Stock market returns and volatility in the BRVM

Transcription

1 African Journal of Business Managemen Vol. (5) pp. 07-, Augus 007 Available online hp:// ISSN Academic Journals Full Lengh esearch Paper Sock marke reurns and volailiy in he BVM N dri, Konan Léon UF of Economics and Managemen, Universiy of Cocody, BPV 43 Abidjan, Côe d Ivoire. konanleond@yahoo.com. Tel+fax: Mobile: Acceped 3 July, 007 This paper sudies he relaionship beween expeced sock marke reurns and volailiy in he regional sock marke of he Wes African Economic and Moneary Union called he BVM. Using weekly reurns over he period 4 January 999 o 9 July 005 and, an EGACH-in-Mean model assuming normally disribued and Suden's disribuion for error erms, he sudy reveals ha: ) expeced sock reurn has a posiive bu no saisically significan relaionship wih expeced volailiy. ) volailiy is higher during marke booms han when marke declines. Key words: egional sock marke, BVM, WAEMU, EGACH-M, isk-reurns radeoff. INTODUCTION The relaionships beween expeced reurns and expeced volailiy have been exensively examined over he pas years. Theory generally predics a posiive relaion beween expeced sock reurns and volailiy if invesors are risk averse. Tha is equiy premium provides more compensaion for risk when volailiy is relaively high. In oher words, invesors require a larger expeced reurn from a securiy ha is riskier. Ye, empirical sudies ha aemp o es his imporan relaion yield mixed resuls. Esimaes of he risk-reurn relaion exploiing he GACH-M framework range from posiive (French e al., 987; Chou, 988; Baillie and DeGennaro (990), Campbell and Henschel, 993; Scruggs, 998; Bansal and Lundblad, 00) o negaive (Nelson, 99; Glosen e al., 993). On he one hand, French e al. (987) examine daily and monhly reurns on he NYSE sock index for he period from January 98 o December 984 and find evidence ha expeced marke risk premium is posiively relaed o predicable volailiy of sock reurns. Using he same source of daa, bu for a differen period, Chou (988) suppored French e al. (987) finding abou he posiive relaion beween he predicable componens of sock reurns and volailiy. Chou sudied weekly daa for he period July 96 o December 985. Baillie and DeGennaro sudy similar daa o French e al. (987) and Chou (988) and reached he same conclusion. They sudy boh daily daa for he period January 970 o December 987, and monhly daa for he period February 98 o December 984. On he oher hand, Glosen e al. (993) use daa on he NYSE over April 85 o December 989, and find negaive relaionship beween expeced sock marke reurn and volailiy. Alernaives o he GACH-M framework have been used bu also yielded mixed resuls. Using an insrumenal variables specificaion for condiional momens, Campbell (987) finds negaive risk-reurn radeoff whereas Harvey (99) finds a posiive relaionship, and Whielaw (994) find mixed evidence on he expeced reurn volailiy radeoff. Turner e al. (989) use a wosage Markov model and find ha he relaionship beween expeced sock reurns and volailiy range from posiive o negaive. Using non-parameric echniques, Pagan and Hong (99) find a weak negaive relaionship, bu Harrison and Zhang (999) find ha he relaionship is significanly posiive a longer horizons. For a specificaion ha faciliaes regime-swiching, Whielaw (000) documens a negaive uncondiional link beween he mean and variance of he marke porfolio. Given he conflicing resuls cied above, i is primary an empirical quesion as o wheher he condiional firs and second momens of equiy reurns are posiively relaed. The purpose of his paper is o conribue o his lieraure by examining he relaion beween expeced sock marke reurns and expeced volailiy in he BVM over he period from 4 January 999 o 9 July 005. The conribuion of his paper is hreefold. Firs, i uses daa on a fronier marke and ess for he risk-reurns radeoff in he BVM for he firs ime. Second, i conribues o he lieraure on his imporan relaion by showing ha

