Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi e-mail: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman, Finance and Economics Institute of Business Administation, Kaachi Phone#-4-4 Fax. 4983867 e-mail: mmnishat@yahoo.com Abstact This pape examines the elationship between aggegate stock maket tading volume and seial coelation of daily stock etuns duing Decembe 99 to Decembe. The esults show that the noninfomational tade has a significant effect on pices and tading activity in addition to pesent etuns, nonlinea volume and volatility. It indicates that stock etuns moved too much due to change in the fundamentals, aggegate expected etuns, and changes in effective isk avesion of maket paticipants. The same esults found in pe-nuclea test peiod (Decembe 4, 99 to May 8, 998). Howeve, the weak and insignificant esult found in post-nuclea test peiod (May 8, 998 to Decembe 3, ). The second ode autocoelation indicates a positive and weak elation as compaed to fist ode autocoelation. Moeove, it is positive when it elates to weighted tading volume in entie sample peiod and two sub-sample peiods. It implies that the ole of infomation is effective afte two days and noninfomatiol ole is less effective.
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Muhammad Nishat. Intoduction The fluctuation in tading activity is not only explained by publicly available infomation but also by noninfomation tade due to events, shot selling, and inside tades. These factos ae exogenous to the geneal pice behaviou in stock maket (Campbell, Gossman and Wang 993). Howeve, these fluctuation ceates the simila effect to those poduced by a change in the isk avesion of significant popotion of maket paticipants (Ali, 997). The academic liteatue povides the association between tading volume and stock etun volatility. It is also found that high stock volume is linked with volatility and positive elation between stock etuns and volume. Mose (98) found that the seial coelation of etuns in high volume and high volume peiods tend to have positively autocoelated etuns. Le Baon (99a) and Sentana and Wadhwani (99) showed that autocoelation of daily stock etuns change with the vaiance of etuns. Duffee (99) established the elation between seial coelation and tading volume in aggegate monthly data. Campbell, Gossman and Wang (993) examined the elationship between aggegate stock maket tading volume and the seial coelation of daily stock etun. They found that a stock pice decline on high volume day is moe likely than a stock pice decline on low volume day to be associated with an incease in the expected stock etun. Oman and Mckenzie () investigated the elation between volume of tade and conditional vaiance of tade and found the significant elation between timing of innovational outlies in etuns and volume. Duing ealy nineties the non-infomational factos geate influence on stock maket activity in Pakistan. These factos ae include stuctued changes in stock maket, constucting the stock pice index, based on maket capitalization. These wee the esult of financial libealisation and deegulation policy (Nishat, 999). This has impotant impact in the fom of uncetainty and isk avesion. Due to inadequate egulatoy and weak enfocement of ules, thee has isen the poblem like as inside tading and unchecked magin equiement tading. As a esult these ceated the leveage (Nishat, ), which can easily foced investos in bankuptcy poblem if the investos expectation about futue pices ae not ealised. A numbe of mega poject in pioity sectos like PTCL, Hubco and othes which attacted the investos specially the foeign investos took away all excess liquidity, which in tuns spaked off the stock selling fo wanted of liquidity and this esulted in pice fluctuations. Pefeential teatment fo boke as jobbe and involvement in speculative tade wee also the eason of undue fluctuation in pices. The deteioating situation of law and ode and gooming political instability advesely affected the stock pices. A lage potion of capital Govenment of Pakistan povided subsidies and special tax teatment to these sectos in 99s (Economic suvey of Pakistan, Ministy of Finance).
