Abstract. Despite the demonstrated benefits from international portfolio diversification into foreign nations including

Transcription

1 Abstract Despte the demonstrated benefts from nternatonal portfolo dversfcaton nto foregn natons ncludng the less developed countres, whch are well documented, the dea s dscouraged by market mperfectons such as poltcal nstablty. In practce, natons may be dfferentated further by many aspects such as border controls or poltcal and socal trends that constran prvate transactons and fnancal decsons. Ths paper attempts to examne (1) whether the home asset bas n a portfolo holdng was assocated wth hgher poltcal nstablty rsk and (2) to what extent nternatonal dversfcaton among stocks, n the presence of poltcal nstablty rsk, outperforms domestc stock portfolos. Usng alternatve nstablty rsk proxes n the context of a mean-varance framework, the mpact of ths type of rsk on nternatonal portfolo nvestment decsons s corroborated. Keywords: Internatonal dversfcaton, Portfolo hedge, Poltcal nstablty rsk, Equty home bas, Corrupton-averse, Mean-varance theory. JEL Classfcaton: F3, G11, G12, G15, C61

2 Internatonal Portfolo Choce and Poltcal Instablty Rsk Introducton Despte the demonstrated benefts and gans of nternatonal equty dversfcaton, nvestors stll fnd t easer to be close to ther domestc markets whle dsregardng the nternatonal prospects. Whereas the gans from nternatonal portfolo dversfcaton nto foregn natons ncludng the less developed countres are well documented, the dea s dscouraged by foregn rsk and market mperfectons caused by poltcal nstablty and taxes. In practce, natons may be further dfferentated by other aspects such as taxes, border controls, and poltcal and socal trends that constran prvate transactons and fnancal decsons. The purpose of the paper s to examne whether the equty home bas n portfolo holdngs s assocated wth hgher poltcal nstablty rsk substtuted by lack of transparency and hgher levels of corrupton. Usng alternatve nstablty rsk proxes n the context of mean-varance framework, the mpact of ths type of rsk on nternatonal portfolo nvestment decsons has been provded. In fact, the gans from nternatonal dversfcaton was well documented (Errunza, Hogan, and Hung (1999); Adler and Dumas (1983); Levy and Sarnat (1970); Grubel (1968)) and dversfcaton n bonds and stocks were noteworthy (Levy and Lerman (1988)). Levy and Lerman (1988) note that the observed bas of nvestors toward ther domestc stocks s due to varous barrers (Stulz (1981)) to nternatonal nvestment, whch may be caused by the lack of nformaton, dscrmnatory taxes, and restrctons on funds flows or smply fear of expropraton. However, Levy and Lerman (1988) do not examne the nternatonal portfolo choce for the nvestor n the presence of fear and other country-specfc rsks. Ther work gnored the mplcatons of those types of rsk on the effcent set theory. The contrbuton of ths paper s the extenson of the adjustment for poltcal nstablty rsk to the nternatonal dversfcaton model. 1

3 Conceptual Framework and Lterature Revew A number of ex-post studes have looked at the gans of nternatonal dversfcaton ncludng the less developed countres (e.g., Levy and Lerman (1988); Errunza, Hogan, and Hung (1999); Ln, Kopp, Hoffman, and Thurston (2004)). Levy and Sarnat (1970) used country stock ndexes to construct effcent fronter portfolos and they found that the Japanese and South Afrcan stocks, whch were not hghly correlated wth other countres, were ncluded n the optmal portfolos. As a result, they suggested that dversfcaton of stock nvestment among countres wth few restrctons on ther captal flowssnotdesrable. Errunza and Rosenberg (1982) stressed the mportance of ncludng corporate securtes of less developed countres n nternatonal portfolos. Usng the varance of returns to nvestment n stocks as a measure of rsk, the authors showed that nternatonally dverse portfolos of such country ndexes domnated a U.S. stock ndex over the consdered perod. Also, they dscussed the reasons behnd the gap between perceved evdence and actual experence where nvestors tend to prefer exclusvely the securtes of the developed world whle gnorng other nternatonal opportuntes. They dscovered the exstence of nvestments barrers n less developed countres such as lack of nformaton, dfferences n captal controls and accountng standards, poltcal nstablty, and taxaton polces. They outlned some procedural shortcomngs whch are due frst to the defnton of rsk as the varance of the ex-post rates of return gnorng other types of rsk such as operatng rsk, poltcal rsk of expropraton, confscaton, and terrorsm and, second to the use of past exchange rates to estmate the exchange rsk. 1 Errunza and Rosenberg (1982), n ther emprcal comparson between nvestment rsk n developed countres (DCs) vs-à-vs less developed countres (LDCs), suggested that the lower busness rsk n LDs s due to the stablty of gross natonal product (GNP) and consumer prces (nflaton), the role of government, the stable culture, the exstence of groups and monopoly power, and the absence of expropraton durng ther sample perod. In another study, Errunza (1983) dscussed the obstacles that should not be gnored such as, currency rsk, captal flow restrctons, and nformaton avalablty. 1 Solnk (1974) concluded that nternatonal dversfcaton s attractve whether exchange rate changes are hedged or uncovered, see Joron (1989) 2

