Genzyme General GENZ 5,820 2,34 29“Indistinguishable companies”Avigen, Inc. AVGN 575 -1,09 n/aDigene Corp. DIGE 663 -0.48 n/aSuperGen, Inc. SUPG 707 -1,59 n/aIn the next chapter, we will first test the selected companies for unit root and then test, whether our consid-erations about factors affecting them really link them in a stable long-run relationship. Page 7 of 17
- 10. 4 Data and Preliminary Results4.1 DataThe sample consists of daily1 stock prices from Datastream for Avigen, Digene, and SuperGen for May 22,1996 through July 28, 2000, resulting in 1093 observations, and for Amgen, Biogen, and Genzyme Generalfor January 1, 1990 through July 28, 2000, resulting in 2759 observations.Prior to analysis the series are de-trended by transforming them in their natural logarithms.4.2 Unit Root TestingBefore testing for cointegration, non-stationarity must be established. In order to determine the number oflags to include in each series, we first inspected the partial autocorrelation function as computed by EViews.The correlogram showed that for each time series the partial correlation of the first lag was significant. Thiscomes as a surprise as we would expect that stock prices are not predictable. Using the Akaike and theSchwartz criteria (see table 4 on the next page), it was decided to include no lags as economic theory sug-gests. The reported Augmented Dickey-Fuller (ADF) test statistics in the Table 2 are thus computed withoutany lag.Table 2: Unit root tests Stock No. of lags Intercept Trend ADF test statistic AMGN 0 √ √ -2.246702 BGEN 0 √ √ -3.019877 SUPG 0 √ √ -3.211599 AVGN 0 √ √ -2.165697 DIGE 0 √ √ -1.757189 SUPG 0 √ √ -1.933291If the absolute value of the computed ADF test statistic is less than the MacKinnon critical values (see table3), we cannot reject the null hypothesis H0: δ = 0, i.e. that there is a unit root, and conclude that the time se-ries is non-stationary. If, on the other hand, the absolute value exceeds the critical values we have to concludethat the series is stationary.Table 3: MacKinnon critical values (MacKinnon, 1991: 275) Variant Size Critical value No constant 1% -2.5658 5% -1.9393 10% -1.61561 Although Shiller and Perron (1985) find that power of tests of the random walk hypothesis “depends more on the span of the data thanon the number of observations” (385), Hooker (1993) concludes that for ADF cointegration tests “researchers can gain power by usinghigher frequency data observations when available” (362). Lahiri and Mamingi (1995) challenge Hooker’s view. The most recent articleby Otero and Smith (2000) concludes that “practitioners ought to rely on data collected over a long period of time, rather than on a largenumber of observations collected over a relatively short period” (9). In this paper we use the maximum span of available data. Page 8 of 17
- 11. No trend 1% -3.4335 5% -2.8621 10% -2.5671 With trend 1% -3.9638 5% -3.4126 10% -3.1279Table 3 shows that the MacKinnon critical values depend on whether there is a constant term and/or trend.Since the computed ADF test statistic are in absolute terms smaller than the 1% and 5% critical values, wecannot reject the null hypothesis that δ = 0. This means that these biotech stock series exhibit a unit root,which is another way of saying that they follow a random walk. Because all the series are integrated of thesame order, cointegration tests are appropriate.4.3 Testing for CointegrationThe following table (table 4) gives the Akaike Information Criterion (AIC) and the Schwartz InformationCriterion (SIC) for a variety of vector autoregression lag lengths. The AIC favors the lag length producingthe smallest AIC value, and the SIC favors the lag length with the smallest SIC value. The difference be-tween them is mainly that the SIC imposes a larger penalty for additional coefficients.Table 4: Order selection using the AIC and SIC Number of lags 0 1 2 3 AMGN AIC -4.453054 -4.453596 -4.461458 -4.463062 SIC -4.446614 -4.445007 -4.450718 -4.450170 BGEN AIC -3.901433 -3.900470 -3.903334 -3.904007 SIC -3.894993 -3.891881 -3.892595 -3.891115 GENZ AIC -4.055850 -4.055679 -4.056864 -4.056484 SIC -4.049410 -4.047090 -4.046124 -4.043592 AVGN AIC -2.790201 -2.791510 -2.788977 -2.786604 SIC -2.776476 -2.773197 -2.766069 -2.759094 DIGE AIC -3.176703 -3.174181 -3.171583 -3.169337 SIC -3.162979 -3.155868 -3.148675 -3.141827 SUPG AIC -3.417032 -3.417593 -3.419402 -3.416877 SIC -3.403307 -3.399280 -3.396494 -3.389367As in the Augmented Dickey-Fuller test, we decided to take no lags in computing the VAR by using the con-sistent results of the Schwartz information criterion, which agrees with economic theory.The Johansen test is basically a multivariate Dickey-Fuller test, which determines the number of cointegrat-ing equations by computing a likelihood ratio statistic for each added cointegrating equation in a sequence ofnested models. If we cannot reject the hypothesis that the number of cointegrating equations is none, the se-ries are not cointegrated. If we cannot reject the hypothesis of at most cointegrating equation, there is onecointegrating vector and the series share a stochastic trend. The following two tables report the abridged re-sults of the Johansen cointegration test in EViews. Page 9 of 17
- 12. Table 5: EViews Output for the cointegration test among “indistinguishable companies”Sample: 22/05/1996 28/07/2000Included observations: 1091Test assumption: Linear deterministic trend in the dataSeries: LAVGN LDIGE LSUPGLags interval: 1 to 1 Likelihood 5 Percent 1 Percent Hypothesized Eigenvalue Ratio Critical Value Critical Value No. of CE(s) 0.021105 41.33468 42.44 48.45 None 0.009288 18.06279 25.32 30.45 At most 1 0.007199 7.882371 12.25 16.26 At most 2 *(**) denotes rejection of the hypothesis at 5%(1%) significance level L.R. rejects any cointegration at 5% significance level Unnormalized Cointegrating Coefficients: LAVGN LDIGE LSUPG @TREND(2/01/90) -0.005599 -0.100418 0.106703 5.36E-05 0.063245 -0.033987 -0.080720 -2.49E-05 0.014998 -0.018418 0.058159 -0.000108We do not find a cointegrating equation in the “indistinguishable companies” at the 1% and 5% significancelevel. But comparing the reported Trace test statistic of 41.33468 with the asymptotic critical values in table10.2 in Franses (1998: 224) we can reject the null hypothesis of no cointegrating equation at the 10% level(critical value: 39.06).Table 6: EViews Output for the cointegration test among “industry leaders”Sample: 1/01/1990 28/07/2000Included observations: 2758Test assumption: Linear deterministic trend in the dataSeries: LAMGN LBGEN LGENZLags interval: 1 to 1 Likelihood 5 Percent 1 Percent Hypothesized Eigenvalue Ratio Critical Value Critical Value No. of CE(s) 0.009664 46.80731 42.44 48.45 None * 0.005282 20.02345 25.32 30.45 At most 1 0.001962 5.416879 12.25 16.26 At most 2 *(**) denotes rejection of the hypothesis at 5%(1%) significance level L.R. test indicates 1 cointegrating equation(s) at 5% significance level Unnormalized Cointegrating Coefficients: LAMGN LBGEN LGENZ @TREND(2/01/90) -0.082836 0.010230 0.123950 1.24E-05 -0.003515 0.076914 -0.048055 -4.46E-05 -0.042558 0.000387 -0.013589 4.96E-05For the Johansen test of the “industry leaders” we find a cointegrating equation at the 5% level of confidence.In the following chapter we will discuss these results in the light of our assumptions. Page 10 of 17
- 13. 5 Discussion of the Cointegration ResultsThe result from our cointegration tests is mixed. On the one hand, the “indistinguishable companies” arecointegrated at the 10% level. This confirms a first impression from the graph (cf. Appendix). While manyempirical studies, which use the theory of cointegration, do not attempt to provide a theoretical explanationfor the existence of cointegration between financial time-series, we started from theoretical considerations,which we subsequently tested. We can therefore, albeit with a 10% chance of being wrong, conclude thatthese more or less randomly selected biotech stocks share a common trend. However, we argued that this is atransitory phenomenon, which contradicts cointegration theory in as far as it is assumed to be identical withlong-run relationships. Granger (1991), for example, summarized the idea underlying cointegration as a toolto capture the belief in economic theory “that certain pairs of economic variables should not diverge fromeach other by too great an extent, at least in the long-run. Thus, such variables may drift apart in the short-runor according to seasonal factors, but if they continue to be too far apart in the long-run, then economic forces,such as a market mechanism or government intervention will begin to bring them together again” (65).Here our second group of biotech companies, the “industry leaders”, come into play. Although our argumen-tation that cointegration is a transitory relationship in the case of