An international Comparison of Volatility in Stock Market Returns Prior and Post Global Financial Crisis

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1 01 Inernaional Conference on Economics, Business and Markeing Managemen IPEDR vol.9 (01) (01) IACSIT Press, Singapore An inernaional Comparison of Volailiy in Sock Marke Reurns Prior and Pos Global Financial Crisis Hsiaofen Chang + Deparmen of Accouning Informaion, Aleheia Universiy Absrac. The aim of his sudy is o compare he volailiy in sock marke reurns prior and pos global financial. From he VIX, before he, Taiwan s VIX is evidenly higher han ha of America s and Europe s. While afer he, Taiwan s VIX is mosly lower han ha of America s and Europe s. In his sudy, he EGACH model is chosen for analysis. From he EGACH model we can deermine wo poins. Firs, he Taiwan sock marke is mainly influenced by he price informaion of he preceding day and has a relaively long flucuaion ime and is following he high flucuaion cos regardless of before or afer he. Second, EURO STOXX 50 and S&P 500 have greaer influences before or afer he on he negaive informaion of he marke prices. TAIEX does no seem o impac he negaive informaion severely. Keywords: global financial ; sock marke reurns; volailiy; EGACHM model 1. Inroducion The global financial really sared o show is effec in he middle of 007 and ino 008. I is believed o have begun wih he credi crunch, he subprime and housing bubble issues in America. The collapse of Lehman Brohers on Sepember 14, 008 marked he beginning of a new phase in he global financial, while many financial insiuions laer faced serious liquidiy issues. Twenyone developed counries share indexes had dropped by 1% he bigges decline in range since The whole world lapsed ino an unprecedened economic. America s economic decline severely affeced various counries expors, leading some expororiened counries o fall ino decline as well. The financial sunami swep over he globe, impacing almos every counry. Taiwan is a small open economy; herefore i has a high probabiliy of being influenced by developed counries. The Taiwanese economy is heavily dependen on expors, and during he financial, he desrucion of wealh in Norh America led o reduced demand for impors, which had a severe impac on Taiwan s expor performance. The global financial made is presence fel in Taiwan as Taiwan s forecas economic growh rae for 009 was 3.34 percen, a sharp decline from a forecas 5.5 percen in 008. Taiwan s share index also fell by half from is high of 9,303 on May, 008. In addiion, hose economies in Europe whose financial secors had been highly inernaionalized and ha were closely linked o he US were also badly affeced. While a number of macroeconomic and financial variables like GDP, ineres rae, exchange rae, unemploymen rae, ec., influence he sock marke, his paper places an emphasis on a comparaive analysis of Taiwan s sock marke and ha of America s and Europe s. The purpose is o find he difference in hese hree marke flucuaions, explain he reasons for flucuaion in Taiwan s sock marke, and provide informaion ha hopefully is helpful for policymakers.. Daa descripion + Corresponding auhor. address: jessica039au@yahoo.com.w 70

2 .1. Daa resource A sock index can represen he general sandards and changes in many sock prices. This hesis uses he share price index o weigh he changes in general sock prices (in he whole sock marke), which, o a cerain exen, reflec he change and endency of he sock marke. I chose hree sock indexes daily closing prices as represenaion for sock prices (A) and (B) as before and afer specimens for Taiwan, S&P 500 (USA), and Europe s sock marke, and used he EVIEW 5.0 sofware for analysis... Daa descripion In his sudy, we analyze he closing price of sock indexes of Europe, America, and Taiwan, which are EURO STOXX 50, S&P 500, and TAIEX respecively. The informaion source of Europe and America s sock index is Yahoo! Finance (hp://finance.yahoo.com) and he informaion source of Taiwan s sock index is Taiwan Economic Journal Co., Ld (hp:// The daa used in his paper cover he daily sock index of he hree counries from 005/1/4 o 011/7/5. We can caegorize