2 08 Afr. J. Bus. Manage. Table : Seleced figures of he BVM Capializaion 3 Dec Dec Dec July 005 BVM BVM Composie Number of firms BVM BVM Composie Some measures Volume raded of socks Toal value raded (CFAfr) # of ransaions # of securiies raded Noes: Euro= CFA Fr. The CFA Fr is he currency uni of he Wes African Economic and Moneary Union (WAEMU) eigh (8) member Saes. Source: Official Newsleer of he BVM. he risk-reurns radeoff in he BVM is conform o hose found in maure markes. Third, i shows ha he asymmeric coefficien is posiive in he BVM conrary o hose found in maure markes. The res of he paper is organised as follows: secion gives an overview of he BVM. Secion 3 describes he daa. Secion 4 exposes he economeric mehodology. Secion 5 concludes he paper. OVEVIEW OF THE BVM The Bourse égionale des Valeurs Mobilières hereafer BVM is a privae corporaion se up on 8 December 996 bu began operaions in Sepember 6, 998. Is mission is o organize he securiies marke; disseminae marke informaion; and promoe he marke. I is he egional Financial Exchange of Benin, Burkina-Faso, Guinea Bissau, Côe d Ivoire, Mali, Niger, Senegal, and Togo which form he Wes African Economic and Moneary Union. The BVM is a cenralized spo exchange driven by orders, ha is, he price of a securiy is fixed by maching bid and ask orders colleced before he quoaion. A incepion, i has hree rading sessions a week, on Mondays, Wednesdays and Fridays. Prices are se a a fixing session ha will gradually become an ongoing process. A second fixing is done before he end of he rading session such ha securiies "unlised" and/or "reserved" during he exchange's firs fixing can evenually be raded. The BVM has an elecronic sysem and a saellie nework ha allows brokerage firms o send orders from he various WAEMU member saes o he cenral sie locaed in Abidjan, Coe d Ivoire. When operaions began, he BVM had wo secions for socks and one secion for bonds: he firs secion for socks is reserved for companies ha can jusify a leas five cerified annual accouns, a marke capializaion of over 500,000,000 CFA francs and disribued public shares of a leas 0%. The CFA franc, which sands for Communaué Financière Africaine is he common currency shared by WAEMU 8 member Saes. Euro = CFA Franc a a fixed rae. The second secion for socks can be accessed by midsized companies wih marke capializaion of a leas 00,000,000 CFA francs and wo years of cerified accouns, and a commimen o disribuing a leas 0% of heir capial o he public wihin wo years, or 5% in he even of a share capial increase; he bond secion can be accessed via bond loans of which he oal number of shares issued is higher han 5,000 and he face value of he share is equal o a leas 500,000,000 CFA francs. Two BVM marke indexes represen he aciviies of sock marke shares: he BVM Composie comprises all securiies lised on he exchange, and he BVM 0 comprises he en mos acive companies on he exchange (Table ). DATA DESCIPTION The daa se used in his sudy is weekly closing prices on he BVM 0 index obained from he Official Newsleer of he egional Sock Marke (BVM). The sudy period ranges from 4 January 999 o 9 July 005. The choice of he BVM 0 over he BVM Composie is moivaed by wo reasons: firs, i is composed of he en mos acively raded socks in he BVM and second, i accouns for abou 70% of he oal marke capializaion of he BVM as shown in Table. I compue he weekly sock marke reurns,, as follows: = 00 *In( P / P - ) ()

