Modelling Environmental Risk

Transcription

1 Modelling Environmenal Risk Suhejla Hoi a, Michael McAleer a and Lauren L. Pauwels b a School of Economics and Commerce, Universiy of Wesern Ausralia b Economics, Graduae Insiue of Inernaional Sudies, Geneva Absrac: As environmenal issues have become increasingly imporan in economic research and policy for susainable developmen, firms in he privae secor have inroduced environmenal and social issues in conducing heir business aciviies. Such behaviour is racked by he Dow Jones Susainable Indexes (DJSI) hrough financial marke indexes ha are derived from he Dow Jones Global Indexes. The susainabiliy aciviies of firms are assessed using crieria in hree areas, namely economic, environmenal and social. Risk (or uncerainy) is analysed empirically hrough he use of condiional volailiy models of invesmen in susainabiliy-driven firms ha are seleced hrough he DJSI. The empirical analysis is based on financial economeric models o deermine he underlying condiional volailiy, wih he esimaes showing ha here is srong evidence of volailiy clusering, shor and long run persisence of shocks o he index reurns, and asymmeric leverage beween posiive and negaive shocks o reurns. Keywords: Environmenal susainabiliy index, environmenal risk, condiional volailiy, Dow Jones Susainabiliy Indexes, GARCH. 1. Inroducion Environmenal susainabiliy is no limied o he domain of policy making and implemenaion, bu also involves he economic and financial behaviour of agens and firms in he privae secor. Invesors increasingly perceive susainable economic behaviour by firms as an improved and disciplined managemen sraegy, pushing invesors o diversify heir financial porfolios and o inves in susainable companies. The Dow Jones Susainabiliy Indexes (DJSI) are par of a family of financial indexes ha are derived in he same manner as he more well-known financial marke indexes, such as he Dow Jones Indusrial Average (DJIA) and he STOXX index. The DJSI is based on a selecion of leading firms ha ake environmenal and social issues seriously in heir business pracices. In his paper, we analyse empirically he risks (or uncerainy) associaed wih invesing in leading susainabiliy-driven firms. Imporan issues o be examined include a consideraion of he volailiy inheren in susainabiliy indexes, and differences in he reurns and volailiy behaviour of hese indexes in comparison wih financial indexes. The echniques used in his paper are derived mainly from he field of financial economerics, which will be used o gain insigh ino he volailiy (or uncerainy) in he underlying susainabiliy indexes. To dae here has been no such empirical analysis of susainabiliy indexes. The plan of he paper is as follows. Secion presens he Dow Jones Susanabiliy Indexes and discusses he key feaures of he various indexes. Univariae condiional volailiy models for daily observaions on he susainabiliy indexes are presened in Secion 3. The daa are described in Secion 4, and he empirical resuls for he univariae models are analysed in Secion 5. Some concluding remarks are given in Secion 6.. Dow Jones Susainabiliy Indexes (DJSI) In financial markes, some firms have paid serious aenion o incorporae environmenal and social issues wihin heir business planning sraegies. The Dow Jones Susainabiliy Indexes (DJSI) were sared in 1999, and repor on he financial performance of leading susainabiliy-driven firms worldwide (his 1

2 informaion is available a hp:// These susainabiliy indexes were creaed by he Dow Jones Indexes, STOXX Limied and he SAM group. The main purpose of he DJSI is o provide asse managers wih a benchmark o manage susainabiliy porfolios and develop financial producs and services ha are linked o susainable economic, environmenal and social crieria. Susainable developmen and social issues are frequenly promoed in he public secor, and are implemened hrough governmen policy, inernaional organisaions or non-governmenal acions. The DJSI, however, quanify he developmen and promoion of susainable values on he environmen and sociey by he business communiy. These indexes enable he promoion of susainabiliy wihin he privae secor by informing invesors abou firms ha behave in an environmenally susainable manner. As in he case of he Dow Jones Global Indexes, he DJSI feaures he same mehods for calculaing, reviewing and publishing daa. The DJSI is used in 14 counries, wih 50 licenses having been sold o asse managers. There are ses of DJSI indexes, namely he DJSI World and DJSI STOXX (a pan-european index). The laer index is also subdivided ino anoher regional index, namely DJSI EURO STOXX, which accouns solely for Euro-zone counries..1 DJSI World and DJSI STOXX Dow Jones Susainabiliy World Indexes (DJSI World) is consruced by selecing he leading 10% of susainabiliy firms (which number more han 300) in he Dow Jones Global Index, which covers 59 indusries over 34 counries. The composie DJSI World is available in four specialised subse indexes, which exclude companies ha generae revenue from (1) obacco, () gambling, (3) armamens or firearms, and (4) alcohol in addiion o he hree previously menioned iems. Two regional indexes, he DJSI STOXX and DJSI EURO STOXX, were firs published on 15 Ocober 001. They include 179 componens and record he financial performance of he leading 0% of European susainabiliy companies chosen from he Dow Jones STOXX 600. Moreover, wo specialised indexes are made available for boh regional composie indexes, which corresponds o caegory (4) given above. The DJSI World and DJSI STOXX are reviewed annually and quarerly o ensure consisency. They accommodae changes in he behaviour and saus of companies which could affec heir susainabiliy performance (such as bankrupcies, mergers and akeovers). Boh indexes comprise companies from 60 indusry groups and 18 marke secors.. Corporae Susainabiliy: Reviewing Process and Crieria The Corporae Susainabiliy Assessmen is a mehodology which assesses he relaive risks and opporuniies for eligible companies according o specific susainabiliy crieria. There are general and indusry-specific crieria, which accoun for 60% and 40% of he assessmen, respecively, in he economic, environmen and social dimensions. This scheme enables a deerminaion of he overall susainabiliy score and assessmen of he eligibiliy of firms o ener he DJSI. More specific informaion is available a hp:// Sources of informaion for such assessmens come from online quesionnaires, company documenaion, publicly available informaion, policies, repors and direc conacs wih a variey of firms. The informaion provided is verified, and heir qualiy and objeciviy are assured hrough an exernal audi of he assessing eams. Moreover, when a company has been seleced o join he DJSI World or DJSI STOXX, is susainabiliy performance is moniored on he basis of all he crieria for which i was seleced. 3. Univariae Models of Condiional Volailiy for Susainabiliy Indexes This secion discusses he specificaion and properies of he condiional volailiy models o be used o esimae he volailiy in he daily Dow Jones Susainabiliy Indexes. The specificaions o be esimaed are based on Engle s (198) auoregressive condiional heeroskedasiciy (ARCH) model and is various exensions. Specifically, his paper uses Bollerslev's (1986) symmeric generalised ARCH (GARCH) model, and he asymmeric GJR model of Glosen, Jagannahan and Runkle (199), which disinguishes beween he impac of negaive and posiive shocks on leverage hrough changes in he deb-equiy raio. Consider he saionary AR(1)-GARCH(1,1) model of y, he reurn on a sock index or on a financial asse (as measured in log-differences): y = ρ + ρ y + ε, ρ < 1 (1) 1 1 where he shocks o reurns, ε, are given by:

3 ε = η h, η ~ iid (0,1) () h = ω + αε 1 + βh 1, in which ω > 0, α 0, β 0 are sufficien condiions o ensure a sricly posiive condiional variance, h > 0. The ARCH (or α ) effec capures he shor run persisence of shocks, and he GARCH (or β ) effec indicaes he conribuion of shocks o long run persisence ( α + β ). In GARCH models, he parameers are ypically esimaed by he maximum likelihood mehod (MLE) o Quasi- Maximum Likelihood Esimaors (QMLE) in he absence of normaliy of he sandardized residuals, η. In he financial economerics lieraure, here are several imporan heoreical resuls ha are relevan for he GARCH model. Ling and McAleer (00a) esablished he necessary and sufficien condiions for sric saionariy and ergodiciy, as well as for he exisence of all momens, for he univariae GARCH(p,q) model, and Ling and McAleer (003) demonsraed ha he QMLE for GARCH(p,q) is consisen if he second momen is finie, E ε ) <, ( and asympoically normal if he fourh momen is finie, E( ε 4 ) <. The necessary and sufficien condiion for he exisence of he second momen of ε for he GARCH(1,1) model is α + β < 1, which is sraighforward o check in pracice. Anoher imporan resul is ha he log-momen condiion for he QMLE of GARCH(1,1), which is a weak sufficien condiion for he QMLE o be consisen and asympoically normal, is given by E (log( αη + β)) < 0. These resuls were derived in Elie and Jeanheau (1995) and Jeanheau (1998) for consisency and Boussama (000) for asympoic normaliy. In pracice, i is more sraighforward o verify he second momen condiion han he weaker log-momen condiion, as he laer is a funcion of unknown parameers and he mean of a random variable. The GARCH model proposes a symmeric reamen of he effecs of shocks on he condiional variance, h, such ha posiive and negaive shocks affec he condiional volailiy in an idenical manner. For his reason, he GJR(1,1) model accommodaes he asymmeric effecs of shocks, whereby negaive shocks are presumed o have a greaer impac on volailiy (hence, greaer leverage) han posiive shocks of a similar magniude. The asymmeric GJR(1,1) model is given as follows: h = ω + ( α + γi( η 1)) ε 1 + βh, (3) 1 where ω > 0, α 0, α + γ 0, β 0 are sufficien condiions for h > 0, and I ( η ) is an indicaor variable defined by: 1, ε < 0 I ( η ) = 0, ε 0 as η has he same sign as ε. The role of he indicaor variable is o disinguish beween posiive and negaive shocks, where he asymmeric effec ( γ > 0 ) measures he conribuion of shocks o boh shor run persisence ( α + γ / ) and long run persisence ( α + β + γ / ). As in he case of he GARCH model, some imporan heoreical developmens are available for he GJR model. In he case of symmery of η, he regulariy condiion for he exisence of he second momen of GJR(1,1) is α + β + γ / < 1 (see Ling and McAleer (00b)). Moreover, he weak log-momen condiion for GJR(1,1), E (ln[( α + γi( η )) η + β ]) < 0, is sufficien for he consisency and asympoic normaliy of he QMLE (see McAleer e al. (00)). 4. Daa Descripion The DJSI World, DJSI STOXX, and DJSI EURO STOXX are available a no charge from he Dow Jones Susainabiliy Indexes websie (he informaion is available a hp:// All he indexes are calculaed as boh he reurns on individual prices and reurns on he index, in boh USD and EURO currencies. The only specialised indexes ha are freely available for he DJSI are hose ha exclude all four componens, as described in secion.1 above. The indexes are available on boh a daily and monhly basis. Daily daa are available from 31/1/93 o 31/03/004 for DJSI World, and from 31/1/98 o 31/03/004 for boh DJSI STOXX and DJSI EURO STOXX. Monhly daa are from January 1994 for DJSI World and from January 1999 for DJSI STOXX, boh unil March 004. Daa for DJSI EURO STOXX are no available on a monhly basis. 3

4 All dividend paymens are included in he price and index reurns. Only dividends from non-operaing income or cash dividends graer han 10% of he share price are included in he price indexes, which are based on he Laspeyres formula. The base dae is 31/1/1998 and he corresponding base value is 1,000 for DJSI World and 100 for DJSI STOXX. Calculaion of he indexes is based on real ime sock prices and currency raes, he number of shares ousanding for each sock class, and corporae acion informaion as inpu daa. Specific informaion on sock prices and he manner in which he financial informaion has been incorporaed are available from he guide o hese indexes (DJSI, 003a, 003b). The empirical analysis in his paper involves he hree indexes and he hree specialised counerpars for he period 31/1/1998 o 31/03/004. The Dow Jones Indexes are calculaed on a 7-days per week basis, whereas he STOXX indexes are calculaed on a 5- days per week basis. We use he oal reurns indexes denominaed in USD for he empirical analysis raher han he price reurns. Using daa for he period January 1999 o March 004, pairwise correlaion coefficiens are calculaed for he six DJSI indexes and wo prominen financial indexes, namely he Dow Jones Indusrial Average (DJIA) and Sandard & Poor's 500 (SP500), as well as heir percenage changes (as expressed in logdifferences) (he correlaion marixes are available upon reques). For he regional DJSI STOXX, he monhly values are calculaed from he daily values, and sar from 31/1/1998. In levels, he SP500 is more highly correlaed wih he DJSI han is he DJSI wih he DJIA. This paern is no repeaed in log-differences (or reurns). No surprisingly, he correlaions are ypically much higher in levels han in log-differences. The hree highes correlaions in boh levels and log-differences are DJSI World, DJSI STOXX and DJSI EURO wih heir XA counerpars, namely hose ha exclude obacco, gambling, armamens or firearms, and alcohol. Finally, all he DJSI are highly correlaed wih heir corresponding specialised indexes in boh levels and log-differences. An implicaion of his resul is ha i does no seem o make any financial difference wheher an invesmen occurs in he susainabiliy index or in is specialised counerpar, excep for possible ehical reasons. The levels and reurns for each of he five principal indexes, namely DJSI World, DJSI STOXX, DJSI EURO, DJIA and S&P500 were also examined (he graphs are available upon reques). Apar form DJIA, he paerns in boh series are remarkably similar, as would be expeced from he simple correlaions coefficiens. There is a subsanial clusering of reurns for each series, wih only he DJIA reurns apparenly being differen from he remaining four series. 5. Empirical Resuls Using he daa on he daily indexes, he condiional mean is modeled in each case as an AR(1) process (hese resuls are available on reques). The univariae AR(1)-GARCH(1,1) and AR(1)-GJR(1,1) models are used o provide esimaes of he condiional volailiies associaed wih he five indexes for he period 31/1/1998 o 31/03/004. The Bernd, Hall, Hall and Hausman (BHHH) (1974) algorihm is used o maximize he condiional log-likelihood funcion. Tables 1- repor wo ses of -raios associaed wih each parameer esimae, namely he asympoic - raios and he Bollerslev and Wooldridge (199) robus -raios. The GARCH(1,1) esimaes in Table 1 show ha he ARCH (or α ) esimaes are always posiive and significan, as expeced, and he GARCH (or β ) esimaes are quie close o uniy and highly significan, which is a sandard resul for financial ime series reurns. Thus, boh he shor run and long run persisence of shocks are highly significan. The log-momen and second momen condiions are saisfied in all five cases, which indicae ha he QMLE are consisen and asympoically normal. These are very srong and robus resuls. In Table, he GJR(1,1) esimaes sugges ha he ARCH (or α ) esimaes are always insignifican, which migh be regarded as being conrary o expecaions, while he GARCH (or β ) esimaes are again quie high, bu no as close o uniy as in he case of GARCH(1,1). The asymmery parameer, γ, is always posiive and significan, which suggess ha negaive shocks have a greaer impac in increasing volailiy han posiive shocks have in decreasing volailiy. Thus, he leverage of negaive shocks exceeds ha of posiive shocks. Moreover, boh he shor run persisence, which arises predominanly from negaive shocks, and he long run persisence of shocks are highly significan. Finally, while he logmomen momen could no be calculaed for any of he five series, he second momen condiion was saisfied in each case. Therefore, he QMLE are consisen and asympoically normal in all cases, which provides anoher srong and robus se of resuls. The rade-off beween GARCH and GJR is problemaic in all five cases as he ARCH effecs are 4

5 insignifican for GJR bu he esimaed asymmery parameers are always significan. The srong empirical evidence of he exisence of condiional volailiy in all five series is compared wih he sample volailiy, which is defined as he squared deviaion from he mean of he respecive series. I is clear ha here is srong evidence of volailiy clusering, wih an absence of ouliers and exreme observaions, which can be pervasive in financial ime series reurns. Overall, S&P500 seems o be more closely relaed o he DJSI han is DJIA o he DJSI. 6. Conclusion Increasingly imporan environmenal issues for susainable developmen have led o firms in he privae secor examining environmenal and social issues. Such behaviour is racked by he Dow Jones Susainable Indexes (DJSI) hrough financial marke indexes derived from he Dow Jones Global Indexes. The susainabiliy aciviies of firms are assessed using crieria in hree areas, namely economic, environmenal and social. Risk (or uncerainy) is analysed empirically hrough he use of condiional volailiy models of invesmen in susainabiliydriven firms ha are seleced hrough he DJSI. In his paper, we analysed empirically he risks (or uncerainy) associaed wih invesing in leading susainabiliy-driven firms. Imporan issues included a consideraion of he volailiy inheren in susainabiliy indexes, and differences in he reurns and volailiy of hese indexes in comparison wih financial indexes. The echniques used in his paper were derived from he field of financial economerics, which were used o gain insighs ino he volailiy in he underlying susainabiliy indexes. The empirical esimaes showed a srong evidence of volailiy clusering, wih boh shor and long run persisence of shocks o he index reurns. Overall, boh GARCH(1,1) and GJR(1,1) were empirically suppored. However, he rade-off beween GARCH and GJR was problemaic in all cases as he ARCH effecs were insignifican for GJR bu he esimaed asymmery parameers were always significan. Acknowledgemens The auhors would like o hank Kahrin Fuellemann of SAM Indexes GmbH for helpful informaion. The firs and second auhors wish o acknowledge he financial suppor of he Ausralian Research Council. References Bernd, E.K., B.H. Hall, R.E. Hall and J.A. Hausman (1974), Esimaion and inference in nonlinear srucural models, Annals of Economic and Social Measuremen, 3, Bollerslev, T. (1986), Generalized Auoregressive Condiional Heeroskedasiciy, Journal of Economerics, 31, Bollerslev, T. and J.M. Wooldridge (199), Quasimaximum likelihood esimaion and inference in dynamic models wih ime-varying covariances, Economeric Reviews, 11, Boussama, F. (000), Asympoic Normaliy for he Quasi-maximum Likelihood Esimaor of a GARCH Model, Compes Rendus de l Académie des Sciences, Série I, 331, (in French). Chan, F., S. Hoi and M. McAleer (00), Srucure and Asympoic Theory for Mulivariae Asymmeric Volailiy: Empirical Evidence for Counry Risk Raings, paper presened o he 00 Ausralasian Meeing of he Economeric Sociey, Brisbane, Ausralia, July 00. Dow Jones Susainabiliy Indexes (003a), Dow Jones Susainabiliy World Indexes Guide, available a hp:// Version 5.0, Sepember. Dow Jones Susainabiliy Indexes (003b), Dow Jones STOXX Susainabiliy Indexes Guide, available a hp:// Version 3.0, Sepember. Elie, L. and T. Jeanheau (1995), Consisency in Heeroskedasic Models, Compes Rendus de l Académie des Sciences, Série I, 30, (in French) Engle, R.F. (198), Auoregressive Condiional Heeroscedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion, Economerica, 50, Glosen, L., R. Jagannahan and D. Runkle (199), On he Relaion Beween he Expeced Value and Volailiy of Nominal Excess Reurns on Socks, Journal of Finance, 46, Hoi, S. And M. McAleer (004), An Empirical Assessmen of Counry Risk Raings and Associaed Models, o appear in Journal of Economic Surveys. Jeanheau, T. (1998), Srong Consisency of Esimaors for Mulivariae ARCH Models, Economeric Theory, 14, Li, W.K., S. Ling and M. McAleer (00), Recen Theoreical Resuls for Time Series Models wih GARCH Errors, Journal of Economic Surveys, 16, Reprined in M. McAleer and L. Oxley (eds.), Conribuions o Financial Economerics: Theoreical and Pracical Issues, 5

6 Blackwell, Oxford, 00, pp Ling, S. and M. McAleer (00a), Necessary and Sufficien Momen Condiions for he GARCH(r,s) and Asymmeric Power GARCH(r,s) Models, Economeric Theory, 18, Ling, S. and M. McAleer (00b), Saionariy and he Exisence of Momens of a Family of GARCH Processes, Journal of Economerics, 106, Ling, S. and M. McAleer (003), Asympoic Theory for a Vecor ARMA-GARCH Model, Economeric Theory, 19, McAleer, M., F. Chan and D. Marinova (00), An Economeric Analysis of Asymmeric Volailiy: Theory and Applicaion o Paens, paper presened o he Ausralasian Meeing of he Economeric Sociey, Brisbane, July 00, o appear in Journal of Economerics. Table 1. AR(1)-GARCH(1,1) Index ω α β Log-momen Second momen DJSI World DJSI STOXX DJSI EURO STOXX DJIA S&P Noe: The hree enries corresponding o each parameer are heir esimaes, heir asympoic -raios, and he Bollerslev and Wooldridge (199) robus -raios. Table. AR(1)-GJR(1,1) Index ω α γ β Logmomen momen Second α + γ / DJSI World NA DJSI STOXX NA DJSI EURO STOXX NA DJIA NA S&P NA

7 Noe: The hree enries corresponding o each parameer are heir esimaes, heir asympoic -raios, and he Bollerslev and Wooldridge (199) robus -raios. 7