inflow in stock maket was due to potfolio investment. The inflow and out flow of capital depends on the political and economic condition of the county. It is also caused of excessive fluctuation in stock maket (Nishat, ). Ali (997) studied the elationship between stock pices and tading volume in context of Kaachi stock maket s daily data fo vey small time peiod i.e. nine months data. He found that significance of non-infomational tade in explaining the fluctuations in stock pices. The pupose of the study is to investigate the non-infomational tade in Kaachi stock maket using tading volume data. It is difficult to test non-infomational tade by using meely the stock etun data (Ali, 997). The basic logic to use the volume is that the tading activity has explanatoy powe in addition to past etuns, and pice changes accompanied by high volume tend to be evesed (Ali, 997). We de-tend the data of volume and etun and check the stationay of the data by using the Phillips Peon test and then estimate the etun on volatility and tading volume. The est of the pape is oganized such that next section discusses the econometic technique, methodology and descibed the data used in this pape. Section thee pesent the empiical esults. Conclusions ae given in section fou.. Econometic Methodology and Data The main etun seies used in this pape is daily etun ( t ) on value weighted index of stock taded on KSE, ove the peiod Decembe 4, 99 to Decembe 3,. Tading volume (V t ) data and stock pice data ae collected fom daily newspape Business Recode. The stock etun seies is geneated by fist diffeence of log pices and tading volume is used as the log of daily tun ove. We test two seial coelation to find the influence of cuent pice on futue pice. t + t + = α + α + β i i () () To check the day of the week effect we intoduced the dummy vaiables. = α + α + t + β + t α i β i D i i D i i (3) (4) The ole of non-infomational tade on stock pices is detemined by intoducing the change in volume as non-infomation facto. We multiply the tading volume with etuns. Tading volume gives the weight to etuns on those days when tading volume is highe than the etuns on the days when it is nomal. By this
3 we ae able to find the impact of etuns on the days of highe tade on the next day etuns so ou equation wil become: = α + α + t + β + t α i β D + α V i t i t 3 t t D + β V 3 t t () (6) To test any non-lineaity in the model we intoduced the squae of tading volume and conditional vaiance, which show the nonlinea elation between stock etuns and tading volume. = α + α + t + β + t α i β D + α V i i i D + β V i t 3 t t 3 t t + α V 4 t 4 t + β V t + α σ + t σ i (7) (8) 3. ESTIMATION AND RESULTS Result with the data fom Dec 4, 99 to Dec 3, is likely to be dominated in pe-nuclea test peiod. That is why we split this peiod into two-sub sample peiod, i.e. Decembe 4,99 to May 8, 998 and May 9, 998 to Decembe 3,. Gaph 8. 7.8 7.6 7.4 8 7. 6 7. 6.8 4 6.6 Log Pices Log Volume Gaph shows high fequency vaiation in pices and volume. To educe this vaiation we have taken diffeence of log volume and log pice. We want to wok with stationay time seies. When we elate ou empiical esults to ou theoetical mo del, we want to measue tading volume elative to the capacity of the Pakistan had nuclea test on May 8, 998 that has significant impact on KSE- and it declines fom 4.9 to 789. and tading volume fom Rs6 million to Rs9 million 3
4 maket to absob volume. To emove low fequency vaiations fom the vaiance we measue tunove in logs athe in absolute value. To de-tend the log tunove seies, we subtact a twenty day backwad moving aveage of log tunove 3. GRAPH.... -. -. -. log of etun - log of volume Gaph shows the tansfomed seies of log stock etun and log of tading volume. The gaphs show that the tend and low fequency vaiations have been emoved. Table shows Phillips-Peon Unit Root Test esults, which test the stationaity of seies of etun and tading volume. It indicates that both seies ae stationay in log fom. Table summaise the evidence on the fist ode autocoelation of the index etun. Fo each of the sample peiod, the table epots the autocoelation with a hetoscedasticity consistent standad eos, and R (Model ) statistics fo egession of the one day ahead etun on a constant etun. R (Model ) is just the squae of the autocoelation. The highest autocoelation is obseved in pe-nuclea test peiod which is.9 and the lowest R is obseved in post nuclea test peiod (Model ) which is.. A egession of one day ahead etun on the cuent etun inteacted with dummies of five day has an R (Model ) statistics. R (Model ) is the geate than R (Model ) in full sample peiod and two sub sample peiods of the basic egession, which shows day of the week effect, is lage in Kaachi stock exchange. The day of the week dummies is significant. We include in all ou subsequent egession. Table 3 shows the elationship between tading volume and the fist autocoelation of value weighted etun index. We egess the one day ahead stock etun on the cuent stock etun inteacted with day of the week dummies, tading volume and tading volume squaed and estimated conditional vaiance. The eason is to take volume squaed is to captue any nonlinealy that may exist in the elationship between tading volume and autocoelation. The esults with full sample i.e. 99- shows that.63 pecent of the vaiance of the one day ahead weighted index etun can be explained by a egession on cuent etun 3 Mitchell, Mak L., and J. Haold Mulhen. (994) used twenty day moving aveage to de-tend the data. 4
inteacted with day of the week dummies. Howeve, it is pointed out that R inceased by 3.47 pecent when the egession one-day ahead egess with dummies and tading volume. The coefficient on the tading volume and stock etun poduct is -.6 with hetoscedaticity consistent standad eo of.3. The standad deviation of tading volume is.47. Thus as moves fom fou standad deviations below the mean to fou standad deviations above, the fist ode autocoelation of the stock etun is educed by.. This esult is not compatible with volatility when volume is excluded fom egession. Howeve, nonlinea tem of tading volume is significantly negative which implies a the stong evidence fo any specification than linea volume egession. The esults fo pe-nuclea test and post nuclea test espectively ae pesented in table 3. As shown in penuclea test peiod, the aveage fist ode autocoelation of the stock etun is.3 and a egession of the one day ahead etun on the cuent etun associated with day of the week dummies ae explained by 8.98%. It is inceased if we incopoate the tading volume. In post nuclea test peiod, the fist ode autocoelation is smalle i.e..38 and the egession of one day ahead etun on cuent associated with day of the week dummies with volatility ae explained by. pecent. In this peiod R inceased by 3.36% if etuns egess on tading volume, volatility and tading volume squaed. The esult points out that the addition of the data afte nuclea test has stong effect of tading volume on the fist ode autocoelation of etuns. In this peiod the tading volume is significant at pecent. Moeove, these dummies ae excluded, the volume effect becomes much stonge in 99-. This is because the stock pice evesal of the nuclea test is captued by the day of the week dummies when these ae included o by tading volume when dummies ae omitted. The second ode autocoelation of etuns ae highlighted in table 4. The esult indicates that the second ode autocoelation of etun is smalle but statistically significant. Howeve, when day of the week dummy is incopoated, with cuent etun the R statistics of the egession is elatively highe. Table also shows the tading volume and volatility effects on the second ode autocoelation. The esults show the elatively weak tading volume effect as compaed to the fist ode autocoelation. Ove a full sample peiod 99-, the coefficients of tading volume and tading volume squaed ae.78 and.3 with standad eo. and. espectively. This implies that the second ode autocoelation incease with tading volumes and highe values of volume the positive quadatic tem dominates and auto coelation should decease. In pe -nuclea test peiod the simila esults ae obseved. Howeve, the esults ae elatively weak. In post nuclea peiod the coefficients of tading volume and tading volume squaed ae.4 and.3 with standad eo.6 and.3 espectively. This implies that the second ode autocoelation falls with tading volume and at highe value of tading volume the positive quadatic tem dominate and autocoelation should incease.
6 4. Conclusion This study investigates the elationship between aggegate stock maket ta ding volume and seial coelation of daily stock etuns duing Decembe 4, 99 to Decembe 3,. The study also identifies any diffeence in this elationship duing pe-nuclea test (Decembe 4, 99 to May 8, 998) and post-nuclea test (May 9, 998 to Decembe 3, ). The esults indicate a fist ode positive autocoelation between futue etuns and pesent etuns. The coelation becomes negative when pesent etuns ae weighted by a change in the tading volume. This implies that non-infomational tade has a significant effect on pices and tading activity has explanatoy powe in addition to pesent etuns, nonlinea tading volume and volatility. The esults also indicate that stock maket moved too much due to change in the fu ndamentals, aggegate expected etuns, and changes in effective isk avesion of maket paticipants. Moeove, the same esults found in pe -nuclea test peiod. Howeve, the weak and insignificant esults wee found in post-nuclea test peiod. It concludes that the addition of post-nuclea test peiod leads to stonge evidence fo tading volume effect on fist ode auto-coelation. The second ode auto-coelation esults indicates a positive and weak elationships as compaed to fist ode autocoelation. Howeve, it positive when it elates to weighted tading volume in entie sample peiod and two sub-sample peiods. It implies that the ole of infomation is effective afte two days and noninfomational ole is less effective. 6
7 Refeences Ali, S. S. (997). Pices and Tading Volume in Pakistan Stock Makets, Jounal of Economic Coopeation Among Islamic Counties, 8, 3, -37. Cambell,J. Y. Sanfod J. Gossman and Jiang Wang. (993). Tading Volume and Seial Coelation in Stock Retun, Quately Jounal of Economics, 9-939. Duffee, Gegoy, (99) Tading Volume and Retun Revesal. Finance and Economics Discussion Seies no. 9, Boad of Govenos of the Fedeal Reseves System. LeBaon, B. (99a) Some Relation between Volatility and Seial Coelation in Stock Maket Retuns. Jounal of Business, LXV, 99-9. Mitchell, Mak L., and J. Haold Mulhen. (994). The impact of public infomation on the stock maket. Jounal of Finance, 49, No.3. pp. 93 9. Mose, D. (98) Asymmetic Infomation in Secuities Makets and Tading Volume, Jounal of Financial and Quantitative Analysis, XV, 9-46. Nishat, M. (999), The Impact of Institutional Development on Stock Pices in Pakistan, Doctoal Dissetation, Auckland Business School, Univesity of Auckland. Nishat, M. (), Institutional Development and Risk Pemia in Pakistan, Pape pesented at Asia- Pacific Finance Association Confeence, held in Shanghai, China. Nishat, M. (), The Systematic Risk and Leveage Effect in Copoate Secto of Pakistan, Pakistan Development Review. Nishat, M. and Mustafa, K. (). Anomalies in Kaachi Stock Maket, (Daft). Oman, M.F. and McKenzie F. (). Hetoscedasticity in Stock Retun Data: Revisited Volume veses GARCH Effects, Applied Financial Economics,, 3-6. Sentana, E. and Sushil Wadhwani (99), Feedback Tades and Stock Retun Autocoelation: Evidence fom a Centuy of Daily Data, Economic Jounal, CII 4-4. Uppal, J. (993), The Intenalisation of the Pakistan Stock Maket: An Empiical Investigation, Pakistan Development Review. 3:4 6-68. 7
8 Table Phillips Peon Unit Root Test Vaiable PP test Result Log of etun -43.48 Stationay Diffeence of Log Volume -.7 Stationay McKinnon citical values fo ejection of hypothesis of a unit oot at significant level of %= -3.43: at %= -.8 at %= -.6 Table I st auto coelation of stock etun. = α + α t + t + Sample peiod α R (Model ) R (Model ) Dec. 4, 99 to Dec. 3, Coefficient.6..3 Standad eo. t-values 6.9 p-values. (Pe-nuclea test ) Dec. 4, 99 to May 8 998 Coefficient.4.6.9 Standad eo. t-values 8.8 p-values. (Post-nuclea test) May 9 998 to Dec. 3, Coefficient.38..38 Standad eo.33 t-values.9 p-values.7 t + β t 8
9 TABLE 3 Volume Volatility and Fist Autocoelation = α + αt + α idi i + α3v t t + α4v t + αtσ i α 3 α 4 α R Dec. 4, 99 to Dec. 3, Volume -.6.3 Standad eo.4 z- statistics -.74 P-values. Volume 8.4.6 Standad eo 9.96 z- statistics.843 P-values.399 Vol. And volatility -. -.89 47.84.37 Standad eo.389.396 9.99 z- statistics.39 -.66 4.78 P-values.69.3. Dec. 4, 99 to May 8 998 Volume -.93.69 Standad eo.9 z- statistics -4.7 P-values. Volatility 37.7.89 Standad eo.44 z- statistics 6.4 P-values. Vol. And volatility.6 -.9 6..69 Standad eo.9..4 z- statistics 7.6-7.8 6.3 P-values... May 9 998 to Dec. 3, Volume -.8.33 Standad eo.8 z- statistics -.4 P-values.8 Volatility -47.38.6 Standad eo. z- statistics -.39 P-values. Vol. And volatility.69 -.3-3.83.36 Standad eo.78.3 7.8 z- statistics.88 -.8 -.77 P-values.37.4.43 9
Table 4 nd ode auto coelation of stock etun. = α + α t + t + Sample peiod β R (Model ) R (Model ) Dec. 4, 99 to Dec. 3, Coefficient.7.9.39 Standad eo. t-values.7 p-values. Dec. 4, 99 to May 8 998 Coefficient.76.8.4 Standad eo.6 t-values.94 p-values.3 May 9 998 to Dec. 3, Coefficient.7.6. Standad eo.33 t-values.7 p-values.88 t + β t
Table Volume Volatility and Fist Autocoelation t + + βt + β idit + γ V tt + γ Vt t + γ 3σ i t γ γ γ 3 R Dec. 4, 99 to Dec. 3, Volume..4 Standad eo.6 z- statistics. P-values.7 Volatility 64.68. Standad eo 9.98 z- statistics 6.47 P-values. Vol. Volatility.78 -. 6.96.46 Standad eo.. 4.7 z- statistics 3.78 -.4 4.4 P-values... Dec. 4, 99 to May 8 998 Volume.9.9 Standad eo.8 z- statistics.6 P-values.68 Volatility -3.6.3 Standad eo 6.7 z- statistics -.8 P-values.86 Vol. And volatility.7 -. 7.4.97 Standad eo.4. 6.9 z- statistics.33 -.68.77 P-values.98.9. May 9 998 to Dec. 3, Volume..6 Standad eo.9 z- statistics.87 P-values. Volatility -3.64.3 Standad eo 6.7 z- statistics -.8 P-values.86 Vol. And volatility -.4.3 -.69.78 Standad eo.68.3.8 z- statistics -.6.9 -.9 P-values.4.34.36