3 N dri 09 Table : Summary saisics for weekly reurn Series Mean S.D. S K J.B. Q(6) Q(0) Q (6) Q (0) BVM Noes: Mean, S.D., S, K, J.B. are he sample mean, sandard deviaion, skewness, and he kurosis respecively. Q(.) and Q (.) are he Ljung- Box Q-saisics and he squared Ljung-Box Q-saisics respecively. P-values are in parenheses. where P is he value of he BVM 0 price index for he period, and represens ime in weeks. P is BVM 0 index price for period ; ln(.) is he logarihm operaor. All reurns are expressed in local currencies and are no adjused for dividends. Table repors summary saisics of weekly sock marke reurns for he BVM equiy marke. The mean and he sandard deviaion are 0.07 and.636 respecively. The skewness saisic of shows ha he disribuion is posiively skewed relaive o he normal disribuion (0 for he normal disribuion). This is an indicaion of a non symmeric series. The kurosis is very much larger han 3, he kurosis for a normal disribuion. This suggess ha for he BVM, large marke surprises of eiher sign are more likely o be observed, a leas uncondiionally. The Ljung-Box es saisics Q(. ) and Q (.) provide ess for he absence of auocorrelaion and homoscedasiciy, respecively. The significance values of Q saisics indicae significan serial correlaion in he mean reurn series. This suggess ha he inclusion of a lag dependen variable in he mean equaion is appropriae. Srong auocorrelaion is also deeced in he squared mean reurns as shown by he values of he Q (.). I resuls in volailiy clusering in he disribuion of sock marke reurns. In addiion, he Jarque-Bera normaliy es rejecs he hypohesis of normaliy. ECONOMETIC METHODOLOGY elaion beween expeced reurn and expeced volailiy In order o examine he relaion beween expeced reurns and expeced volailiy, I exploi he GACH-in-Mean echnology (Engle e al., 987). The moivaion for his choice sems from he fac ha he expeced reurn on an asse is proporional o he expeced risk of ha asse. I assume ha he mean componen in he GACH (, )-in-mean framework describes he expeced reurns-volailiy radeoff for he equiy marke reurns as follows: +δ + = b + b () 0 where represens sock marke reurns a ime, he lag order of he auoregressive process for equaion () is deermined by he Schwarz (978) crieria. The opimum lag is one. is he accouning for auocorrelaion, b 0 is comparable o he risk-free rae in he Capial Asse Pricing Model, δ is he marke risk premium for expeced volailiy, is he disurbance erms wih mean zero and condiional variance. The expeced volailiy is approximaed by, he condiional variance of such ha: reurns a ime = var( / ψ ) (3) where is defined as above, ψ is he informaion se up o ime and, var(.) is he variance operaor. The volailiy measure defined by he condiional variance above is in an expecaion formulaion. If he forecass of his variance can be used o predic expeced reurns, hen we should expec he coefficien δ in equaion () o be posiive and significan for a risk averse invesor. In oher words, if invesors are rewarded for heir exposure o risk, hen we should expec a posiive relaion beween condiional expeced reurns and condiional variance. This supposes ha markes are fully segmened, ha is invesors do no diversify heir porfolio inernaionally. Therefore, hey should be rewarded for heir exposure o counry specific risk. The coefficien δ in equaion () ha links firs and second momen of reurns can be inerpreaed as he price of domesic marke risk. Esimaing and esing he risk reurns radeoff described in equaion () requires an empirical model for he condiional volailiy. My choice of models is moivaed by he empirical lieraure on marke volailiy. I assume ha he condiional variance follows an Exponenial Generalized Auoregressive Condiional Heeroscedasiciy (EGACH) process (Nelson, 99). The GACH (Bollerslev, 986) family of models assumes ha he marke condiions is expecaion of marke variance on boh pas condiional marke variance and pas marke innovaions. The EGACH model, a refinemen of he GACH model imposes a nonnegaiviy consrain on marke variance, and allows for condiional variance o respond asymmerically o reurn innovaions of differen signs. I specify he model as follows: ln ln = w+ β + α + γ (4) π wherew,β, α, γ are consan parameers, ln( ) is he one-period ahead volailiy forecas. This implies ha he leverage effec is exponenial raher han quadraic and forecas of condiional variance are guaraneed o be nonnegaive, w is he mean level, β is he persisence parameer, ln( ) is he pas

4 0 Afr. J. Bus. Manage. Table 3 : isk-eurns esimaes b 0 b δ ω β α γ LF Model (0.085) 0.93* (4.76) (0.905) -0.68* (-.8) 0.78* (8.35) 0.594* (6.080) 0.5* (.353) Model (-0.06) 0.78* (4.99) 0.0 (0.338) -0.70* (-.00) 0.70* (8.49) 0.757* (3.555) 0.9* (.37) Noes: Model is he A()-EGACH(,)-M wih normally disribued error erms; model is he A()-EGACH(,)-M wih Suden's disribuion for error erms. The degree of freedom s coefficien of Model, υ is 3.09 wih a -saisics of L.F. is he maximum value of he log-likelihood funcion; -saisics are in parenheses. * indicaes saisically significance a he 5% level. period variance. Unlike he GACH model, he EGACH model allows for leverage effec. If γ is negaive, leverage effec exiss. Tha is an unexpeced drop in price (bad news) increases predicable volailiy more han an unexpeced increase in price (good news) of similar magniude (Black, 976; Chrisie, 98). If α is posiive, hen he condiional volailiy ends o rise (fall) when he absolue value of he sandardized residuals is larger (smaller). Equaions and 4 are joinly esimaed afer specifying he assumpions abou he disribuion of error erms. I consider wo disribuions for error erms: he normal disribuion and he Suden's disribuion. The choice of he former is dicaed by he fac ha esimaion radiionally assumes normally disribued error erms. This case will serve as a benchmark for comparison. The fac ha excess skewness and kurosis displayed by he residuals of condiional heeroskedasic models will be reduced if a more appropriae disribuion is used, jusifies he use of Suden's - disribuion for error erms. Equaions and 4 can be summarized in he following wo models: Model : ln = b0 + b +δ + (5) / ψ N(0, ) (6) ln = w+ β + α + γ (7) π Model : = b0 + b +δ + (8) / ψ (0,, υ ) ln, υ is he degree of freedom (9) ln = w+ β + α + γ (0) π Empirical resuls The resuls of esimaing models and show ha he differences in maximum log-likelihood beween he wo models are very small. Model produces a marginally higher log-likelihood value. However, in all cases, he differences are very insignifican a he 5% level (Table 3). In he mean equaions 5 and 8, he coefficien δ of he erm urns ou o be posiive bu saisically insignifican a he 5% level. This resul implies ha sock reurns are no affeced by volailiy rends. In oher words, condiional variance lacks predicive power for sock reurns. This resul is similar o hose reached by French e al. (987), Baillie and DeGennaro (990) and Chan e al. (99). However, he lieraure has no reached ye a consensus on his imporan relaion. According o finance heory, condiional expeced reurns should be posiively and saisically significan in relaion o condiional variance (Campbell and Henschell, 99). The presen sudy suggess ha invesors are no rewarded for he risk hey ake on he regional sock exchange. If hey were, he coefficien δ should have been posiive and saisically significan. In erms of he condiional volailiy, he persisence parameersβ in equaions 7 and 0 are 0.78 and 0.70 respecively. This suggess ha he degree of persisence is high and very close o one. In oher words, once volailiy increases, i is likely o remain high over several periods. The posiive and saisically significan coefficien α in boh models confirms he presence of volailiy clusering. Condiional volailiy ends o rise (fall) when he absolue value of he sandardized residuals is larger (smaller). The posiive and saisically significan coefficien γ in boh models implies he presence of asymmery; ha is volailiy is higher during marke booms han when marke declines. This resul is a odd wih hose found in he U.S. equiy marke (Pagan and Schwer, 990; Nelson, 99). An explanaion of his conradicory resul is ha invesors believe ha marke booms are no suppored by economic fundamenals and marke reurns behave as speculaive bubbles.

