RELATIONSHIP BETWEEN VOLATILITY AND TRADING VOLUME: THE CASE OF HSI STOCK RETURNS DATA

Transcription

1 RELATIONSHIP BETWEEN VOLATILITY AND TRADING VOLUME: THE CASE OF HSI STOCK RETURNS DATA Mchaela Chocholaá Unversy of Economcs Braslava, Slovaka

2 Inroducon (1) one of he characersc feaures of sock reurns s he me-varyng volaly he poneerng work n he area of modellng volaly was presened by Engle [1982] nowadays a large number of modfcaons of he sandard ARCH and GARCH models have been developed hough he ARCH/GARCH class models allow he volaly shocks o perss over me, hey ddn provde he economc explanaon for hs phenomenon

3 Inroducon (2) he paper of Lamoureux and Lasrapes [1990] offers he explanaon for volaly perssence her approach has been appled n varous sudes o boh ndvdual socks (sock-level analyss) and sock marke ndces (marke-level analyss) hey proved ha he daly radng volume has a sgnfcan explanaory power regardng he varance of daly reurns

4 The am of he presenaon: o analyse he relaonshp beween he radng volume and he daly volaly of he Hong Kong HSI sock reurns daa usng he GJR-GARCH models and applyng he approach of Lamoureux and Lasrapes [1990]

5 Daa and Mehodology he whole analyss was done on logarhmc ransformaon of daly ndex reurns and daly radng volume he logarhmc sock reurns are calculaed as he logarhmc frs dfference of he daly closng values of he analyzed sock ndex,.e. P r P d(ln( P)) ln P where s he closng value of he sock ndex a me and r denoes logarhm of he correspondng sock reurn 1

6 Closng values of he HSI sock ndex and descrpve sascs of he logarhmc reurn seres CLOSE Seres: DLCLOSE Sample 1/03/2005 3/31/2011 Observaons 1535 Mean Medan Maxmum Mnmum Sd. Dev Skewness Kuross Jarque-Bera Probably

7 Mehodology condonal mean equaon he logarhmc sock reurns equaon,.e. he condonal mean equaon, can be n general wren as a Box-Jenkns ARMA(m,n) model of he form: r m n 0 + φ jr j + θkε k j 1 k 1 ω + ε where ω0 s unknown consan, φ ( j j 1,2,...m ) and θ k ( k 1,2,...n ) are he parameers of he approprae ARMA(m,n) model, s a dsurbance erm. ε

8 Mehodology condonal varance equaon he condonal varance equaon n case of a GJR-GARCH(p,q) model can be specfed as: where from, s clear he dfferen mpac of he posve shocks and negave shocks on he condonal varance o examne he effec of radng volume on sock reurns volaly, he followng modfcaon of he condonal varance equaon s used q p q I h h ε γ β α ε α > < 0 0, 0 1, f f I ε ε > 0 ε 0 < ε q p q V I h h δ ε γ β α ε α V

9 Emprcal resuls he analyss was done n wo seps whou and wh radng volume ncluded no he condonal volaly equaon he approprae ARMA (m,n) model for logarhmc sock reurns was esmaed (able 1) he esmaon resuls of condonal varance equaons whou and wh he radng volume ncluded usng he GJR-GARCH(1,2) model are n able 2 and able 3, respecvely

10 Table 1 Dependen Varable: D(LOG(CLOSE)) Mehod: Leas Squares Dae: 11/20/11 Tme: 18:59 Sample (adjused): 1/04/2005 3/31/2011 Included observaons: 1534 afer adjusmens Convergence acheved afer 5 eraons Backcas: 12/21/2004 1/03/2005 Varable Coeffcen Sd. Error -Sasc Prob. C MA(10) R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regresson Akake nfo creron Sum squared resd Schwarz creron Log lkelhood F-sasc Durbn-Wason sa Prob(F-sasc) Invered MA Roos