he daa ino hree periods: he whole period (005/1/4 o 011/7/5), before he (005/1/4 o 008/9/13), and afer he (008/9/14 o 011/7/5). Sock marke reurns: R = (ln P ln P ) *100%, i = 1,,3 (1) i i i 1 Fig. 1: The Sock Marke Reurns of America, Europe and Taiwan before and afer Global Financial Crisis. Fig.1 is a comparison of sock price flucuaions in America, Europe and Taiwan. The flucuaion margins of America and Europe have obviously widened afer he financial (America s widening of margin was especially dramaic), bu he financial has no been coninuous, and here are no severe impacs on Taiwan s flucuaion margin (Taiwan has price limis). Alhough recenly he flucuaion margins of America, Europe and Taiwan have narrowed, hey have no reurned o heir original flucuaion range of 007. Fig. : The graph above compares he volailiy index beween Taiwan, America and Europe. 71

3 .3. VIX Afer he global sock in 1987, NYSE impored circui breakers in 1990 o sabilize he sock marke and proec is invesors. These circui breakers allowed us o observe dynamic flucuaions of he marke. To measure he flucuaion rae of he marke, he Chicago Board Opions Exchange (CBOE) esablished VIX (Marke Volailiy Index) in The VIX represens one measure of he marke s expecaion of sock marke volailiy over he nex 30day period. Before he (shown o he lef of he red verical line on he graph), Taiwan s VIX is evidenly higher han America s and Europe s. Afer he, (shown o he righ of he red verical line on he graph), Taiwan s VIX is mosly lower han America s and Europe s. Table1. Descripive Saisics TW S&P 500 EURO Index Enire period Before Afer Enire period Before Afer Enire period Before Afer Mean Medi an Sd Skew Kur Jarqu e Bera p value ADF p value Samp le size Noe: The rows Mean, Sd., Skew., and Kur. sand for he sample mean, sandard deviaion, skewness coefficien, and kurosis coefficien of he five indices. Table 1. repors descripive saisics for hese sample daa. We can see ha he European sock index was he mos affeced index afer he. Is mean and median are negaive, and i has he bigges flucuaion. Taiwan s TAIEX was no nearly as affeced. Is mean is five imes ha of he indexes of Europe and he USA. The kurosis coefficien of all hree indexes for he enire period is greaer han hree, meaning ha all he indexes have Lepokurosis characerisics. The kurosis coefficien of he indexes of boh he USA and Europe is higher, which demonsraes is response from he impacs of he laes news. The pvalue of he JarqueBera examinaion is far smaller han he significance level, so i doesn conform o he normal disribuion. The higher he JarqueBera value, he more obvious he characer of Lepokurosis, he furher away i is from he normal disribuion, and he greaer he inernal uncerainy. ADF (Augmened DickeyFuller) is used o proceed wih a uni roo es on he daa of he hreeime series (Enire period, Before, Afer ). The null hypohesis of he uni roo was rejeced, which shows ha he hree sock marke reurns are saionary. 3. Model consrucion and parameers esimaion 3.1. Model consrucion The daily sock marke reurn s disribuion usually has wo characerisics. The firs is volailiy clusering as menioned by Mandelbro [5] (p. 418) large changes end o be followed by large changesof 7

4 eiher sign and small changes end o be followed by small changes This saemen is observed in many financial applicaions. The second is a lepokuric (wih he sample kurosis coefficien>3) and asymmeric disribuion. This srongly rejecs he Gaussian whie noise hypohesis for he reurn sequence. Wha asymmery refers o is ha new informaion ends o cause volailiy, and negaive informaion generaes a greaer impac on volailiy han posiive informaion of he same magniude. A GARCH (generalized auoregressive condiional heeroskedasiciy) model was proposed by Engle [3] and generalized by Bollerslev [1]; he GARCHM model was inroduced by Engle, Lilien and Robins [4]. Under he assumpion of condiionally normal or disribuion, he EGARCHM model s coefficiens are nonnegaive; herefore, he GARCHM model canno explain eiher he lepokuric disribuion or volailiy clusering of he reurn series, especially no for he volailiy asymmery. To ake he asymmeric volailiy effec ino accoun, some nonlinear mechanisms were inroduced ino he condiional variance specificaion of he GARCH model. Nelson [6] developed he exponenial GARCH (EGARCH) model and replaced he normaliy assumpion of sandardized innovaions wih he generalized error disribuions assumpion. We prefer he EGARCHM model, which accommodaed more precise esimaions of he asymmeric relaionship beween sock price reurns and volailiy changes. The EGARCH(1,1)M model : Mean equaion: Variance equaion: p q 1 R i i i i = c+ λ σ + air 1 + bi R 1 1 Z i 1 i 1 i j + ε, ε = σ = = + i= 1 () ε ε 1 1 log( ) σ = ω + α + γ + β log( σ 1 ) σ σ 1 1 (3) The mean equaion akes he effecs of various elemens ino accoun, such as risk premium and he course of ARMA(p,q). These elemens economic significance is as below: Mos invesors are risk averers. The bigger he sock flucuaion, he greaer he reurn hey expec from i; herefore, he more obvious he risk premium. On how he i value was chosen; firsly, he sofware did a correlaion analysis on he acily acknowledged lag 36 seps variables. And he value of p,q was chosen due o he ACF (Auocorrelaion Funcion) and PACF (Parial Auocorrelaion Funcion). The σ in equaions () and (3) are condiional variance. The larger σ, he larger he range of sock price flucuaion. Generally speaking, σ is a measuremen for risk, and λ reflecs he posiive correlaion beween risk and reurn []. c and ω are boh consans; hey represen he nonrisk reurns of sock invesmen. ε is he error erm series. Z is a process of sandardizaion, is mean is zero, and variance is one. Generally, we use he Lagrange Muliplier Tes (LM Tes) o es for he exisence of he ARCH effec. This hesis uses he LM Tes o examine he residual series of EURO STOXX 50, S&P 500, and TAIEX. If he pvalue is less hen significance level 0.05, his indicaes ha he oucome of he examinaion is significan, and ha he residual series has an ARCH characer. Using he maximum likelihood mehod and EVIEWS5.0 sofware o solve he equaion se from above, we have he esimaed value of maximum likelihood of all parameers from equaion () o (3). For resuls of he esimaed value of each parameer, please refer o Table 3. Table locaion The opimal model Enire period Before Afer TAIEX AR(1) a EGARCH(1,1) AR(1) a EGARCH(1,1) AR(1) a EGARCH(1,1) S&P 500 MA(1) EGARCH(1,1) ARMA(,1) EGARCH(1,1) EGARCH(1,1) b Euro 50 ARMA((),()) EGARCH(1,1) EGARCH(1,1) b ARMA((1,4),(4,)) EGARCH(1,1) 73

5 Noe: The symbol a indicaes ha i is enough o find he fied model wihou he MA (Moving Average process) erm o adjus he residuals. The symbol b indicaes by he Q saisics and he graph of ACF, he PACF may judge he residuals are wrie noises,so we do no need o esablish ARMA(p, q) o adjuss he residual iem. From Table, in he ARMA process, we can see ha in differen naions he sock price reurns are influenced by price informaion. Take TAIEX for example; regardless of before or afer he, i is mainly influenced by he price informaion of he preceding day. However, before he, he S&P 500 index is affeced by he previous wo days; afer he, EURO STOXX 50 is affeced by he preceding day and he previous four days. Ye he S&P 500 index of afer he and EURO STOXX 50 of before he are simply no affeced by he before price informaion. According o he marke efficiency heory, in he weakform efficien marke, he presen's price may reflec he beforehand price informaion, especially recen informaion. Therefore, he S&P 500 index of afer he and EURO STOXX 50 of before he are more effecive. Table3 locaion During ime ˆλ ĉ ˆω ˆ α TAIEX S&P 500 Euro 50 Enire period 0.54** 0.35*** Before 0.9*** 0.347*** Afer 0.574** 0.635*** Enire period 0.105*** 0.078*** 0.140*** 0.088*** ˆ γ ˆ β 0.145*** 0.108*** 0.986*** 0.111*** 0.1*** 0.99*** 0.18*** 0.093** 0.939*** 0.117*** Before 0.051** 0.054* Afer Enire period Before 0.061*** 0.077*** 0.084*** 0.108*** 0.157*** 0.1*** 0.983*** 0.971*** 0.986*** 0.108*** 0.17*** 0.978*** 0.0*** 0.96*** Afer 0.048*** 0.048* 0.08** 0.17*** 0.979*** *** Noe: The symbol*** signifies significance a 1% level; he symbol** signifies significance a 5% level; he symbol* signifies significance a 10% level. Blanks indicae ha he argumen independen variable is insignifican a 10% level in regression, so i has been eliminaed from he model. 