GOOD NEWS, BAD NEWS AND GARCH EFFECTS IN STOCK RETURN DATA

Transcription

1 Journal of Applied Economics, Vol. IV, No. (Nov 001), GOOD NEWS, BAD NEWS AND GARCH EFFECTS 313 GOOD NEWS, BAD NEWS AND GARCH EFFECTS IN STOCK RETURN DATA CRAIG A. DEPKEN II * The Universiy of Texas a Arlingon I is shown ha he volume of rade can be decomposed ino proporional proxies for sochasic flows of good news and bad news ino he marke. Posiive (good) informaion flows are assumed o increase he price of a financial vehicle while negaive (bad) informaion flows decrease he price. For he majoriy of a sample of en spli-socks i is shown ha he proposed decomposiion explains more GARCH han volume iself. Using he proposed decomposiion, he variance of reurns for younger spli socks reacs asymmerically o good news flowing ino he marke, while he variance for older spli-socks reacs symmerically o good news and bad news. JEL classificaion codes: C3, G14 Key words: informaion flows, auocorrelaion I. Inroducion The second momen analysis of Engle (198) has inroduced a wide lieraure invesigaing he persisence of variance in ime series daa, especially in financial conexs. The Auoregressive Condiional Heeroskedasiciy (ARCH) model, and he exension by Bollerslev (1986) o he Generalized ARCH (GARCH) model, can be used o explain he serial correlaion ha is someimes observed in daily reurns o sock shares. The noiceable clusering of like-magniude reurns can be modeled using GARCH, and hypohesis esing is sraighforward. One possible inerpreaion of he observed like-magniudes in variance is * Correspondence should be addressed o Deparmen of Economics, Arlingon, Texas , or by o depken@ua.edu.

2 314 JOURNAL OF APPLIED ECONOMICS ha informaion may be received and aced upon a differen imes by he agens in he marke. Thus here is a difference beween calendar ime, which daily reurns are based upon, and economic ime ha is acually generaing he daa. Considering how o measure he informaion flows ha can affec he variance of reurns; Lamoureux and Lasrapes (1990) invesigae he role ha volume plays in explaining he persisence of volailiy shocks by inroducing i as a mixing variable. Their work aemps o jusify he suggesions of Diebold (1986) and Sock (1987, 1988) ha sochasic informaion flows can explain he persisence of volailiy shocks. Using volume as a proporional proxy for informaion flows, Lamoureux and Lasrapes explain away he GARCH effecs found in daily sock reurn daa. This paper offers an exension o his lieraure by replacing he proxy for informaion (daily rading volume) wih a decomposiion of volume which proxies as a proporional measure of good news and bad news enering ino he marke. Using en spli-socks ha are differeniaed by age, I find ha younger splis reac asymmerically o good news and bad news, wih good news having a greaer effec on he persisence of variance. On he oher hand, older splis reac symmerically o good news and bad news, suggesing ha he marke has more complee informaion leading o more compleely formulaed expecaions on he reurns of older splis han younger. The paper is developed as follows. Secion II discusses he heoreical moivaion of GARCH in sock reurn daa and proposes a decomposed measure of volume ino good news and bad news flowing ino he marke. Secion III repors he empirical analysis. The final secion conains concluding remarks. II. GARCH in Sock Daa A. The Basic Model The ARCH model inroduced by Engle (198) was enhanced by Bollerslev (1986) o include only he squares of he pas residuals, leading o he

