MPRA Munich Personal RePEc Archive On he Impac of Inflaion and Exchange Rae on Condiional Sock Marke Volailiy: A Re-Assessmen OlaOluwa S Yaya and Olanrewaju I Shiu Deparmen of Saisics, Universiy of Ibadan, Nigeria, Deparmen of Saisics, Universiy of Ibadan, Nigeria 010 Online a hps://mpra.ub.uni-muenchen.de/88759/ MPRA Paper No. 88759, posed 1 Sepember 018 17:30 UTC
On he Impac of Inflaion and Exchange Rae on Condiional Sock Marke Volailiy: A Re-Assessmen OlaOluwa S. Yaya Deparmen of Saisics Universiy of Ibadan, Nigeria E-mail: os.yaya@mail.ui.edu.ng Olanrewaju I. Shiu Deparmen of Saisics Universiy of Ibadan, Nigeria E-mail: oi.shiu@mail.ui.edu.ng Absrac This paper sudies he impac of inflaion and exchange rae on condiional sock marke volailiy. Senana s QGARCH model is generalized o include he asymmeries in inflaion and exchange rae ha are no allowed in linear GARCH (p, q) model of Bollerslev (1986). Nonlinear specificaions of QGARCH model hen show he significan relaionship of inflaion and exchange rae o condiional sock marke volailiy. JEL Classificaions: C, C51, C3, D53, E3. Keywords: Condiional Volailiy, Exchange raes, Inflaion raes, Quadraic-GARCH, Sock prices, volailiy clusering. Corresponding Auhor: Yaya, O. S. (Email: os.yaya@mail.ui.edu.ng) Dep of Saisics, Universiy of Ibadan, Ibadan, Nigeria. 1
1. Inroducion Volailiy, he condiional sandard deviaion of he sock reurn and is deerminans has been sudied over he years and many facs have been presened in he lieraure. Schwer (1989) in his classic paper sudied he relaionship beween sock marke volailiy and volailiy of real and nominal macroeconomic variables. He looked a he impac of he level of economic aciviy, financial leverage and sock rading. He concluded ha movemens in inflaion and real oupu have weak predicive power on volailiy of sock marke and reurn. Davies and Kuan (003) exended Schwer s sudy by accouning for volailiy in an inernaional seing. Oher sudies carried ou by Huang and Kracaw (1984); Kaul (1987) and Hamilon and Lin (1996) have variously found from heir sudy ha oher macroeconomic facors such as GDP growh, and shor erm ineres raes are imporan explanaory variable in explaining volailiy in sock marke reurns. None of hem have looked a he impac of he combinaion of inflaion and exchange rae and volailiy of sock reurns having known ha exchange rae provides evidence for he impac of inernaional marke on he overall healh of an economy. This is paricularly so in a developing economy like Nigeria wih high inflaion rae and very srong dependence of is economy on foreign rade. This sudy herefore focuses on he examinaion of he predicive power of inflaion and Naira/US Dollar exchange rae on Nigerian s socks marke volailiy. The resul of his research would give imporan implicaion for policy makers, invesors and economic forecasers.. Mehodology Mos economic and financial ime series and especially condiional sock marke volailiy have always been sudied using he ARCH and GARCH models inroduced by Engle (198) and Bollerslev (1986) respecively. These models help o sudy volailiy clusering. Assuming lineariy, he firs and second condiional momens of reurn series (given is pas behaviours) can be joinly esimaed by GARCH (p,q) in order o characerize he dependence of fuure observaions on pas values. Consider a univariae sochasic process for sock marke reurns where he informaion se of monhly reurns is defined o be r, r 1,..., r q,...,1. The joinly esimaed GARCH (1,1) model inroduced by Bollerslev (1986) is given by, r, z, 0,1 z N (1) () 1 1 where is measurable wih respec o 1 and 0, 0, 0 and 1 such ha he firs wo momens of he uncondiional disribuion of he series are ime invarian. I should be noed ha he condiional variance is only linear in he squares of he pas values and no in he informaion se r 1 (Senana, 1995). In his work, he impac of volailiy on he reurn series will be measured using he GARCH- M model, r c 1 z z N 0,1 (3),
1 1 (4) where c is he risk premium parameer which indicaes ha he reurn is relaed o is volailiy (Tsay, 005). Following Saryal (007), he impac of asymmeric effec of shocks on volailiy will be esimaed using Senana s QGARCH (1,1) model, r, z z N 0,1 (5), 1 1 1 (6) where he erm 1 makes i possible for posiive and negaive shocks o have differen effecs on condiional volailiy. Once he appropriae model is deermined, hus he esimaion of he impac of inflaion and exchange rae on sock marke volailiy can be invesigaed by specifying wo models: Model I r Inflaion Exchrae 1, z Inflaion Exchrae 1 1 1 1, 0,1 z N (7) (8) The above model esimaes he impac of he previous period inflaion rae and exchange rae in order o capure ime-variaion in he (condiional) mean and variance equaions. Model II r Inflaion Exchrae 1 1, 1 z Inflaion Exchrae 1 1 1 1, 0,1 z N (9) (10) Here, he sandard GARCH (1,1) model is exended by including he impac of changing inflaion rae and exchange rae. Whenever here is evidence ha an asymmeric GARCH specificaion is suiable for condiional volailiy esimaion, hen he above models should be replaced wih he appropriae condiional variance specificaion given by QGARCH. 3. Resuls and Discussion The monhly share indices, inflaion rae and average monhly Nigeria/US dollar exchange rae from 1991 o 008 were used in his sudy. The daa were colleced from Cenral Bank of Nigeria (Exchange raes and Share indices) and Nigerian Bureau of Saisics (Inflaion raes). These daa range from 1991 o 008. Nominal Sock reurn is given by, S r 100 ln where S is he sock index. Table 1 shows he descripive saisics for all S 1 he hree variables under sudy. The resuls indicae ha he average monhly reurn on sock is 1.9%, he average exchange rae is N75.48/ 1 US Dollar and inflaion rae is.60% per monh. I can be observed ha inflaion rae is very high and one could expec higher nominal sock reurn in line wih he simple Fisher effec. 3
The sandard deviaion of he reurn series, exchange rae and inflaion are 5.5, 50.6 and 0.30% respecively. I could be seen ha he figure are quie high as well. This is due o frequen poliical changes in Nigeria along wih incessan fiscal and economic changes ha ook place wihin his period. Table 1: Descripive Saisics on Reurn Series, Exchange raes and Inflaion raes Saisics Nominal Sock Exchange Raes, Inflaion Raes, Change in Exchange Change in Reurns, r E I Raes, E Inflaion, Minimum 4.0799 8.869000 0.900000-10.07600-4.800000 Maximum 19.1879 137.30 78.50000 64.11400 3.900000 Mean 1.90035 75.48187.59674 0.545400 0.0651 Sandard Dev. 5.510498 50.60006 0.30065 4.656747 1.537140 Skewness -0.44445-0.138914 1.73709 11.95399-0.344580 Kurosis 6.13819 1.144679 3.315890 163.3378 3.99544 Jarque-Bera 95.9574 31.5800 59.0755 3543.1 13.1801 Prob. (0.00000) (0.00000) (0.00000) (0.00000) (0.001410) I The Impac of Inflaion and Exchange Rae on Sock marke Volailiy The appropriae model for sock reurn volailiy considering he effec of exchange rae and inflaion rae is given as, r 13.4167 0.3746r 0.0714I 0.0543E 5.085log 1 1 1 (0.0000) (0.0000) (0.0770) (0.0193) (0.0000) 1.650 0.3017 0.131E 0.1670I 0.4155 1 1 1 1 (0.0004) (0.0004) (0.0054) (0.0001) (0.0074) R = 0.159, Adj. R = 0.119, DW =.1300, AIC = 5.8547, SIC = 6.015, Sk. = -0.77, Kur. = 7.630, JB. = 19.4050 (0.0000), ARCH-LM (3) = 0.9465 (0.4191) The impac of inflaion and exchange raes on he mean equaion is no significan, bu he effec of exchange rae on condiional variance is posiive and significan. The esimaed 1 is 18.08 which indicaes ha he impac of shocks on he sample variance condiional variance will las for a long ime period. Model I Here he predicive power of he previous period Inflaion and Exchange rae on sock marke volailiy is examined by using ARCH (1). As seen from he model, he esimaed coefficien of exchange and inflaion raes are 0.179684 and -0.07760 respecively and hese are significan. r.1616 0.5503r 0.1383log 1 (0.0000) (0.0000) (0.3149) 3.656 0.5087 0.1797E 0.0776I 1.4175 1 1 1 1 (0.0053) (0.0001) (0.0000) (0.0000) (0.0030) 4
R = 0.114, Adj. R = 0.0914, DW =.449, AIC = 5.6753, SIC = 5.8016, Sk. = 0.4331, Kur. = 4.6350, JB. = 30.3850 (0.0000), ARCH-LM (3) = 0.857 (0.4666) A 1% increase in exchange rae causes increases in he condiional volailiy of socks in 1 is 7.5 which indicae a high Nigeria by 1%. The esimaed sample variance persisen volailiy of sock reurns. Model II The impac of variabiliy in he inflaion and exchange rae is invesigaed by Model II. This is achieved by modelling condiional variance on he changes in he predicor variables. r.3909 0.3996r 0.1737 log 1 (0.08) (0.0000) (0.7335) 13.484 0.7173 0.034 0.161 E.0054I.7544 1 1 1 1 1 (0.0000) (0.0000) (0.6680) (0.7906) (0.0000) (0.0065) R = 0.1479, Adj. R = 0.1145, DW =.1154, AIC = 5.8983, SIC = 6.0404, Sk. = 0.1947, Kur. = 4.748, JB. = 15.7695 (0.0004), ARCH-LM (3) = 1.776 (0.831) As seen from he model, he esimaed coefficiens are all significan bu surprisingly wih differen signs indicaing differen ype of impac on he volailiy of sock marke reurn. The 1 is 47.50 which indicae a higher persisen volailiy esimaed sample variance of sock reurns. 4. Conclusion In his paper, we have shown ha previous exchange raes and inflaion raes have significan effecs on condiional sock marke volailiy. Changes in exchange raes and inflaion raes, as measured by changes in hese raes also have greaer impac in predicing he sock marke volailiy in Nigeria. These resuls are in agreemen wih Fisher s effec in inernaional sock marke. his resul will serve as a guide o he policy makers on finance, he sock brokers and invesors. Our findings are in line wih ha of Saryal (007). 5
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