3.. Esimaion and empirical resul From Table 3, we can see ha he ĉ value of he European sock marke is negaive afer he financial, indicaing ha he nonrisk repaymen is negaive in his marke. Because he oal reurns raio is equal o he nonrisk rae of reurn plus he risk premium, and since all marke average gross revenues are nonnegaive, herefore he high risk premium rises o make up for negaive nonrisk repaymen, hus an invesor migh obain an average reurn. In oher words, as he high risk premium rises, i aracs risk invesors by chance. In he condiion variaion equaion, he consan ˆω has promulgaed a longerm flucuaion fixed cos. In able III, regardless of before or afer he, he TAIEX absolue value of ˆω is higher han he oher wo indices. This indicaes ha he Taiwan sock marke has a relaively long flucuaion ime and is following he high flucuaion cos. Anoher disincive resul is ha he coefficien ˆ α values of Taiwan are sill he larges; his demonsraes ha he Taiwan sock marke has a very ousanding volailiy clusering effec, and ha he duraion of is price flucuaion is longer. Once some kind of impac causes sock price reurns o have an abnormal flucuaion, his kind of abnormal flucuaion is unable o eliminae iself in he shor erm (i may be because of he rise and decline percenage limi, which is why i was longer during imes when Taiwan s sock marke (boh before and afer he ) saw abnormal flucuaions. 74

6 Oher han his, he resul of he coefficiens of ˆ γ shows ha none of he indexes coefficien is zero and all of he coefficiens are significan, which means ha he impac of informaion is no symmerical; i is also an indicaion of he leverage effec menioned elsewhere. From his, we can conclude ha in EURO STOXX 50 and S&P 500, negaive ˆ γ values mean he greaer influences ha negaive informaion has on he marke prices. TAIEX does no seem o have a severe impac on he negaive informaion. As can be seen by he empirical analysis above, compared wih he oher wo sock markes, sock prices of Taiwan sock marke volailiy has shown a relaively long period. This is because of Taiwan has price limis, i is no possible o eliminae in he shor erm, i requires higher flucuaion cos o diges he risk which he flucuaion brings. In addiion, due o he social sabiliy and oher reasons, i will usually carry on he guaranee o invesor's invesmen loss explicily or implicily, such as, naional securiy fund or posal funds ino he sock marke, so invesors will relax heir awareness of he risk and managemen, hereby affecing he volailiy of asse prices, his acion, wheher really exiss or only in concep, has affeced invesors in deermining asse prices and volailiy o a cerain exen. 4. Conclusions This aricle examines Taiwan, Europe and he U.S. sock marke price flucuaions: From he VIX, before he, Taiwan s VIX is evidenly higher han America s and Europe s. While afer he, Taiwan s VIX is mosly lower han America s and Europe s. Obviously, invesors in Taiwan are raher more opporunisic when invesing in longerm invesmen holdings. From he EGACH model we can deermine wo poins. Firs, he Taiwan sock marke is mainly influenced by he price informaion of he preceding day and has a relaively long flucuaion ime and is following he high flucuaion cos regardless of before or afer he. Second, EURO STOXX 50 and S&P 500 have greaer influences before or afer he on he negaive informaion of he marke prices. TAIEX does no seem o impac he negaive informaion severely. 5. References [1] T. Bollerslev. Generalized auoregressive condiional heeroskedasiciy, Journal of Economerics, 1986, 31: [] J.Y.Campbell, and L. Henschel. No News is Good News: An Asymmeric Model of Changing Volailiy in Sock Reurns. Journal of Financial Economics. 199, 31: [3] R.F. Engle. Auoregressive Condiional Heeroskedasiciy wih Esimaes of he Variance of UK inflaion, Economerica. 198, 50: [4] R.F. Engle, D.M. Lilien, R.P. Robin. Esimaing Time Varying Risk Premia in he Term Srucure: The ARCHM Model. Economerica. 1987, 55: [5] B. Mandelbro. The Variaion of Cerain Speculaive Prices. Journal of Business. 1963, 36: [6] D. Nelson. Condiional Heeroskedasiciy In asse Reurns: A New Approach. Economerica. 1991, 59: