Journal of Applied Finance & Banking, vol. 4, no. 1, 2014, 91-102 ISSN: 1792-6580 (prin version), 1792-6599 (online) Scienpress Ld, 2014 Macroeconomic Variables Effec on US Marke Volailiy using MC-GARCH Model Jang Hyung Cho 1 and Ahmed Elshaha 2 Absrac Forecasing equiy volailiy was horoughly invesigaed during he pas hree decades. The majoriy based heir forecass on he dynamics of he underlying equiy ime series. They helped beer undersand he dynamics of hese ime series and undersand differen aspecs of volailiy. Oher models wen a sep furher o include he effec of news announcemen on equiy volailiy. The vas majoriy ignored he effec of macroeconomic variable or he sae of he economy. This paper proposes a volailiy-forecasing model ha accouns for effec of fundamenal macroeconomic variables ha reflec he sae of he economy. The explanaory variables used measure he sage of business cycle, uncerainy abou he fundamenal economic variables, and a predicion of he fuure sae of he economy. All hese variables have been documened in he empirical lieraure or in he economic heory o have an effec on equiy volailiy. Anoher major conribuion is he way volailiy is being measured. The proposed model uses MC-GARCH model o measure he long-erm volailiy wihou losing much of he relevan informaion or he characerisics of he volailiy ime series. This paper also has some policy implicaions as i shows he relaionship beween fundamenal macroeconomic variables and equiy marke volailiy. JEL classificaion numbers: E27, E37, E32, E44. Keywords: Modified Componen GARCH; long-run volailiy; macroeconomic effec, Forecasing, Business cycles. 1 San Jose Sae Universiy. 2 Bradley Universiy. Aricle Info: Received : Sepember 23, 2013. Revised : Ocober 21, 2013. Published online : January 1, 2014
92 Jang Hyung Cho and Ahmed Elshaha 1 Inroducion During he pas hree decade a large number of models have been developed o forecas equiy volailiy. These models aemped o forecas volailiy based on hree ypes of informaion; characerisics of equiy ime series, effec of news or announcemens, and effec of macroeconomic variables. The vas majoriy of research in his area focused on forecasing volailiy based on he characerisics of he equiy ime series. See for example of work of [1], [2], [3], and [4]. This line of research led o he developmen of more accurae and sophisicaed models o forecas volailiy, namely univariae and mulivariae GARCH models. [5] provided a survey for he univariae and mulivariae GARCH models respecively. Oher researchers aemped o forecas volailiy as a reacion o news or announcemens. [6] for insance sudied he shor-erm volailiy movemens as he US macroeconomic informaion is released. [7] evaluae he forecasing performance of ime series models for realized volailiy aking ino consideraion a number of facors including macroeconomic announcemens. Oher aemps include [8] who found ha imporan poliical evens end o be associaed wih sudden jumps in volailiy. [9] and [10] who found ou ha on average he porion of volailiy relaed o world facors is quie small for emerging markes. [11] examined global and local evens (social, poliical, and economic) o assess heir effec on volailiy in emerging markes. More recen aemps using inra-daily reurn daa include [12], [13], [14] and [15]. These wo ypes of models failed o use oher ype of available criical informaion. They ignore he relaionship beween he sae of he economy and he equiy volailiy, a hird caegory of models incorporae his relaionship. These models are relaively scarce. Even he aemps made generally provided weaker relaionships han wha would be expeced. Among he early aemps o incorporae he sae of he economy, [16] used leverage and he volailiy of indusrial producion o explain he high volailiy during he 1930s. [17] and [18] used he US macroeconomic and microsrucural facors o explain he US ime varying volailiy. Schwer used a long ime series daa saring from he 19 h cenury o measure he relaionship beween equiy volailiy and 3 variables; real and nominal macroeconomic volailiy, level of economic aciviy, and financial volailiy. [19] proposed o model equiy volailiy as a produc of boh macroeconomic effecs and he dynamics of he equiy volailiy ime series. [20] proposed he same idea bu used a class of componen models ha disinguished beween shor erm and secular volailiy movemens. Volailiy is no jus volailiy any more. There are condiional and uncondiional volailiy, shor erm and long erm volailiy, saic and dynamic volailiy. Also, he arrival of new heerogeneous informaion affecs he volailiy dynamics wih differing frequencies; hus, he equiy volailiy aggregaes numerous independen volailiy componens [21]. Furhermore, [22] showed ha raders wih differen holding periods could lead o differen volailiy componens. [23] and [24] showed ha he acual sample volailiy decays much slower han he exponenial decay paern as prediced by he classic GARCH models. Mos models disinguish he oal condiional variance ino shor-run, long run variance componens and oher componens, such as seasonal variance componen. [25] proposed a wo componen model ha decomposes he oal condiional variance ino permanen and ransiory variance componens. The goal of his paper is o develop a model ha uilizes informaion provided by he sae of he economy. The proposed model inegraes he effec of fundamenal macroeconomic
Macroeconomic Variables Effec on US Marke using MC-GARCH Model 93 variables ino he volailiy-forecasing model. Anoher key improvemen in his model is he way volailiy is defined. The proposed model uilizes a newly developed class of he componen GARCH, namely Modified Componen GARCH (MC-GARCH), developed by [26]. The MC-GARCH provides a superior filraion ha filers ou he shor-erm volailiy from he ime-varying long run condiional variance. This paper furher explores he policy implicaions of esablishing he relaionship beween he equiy markes volailiy and macroeconomic variables. We proceed in his sudy as follows: In secion 2, he variables used are described along wih he process of selecing hem and heir sources. Then he mehodology and he proposed model are discussed followed by he daa used. Secion 3 presens he empirical resuls and heir inerpreaions. In secion 4 he conclusion is presened. 2 Daa and Mehodology 2.1 Mehodology The purpose of his paper is o find ou which macroeconomic variables has significan effec on he long run volailiy of marke porfolio. We use he S&P 500 index as he proxy for marke porfolio. I is needless o say ha empirical resuls are significanly affeced by he employed mehodologies. Therefore, i is indispensable o examine he effeciveness of alernaive mehodologies before we draw any conclusions abou he opic. I is well known ha he popular mehodologies o filer he long run volailiy are he [19] and [25]. [26] modify he Engle and Lee model and show heir modified model capures he long run volailiy beer. This sudy uses he daily reurns from he S&P 500 index and average he filered daily long run volailiy for each year. We compare he empirical resuls using he annualized long run volailiies from Engle and Rangel model and Cho and Elshaha model. 3 The empirical findings will be discussed wih he resuls from he beer-performed mehodology. [26] idenify he wo main condiions of coefficiens of he [25] model under which he long-run variance componen is no filered from he oal condiional variance. These wo mal-adjusmen condiions are caused by he innovaion erm in he long run variance equaion in Engle and Lee model. Hence, Cho and Elshaha redefine he innovaion in he long run variance based on he definiion of innovaion in ime series as saed in [27]. Specifically, Cho and Elshaha s modified componen GARCH model (MC-GARCH hereafer) model is as follows: r r E e (1) wih e h v (2) 3 This paper does no specify he [19] model. Only he empirical resuls from heir model will be discussed.
94 Jang Hyung Cho and Ahmed Elshaha h q q 2 e q h q (3) 1 1 1 1 1 1 h 1 q 1 q 1 w (4) Noe ha he long run variance equaion in (4) is differen from ha in he [25] model as shown below: q 2 e 1 h 1 q 1 w (5) The mehodology o examine he macroeconomic deerminans of he long run volailiy is regression analysis. The dependen and independen variables are all annual values for he regression analysis. 2.2 Daa I is worh menioning again here ha volailiy is no jus volailiy. Afer hree decades of volailiy research and developmen i became a fac ha no any measure of oscillaion is he correc measure of volailiy. A major conribuion of his paper is he aenion paid o measuring he dependen variable of he proposed model. The dependen variable used is he long run volailiy using he daily reurns on S&P500 index. Specifically, P ln P r 100 ln 1 (6) The long run volailiy is measured using he MC-GARCH model. While he principle of muliple componens is widely acceped, here is neiher a clear agreemen on how o specify he dynamics of each of he componens nor an agreemen on he filering mehod. The MC-GARCH is found o provide a long run forecas wihou losing much of informaion available. The use a model ha filers oo much informaion simply would fail o capure an exising effec. The esimaed daily long run volailiies are annualized by average each year o be used in regression analysis. There are many poenial macroeconomic variables ha affec he long run marke volailiy. In his paper we use he [19] model as a benchmark o compare our resuls. To make a fair comparison, he same variables used by [19] are used in his research. The variables used are inspired by prior empirical research or economic heory. The variables are inended o measure he following; he effec of business cycles, he uncerainies abou fundamenals, and predicion of economic facors or fuure saes of he economy. [19] esed heir model using a sample ha covers differen counries, developed and under developed. Thus, hey used conrol variables o conrol for he marke developmen level and economy size. These wo caegories are ou of he scope of his paper, as our focus is only on he US marke. The real GDP growh rae is used o measure he sage of he business cycle. Our hypohesis here is he negaive relaionship beween volailiy and he business cycle [28]. Tha is o say ha during recession volailiy is expeced o be higher. [29] and [30] documened he empirical regulariy ha risk-premia are couner cyclical. To measure he uncerainy or he volailiy of he fundamenal macroeconomic variables and heir effec
Macroeconomic Variables Effec on US Marke using MC-GARCH Model 95 on he equiy marke volailiy, we used he volailiy of hree macroeconomic variables; real GDP, shor erm ineres raes and exchange raes. For insance, [31] used sochasic volailiy models of macroeconomic variables o forecas volailiy; [32] documened ha equiy marke volailiy are affeced by inflaion and earnings uncerainy. The level of inflaion is used as a predicor of he fuure sae of he economy as i is a major goal for any cenral bank. Inflaion level is associaed wih any moneary policy decision and fuure economic growh as documened by he economic heory. Here we add one more independen variable, which is he growh rae of M2. The main macroeconomic effec of growh of M2 is relaed o inflaion. The CPI reflecs wo differen sources of inflaion: moneary inflaion and srucural (non-moneary) inflaion. Hence, i is meaningful o separae he effec of moneary inflaion on he long run marke volailiy by including he growh rae of M2. The growh raes of M2 are annual values. We use he hree-monh Treasury bill rae as [32] shor-erm ineres rae and he dollar index as he exchange rae. Boh variables are downloaded from he federal funds reserve websie. The inflaion rae is defined as he annual growh of CPI (consumer price index). The inflaion rae is he growh rae of CPI using December CPI values of each year. Inflaion is downloaded from he Bureau of Labor saisics (BLS) Web sie. The dollar index is calculaed using he exchange raes of six major currencies: he Briish pound, Canadian dollar, euro, Japanese yen, Swedish krona and Swiss franc. This index was iniiaed in 1973 wih a base of 100 and he dollar index calculaed is relaive o his base. Following [19], all he annualized volailiy values of monhly shor erm ineres, exchange rae, GDP and inflaion are compued by MA(1). Using he monhly daa he annual sandard deviaions of residuals of MA(1) models are compued. 3 Empirical Resuls 3.1 Performance of Alernaive Mehodologies Before discussing he resuls of regression analysis on he U.S. macroeconomic deerminans of he long run marke volailiy, we compare he performance of he alernaive mehodologies. Figure 1 shows he esimaed oal volailiy and he filered long run volailiies from Engle and Rangel and Cho and Elshaha models. Since he Engle and Rangel model use spline mehod, he filered long run volailiy seems o lose he innovaions in he long run volailiy series. Wihou reflecion of innovaions in long run volailiy, i is possible ha imporan macroeconomic variables may lose he explanaory power for he long run marke volailiy. The small value of R square of Engle and Rangel in Table 1 indicaes ha he long run variance from heir model loses imporan macroeconomic informaion ha affec he marke uncerainy. In addiion o he small R square, here is only one macroeconomic variable ha significanly affec he long run marke volailiy obained from he Engle and Rangel s model. For he comparison purpose, we also use he oal condiional variance (h ) as he dependen variable o examine how he macroeconomic variables affec he annualized. We should expec ha here are few macroeconomic variables ha deermine he oal volailiy because he oal volailiy (h ) conains shor-erm volailiy componen in i. In accordance wih his expecaion, only wo independen macroeconomic variables have saisically significan explanaory power. Figure 1 shows ha unlike he long run volailiy from Engle and Rangel model, ha from
1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 96 Jang Hyung Cho and Ahmed Elshaha Cho and Elshaha model capures he innovaions in he long run volailiy process. The esimaion resuls in Table 1 also prove ha he filered long run volailiy using Cho and Elshaha model beer reflec he macroeconomic effecs. Pu differenly, mos of macroeconomic variables are saisically significan wih he expeced signs of coefficiens. Hence, he regression resuls are discussed using he resuls from [26] model. 14 12 10 8 6 4 2 0 Toal Variance Long Run Variance (Engle and Rangel) Figure 1: Filered long run volailiies The oal volailiy conains boh he emporary componen and long run componens. The long run volailiies are esimaed using wo differen models from Engle and Rangel (2008) and Cho and Elshaha (2011). The esimaed values of oal volailiy larger han 15 is rimmed for he beer visibiliy of he filered long run volailiies. For he GARCH models he reurns on S&P500 index are used. Specifically: P ln P Long Run Variance (Cho and Elshaha) r 100 ln 1 (6) Because he percenage reurns (as shown by muliplicaion by 100 in (6)) are used, he scale of he esimaed volailiies is large. Table one shows he resuls of he model proposed. Using he same independen macroeconomic variables, hree differen models yield differen resuls mainly because hey use differen dependen variable. The hree models use volailiy as he dependen
Macroeconomic Variables Effec on US Marke using MC-GARCH Model 97 variable, bu measured differenly. Our model provides a srong forecasing power wihou losing much informaion. The esimaed daily long run volailiies are annualized by average each year. Grgdp = Growh rae of real GDP, Irae = Shor erm ineres rae. * represens he saisical significance a or less han he 10% criical value. Table 1: Resuls of regression analysis Dependen variable Long variance (q ) (Cho&Elshaha) Long variance (q ) (Engle&Rangel) Toal Condiional variance (h ) Independen variable Coeff. Value Coeff. Value Coeff. Value Inercep -5.886-2.04* -4.585-2.05* -3.512-1.04 (1) Log nominal GDP 0.736 2.59* 0.580 2.63* 0.487 1.47 (2) Growh rae real GDP -0.289-3.76* -0.062-1.04-0.305-3.39* (3) Annual inflaion rae 0.017 0.25 0.003 0.05-0.057-0.69 Growh rae of M2-0.050-0.95 0.047 1.15-0.005-0.09 (4) Growh rae of M2 lagged by 1 year 0.148 3.04* 0.048 1.27 0.120 2.10* (5) Volailiy of grgdp 0.983 2.52* 0.510 1.68 0.648 1.42 (6) Volailiy of dollar index 0.347 1.85* 0.186 1.27 0.226 1.03 Volailiy of irae -1.419-0.96-0.626-0.55 0.209 0.12 (7) Volailiy of irae lagged by 3 monh -3.139-1.66 0.249 0.17-3.123-1.41 Volailiy of irae lagged by 6 monh 3.407 2.90* -0.163-0.18 2.072 1.50 (8) Volailiy of inflaion rae -1.068-0.92-1.363-1.52 0.557 0.41 R-Square 0.68 0.436 0.633 N 37 37 37 3.2 Macroeconomic Deerminans of he Long Run Marke Volailiy The esimaion resuls in Table 1 are very good given he small number of observaions. The number of observaions (number of years) is 37. The reason for he small number of observaions is due he independen variable, Dollar Index. Unlike oher variables, he values of Dollar Index are available from 1973. The effecive number of independen variables for he regression is 8: (1) Log nominal GDP, (2) growh rae of real GDP, (3) Inflaion rae, (4) Growh rae of (lagged) M2, (5) volailiy of real GDP, (6) volailiy of exchange rae (dollar index), (7) volailiy of (lagged) shor erm ineres rae, and (8) volailiy of inflaion rae. Among hese eigh independen variables, six variables deermine he long run marke volailiy saisically significanly. The wo inflaion variables (3) and (8) are insignifican. The raionale of using nominal GDP as independen variables is o examine which of he leverage effec and diversificaion effecs dominaes on he long run marke volailiy as he size of he U.S. economy grows bigger. Resuls in Table 1 shows ha he leverage
98 Jang Hyung Cho and Ahmed Elshaha effec dominaes he diversificaion, as he size of U.S. economy grows bigger. This resul is also observed in [19]. [17] and [28] show ha economic recession is he mos imporan facor ha affecs he US sock-reurn volailiy. Our resuls also suppor heir resuls in ha he long run marke volailiy increases as he real economic aciviies diminish. The resuls wihou Argenina sample in [19] also suppor his resul. I is well known ha he sock can be a perfec hedge agains inflaion only if prices and coss increase uniformly and hence a firm passes on all increased coss o is buyers. However, inflaion is rarely uniform in affecing prices and coss. As a resul, inflaion increases earning volailiy and hence reduces value. We expec o find he negaive relaion beween he long run marke volailiy and hese inflaion variables (3) Inflaion rae and (8) volailiy of inflaion rae). However, resuls show ha hese wo inflaion variables are no significan. The explanaory power of volailiy of inflaion rae disappear when oher explanaory variables are included, especially, growh rae of real GDP, he regression model. Also he correlaion coefficien in Table 3 shows ha here is significan posiive relaion of inflaion volailiy o he long run sock reurn volailiy as shown by 34.4%. The level of inflaion rae does no have any explanaory power for he long run volailiy. The reason can be ha level of inflaion may be adjused ino prices and coss in he long run. Hence, only uncerainy in inflaion rae causes he increase in long run volailiy. This able shows he esimaion resuls of Cho and Elshaha s (2011) modified componen GARCH model. In he following model, h represens he oal volailiy and q he long run volailiy. * represens he saisical significance a or less han he 10% criical value. MC-GARCH model is specified as follows: r r E e (1) wih e h v (2) h q 2 e q h q (3) 1 1 1 1 1 1 h 1 q 1 q 1 q w (4) Table 2: The esimaion resuls of long run volailiy Coefficien Value ALPHA1 0.078 14.94* BETA1 0.877 53.96* W 0.002 3.59* RHO 0.998 1141.26* PHI 0.019 2.50* N 2,777 LOGLIK -15,592
Macroeconomic Variables Effec on US Marke using MC-GARCH Model 99 Table hree shows he correlaion coefficiens for he variables used in he regression analysis. To compue he correlaion coefficiens, he same number of observaions (37) ha was used for he regression analysis was used. The compued correlaion coefficiens are muliplied by 100 in he able. Grgdp = Growh rae of real GDP, Irae = Shor erm ineres rae. *represens he saisical significance a or less han he 10% criical value. Log nominal GDP Growh rae of real GDP Annual inflaion rae Growh rae of M2 lagged by 1 year Volailiy of grgdp Volailiy of dollar index Volailiy of irae/ lagged by 3 monh/ lagged by 6 monh Volailiy of inflaion Long run volailiy 33.5 Log GDP -40.4* -10.2 Table 3: Correlaion coefficiens Growh rae of real GDP -22.4-73.7* -14.9 Annual inflaion rae 15.1-47.7* 15.8 31.9 Growh rae of M2 lag by 1 year 10.2-51.6* -21.1 58.0* 37.8* Volai. of grgdp 23.5-13.7-9.7 6.7 24.1 17.7-9.0-4.0 1.3-51.0* -47.3* -49.9* -39.2* -45.4* -36.3* 65.6* 59.6* 54.5* 27.4* 23.8 25.6 67.3* 63.7* 61.3* Volai. of dollar index 36.2* 35.3* 34.7* 34.4* 13.0-56.0* -0.2 15.8 31.5* 3.1 rae Growh rae of M2 2.1-43.9* 1.9 19.2 56.4* 37.9* 11.2 Volai. of irae/ lagged by 3 mon/lagged by 6 mon. 24.2 23.7 20.8 34.5* 33.4* 44.4* We add new empirical findings abou he effec of M2 on he long run volailiy. As menioned earlier, he growh of M2 can cause moneary inflaion in he long run. Then, we should expec ha he lagged growh rae of M2 should increase he uncerainy in earnings. In accordance wih his expecaion, here is significan posiive correlaion beween lagged growh rae of M2 and volailiy of real GDP as shown by 37.8%. Regression resuls also show ha he lagged growh rae of M2 significanly increases he long run volailiy. Volailiies of fundamenals are imporan facors ha affec he marke volailiy. As done in [19], we include he volailiies of real GDP, exchange rae (dollar index), ineres rae and inflaion rae. As expeced hese uncerainy in fundamenals significanly increase he long run marke volailiy. Unlike [19], we find ha volailiy of ineres rae lagged by wo quarers increases he marke volailiy.
100 Jang Hyung Cho and Ahmed Elshaha 4 Conclusion This paper provides evidence ha he fundamenal macroeconomic variables and he sae of he economy have a significan effec on he equiy marke s volailiy. The auhors jusificaion for he mixed resuls in he lieraure or non-significan relaions are due o he use of conaminaed volailiy measures. Some of he measures of condiional volailiy do no filer noise, and jus use he oal condiional volailiy. The exisences of oo much noise obviously affec he relaionship. Oher models filer oo much informaion and leave a long-erm volailiy measure ha is unable o capure exising relaions. The proposed model provides a model ha can forecas long-erm volailiy wihou filering ou relevan informaion. In his paper, he proposed model is compared o he spline-garch model proposed Engle and Rangel 2008 and o he oal condiional volailiy. The resuls reached showed ha he proposed model offers a sronger explanaory power and forecasing abiliy for equiy volailiy. The resuls reached in his paper provide valuable insighs for he policy makers, as i provide evidence of significan relaionships beween some fundamenal macroeconomic variables and he equiy marke volailiy. Saring wih he effec of he business cycle as measured by he growh rae of real GDP, unlike he resuls reached by [19] our resuls are consisen wih he economics lieraure ha shows a significan negaive relaionship beween he business cycle and he equiy marke volailiy. Thus, our model expecs volailiy o be higher during recessions, consisen wih [28] and [29]. To reflec he uncerainy abou he fundamenal macroeconomic variables, we used he volailiy of hree variables; real GDP, shor-erm ineres raes, and exchange rae index. Consisen wih he economic heory and he empirical lieraure, hese hree variables showed significan posiive relaionship wih long-erm equiy volailiy using he proposed model and no significan relaionship using he Engle and Rangel Spline-GARCH model. This finding is jus inuiive. As hese macroeconomic variables become more volailiy, he risk premia for equiy securiies will become more volailiy, and hus he risk of he equiy marke volailiy increase. The hird explanaory variable used as a predicor of fuure sae was he level of inflaion. Consisen wih he lieraure, our model showed a posiive relaionship beween annual inflaion rae and he equiy marke volailiy, bu he relaion was no saisically significan. Even hough our model did no resul in a significan relaion, i resuled in sronger relaion as compared o he resuls reached by [19]. References [1] Andersen, T., Bollerslev, T., Huang, X. A reduced form framework for modeling volailiy of speculaive prices based on realized variaion measures, Journal of Economerics, 160(1), January 2011, pages 176-189, ISSN 0304-4076. [2] Ding, J., Nigel, M. Forecasing accuracy of sochasic volailiy, GARCH and EWMA models under differen volailiy scenarios. Applied Financial Economics. 20(10), 2010. [3] Hansen, R. and Lunde, A. A forecas comparison of volailiy models: does anyhing bea a GARCH(1,1)?. Journal of Applied Economerics, 20, 2005, 873 889.
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