3 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 315 Generalized ARCH (GARCH) model. The model used here conains a GARCH formulaion similar o ha of Lamoureux and Lasrapes (1990), i.e., r = µ 1 ε ε ( ε 1, ε,...) ~ N(0, h ) h = α αε 1 1 α h 1 where r is he rae of reurn and µ is he condiional mean of r based upon all pas informaion. The condiional variance is a deerminisic funcion based upon he previous period s poinwise variance and he overall variance given he informaion a ime -1. Lamoureux and Lasrapes (1990) moivae heir analysis by considering ε he innovaion upon sock reurns, as a linear combinaion of inraday price movemens, i.e., n ε = δ ι (1) i= 1 where δ i is he i h inraday price incremen in day due o an informaion flow ino he marke, and n is he number of informaion flows wihin a given day. Thus, ε is an aggregaion of price innovaions from informaion flows ino he marke bu does no differeniae on he ype of informaion flows ino he marke. Differen ypes of informaion flows would be expeced o cause differen innovaions on price. Inroduced as a proporional proxy for informaion arrivals o he marke, volume acs as a mixing variable. This is imporan because ε is assumed o be random draws upon alernaive disribuions, wih variances depending upon informaion available a he ime. This use of volume leads o a model of he condiional variance of h = α h 0 αε 1 1 α 1 β1v ()

4 316 JOURNAL OF APPLIED ECONOMICS where V is he volume of rade ha occurs in ime. I use he same approach in aemping o explain he persisence of volailiy in daily sock reurns. 1 One mehod of measuring he persisence of volailiy shocks is o consider γ = (α 1 α ). As γ approaches 1, he persisence of volailiy shocks increases; ha is here is more evidence of GARCH. B. Good News and Bad News: Theoreical Foundaions In equaion (1), ε is presened as an aggregaion of inraday price changes caused by informaion flows ino he marke. However, ε can be decomposed ino posiive price changes summed over posiive informaion flows (good news), and negaive price changes summed over negaive informaion flows (bad news). This leads o an alernaive formulaion of n n δ i i= 1 j= 1 ε = δ (3) j where n is he number of posiive informaion flows ino he marke, and n is he number of negaive informaion flows ino he marke on a given day. Furher, le δ i be he absolue values of he inraday price changes due o good news on day, and δ j he absolue values of he inraday price changes due o bad news on day. This decomposiion is moivaed by he following inuiion. If an iem of bad news flows ino he marke hree possibiliies can lead o a decrease in he price: agens wishing o sell will do so only a a lower price; agens willing o buy will do so only a a lower price, or boh may occur. This is because bad news, e.g., a change in managemen, desrucion of capial, liigaion or new governmen regulaions, decreases he expeced reurn of he firm and hence 1 One problem wih using volume as a proxy for informaion is invesigaed in Lamoureux and Lasrapes (1994) where hey acknowledge possible problems associaed wih assuming he exogeneiy of volume in he marke and find ha a single laen variable canno explain boh volume and GARCH. Here, I assume ha volume is weakly exogenous.

5 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 317 lowers he price of he sock. Likewise, good news, e.g., higher han expeced profis, produc innovaion, increased marke share, or deregulaion, increases he expeced fuure reurns of he firm and causes an increase in he price of he sock. Normalizing he absolue price changes associaed wih each ype of informaion flow so ha δ i = δ j = δ, rewrie equaion (3) as ε = ( n n ) δ This normalizaion of he absolue price response o an informaion flow allows for up o hree addiional iems of he informaion se a ime o be uilized in he explanaion of GARCH. This follows because he price of a sock ypically flucuaes over he course of a rading day and is frozen a he end of he rading day (see Figure 1). These inraday price changes can be used o develop proporional proxies for posiive and negaive informaion flows. Figure 1. Price Changes from Sochasic Informaion Flows - info HI C info - info C -1 LO LO C -1 info

6 318 JOURNAL OF APPLIED ECONOMICS The difference beween he high price of he day (HI ) and he low price of he day (LO ) gives a oal aggregaion of posiive incremens in he price during he day. Furher, if he close of he previous day (C -1 ) is lower han he low of he curren day, hen we have a furher measure of posiive informaion ha is no capured by he difference beween high and low price. This will occur if good news has accumulaed while he marke was closed. A proporional proxy for he number of posiive informaion flows, n, can be derived by he oal aggregaion of posiive price incremens divided by he size of he posiive incremen δ i. An analogous proporional measure for he number of negaive informaion flows, n, can be measured by he difference beween he high price of he curren day (HI ) and he closing price of he curren day (C ). If he difference beween he closing price of he previous day and he low price of he curren day is posiive hen more negaive informaion flows have accumulaed in he marke during non-rading hours. Therefore, a proporional proxy for oal negaive informaion flows is he aggregaion of negaive price incremens divided by he size of he negaive incremen δ i. Resricing he normalizaion of incremenal price changes o being discree raher han coninuous allows for closed-form soluions for n and n in erms of observed daa available a ime. Using he definiions developed above, define HI = HI = V = ζ ( n n n n C LO ), max(0, LO C max(0, C δ δ 1 1 LO ), ), (4-6) where ζ > 0 is a proporioning facor. Equaions (4)-(6) comprise a sysem of hree equaions and hree unknowns (δ, n, and n ), which can be solved for he following closed-form soluions,