biotech stocks suggest that the “industryleaders” will not be cointegrated, the results show the opposite at the 5% level of significance. Several expla-nations for this result come to mind.First of all, the 5% chance of having an erroneous result. However, the same applies to the results in our firstgroup.Second, the frequency of data may cause this phenomenon. Small companies will have quite volatile stockprices when they are subjected to large trades. High frequency data may then contain considerable short-termnoise. This may cause the cointegration to appear less probable. For big companies, the opposite result holds.An additional factor would be the price discovery, which is assumed to take longer for smaller stocks that arenot covered by analysts.Third, the span of ten years might not yet be long enough for the transitory cointegration relationship to end.Fourth, the cointegrating relationship might not be transitory at all but in fact a long-run one. This howeverwould be at odds with the efficient market hypothesis, which is generally accepted in its weak and semi-strong form.2Fourth, a slightly altered argumentation as the one presented for the “indistinguishable companies” might beapplicable for the “industry leaders”. We noted before that some stock analysts advise to buy these “industryleaders”. Not only individual investors may follow this advice but also institutional investors because thesewell-known stocks are “easier to justify to clients and superiors as prudent investments” (La Porta et al.,1997: 873). Thus, the fact that there are only a few companies, which are distinct (“prudent investments”),causes them to be cointegrated.2 Our finding of predictability does not result in regression equations where the cointegrating vector can predict a significant part of themovements of the individual stock. The adjusted R2’s for these equations are below 0.5%, with Digene being higher but still very low(1.7%). Page 11 of 17
- 14. 6 ConclusionIn the beginning of this paper was Krämer’s (1999) research on cointegration among chemical companies inthe German DAX. He found fractional cointegration, which he ascribed to a common origin in the samecompany and to similar market conditions. An alternative explanation would be that investors, who start bypicking a sector to invest in, have only a limited choice for blue chip companies in this sectors, especiallywhen home bias guides their investment decisions. These few companies then share some common percep-tion and are subjected to similar market forces.This paper argued that a common perception of investors is even more likely in the biotech sector, whereinvestors are not able to make distinctions between smaller companies with negative earnings. This indeci-siveness, it was argued, would subject these companies to a common transitory trend. Although we were ableto support the notion of a common trend with cointegration analysis, the results for the industry leaders cameas a surprise. According to our argumentation, these companies should no longer share this common trend asinvestors are able to make distinctions between them as they have physical products and positive earnings.However, the cointegration results showed that they share a common trend, too.The above alternative explanation for fractional integration among chemical companies in Germany may alsoexplain the results for biotech companies listed on the NASDAQ. For portfolio managers and uninformedinvestors industry leaders are the first choice. With a limited number of these companies, which show posi-tive earnings, their prices may tend to move together.To narrow down possible interpretations of the results further research, which takes data series with differentfrequency of observations and considers other sectors for which similar arguments hold (e.g. internet compa-nies sharing certain characteristics), will be required. Page 12 of 17
- 15. ReferencesBewley, Ronald and Yang Minxian (1995) “Testing for cointegration: the effects of mis-specifying the lag length”, Mathematics and Computer in Simulation, 39, 251-255Charemza, Wojciech W. and Deadman, Derek F. (1992) New directions in econometric practice: general to specific modelling, cointegration and vector autoregression, Aldershot: Edward ElgarCheung, Yin-Wong and Lai, Kon S. (1993) “Finite sample sizes of Johansen’s likelihood ratio tests for coin- tegration“, Oxford Bulletin of Economics and Statistics, 55, 313-328Corhay, A. et al. (1993) “Common stochastic trends in European stock markets“, Economics Letters, 42, 385-390Engle, Robert F. and Granger, C.W.J. (1991) “Co-integration and error correction: representation, estimation, and testing”, in: Engle, R.F. and Granger, C.W.J. (eds) Long-run economic relationships – readings in cointegration, Oxford: Oxford University Press, pp. 81-111 [reprinted from Econometrica, 55, (1987), pp. 251-276]Fama, Eugene F. (1970) “Efficient capital markets: a review of theory and empirical work”, Journal of Fi- nance, 25, 383-417Franses, P.H. (1998) Time series models for business and economic forecasting, Cambridge: Cambrige Uni- versity PressGodbout, Marie-Josée and Van Norden, Simon (1997) “Reconsidering cointegration in international finance: three case studies of size distortion in finite samples”, Bank of Canada Working Paper 97-1, online avail- able at http://www.bankofcanada.ca/en/res/wp97-1.htmGranger, C.W.J. (1991) “Developments in the study of cointegrated economic variables”, in: Engle, R.F. and Granger, C.W.J. (eds) Long-run economic relationships – readings in cointegration, Oxford: Oxford University Press, pp. 65-80Hooker, Mark A. (1993) “Testing for cointegration – power versus frequency of observation”, Economics Letters, 41, 359-362Johansen, Søren (1991) “Statistical analysis of cointegration vectors”, in: Engle, R.F. and Granger, C.W.J. (eds) Long-run economic relationships – readings in cointegration, Oxford: Oxford University Press, pp. 132-152 [reprinted from Journal of Economic Dynamics and Control, 12, (1988), pp. 231-254]Johansen, Søren (2000) “Modelling of cointegration in the vector autoregressive model”, Economic Model- ling, 17, 359-373Kasa, Kenneth (1992) “Common stochastic trends in international stock markets”, Journal of Monetary Eco- nomics, 29, 95-124Kennedy, Peter (1998) A guide to econometrics, 4th edition, Cambridge, Massachusetts: MIT PressKrämer, Walter (1999) “Kointegration von Aktienkursen”, zfbf, 51, 915-936Lahiri, Kajal and Mamingi, Nlandu (1995) “Testing for cointegration: power versus frequency of observation – another view”, Economics Letters, 49, 121-124La Porta, Rafael et al. (1997) “Good news for value stocks: further evidence on market efficiency”, Journal of Finance, 52/2, 859-874 Page 13 of 17
- 16. MacKinnon, James G. (1991) “Critical values for cointegration tests”, in: Engle, R.F. and Granger, C.W.J. (eds) Long-run economic relationships – readings in cointegration, Oxford: Oxford University Press, pp. 267-276Maddala, G.S. and Kim, In-Moo (1998) Unit roots, cointegration, and structural change, Cambridge: Cam- bridge University PressOtero, Jesus and Smith, Jeremy (2000) “Testing for cointegration: power versus frequency of observations”, Economics Letters, 67, 5-9Richards, Anthony J. (1995) “Comovements in national stock market returns: evidence of predictability, but not cointegration”, Journal of Monetary Economics, 36, 631-654Sanchez Valle, Rene (1998) “A cointegration analysis of Latin American stock markets and the U.S.”, Uni- versity of Exeter Working Paper, online available at http://papers.ssrn.com/paper.taf?ABSTRACT_ID=86604Shiller, Robert J. and Perron, Pierre (1985) “Testing the random walk hypothesis – power versus frequency of observation”, Economics Letters, 18, 381-386Stengos, Tanasis and Panas, Epaminodas (1992) “Testing the efficiency of the Athens stock exchange: some results from the banking sector”, Empirical Economics, 17, 239-252Newspaper ArticlesFinancial Times Deutschland (FTD)03/082000 “Angriff der Biotech-Zwerge” by Karen KleinwortHandelsblatt (HB)16/05/2000 “Wenn Aktienkurse zueinander finden – Dortmunder Professor untersucht ähnlich verlaufende Charts”02/08/2000a “Größe zählt zunehmend auch im Biotech-Sektor” by Siegfried Hofmann02/08/2000b “Biotech boomt woanders”17/08/2000 “Biotech-Aktien für das Renditeplus”Welt11/07/2000 “Bei Biotech-Aktien kommt es auf die richtige Auswahl an” Page 14 of 17
- 17. Appendix Page 15 of 17
- 18. Figure 1: Graph of the natural logarithms of the Avigen (LAVGN), Digene (LDIGE), and SuperGen (LSUPG) time series 5 4 3 2 1 0 22/05/96 22/04/98 22/03/00 LAVGN LDIGE LSUPG Page 16 of 17
- 19. Figure 2: Graph of the natural logarithms of the Amgen (LAMGN), Biogen (LBGEN), and Genzyme General (LGENZ) time series 5 4 3 2 1 0 -1 1/01/90 1/11/93 1/09/97 LAMGN LBGEN LGENZ Page 17 of 17

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