11 Table 2 Dependen Varable: D(LOG(CLOSE)) Mehod: ML - ARCH (Marquard) - Normal dsrbuon Dae: 11/20/11 Tme: 19:03 Sample (adjused): 1/04/2005 3/31/2011 Included observaons: 1534 afer adjusmens Convergence acheved afer 14 eraons MA backcas: 12/21/2004 1/03/2005, Varance backcas: ON GARCH C(3) + C(4)*RESID(-1)^2 + C(5)*RESID(-1)^2*(RESID(-1)<0) + C(6)*RESID(-2)^2 + C(7)*GARCH(-1) Coeffcen Sd. Error z-sasc Prob. C MA(10) Varance Equaon C 3.07E E RESID(-1)^ RESID(-1)^2*(RESID(-1)<0) RESID(-2)^ GARCH(-1) R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regresson Akake nfo creron Sum squared resd Schwarz creron Log lkelhood F-sasc Durbn-Wason sa Prob(F-sasc) Invered MA Roos

12 Table 3 Dependen Varable: D(LOG(CLOSE)) Mehod: ML - ARCH (Marquard) - Normal dsrbuon Dae: 11/20/11 Tme: 19:04 Sample (adjused): 1/04/2005 3/31/2011 Included observaons: 1534 afer adjusmens Convergence acheved afer 25 eraons MA backcas: 12/21/2004 1/03/2005, Varance backcas: ON GARCH C(3) + C(4)*RESID(-1)^2 + C(5)*RESID(-1)^2*(RESID(-1)<0) + C(6)*RESID(-2)^2 + C(7)*GARCH(-1) + C(8)*LOG(VOLUME) Coeffcen Sd. Error z-sasc Prob. C MA(10) Varance Equaon C E RESID(-1)^ RESID(-1)^2*(RESID(-1)<0) RESID(-2)^ GARCH(-1) LOG(VOLUME) 6.31E E R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regresson Akake nfo creron Sum squared resd Schwarz creron Log lkelhood F-sasc Durbn-Wason sa Prob(F-sasc) Invered MA Roos

13 he receved resuls show que hgh degree of he q p volaly perssence, snce he sum ˆα + s 1 ˆβ 1 hgh n model whou radng volume varable akes value of 0, and besdes hs fac also he exsence of he leverage effec was proved (snce he correspondng parameer s sascally sgnfcan and posve) n model wh radng volume varable he volaly perssence slowly declned o 0,866518

14 The dagnosc check sascs of he sandardzed resduals n order o have he nformaon abou adequacy of he presened esmaes, we esed he sandardzed resduals he uncorrelaedness of he sandardzed resduals and squared sandardzed resduals was proved usng he Ljung Box Q sascs and Q 2 sascs, respecvely he normaly was no confrmed (Jarque Bera es)

15 Condonal varance whou and wh he radng volume ncluded Condonal varance whou he radng volume Condonal varance wh he radng volume ncluded

16 Concludng remarks he logarhm of he radng volume was ncluded no he condonal volaly equaon n order o nvesgae f s a good proxy for nformaon arrval akng no accoun some oher papers (e.g. [Grard and Bswas 2007], [Gursoy e al. 2008], [Sharma e al. 1996]), he resuls of our analyss concde wh hers,.e. ha he radng volume can be n general consdered (n case of he marke-level analyss) o be only a poor proxy for nformaon flow

17 References (Exrac) Engle R.F. (1982) Auoregressve Condonal Heeroscedascy wh Esmaes of he Varance of Uned Kngdom Inflaon, Economerca, 50, No. 4. Grard E., Bswas R. (2007) Tradng Volume and Marke Volaly: Developed versus Emergng Sock Markes, The Fnancal Revew, 42, pp Gursoy G., Yuksel A., Yuksel A. (2008) Tradng volume and sock marke volaly: evdence from emergng sock markes, Invesmen Managemen and Fnancal Innovaons, Vol. 5, Issue 4, pp Lamoureux C., Lasrapes N. (1990) Heeroscedascy n sock reurn daa: volume versus GARCH Effecs, The Journal of Fnance, Vol. XLV, No. 1, pp Sharma J.L., Mougoue M., Kamah R. (1996) Heeroscedascy n sock marke ndcaor reurn daa: volume versus GARCH effecs, Appled Fnancal Economcs, Vol. 6, pp