7 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 319 δ I I = ζ ( V ' ), ζn ζn V I = I = I ' I ' VI ' I, (7-9) where I = HI LO max(0, LO C 1 ), I ' = HI C max(0, C 1 LO ). Using hese closed-form soluions for proporional proxies of posiive and negaive informaion flows on a given rading day offers a possible advanage over using only he volume of rade. Firs, he decomposiion allows for more informaion available a ime o be used in he explanaion of GARCH effecs: he curren day s high and low prices and possibly he previous day s closing price. Furher insigh is available as o how GARCH is affeced by qualiaively differen informaion ypes; ha is wheher GARCH is driven by negaive or posiive informaion flows ino he marke. This decomposiion explicily includes informaion flows ha occur while he marke is closed. Previous sudies such as Baillie and Bollerslev (1989) and Bollerslev, Engle and Nelson (1993) have included qualiaive variables o indicae imes when markes are closed o conrol for asymmeric informaion flows beween marke and non-marke hours. Laux and Ng (1993) furher propose o remove volume compleely, because i is an incomplee measure of informaion flows, and describe he flow as a linear combinaion of announcemen-induced price changes and liquidiy-preference-induced price changes. However, my purpose is o deermine if volume used as a

8 30 JOURNAL OF APPLIED ECONOMICS proporional proxy for informaion flows can be decomposed so as o beer explain he persisence of variance eviden in sock reurn daa. Wih he proporional proxies for he aggregaed flows of good news and bad news ino he marke given in equaions (7)-(9), subsiuion of ζ n, and n for V yields a new specificaion of variance as ζ h ( = α α ε α h φ ζn ) φ ( ζn ). (10) Inferences can be made on how good news and bad news explain he persisence in variance. In paricular, he symmery of good news and bad news in explaining he variance in sock reurns can be invesigaed. If φ 1 and φ are saisically equal o each oher, he decomposiion offers no advanage over he approach used by suppors he resuls of Lamoureux and Lasrapes (1990) in ha he effecs of good news and bad news are symmeric. III. Good News and Bad News: Empirical Resuls To es he hypohesis ha good news and bad news affecs variance asymmerically, a sample of 100 socks was randomly seleced. As GARCH is ypically appropriae for ime-series of 00 observaions or more, of he one hundred seleced socks, all series shorer han 5 observaions were discarded. Of he original hundred socks, en series were subsequenly used. Five socks in he sample are ermed old in ha hey have been spli for a leas six hundred rading days. The remaining five socks in he sample are ermed young in ha hey have been spli for less han 600 bu more han 5 rading days. The series include he high price, low price, closing price, and volume of rade for each sock. Table 1 liss he socks, heir icker symbols and ime series lenghs. These socks are firs modeled using he GARCH(1,1) specificaion in equaion (), consraining he coefficien on he volume of rading, β 1, o zero. The resuls are lised in Table. For all socks oher han socks 6 and 7

9 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 31 Table 1. The 10 Companies in he Sample Company Name Ticker Series Lengh (observaions) Type 1 CNVX CNVX o (716) Old General Moors GM o (556) Old 3 Hewle-Packard HWP o (564) Old 4 IBM IBM o (90) Old 5 Inergraph Corp. INGR o (761) Old 6 QMS, Inc. AQM o (48) Young 7 CDNC CDNC o (08) Young 8 Carolina Power CPL o (08) Young 9 Texaco TX o (08) Young 10 Florida Power Corp. FPC o (71) Young he γ measuremen of volailiy persisence is above 0.7, indicaing ha hese ime series have persisence in variance. I hen model he variance of he en socks in he sample using he specificaion offered in (), ha is resricing φ 1 = φ in equaion (10), and resuls are repored in Table 3. Volume is saisically significan a he 0.05 level for all he en socks in he sample. For every sock in he sample he measure of GARCH is driven owards zero, suggesing ha he specificaion given in Lamoureux and Lasrapes (1990) is successful in explaining much of he persisence in variance. However, he specificaion in equaion () is a special case of equaion (10). Therefore, I relax he resricion of φ 1 = φ and re-esimae he model using he specificaion of variance in equaion (10). Upon esimaion, he null hypohesis ha φ 1 = φ is esed. If he null canno be rejeced hen he specificaion of variance is idenical o ha proposed by Lamoureux and Lasrapes (1990) and here is no advanage in using he decomposed informaion flows. The resuls of he esimaion and asympoic -saisics for he null hypohesis are repored in Table 4.

10 3 JOURNAL OF APPLIED ECONOMICS Table. GARCH(1,1) Resuls Company α 0 α 1 α γ (9.05) * (6.97) * (1.60) * (4.0) * (5.3) * (18.93) * (6.15) * (11.45) * (11.14) * (7.59) * (1.47) * (18.16) * (5.73) * (4.33) * (11.57) * (1.53) (1.9) (1.85) * (.47) * (3.18) * (3.3) * (0.91) (0.83) (.78) * (3.0) * (.9) * (6.75) * (1.76) * (0.79) (13.70) * Noes: Asympoic -saisics in parenheses. * denoes significance a he 5% level. The resuls obained in his sample are encouraging. For seven of he en socks, he decomposiion of aggregaed informaion flows capures more of he observed persisence of variance han using volume alone, ha is γ is driven closer o zero. Furher, he good news proxy is significan a he 0.05 level for nine of he en socks, and significan a he 0.10 level for Company

11 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 33 Table 3. GARCH(1,1) wih Daily Volume of Trade Company α 0 α 1 α β 1 γ (0.76) (.84) * (0.75) (15.9) * (0.00) (.46) * (0.33) (0.44) * (-10.95) * (3.14) * (0.69) (16.73) * (-10.14) * (.18) * (1.11) (3.47) * (0.00) (.47) * (-1.59) (18.69) * (0.00) (-0.14) (1.77) (8.30) * (0.00) (0.0) (1.15) (9.7) * (.49) * (1.17) (0.00) (3.84) * (0.91) (0.91) (0.00) (8.15) * (.73) * (0.3) (0.30) (.68) * Noes: Asympoic -saisics repored in parenheses. * denoes significance a he 5% level. 4. The bad news proxy is significan a he 0.05 level for eigh of he en socks and is insignifican for Company 7 and Company 10. Older splis in he sample fail o rejec he null hypohesis ha φ 1 = φ hree of five imes. Companies 1, 3 and 4 herefore suppor he specificaion

12 34 JOURNAL OF APPLIED ECONOMICS Table 4. GARCH(1,1) wih Decomposed Volume and H : f = f 0 1 Company γ φ 1 φ Η 0 :φ 1 = φ (4.77) * (6.03) * * (8.68) * (4.41) * (7.36) * (11.0) * (1.75) (.03) * * (8.94) * (3.80) * (4.34) * (.94) * * (7.43) * (1.03) (.) * (.41) * * (5.87) * (.63) * * (3.38) * (-0.34) Noes: Asympoic -saisics repored in parenheses. * denoes significance a he 5% level. of variance offered in Lamoureux and Lasrapes (1990). However, Companies and 5 rejec he null hypohesis wih posiive informaion holding more srengh in explaining he variance of reurns. For Company posiive informaion has a coefficien approximaely hree imes as large as he