5 N dri Table 4 : Diagnosic checks aw series Model Model Mean Sandard deviaion Skewness Kurosis Q (6) Q (0) Q (6) Q (0) J.B (0.386).39 (0.374) 3.99 (0.688) 3.09 (0.873) (0.30).9 (0.345) (0.680).480 (0.899).976 Noes: Table 4 shows he summary saisics for he raw reurns and he sandardized residuals for Model and Model. Q (.) is he Ljung-Box Q-saisics for he absence of auocorrelaion and Q (.) is he squared Ljung-Box Q-saisics for he absence of heeroskedasiciy. P-values are in parenheses and, J.B. is he Jarque Berra es for normaliy. Diagnosic checks Table 4 repors he summary saisics for he raw reurns and he sandardized residuals for models and. The purpose of his diagnosic check is o es wheher he models are correcly specified. The kurosis is now 5.88 for model and for model, which is quie an improvemen from he raw series (7.634). Furhermore, he skewness is close o zero for boh models. The Q-saisics for he absence of auocorrelaion in he sandardized residuals have p- values ranging from o while hey were in he original series. This confirms he fac ha reurns have no remaining ACH effecs. The p-values of he Q - saisics for he absence of heeroscedasiciy range from o relaive o in he original series. All hese ess sugges ha he models are fairly specified. They can herefore be used for forecasing purposes. Conclusion This sudy has analyzed he relaionship beween sock marke reurns and volailiy in he regional sock marke of he Wes African Economic and Moneary Union called he Bourse égionale des Valeurs Mobilières (hereafeer BVM). Using weekly daa on sock prices from he Official Newsleer of he BVM over he period 4 January 999 hrough 9 July 005, he sudy ess for he risk-reurns radeoff wihin an EGACH-in-Mean framework. The sudy reveals ha coefficiens linking condiional marke reurns o condiional volailiy are posiive bu saisically insignifican. This resul is conform o resuls found in maure markes bu is a odd wih he posiive and saisically significan risk-reurn radeoff prescribed by finance heory. The resul also shows ha volailiy is persisen bu conrary o he EGACH model of Nelson (99), here is no leverage effec. The resuls of his paper have wo imporan policy implicaions. Firs, he posiive and saisically insignifican riskreurn relaionship is an indicaion ha invesors are no rewarded for he risk hey ake in he BVM. While his resul is no consisen wih porfolio heory, i may resul from he ax reamen of ineres income and dividend income, and weaker corporae profi performance. The fac ha sock marke variance can no be used o predic sock reurns in he BVM imply ha invesors should look a oher macroeconomic and financial deerminans of sock reurns. Second, he presence of persisence in volailiy, ha is, he fac ha periods of high volailiy as well as low volailiy end o las, implies he inefficiency of he BVM since persisence in volailiy implies ha ) he riskreurn radeoff changes in a predicable way over he business cycle and, ) persisence can be used o predic fuure economic variables. Given ha marke inefficiency affecs he consumpion and invesmen spending and hereby he overall performance of he economy, marke regulaors should improve he echnical organizaion of he marke, and encourage quoed companies o provide periodic repors as policies o improve he sock marke s

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