Time-series modeling of returns from the NSE 20-share index: An empirical study of the impact of political climate on market volatility

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1 Time-series modeling of reurns from he NSE 0-share index: An empirical sudy of he impac of poliical climae on marke volailiy T N O Achia, A Wangombe and Emma Anyika Absrac A ime series analysis of he Nairobi Sock Exchange (NSE) 0-Share index from January 1998 o March 007 is provided. A comparison of he daily raes of reurn and volailiies for periods immediaely preceding and following elecion years (00-003) and periods prior o and afer his elecoral season ( and ). Volailiy, as measured by he absolue change in he rae of reurn, has posiive serially correlaions in he markes as expeced. This paper also ess wheher he efficien marke hypohesis (EMH) hold in he case of he NSE 0 share index. The resuls indicae ha his hypohesis is no saisfied as in his paper boh he ARIMA(1,1,1) and he GARCH(1,1) models are fi o he daa. The random walk process ha holds under he EMH does no hold for his daa. Predicion for he NSE index for a range of periods is given. KEY WORDS : Time series analysis; Auoregressive inegraed Moving Average (ARIMA) process; Generalised Auoregressive Condiional Heeroskedasic (GARCH) process; Rae of reurn; Volailiy; Auocorrelaion funcion (ACF); Parial Auocorrelaion funcion (PACF); Nairobi Sock exchange (NSE). Inroducion World over a sock exchange index is assumed o be an indicaor of he economical, social and poliical volailiy of a naion. Therefore when he economy of a counry is hriving and he poliical environmen is sable, he sock exchange index is high. Share socks are a form of invesmen. Invesors buy shares a a cerain price hoping ha he share price of a sock will increase in fuure enabling hem make profis. These share prices are expeced o be deermined by he basic marke principle of supply and demand. However his is no normally he case. Various oher facors are seen o influence he prices of sock. These include, governmen policy as seen in he US farm policy by Sergio e al (00), increased inernaional influence as researched by John (1999), ransacion coss and securiies ransacion axes as implicily seen by Allen e al (1997). Mos of he above facors hinge on availabiliy of informaion or speculaion as normally refered o in he sock exchange environmens. Using he Kenyan sock exchange scenario in he pas en years, his paper posulaes o illusrae how informaion affecs he changes in prices of sock a he Nairobi Sock exchange in line wih he efficien marke hypohesis. Background December 00 marked he end of a 40 year Kenya African Naional Union (KANU) rule in Kenya. The las 10 years of KANU s rule saw he re-esablish and srenghening of muli-pary poliics in Kenya, a clamor for a new consiuional dispensaion and increase public demand for perperaors of grand corrupion o be brough o book.

2 The opimism ha surrounded he elecion of a Naional Rainbow coaliion (NARC) governmen was shor-lived as immediaely afer he new governmen ook office, cries of dissaisfacion were heard. The governmen, however, reduced domesic borrowing, inroduced sringen ax collecion measures, and wen on o inspire local and inernaional invesor confidence. These measures led o an economy recovery from a zero growh rae in 001 o a seven percen growh rae in 007. This period saw he Nairobi Sock Exchange, esablished in 1954, arac local and inernaional invesor ineres. The pos-elecion crisis ha followed he December 007 general elecion in Kenya, deep-rooed ehnically issue and perceived socio-economic dispariies, hreaened o nullify he gains made in he 5 years of he NARC. The campaign period only served o excie ehnic ension and made i difficul for businesses o hrive and for he economy o arac or inspire boh local and/or inernaional invesmen. This paper is o sudy he characerisics of he Nairobi Sock Exchange (NSE) index from January 1998 o March 007. The paper also aemps o evaluae wheher marke index saisfies he efficien marke hypohesis, o deermine, esimae and inerpre, an appropriae a Garch(p,q) model o he NSE 0-share index and o compare he volailiy of he marke during pre and poselecion years. We also compare he performance of he marke index during periods of relaive elecoral calm and periods immediaely prior o or afer an elecion. The efficien marke hypohesis Ross (1987) saes ha a marke is efficien wih respec o a se of informaion if i is impossible o make economic profis by rading on he basis of his informaion se and ha consequenly no arbirage opporuniies, afer coss, and afer risk premium can be apped using ex ane informaion as all he available informaion has been discouned in curren prices. Müslümov e al (004) noed ha capial markes wih higher informaional efficiency are more likely o reain higher operaional and allocaional efficiencies. According o Samuelson (1965) and Fama (1970), under he efficien marke hypohesis (EMH), sock marke prices mus always show a full reflecion of all available and relevan informaion and should follow a random walk process. Successive sock price changes (reurns) are herefore independenly and idenically disribued (iid). Based on he informaion se, Fama (1970) caegorizes he hree ypes of efficien markes as weak-form, semi-srong-form, and srong-form efficien if he se of informaion includes pas prices and reurns only, all public informaion, and any informaion public as well as privae, respecively. The implicaion here is ha all markes can be weak-form bu he reverse canno be he case. Furhermore, sock marke reurns unlike oher economic ime-series, ypically exhibi a se of peculiar characerisics such as clusers or pools of volailiy and sabiliy (i.e. large changes in hese reurns series end o be followed by large changes and small changes by small changes) Mandelbro (1963) and Fama (1965), and lepokurosis, (i.e. he disribuion of reurns ends o be faailed) Fama (1965).

3 Mehodology Daa The daa, y, for his paper were daily NSE 0-share index from January 1998 o March 007. Using he Splus finmeric package, daily reurns, r, were calculae as follows: r y ln y 1 (0.1) Generalised heeroskedasic condiional heeroskedasic (Garch) modeling In his paper we fi a Garch (1,1) process o daily reurns on he NSE 0-share index. A sochasic process, r c r 1 is Garch (p,q) if var 1 var 1. denoing he condiional variance on informaion a ime 1, z, and, wih , where z are independen and idenically disribued random variables wih zero mean. Before fiing Garch (1,1) models o each of he daily reurns series we firs es for he presence of ARCH effecs in he residuals. A sochasic process y c, is said o be Arch (p) if var 1, z, and i i i1 q. If here does no exis a significan ARCH effec in he residuals hen he ARCH model is unnecessary or mis-specified. Tesing he hypohesis of no significan ARCH effecs is based on he Lagragian Muliplier (LM) approach, where he es saisic is given by LM nr, (0.) where n is he sample size and R is he coefficien of deerminaion for he regression in he ARCH model using he residuals. Model Idenificaion To idenify he GARCH (1,1) model ha bes explains reurns for he NSE daa we deermine he Bayesian informaion crierion (abbreviaed BIC) values for he following candidae Garch models: Model 1: r c, z, and, where ~ 0, z WN.

4 Percen Model :, r c 1 z, and Model 3: r c r, z, and , where ~ 0, z WN., where ~ 0, Model 4:, r c r 1 z, and z WN , where ~ 0, z WN. The model wih he lowes BIC value is viewed as he bes fiing model. The BIC saisic is given as BIC= ln L k ln n, (0.3) where L denoes he maximized value of he likelihood funcion for he esimaed model, k represens he number of free parameers o be esimaed and n is he number of observaions. Exploraory analysis In his secion we use graphical echniques o idenify possible paerns ha exis in he NSE daa. Based on his exploraion we aemp o idenify an appropriae model for he daa. NSE index Figure 1 Time-series plo he daily NSE 0-share index from January 1, 1998 o March 1, 007

5 ACF Parial ACF ACF ACF Series : nse.re Series : abs(nse.re) Lag Series : nse.re^ Lag Series : nse.re^ Lag Lag Figure Sample ACF and PACF of various funcions of daily log sock reurns of he NSE 0-Share index from January 1, 1998 o March 1, 007: (a) ACF of he log reurns, (b) ACF of he squared reurns (lower lef), (c) ACF of he absolue reurns (upper righ), and (d) PACF of he squared reurns. From Figure 1, he marke index exhibis a decline from a relaive high value in 1998 o an allime low ha was experienced in lae 00. The marke index from ha poin exhibis a seady growh ha may be explained by he posiive invesor confidence experienced during he NARC era. Figure illusraes 4 imporan plos of he marke index. The upper lef plo is an ACF plo of he index, which indicaes significan serial correlaions and also he fac ha he index exhibis some form of non-saionariy. The upper righ and lower lef plos are he ACF s of he absolue and squared reurns, respecively. These plos sugges ha he daily reurns are no independen. These plos indicae ha he reurns are serially correlaed and dependen. Summary saisics Summary saisics for he NSE reurn series are presened in Table 1. The mean coninuously compounded reurn for he NSE is 0.019(±0.767). The resuls indicae high volailiy and he risky naure of he marke since he sandard deviaion of he marke reurns is high in comparison wih he mean.

6 Table 1 Descripive saisics for he NSE reurn series Mean Sd. Dev. Min. Max. Skewness Kurosis NSE index ( ) NSE index ( ) NSE index (00-003) NSE index ( ) Table Summary saisics for Annual NSE reurns N mean abs(mean) Sd. Dev Skewness Kurosis Min Max ARIMA(p,d,q) modeling Table 3 AIC values for he candidae ARIMA(p,d,q) models Model AIC AR(1) MA(1) ARMA(1,1) ARIMA(1,1,0) ARIMA(0,1,1) ARIMA(1,1,1)

7 Based on he AIC values presened in Table 3, he ARIMA(1,1,1) model is idenified o be he one ha bes fis he daily reurns on he NSE 0-share index from January 1998 o March 007. The equaion of he ARIMA(1,1,1) model idenified is given as Garch (p,q) modeling r r (0.4) 1 1 Table 4 Lagragian Muliplier es for Arch effecs Reurns Chi-square df p-value NSE index ( ) <0.001 NSE index ( ) NSE index (00-003) <0.001 NSE index ( ) <0.001 From Table 4, significan arch effec in he daily reurns on he NSE 0-share index for he January 1, 1998 o March 1, 007 period deeced. The resuls also indicae a significan arch effec in he NSE 0-share index for he period spanning January 00 o December 003 and for he period hereafer, spanning January 004 and December 006. Table 5 Model selecion Model AIC BIC p Model Model Model Model From Table 5, i is noed ha model 4 is he bes fiing model. The Garch (1,1) model obained is hus r 0.008( 0.006) r , and From he volailiy equaion, he implied uncondiional variance of is 0.03 F var (0.5) Figure 3 and Figure 4 respecively, provides he sample ACF of he sandardized shocks and he squared process. These ACFs fail o sugges any significan serial correlaions in he wo processes.

8 More specifically, we have he values of he Lagrange muliplier and Ljung-Box saisic as Q(1) = 16.46(0.1711) and Q(1) = 7.91(0.791) for,, and also hese saisics Q(10) = 8.83(0.55) and Q(0) = 15.8(0.73) for, where he number in parenheses is he p value of he es saisic. Thus, he model appears o be adequae. Noe ha he fied model shows , which is close o 1. This indicaes a covariance saionary model wih a high degree of persisence in he condiional variance. ACF of Sd. Residuals 1.0 ACF Lags Figure 3 Auocorrelaion plo for he residuals of he bes fiing GARCH (1,1) model

9 ACF of Squared Sd. Residuals 1.0 ACF Lags Figure 4 Auocorrelaion plo for he squared sudenised residuals of he bes fiing GARCH (1,1) model Discussion Table 3 gives forecass of he nse index for a period of 3-7 monhs in he year 008. This is more or less he scenario ha has been seen in he Kenyan markes in he pas few monhs unil he global slum in Ocober 008. The high volailiies seen jus before elecion periods indicaes lack of informaion or uncerainy leads o low sock exchange index. More research needs o be done o deermine he righ informaion he invesors need o be given o be boos heir invesmen confidence. In his paper we use boh he Box-Jenkins (ARIMA) modeling approach and he GARCH approach o model reurns from he NSE 0-share index. A comparison of he AIC and BIC values for hese models reveals ha he Garch model idenified provides a beer explanaion of he dynamics of he marke reurns. References 1. Akins, A. B. and Dyl, E. A. (1997) Sock price volailiy, ransacion coss and securiies ransacion axes. Managerial and Decision Economics. pp Bollerslev, T. (1986). Generalised Auoregressive Condiional Heerscedasiciy. Journal of Economerics 31: Brock, W.A., W. Decher, H. Scheinkman, and B. LeBaron (1996). A es for Independence Based on he Correlaion Dimension. Economeric Reviews 15,

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