13 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 35 coefficien on bad news, while for Company 5 good news has a coefficien approximaely wice as large as bad news. On he oher hand, four of he five younger splis in he sample rejec he null hypohesis; Company 8 is he only young spli ha fails o rejec he null hypohesis. The asymmeric effec of posiive informaion on he volailiy of reurns is pronounced for young splis. Company 7 exhibis he mos asymmeric effec in ha he coefficien on good news is approximaely seven imes as large as he coefficien on bad news. The fac ha more young splis rejec he null hypohesis may indicae ha he marke has incompleely formulaed expecaions on he fuure reurns of he firm. As he marke has more compleely formed expecaions of he fuure reurns of he firm, he less an individual sochasic informaion flow will have on he variance of price. The older splis of he sample suppor he Lamoureux and Lasrapes (1990) formulaion for explaining away he persisence of variance eviden in he daa. In modeling he variance of he older splis, he aggregaed informaion flows ino he marke holds as much power as he decomposed levels of good news and bad news. Therefore, he decomposiion offers no advanage in explaining he variance of price. On he oher hand, younger splis are more vulnerable o he level of posiive and negaive informaion flows as refleced in he proxies developed here. These findings may indicae ha he marke has incompleely formulaed expecaions on he firm s abiliy o provide posiive reurns in he fuure. IV. Conclusions This paper uilizes a sample of en firms ha have spli heir sock in rade. The resuls of Lamoureux and Lasrapes (1990) are replicaed, and he gross level of informaion flows, as proxied by he volume of rade, does explain much of he persisence in variance apparen in he daa. A decomposiion of aggregaed informaion flows ino he marke is developed. I is possible o derive closed-form soluions for proporional proxies of good news and bad news enering ino he marke, he former

14 36 JOURNAL OF APPLIED ECONOMICS raising he price of financial insrumen and he laer decreasing he price. These proxies are based upon he volume of rade, he closing price of he previous day and he high and low-price of he curren rading day. Thus up o hree addiional iems of informaion are available for explaining he persisence of variance. I model he variance in sock marke reurns by subsiuing he proporional proxies for posiive and negaive informaion flows for he aggregaed proxy for informaion flows. For nine of he en socks in he sample, he amoun of persisence in variance explained by decomposed informaion flows is greaer han using he aggregaed measure. I find ha he variance of younger socks reacs asymmerically o good news perhaps reflecing incompleely formulaed expecaions on he par of he marke, while older socks in he marke respond symmerically o he ype of informaion flows ino he marke. References Baillie, Richard T. and Bollerslev, T. (1989), The Message in Daily Exchange Raes: A Condiional Variance Tale, Journal of Business and Economic Saisics, 7: Bollerslev, Tim (1986), Generalized Auoregressive Condiional Heeroskedasiciy, Journal of Economerics, 31: Bollerslev, Tim, Rober F. Engle, and Daniel B. Nelson (1993), ARCH Models, The Handbook of Economerics, Volume 4. Diebold, Francis X. (1986), Commen on Modeling he Persisence of Condiional Variance, Economeric Review, 5: Engle, Rober F. (198), Auoregressive Condiional Heeroskedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion, Economerica, 50: Lamoureux, Chrisopher and William D. Lasrapes (1990), Heeroskedasiciy in Sock Reurn Daa: Volume versus GARCH Effecs, Journal of Finance, 45: 1-9. Lamoureux, Chrisopher and William D. Lasrapes (1994), Endogenous

15 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 37 Trading Volume and Momenum in Sock Reurn Volailiy, Journal of Business and Economics Saisics, 1: Laux, Paul A. and Ng, Lilian K. (1993) The Sources of GARCH: Empirical Evidence from an Inraday Reurns Model Incorporaing Sysemaic and Unique Risks, Journal of Inernaional Money and Finance, 1: Sock, James H., (1987), Measuring Business Cycle Time, Journal of Poliical Economy, 95: Sock, James H., (1988), Esimaing Coninuous-ime Processes Subjec o Time Deformaion, Journal of he American Saisical Associaion, 83: