ASIA ACADEMY of MAAGEMET JOURAL of ACCOUTIG and FIACE AAMJAF, Vol. 10, o. 1, 151 165, 014 THE PERSISTECY OF ITERATIOAL DIVERSIFICATIO BEEFITS: THE ROLE OF THE ASYMMETRY VOLATILITY MODEL Ung Sze ie 1*, Choo Wei Chong, Murali Sambasivan 3 and Annuar Md. assir 4 1 Graduae School of Managemen, Universii Pura Malaysia, 43400 UPM Serdang, Selangor, Malaysia Deparmen of Managemen and Markeing, Faculy of Economics and Managemen, Universii Pura Malaysia, 43400 UPM Serdang, Selangor, Malaysia 3 Taylor's Business School, Taylor's Universiy Lakeside Campus, 1 Jalan Taylor s, 47500 Subang Jaya, Malaysia 4 Deparmen of Accouning and Finance, Faculy of Economics and Managemen, Universii Pura Malaysia, 43400 UPM Serdang, Selangor, Malaysia *Corresponding auhor: janys119@gmail.com ABSTRACT This sudy resaes he issue of inernaional porfolio diversificaion benefis by considering he problem of perfec foresigh assumpion and consan variancecovariance esimaion. Whils emphasising he role of he asymmery volailiy model in porfolio formaion, we also invesigae he economic implicaion of he smooh ransiion exponenial smoohing (STES) mehod in porfolio risk managemen. Our resuls sugges ha all porfolios perform beer in he ex-pos period compared o he ex-ane period. However, invesors may no be able o obain any benefis from diversifying heir porfolio in developed sock markes in boh ex-ane and ex-pos periods. Furher invesigaion on he economic implicaions of he STES mehod also show ha he STES mehod does help o cushion losses generaed from he inernaional diversificaion porfolio. Hence, his suggess he use of he STES mehod in compuing and monioring he risk of an inernaionally diversified porfolio. Keywords: inernaional porfolio diversificaion (IPD) benefis, smooh ransiion exponenial smoohing (STES), ex-pos, ex-ane, asymmery volailiy model ITRODUCTIO There has been a grea deal of ineres on he benefis of inernaional porfolio diversificaion (IPD) over he pas few decades. I is believed ha diversifying domesic porfolios inernaionally will provide significan risk-reducion benefis. Despie he conclusion of a large amoun of lieraure ha looks favourably on IPD benefis (see, for example, Solnik, 1974; Flecher & Marshall, 005; De Sanis & Gérard, 009), some sudies find ha IPD benefis diminish due o Asian Academy of Managemen and Penerbi Universii Sains Malaysia, 014
Ung Sze ie e al. increasing correlaions among inernaional sock markes (Driessen & Laeven, 007; Smih & Swanson, 008). The incorporaion of he ime-varying condiional correlaion model was shown o be imporan in he IPD benefis compuaion (see, Guidolin & Hyde, 008; You & Daigler, 010). However, mos of he lieraure evaluaes he IPD benefis based on he degree of consan correlaion (Chiou, 009; Flecher & Marshall, 005; Laopodis, 005; Markellos & Siriopoulos, 1997). Apar from he use of he consan correlaion approach, he evaluaion of IPD benefis based on a porfolio consruced from hisorical daa is a common pracice in financial lieraure. Such perfec foresigh is impracical in he real world. The benefis delivered in he porfolio formaion period could be differen from hose in he pos-porfolio formaion period (Meyer & Rose, 003). Inernaional diversificaion benefis may be oversaed, especially when a large marke disurbance exiss afer he porfolio has been formed and when he associaed risks canno be accuraely forecased. To our knowledge, no research has explicily sudied he benefis of IPD on an ex-pos basis in conjuncion wih he use of ime-varying condiional correlaion models, wih he excepion of Aslanidis, Osborn and Sensier (009). This paper examines he persisency of IPD benefis from he ex-ane period o he ex-pos period. To incorporae he ime-varying variance-covariance feaure, his sudy has adoped he STES mehod o compue he IPD benefis. The adapive smoohing parameer of he STES mehod is able o capure he ime-varying condiional correlaion. I was proven o be he superior model in forecasing sock marke volailiy (Taylor, 004a; Choo, 008) and monhly porfolio risk (Ung, Choo, assir, & Sambasivan, 010). PRIOR RESEARCH Earlier sudies conduced on he benefis of IPD can be raced back o he work of Grubel (1968), Harvey (1995), Levy and Sarna (1970), Markellos and Siriopoulos (1997), Odier and Solnik (1993) and Solnik (1974). These sudies conclude ha invesors can gain from invesing in oher pars of he world. This viewpoin has also been proven in recen lieraure, such as Bonfiglioli and Favero (005), Flavin and Panopoulou (009), and Rezaya and Yavas (006). However, anoher group of sudies reaches he opposie conclusion, which includes Click and Plummer (005), Driessen and Leaven (007), Shawky, Kuenzel and Mikhail (1997), and Smih and Swanson, (008). They claim ha he reducion of IPD benefis is due mainly o he increasing level of inerdependence among inernaional sock markes. 15
IPD Benefis and Asymmery Volailiy Model The aforemenioned sudies used he consan correlaion approach o draw heir conclusions on IPD benefis. Goezmann, Li and Rouwenhors (005), Longin and Solnik (1995), and Rua and unes (009), among ohers, have found ha correlaions beween sock markes were ime varying. Oher sudies even documened ha correlaions end o srenghen during he bear marke periods (e.g., Barram & Bodnar, 009; Campbell, Koedijk, & Kofman, 00; Haas, 010; King & Wadhwani, 1990; Longin & Solnik, 001; Yang, Tapon, & Sun, 006). Thus, invesors should carefully monior he porfolio risk because he IPD benefis are ime varying and resuled from he increased marke inegraion (Kearney & Lucey, 004). There are sudies ha explicily employ a ime-varying condiional correlaion model o examine he IPD benefis. By using he Mulivariae GARCH model, Aslanidis e al. (009) reveal ha US and UK markes provide limied diversificaion benefis o invesors in he ex-pos period. Similarly, You and Daigler (010) also reach he same conclusion wih he use of US and European sock markes as heir daa se. Early sudies ha examined he ex-pos diversificaion benefis include Eun and Resnick (1988, 1994), and Cumby, Figlewski and Hasbrouck (1994). They reveal ha he performances of inernaional porfolios are superior o ha of domesic porfolios in he ex-pos period. In he synhesis lieraure, Shawky e al. (1997) reveal he exisence of IPD benefis in an ex-pos period. Recenly, Meyer and Rose (003) menion ha an opimal ex-ane porfolio may be unable o deliver he maximum inernaional diversificaion benefis o he invesors on an ex-pos basis. Conrarily, Chiou (009), and Chiou, Lee and Chang (009) show ha considerable risk reducion is achievable wih he Markowiz model in he ex-pos period. EMPIRICAL STUDY Descripion of he Sudy Daily closing prices of eigh inernaional sock indices have been used in his sudy. These include he Sandard and Poor s 500 (S&P 500, ew York), he Financial Times and London Sock Exchange 100 (FTSE 100, London), he Hang Seng Index (HIS, Hong Kong), he Srai Times Index (STI, Singapore), he ikkei 5 (Tokyo), he Deuscher Akien Index (DAX, Frankfur), he European Opion Exchange (EOE, Amserdam) and he Coaion Assisée en Coninu (CAC 40, Paris). 1 To evaluae he inernaional diversificaion benefis, he US monhly 3-monh T-bill raes will be used as a proxy for he risk-free ineres rae. The sample period spanned from early 1995 o he end of 010. 153
Ung Sze ie e al. We spli he daa ino ex-ane (1995 003) and ex-pos (004 010) periods o examine he persisency of IPD benefis in he ex-pos period and he pos-sample forecasing performance of he asymmery volailiy model. Parameer esimaes are drawn from 1995 o 003 for he forecasing mehod. The remaining periods are used for pos-sample forecasing performance evaluaion. We focused on he muli-period forecass (i.e., forecass produced over a holding period of differen lenghs in every monh) raher han on a onesep-ahead forecas in he forecasing evaluaion; in view of he porfolio, rebalance aciviy is carried ou once a monh (Akgiray, 1989). The muli-period forecass of he smooh ransiion exponenial smoohing (STES) mehod will be discussed laer. Furhermore, he rolling window basis is applied on he parameer esimaion in his sudy. We esimae parameers on R observaions running from R, R + 1,.... The fixed window size, R, spanned over 96 monhs, in which our firs window is from March 1995 o February 003. The esimaed parameers are used o produce he one-sep-ahead forecas on he firs day of he following monh. The window is hen rolled over o include he daa in March 003 for he following parameer esimaes. This esimaion procedure updaes he parameer esimaes on a monhly basis such ha he laes informaion se is included. This process provides us wih 94 forecass for every porfolio in he ex-pos period. Minimum Variance Porfolio (MVP) Formaion Benchmark porfolio The daa in he ex-ane period will be used o calculae he variances ij( i() ) covariances of sock index reurns based on convenional formulae, as saed below: and r i( ) ri ri ( ri i( ) where r i() is he reurn for sock index i a ime, 1 ) (1) ij( ) r i( ) ri rj( rj ) 1 () 154
IPD Benefis and Asymmery Volailiy Model r where is he number of rading days in a monh and i is he mean reurn of sock index i for a specific monh. The compued variance-covariance marices will hen serve as a basis for he minimum variance porfolio (MVP) formaion. The seven MVPs ha combined he US sock marke wih oher developed markes are as follows. These MVPs were based solely on hisorical daa and will serve as he benchmark porfolio. Porfolio 1: S&P 500 combined wih ikkei 5 Porfolio : S&P 500 combined wih STI Porfolio 3: S&P 500 combined wih HSI Porfolio 4: S&P 500 combined wih EOE Porfolio 5: S&P 500 combined wih DAX Porfolio 6: S&P 500 combined wih CAC 40 Porfolio 7: S&P 500 combined wih FTSE 100 We assumed ha shor selling is prohibied and ha no risk-free asse will be chosen in he porfolio. The MVP formaion model is hen: Minimise p xi i Subjec o: where p x x (3) i1 xi i1 i1 j1 x i 0 1 i 1,..., i is denoed as porfolio variance and x i is he monhly porfolio composiion for sock index i. The resulan monhly porfolio composiion (x i ) will be used o compue he monhly porfolio reurn in he ex-ane period. Porfolio reurn (r p ) is simply rp xiri he summaion of consiuen sock index reurns i1, where r i is he reurn of sock index i. Given each ex-ane MVP s risks and reurns, a imeseries of 96 monhly Sharpe raios are being calculaed. Thereafer, he mean Sharpe raio as employed by Berger, Pukhuanhong and Yang (011) is compued for each of he MVPs. j ij n 155
Ung Sze ie e al. Ex-pos porfolio We recalculae he monhly porfolio risk and reurn using ex-pos daa bu wih an ex-ane porfolio composiion. This procedure ensures ha ex-pos MVPs are being consruced using ex-ane porfolio composiion o evaluae he persisency of IPD benefis beyond he porfolio formaion period. Similarly, he mean Sharpe raio is compued for each ex-pos MVP, and he value will be compared agains ha of he ex-ane MVPs o deermine he persisency of IPD benefis. A procedure similar o he one saed above is hen repeaed in conjuncion wih he use of he STES mehod in esimaing he variance-covariance marices. Smooh Transiion Exponenial Smoohing (STES) Exponenial smoohing is a simple volailiy forecasing mehod. The one-sepahead variance forecas under his mehod is an exponenially weighed moving average of pas squared shocks. Mos of he lieraure has generally applied a consan smoohing parameer on his mehod. everheless, some previous sudies argue ha he smoohing parameer should be allowed o vary over ime. The raionale of applying varying a smoohing parameer is ha he characerisics of he ime series are no saic over ime. Hence, several adapive exponenial smoohing mehods have been developed (see Snyder, 1988; Trigg & Leach, 1967). The smoohing parameer of hose adapive exponenial smoohing mehods varies according o he value of he racking signal bu someimes leads o unsable forecass. Taylor (004a, b) has developed a new adapive exponenial smoohing, which is based on he smooh ransiion model. The STES was found o have a comparaively sable forecas. This new adapive exponenial smoohing is formulaed as follows: one-sep-ahead variance forecas ˆ ˆ i( 1) i( ) (1 ) i( ) (4) where is he one-sep-ahead variance forecas, ˆi( 1) α is he smoohing parameer, is he price shock, i() ˆ i ( ) is he esimaes of variance of he reurn for sock index i a ime, 156
IPD Benefis and Asymmery Volailiy Model one-sep-ahead covariance forecas ˆ ˆ ij( 1) ( i( ) j( ) ) (1 ) ij( ) (5) where ˆ ij( 1) ˆ ij ( ) is he one-sep-ahead covariance forecas, is he esimaes of covariance beween sock index i and j a ime, 1 and 1 exp( V ) under consrain 0 1. The daily residual of a sock index reurn i() was also considered as price shock, defined by r E( r I 1). E ( r I 1) is he mean erm a ime condiional upon I 1, he informaion se of all observed reurns up o ime 1. β and γ are consan parameers. I is noed ha he smoohing parameer α is a logisic funcion of a user-specific ransiion variable, V. The smoohing parameer will always be bound beween 0 and 1, regardless of he value of he ransiion variable, because he resricion is imposed by he logisic funcion. If γ>0, he weigh will gradually shif from pas shocks o pas condiional variances as V increases. The ransiion variable is he crucial componen in deermining he performance of he STES mehod. Taylor (004b) has proven ha he daily squared residual is more suiable when used as a ransiion variable compared o he absolue value of he daily residual he price shock.. Boh and are he size of The parameers of he STES mehods are obained via minimising he sum of he in-sample one-sep-ahead forecas error: min i ( ˆ ) (6) i Following his formula, he in-sample daily squared residual acs as a proxy for acual variance. Transiion variables V of he daily squared residual and daily esimaed covariance are used in he variance and covariance forecas, respecively. The daily esimaed covariance can be calculaed by muliplying he daily residuals of wo sock index reurns i j. As he V changes, he smoohing parameer will vary accordingly. The muli-period forecas of he i i 157
Ung Sze ie e al. STES mehod is he one-sep-ahead forecas muliplied by he number of days in a monh, k, as shown below: monhly variance forecas monhly covariance forecas ˆ i(, k) ˆ i( 1) k (7) ˆ ij(, k) ˆ ij( 1) k (8) Evaluaion Crierion The Sharpe raio (Sharpe, 1966) is used o evaluae he inernaional diversificaion benefis. I is a reward-o-variabiliy raio and measures he excess reurn (difference beween porfolio reurn and risk-free rae) over porfolio reurn volailiy, which is measured by sandard deviaion. Hence, a higher Sharpe raio indicaes ha larger benefis can be delivered from ha porfolio. The formula can be wrien as: S rp r f p where S is he Sharpe raio, r p is he porfolio reurn, σ p is he porfolio reurn volailiy as measured by sandard deviaion, wih 3-monh US Treasury Bill raes (r f ) used as a proxy for he risk-free rae o evaluae he inernaional diversificaion. (9) EMPIRICAL EVIDECE Descripive Saisics of Daa Table 1 summarises he descripive saisics of he daily raes of reurn. The ln r ln P P. naural log reurn, as used in his sudy, is compued based on All sock markes have a posiive average reurn, excep he Japanese and Singapore sock markes. The reurn of he U.K. sock marke is he leas varied wih a sandard deviaion of 1.19%, while Hong Kong has he highes reurn volailiy wih a sandard deviaion of 1.86%. The skewness and kurosis 158 1
IPD Benefis and Asymmery Volailiy Model coefficiens clearly show ha all reurn series are asymmeric and lepokuric. These have been furher srenghened by he Jarque-Bera es, which srongly rejecs he null hypohesis of a normal disribuion. Table 1 Summary saisics of daa on daily raes of reurn from March 1995 o February 003 Index Mean ( 10 4 ) Sandard deviaion Skewness Kurosis Jarque-Bera (p-value) Panel A: Developed markes S&P 500.71 0.011 0.1090 5.805 671.90* FTSE 100 1.06 0.0119 0.0 5.1454 401.18* HSI 0.51 0.0186 0.1453 1.5985 7584.7* IKKEI 5 3.90 0.0153 0.1101 4.780 64.91* STI.6 0.0150 0.36 11.483 5963.10* CAC 40.18 0.0153 0.1091 5.1088 376.79* DAX 1.5 0.0166 0.6 5.5585 57.09* EOE 1.70 0.0133 0.199 5.747 647.19* oes: * Rejecion of null hypohesis a 1% level of significance. The Jarque-Bera es is a goodness-of-fi es ha ess for he exisence of skewness and kurosis in a disribuion. The null hypohesis assumes he daa are from a normal disribuion. The average monhly correlaions beween sock markes from March 1995 o February 003 are shown in Table. I is noed ha he correlaions of wo sock markes formed from he same region are higher compared o ha of sock markes in differen regions. The Persisency of IPD Benefis Invesors are concerned wih he persisency of inernaional diversificaion benefis beyond he porfolio formaion period. Table 3 summarises he mean Sharpe raio from differen porfolios o reveal wheher he diversificaion benefis found in he ex-ane period will las in he ex-pos period. From he resuls, we find ha all porfolios have a negaive mean Sharpe raio in boh he ex-ane and he ex-pos periods. This resul indicaes ha invesors would no be beer off wih inernaionally diversified porfolios. The resul is consisen wih he findings of You and Daigler (010). Their findings reveal ha inernaionally diversified porfolios had much higher losses agains a US porfolio alone. Similar o You and Daigler (010), as shown in our resuls, US Asian porfolios deliver a smaller mean Sharpe raio compared o US European porfolios. For example, he mean Sharpe raio for US Singapore is 6.39 in he ex-ane period 159
Ung Sze ie e al. and 3.84 in he ex-pos period. On he oher hand, he mean Sharpe raios for US France porfolios in he ex-ane and ex-pos periods are 5.87 and 3.16, respecively. Table Correlaions beween he reurn of developed sock markes from March 1995 o February 003 Index CAC 40 DAX EOE FTSE 100 HSI IKKEI S&P 500 STI CAC 40 1 DAX 0.77167 1 EOE 0.877671 0.830343 1 FTSE 100 0.77847 0.705479 0.87540 1 HIS 0.96343 0.335706 0.371176 0.331976 1 IKKEI 0.377 0.0879 0.51544 0.661 0.40939 1 S&P 500 0.4361 0.474856 0.43118 0.411301 0.1199 0.105609 1 STI 0.4544 0.19479 0.6600 0.46871 0.54634 0.30777 0.107313 1 Conrary o he resuls of Meyer and Rose (003), our resuls show ha opimal porfolio composiions implied in hisorical daa do cushion he loss in he ex-pos period. All porfolios deliver a mean Sharpe raio ha is smaller han 6 in he ex-ane period bu have mean Sharpe raios beween 3 o 4 in he ex-pos period. The differences of our resuls from he previous lieraure may be aribuable o he differen ime periods being used for examinaion (Shawky e al. 1997). The sample period used by Meyer and Rose (003) was from May 199 o May 1998 only, whereas our analysis covers from 1995 unil 010. The poenial impacs of he 1997 Asian Financial Crisis and of he 00 bear marke, which were excluded in he ex-ane period of Meyer and Rose (003), have been included in our ex-ane period. Thus, he porfolio composiions obained in he ex-ane period do ake ino accoun he financial crisis risk, and his helps o cushion he loss in he ex-pos period even hough he subprime crisis is occurring during our ex-pos period. Meanwhile, uni rus was used as heir daa series, which is differen from our daa series. 160
IPD Benefis and Asymmery Volailiy Model Table 3 Mean Sharpe raios for porfolios formed using he convenional mehod Period Mean Sharpe raio (porfolio) 1 3 4 5 6 7 Ex-ane 6.39 6.93 6.17 6.40 6.13 5.87 6.69 Ex-pos 3.39 3.84 3.39 3.3 3.09 3.16 3.41 oe: The abbreviaions for he porfolios are as follows: Porfolio 1 (US and Japan), Porfolio (US and Singapore), Porfolio 3 (US and Hong Kong), Porfolio 4 (US and he eherlands), Porfolio 5 (US and Germany), Porfolio 6 (US and France) and Porfolio 7 (US and UK). The Role of he Asymmery Volailiy Model in Porfolio Formaion To evaluae he role of he asymmery volailiy model in porfolio formaion, he ex-pos IPD benefi is compued using he STES mehod. Meanwhile, his sudy enables us o gauge he economic implicaion of he STES mehod. Table 4 displays he inernaional diversificaion benefis in erms of he mean Sharpe raio compued using he STES mehod and he convenional mehod. Alhough boh mehods yield negaive mean Sharpe raios, he STES mehod yields a smaller negaive mean Sharpe raio for all porfolios. Apparenly, he STES mehod does help o cushion some losses incurred from porfolios formed using he convenional mehod. This resul is in accordance wih he findings of Aslanidis e al. (009), which saed ha he smooh ransiion condiional correlaion model is able o capure he dynamic co-movemen beween sock markes and herefore helps o improve he performance of he porfolio and reduce losses. Table 4 Mean Sharpe raios based on pos-sample weighing compued via he STES and he convenional mehods Mehod Mean Sharpe raio (porfolio) 1 3 4 5 6 7 Convenional 3.39 3.84 3.39 3.3 3.09 3.16 3.41 STES 0.76 0.75 0.81 0.73 0.78 0.70 0.75 oes: Every porfolio being analysed here was formed from wo sock markes: Porfolio 1 (US and Japan), Porfolio (US and Singapore), Porfolio 3 (US and Hong Kong), Porfolio 4 (US and he eherlands), Porfolio 5 (US and Germany), Porfolio 6 (US and France) and Porfolio 7 (US and UK). Equaions (1) and () were used o calculae he variance-covariance marix under he convenional approach. The pos period sample was from March 1995 unil February 003. 161
Ung Sze ie e al. COCLUSIO Research on inernaional diversificaion benefis has hus far employed he consan correlaion model, which is no suppored by empirical evidence and heory. Only a few sudies have examined diversificaion benefis based on imevarying correlaions. Furhermore, unrealisic perfec foresigh assumpions have been widely applied in his research area wih he conclusion ha diversificaion offers benefis; his conclusion has been based on a porfolio formed from hisorical daa, which may no reflec he acual IPD benefis in he fuure. This paper conribues by addressing he persisency of inernaional porfolio diversificaion benefis from he ex-ane period o he ex-pos period in conjuncion wih he use of he ime-varying porfolio risk forecasing mehod. We provide a more realisic view on boh compuaional and evaluaion issues relaing o diversificaion benefis. The findings indicae ha he diversificaion benefis disappeared in boh he ex-ane and he ex-pos periods for all porfolios. Ineresingly, all porfolios yield a beer performance in he ex-pos period compared o he ex-ane period. The combinaion of he U.S. and Singapore sock markes faces he mos severe loss, whereas he porfolio consising of he U.S. and French sock markes has he smalles loss compared o oher porfolios. oneheless, hese findings are based on he benefis generaed from he convenional variance-covariance formulae. The benefis generaed from he ime-varying porfolio risk forecasing mehod are worh examining. This sudy furher examines he role of he asymmery volailiy model STES mehod in porfolio formaion. By comparing he IPD benefis compued from he STES mehod o he convenional mehod, he STES mehod is shown o cushion losses in porfolios consruced using he convenional mehod. Therefore, our resuls sugges he use of he STES mehod in porfolio risk managemen o opimally allocae he fund. OTES 1. Daa are no adjused for exchange raes for several reasons. Firs, sudies have proven ha exchange rae effecs on inernaional diversificaion benefis, especially on sock markes, are no maerial and are insignifican (Heson & Rouwenhors, 1994; Meyer & Rose, 003). Second, currency risk can be hedged away using derivaive insrumens, and hedging sraegies can reduce porfolio risk (see Soenan & Lindvall, 199; Dumas & Solnik, 1995; Eun & Resnick, 1994; Bugár & Maurer, 00). Third, sudies ha mainly focus on inernaional diversificaion benefis also ignore currency effecs (Aslanidis e al., 009; You & Daigler, 010). 16
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