4 Errunza (1983) ponted out that Even though t s natural to perceve the barrers to be more onerous n the case of EMs, they are not as bad as they seem to appear. Moreover, Errunza (1983) ponted out that even though the poltcal rsk s apparent n emergng markets, contemplaton of ths rsk n asset prces depends on the opportunty set of the nvestor and the underlyng factors. It s often sad that as captal markets around the world become more ntegrated over tme, the gans of dversfcaton wll be reduced. Ths nference was acheved by comparng selected correlaton coeffcents between stock markets for dfferent tme perods, and the overall pcture show that correlatons have ncreased over tme. Yet, although captal market ntegraton has decreased some benefts of nternatonal portfolo dversfcaton, the correlaton coeffcents between markets are stll far from perfect postve correlaton stuaton. Thus, there are plenty of rsk-reducton opportuntes for nternatonal portfolo dversfcaton by holdng nternatonal assets abroad. 2 Informaton Imperfecton and Barrers to Investments Extensve prevous studes (Adler and Horesh (1974); Bergstrom (1975); Maldonado and Saunders (1981); Errunza and Rosenberg (1982); Adler and Dumas (1983); Errunza (1983); Joron (1985); Levy and Lerman (1988); Errunza, Hogan, and Hung (1999)) made strong arguments favorng nternatonal stock dversfcaton and/or bond dversfcaton, and call nto queston why ndvdual nvestors do not take advantage of nternatonal opportuntes. Home-asset bas runs counter to the strand of lterature, s when nvestors tend to nvest n asset from ther own country. Ths tendency to nvest n local assets exsts n many dfferent markets, ncludng stock and bond markets and real estate. 3 Lews (1999) suggests that stock-market ntegraton may stll be restrcted by home bas n equty portfolos dsplayed by many nvestors. She defnes equty home bas as ndvduals who hold too lttle of 2 Many natonal economes are denomnated by only a few ndustres, and stock markets retan a dstnctve natonal character and are only loosely lnked to other markets. It s easy to fnd examples of natonal markets wth frms concentrated n a few ndustres. Ol and constructon companes domnate the economes of Saud Araba and ts Persan Gulf neghbors. The economes of Brazl and Indonesa are smlarly dependent on ther natural resources. Stock markets n these countres reflect nternatonal commodty prces and hence the fortunes of the local economy. 3 For a survey of ths ssue, readers are referred to Uppal (1992) and Lews (1999). 3

5 ther wealth n foregn assets. Her essay examnes three explanatons for equty home bas and consumpton home bas. Wthout acknowledgng the exstence of home bas and wth no defntve explanaton, n fact, her study has rased questons to gude further studes. One explanaton that may relate to the present paper s the second and thrd explanatons; Lews (1999) states: On the other hand, f the costs of acqurng and/or holdng foregn equtes are suffcently hgh, then nvestors may be nduced to keep ther savngs at home. The costs of nternatonal dversfcaton nclude nternatonal taxes, nformatonal costs, and other barrers to trade equty. Frst, she ponted out that home bas could be explaned by dversfcaton costs that may exceed the gans, whch s possble f the costs are extremely large and thus dscourage an effcent domestc nvestor from nternatonal dversfcaton. Then she concluded that costs declne over tme and there s no reason to suggest that the costs exceed the gans. We suggest that unexpected costs as measured by poltcal nstablty rsk could exceed gans, notably n the case of dversfcaton that ncludes emergng or developng countres as some past studes have suggested (e.g., Errunza and Rosenberg (1982)). In her thrd explanaton of the equty bas, Lews looked at emprcal msmeasurement as the possble reason for equty home bas. She outlned that the gans from nternatonal dversfcaton have been calculated based on the measurement of the hstorcal means and varances. In realty, the mean and standard devatons of returns are not the specal elements that are of much nterest to nternatonal nvestors. For example, poltcal rsk assessment was always one of the challenges that nternatonal nvestors faced (e.g., Bourgugnon and Boussema (2004); Damodaran (2003); Bloomfeld and O Hara (2000); Rvol and Brewer (1997); Ctron and Nckelsburg (1987)). We augment ths conjecture by addng poltcal rsk n the modelng and measurement context to show that t does matter to the nvestor. Ths mples that f theresmsmeasurementofequtyhomebas,tcouldbepossblebygnorngotherrelevantrsksnthe modelng framework n addton to the degree of uncertanty n the estmates of the mean returns and varances as dscussed by other studes (e.g., Bekaert and Uras (1996); Gorman and Jorgensen (2002)). 4

6 [TABLE 1 HERE] Table (1) n the study by Tesar and Werner (1995) shows the opposte pattern that the flow of captal on nternatonal equty transactons s hgher than those on domestc flow. But as was ndcated by Lews (1999), the sgnfcance of the result presented n Table (1) s questonable. In addton to Lews s (1999) suggeston that the varablty n equty markets affects the measurement of portfolo allocatons and decsons, poltcal nstablty s also a rsk that nfluences portfolo decsons (Gentle (1998)). Investors are better nformed about domestc (or regonal) market condtons or are more optmstc about the future performance of domestc markets (nvestor sentment). Baxter and Jermann (1997) showed that the nternatonal dversfcaton puzzle s deepened when we consder the mplcatons of nontraded human captal for portfolo composton. Whle growth rates of labor and captal ncome are not hghly correlated wthn countres, they found that the returns to human captal and physcal captal are very hghly correlated wthn four Organzaton for Economcs Co-operaton and Development (OECD) countres and they suggested that a dversfed world portfolo wll nvolve a negatve poston n domestc marketable assets. What could account for ths strong home bas n equty portfolos? Two classes of explanatons have been suggested, based on nternatonal asset prcng model, and also on market mperfectons. The frst explanaton suggests that snce nvestors are exposed to nflatonrskntherdomestccur- rences, the domestc assets have the ablty to hedge domestc nflaton (e.g., Adler and Dumas (1983)). But Cooper and Kaplans (1994) rule out nflaton hedgng as a prmary cause of home bas. They found that the emprcal evdence was consstent wth ths motve only f nvestors have very hgh levels of rsk tolerance, as equty returns are negatvely correlated wth domestc nflaton. Also, for a level of rsk averson consstent wth standard estmates of the domestc equty market rsk premum, deadweght costs are a few percent per annum greater than observable costs such as wthholdng taxes. Thus, the home bas cannot be explaned by ether nflaton hedgng or drect observable costs of nternatonal nvestment unless nvestors have very low levels of rsk averson. 5

7 Although fnancal market mperfectons are less mportant as markets are progressvely opened to foregn captal, the second explanaton emphaszes that there are stll many barrers to nternatonal nvestment. Some studes have explaned that effect as behavor mperfecton of nvestors (e.g., Levy and Lerman (1988)) or market mperfectons (e.g., Madura (1985)) or cost to nvestors attached to the holdng of nternatonal assets (e.g., Stulz (1981); Adler and Dumas (1983)). Levy and Lerman (1988) suggest the motves behnd the exstence of the barrers to nternatonal nvestment are due to a lack of nformaton related to nternatonal nvestment and the nablty of nvestors to montor and track many nternatonal stocks and bonds notably those nvestment opportuntes exstng n LDCs. 4 Other mpedments could be the exstence of dscrmnatory taxes and restrctons on fund flows or smply a fear of expropraton, whch are commonly present n emergng countres or LDCs. Ther modelng effort and results gnore the mpact of these mperfectons on the nternatonal dversfcaton decson; n ths mleu, the paper wll attempt to examne what would happen f nvestors felt some nhbtons aganst dversfyng globally and how those obstacles and complcatons wll mpact ther nternatonal nvestments. Dealng wth market mperfectons and the exstence of other types of rsk, prevous research suggests the purchase of shares of multnatonal corporatons (MNCs) as a substtute or proxy for an nternatonal stock portfolo. Yet, other studes (e.g., Jacullat and Solnk (1978)) rejected the substtuton hypothess, because MNC shares behave lke domestc returns and are n the same busness envronment. Thus, the nternatonal nvestor gans addtonal benefts by tradng abroad. Stulz (1981) presented a smple model n whch there s a holdng cost for rsky foregn assets, where the composton of optmal portfolos at home and abroad wll dffer accordngly. In fact, he ponted out that barrers to nternatonal nvestment can be represented by other nonpecunary forms ncludng taxes. 5 Snce barrers decrease trade n the least rsky assets, as ponted out by Stulz, there s a need to test whether the expected return on nternatonal assets s large enough to offset the cost of holdng them. 4 Merton (1987) argued that nvestors tend not to hold assets wth whch they are not famlar. 5 In hs model Stulz (1981) defned the barrer as a penalty for holdng foregn shares long or short. 6

8 Poltcal Instablty and Corrupton Corrupton (Shlefer and Vshny (1993); Roy (1970)) has been ntroduced as a proxy for poltcal nstablty rsk snce much research supports ths nducton by expressng the mportance of such rsk (We and Shlefer (2000); Rvol and Brewer (1997); Bac (1996); Mauro (1995); Ctron and Nckelsburg (1987)). Corrupton s defned as excessve red tape and absence or lmtaton of the rule of law, or poor publc governance. In support of our proposton, other studes show that poltcal rsk s one of most mportant factors that nfluence fnancal decson (Erb, Harvey, and Vskanta (1996)). Kobrn (1978) suggests that an assessment and evaluaton of poltcal rsk s dffcult, but some of the problems can be allevated wth more rgorous and objectve procedures. From a practcal perspectve, whle most managers rank poltcal nstablty as one of the most mportant factors n decsons on foregn drect nvestment (FDI), formal assessment and evaluaton of the poltcal envronment and ts potental mpact upon operatons s rare. Poltcal assessments tend to be subjectve, mpressonstc, and superfcal. Ths can lead to a sgnfcant overstatement of poltcal rsk. Poltcal nstablty, however, s not poltcal rsk. The relatonshp between conflct and flows of manufacturng FDI depends on both the nature of the conflct and the socoeconomc condtons under whch t occurs. Only hghly focused generally covert ant-regme volence offered any sgnfcant relatonshp. The effects of conflct are also dependent upon the nature of the frm. Frms should determne what the poltcal envronment wll look lke and how t wll affect them. Lterature on corrupton and ts mpact on development s not lmted (e.g., Ward (1949); Roy (1970)), but economc studes on corrupton are (e.g., Shlefer and Vshny (1993)). Whle corrupton s persstent and exsts around the globe, especally n the LDCs and common n the DCs. Shlefer and Vshny (1993) defne corrupton as government corrupton where the sale of government property by offcals results n personal gan. 6 They explored the reasons why corrupton s costly to economc development usng a 6 Ths paper uses the poltcal nstablty rsk nterchangeably wth corrupton rsk (measures pre-nstablty condtons) snce We (2000) showed that poor nsttutons of law and corporate governance are seen as far more responsble than poor macroeconomc condtons of even macroeconomc polces for the depth of the Asan fnancal crss. Johnson, Boone, Breach, and Fredman (2000) found that macroeconomc varables, whether measurng pre-crss condtons of crss polces, have only lmted power n explanng the varaton n the extent of the crss across countres. 7

9 smple model. They argue that economc and poltcal competton could reduce the level of corrupton and ts mpacts. The defnton of corrupton proposed by We and Shlefer (2000) s mantaned n ths study. We and Shlefer (2000) defned corrupton as poor publc governance, whch could be nterpreted as bureaucratc corrupton, excessve red tape, corrupton n the judcal system, and absence of the rule of law. Because of the hgh correlaton among other varables such as poor securty of property rghts or poor qualty of the judcary and low nsttutonal qualty, the corrupton measure could be a proxy for these nfluences as well. We and Shlefer (2000) used three measures of corrupton that are percepton-based subjectve ndexes: Internatonal Country Rsk Gude (ICRG) and the Global Compettveness Report (GCR) and World Development Report (WDR), and the type whch s based on an average of exstng ndexes. The latter s the ndex produced by Transparency Internatonal, a non-governmental organzaton. We and Shlefer (2000) look at the mpact of corrupton on foregn drect nvestment (FDI), but the authors attempted to test the mpact on portfolo nvestment (PI). Besdes fndng a negatve statstcally sgnfcant effect of corrupton on FDI, they concluded that corrupton affected composton of captal nflows n such a way that the host country was more lkely to experence a currency crss. Thus, corrupt countres tend to have a small porton of FDI and rely heavly on bank borrowng and perhaps more on portfolo captal. Ther conjecture s that the more corrupt country wll receve less n the form of FDI relatve to portfolo nvestment. That concluson suggests the mportance of consderng the mpact of corrupton on the nternatonal portfolo nvestment. Two ponts are worth notng. Frst, the emphass n ths paper s on the last ndex, whch s an average of GCR ICRG and WDR. Second, corrupton and ts mpact on the composton of a country s captal nflows, as presented by We and Shlefer (2000), may make the country more at rsk to a currency crss and that s the motvaton behnd our consderaton of the corrupton mpact on the nternatonal nvestment decson. 8

10 Leblang and Bernhard (2000) fnd that poltcal factors strongly nfluence the probablty of a speculatve attack, suggestng that currency traders do ncorporate poltcal nformaton nto ther expectatons. Edwards (1993) fnds evdence that the nflaton tax depends postvely on the degree of poltcal nstablty n the country n queston, but he advances one more step by showng that countres wth more volatle poltcal sectors are less lkely to have successful stablzaton. Instablty measure Many managers and researchers tend to be more concerned wth poltcal nstablty and/or poltcal rsk as one of the most mportant element n the foregn drect nvestment (FDI) decson, however, the mportance of poltcal nstablty n the nternatonal portfolo nvestment decson dd not get much attenton. The apparent dscrepancy between poltcal nstablty, ts lkely ncdence, and nvestment decson s stll perceved to be an unresolved ssue n the fnance lterature. Ths paper takes a new look at the exposure puzzle by studyng the potental mpact of the poltcal nstablty and nternatonal dversfcaton. We understand that the quantfcaton of poltcal or socal concepts ntroduces a challengng practcal task. Rajan and Fredman (1997) studed the mpact of country rsk on nternatonal portfolo nvestment, usng alternatve country rsk proxes n the context of the two-factor model. They used country ndex by nsttutonal nvestor magazne and nternatonal country rsk ndex publshed by nternatonal reports. 7 The latter ndex conssts of sx economc ndcators, fve ndcators of fnancal rsks and thrteen poltcal rsk ndcators some of whch drectly represent the corrupton measures such as law and order tradton and qualty of bureaucracy and corrupton n government. Snce ths ndex s a weghted average of all ndcators, the mportance of each ndcator has been assumed equal. Thus, we wll emphasze the corrupton ndcators and examne emprcally the mpact on the nternatonal portfolos. Gentle (1998) dscussed that poltcal rsk:... s a measure of nstablty whch covers a range of overlappng factors : economc expectatons 7 One of the shortcomngs of the country ndex by nsttutonal nvestor magazne s the heavy emphass on credt ratngs wthout provdng the detals about the constructon of the ndex, and that s not the purpose of our paper. 9

11 versus realtes, economc plannng falures, poltcal leadershp, external conflct rsk, corrupton n government, the nfluence of the mltary and organzed relgon n poltcs, law-and-order tradton, racal and ethnc tensons, poltcal terrorsm, chances of cvl war, developments wthn poltcal partes and the qualty of bureaucracy. Note that stocks nvestment n foregn companes, notably the ones that are not cross-lsted n home country, requres an understandng of foregn accountng practces and corporate relatonshps, corporate governance practces, and legal envronment. It was ponted out by Kang and Stulz (1997) that the nformaton - ts qualty and relablty - about the companes makes nvestors nvest n known Japanese stocks, though the returns are lower, and not n the unknown stocks wth hgher returns. Ths result provdes strong support to our conjecture that the nvestors ncorporate addtonal nformaton before makng the nternatonal nvestment decson. Also, ths analyss lends support to our contenton that nvestors are wllng to gve up or compromse and make trade-offs between return and nformaton wth respect to the company. In the context of our study, we could add the qualty and relablty of nformaton for a better optmal decson s nevtable (Bloomfeld and O Hara (2000); Bloomfeld and O Hara (1997)) Research Contrbuton We make mportant contrbutons to related research. We attempt to address the followng: addng to the equty home bas lterature unstated explanaton on how the nvestor allocates her portfolo gven ts varablty and gven the exstence of other types of rsk. How do we model such a problem f we want to add other types of rsk? What are we learnng for that modelng effort from a practcal perspectve? The research rases further questons to assst practtoners and academcs when tacklng other studes on the ssue. As a frst contrbuton to ths lterature, the paper presents data on a new cross-country measure of restrctons on nternatonal portfolo nvestment. The paper s second contrbuton s an examnaton of the mpactofnstabltyrskmeasuredbythecorruptonndex on the composton of nternatonal portfolo 10

12 constructon. Ths s done by effectvely comparng possble mpacts of corrupton and provdng a possble explanaton for the equty home bas puzzle. It s a natural extenson of nternatonal dversfcaton to add the poltcal nstablty rsk when consderng nternatonal portfolo management. The paper attempts to address the followng: To what extent does nternatonal dversfcaton among stocks, n the presence of poltcal nstablty rsk, outperform domestc stock portfolos? Poltcal rsk s a measure of nstablty, whch covers a range of overlappng factors: economc expectatons versus realtes, economc plannng falures, poltcal leadershp, external conflct rsk, corrupton n government, the nfluence of the mltary and organzed relgon n poltcs, law-and-order tradton, racal and ethnc tensons, poltcal terrorsm, the chance of cvl war, developments wthn poltcal partes, and the qualty of bureaucracy. Corrupton s the sngle most mportant factor (one of many other forms of poltcal nstablty (Brewer (1983)) contrbutng to poltcal nstablty and economc declne. It ncreases economc nequalty and captal flght and that reduces nvestment and productvty and eventually leads poltcal declne and the system rsks hgh levels of nstablty. Unfortunately, corrupton s an mportant factor n understandng poltcal rsk n emergng markets, and s the key factor that many nternatonal portfolo managers have not ncluded n the decson to nvest (not ncluded n ether the poltcal stablty ndex, polcy foundatons ndex, and nsttutonal strength ndex (Zons, Lefkovtz, and Wlkn (2003)). What s the mpact of nstablty rsk substtuted by two possble measures (corrupton ndex and nstablty governance ndcator 8 ) of nternatonal dversfcaton made up of stocks from varous markets? Under ths crcumstances does the quadratc programmng optmzaton suffce n the modelng effort to derve the optmal nvestment proportons that mnmze the portfolo varance for a gven rate of 8 Duetospacelmtatonstheresultsofthestabltygovernance ndcator are omtted but avalable upon request from the author. 11

13 return? Frst, the mathematcal mean-varance model s proposed for portfolo selecton wth poltcal nstablty constrant, and second, a mult-objectve optmzaton approach s suggested, gven that poltcal nstablty rsk s another objectve that should be mnmzed as well. The paper s organzed as follows. Secton I presents varous mathematcal quadratc and multobjectve models for generatng decson allocaton of low rsk across a set of countres. Also, dfferent soluton technques have been proposed. Secton II emprcally nvestgates the mpact of nstablty rsk proxes on the effcent fronter and dscusses the results. Secton III concludes wth a summary. 1 Mathematcal Approaches 1.1 Approach I The model and problem The theoretcal paper consders two methods n nternatonal markets ncludng less developed countres (Errunza (1977); Errunza and Rosenberg (1982); Errunza (1983)) n the context of poltcal nstablty rsk, whch extends prevous models (Rajan and Fredman (1997); Levy and Sarnat (1970); Bourgugnon and Boussema (2004); Cosset and Suret (1995)) to an envronment wth poltcal nstablty rsk. In a mean-varance framework, a probablty dstrbuton of securty prces s assumed to be known, and the return of any portfolo s quantfed as ts expected value and ts rsk s quantfed as ts varance. Our economy conssts of N countres, ndexed by j, wherej =1,...,N. Let the symbol desgnate random varables. Let R j represent the one-perod rate of return on common stock ndex j at the end of month t such that t =1,...,m.Wedefne P jt as the dollar value of the j th country common stock ndex at country j. The returns have been computed n dollars, therefore, the ndexes have been adjusted to reflect changes n exchange rates. 9 We use the followng set of mantaned assumptons: 9 Foregn currency values were adjusted nto dollars (US$) usng monthly averages of exchange rates. Data for exchange rates were taken from Pacfc ExchangeRateServce(PERS)atUBC. 12

14 (A1) Perfect markets: The markets for all assets are perfect wth no taxes or transacton costs. Unlmted borrowng and short sales are not permtted. Each asset s nfntely dvsble. (A2) (A3) (A4) Competton: All nvestors act as prce takers n all markets. Homogenous expectatons: All nvestors have dentcal probablty belefs. State-ndependent utlty: Investors are rsk averse and maxmze the expectaton of a Von Neuman-Morgenstern utlty functon, whch depends solely on wealth. (A5) Complete markets: Each compettve nvestor can obtan any pattern of returns through the purchase of marketed assets (subject only to her own budget constrant) f the number of marketed assets wth lnearly ndependent returns s equal to the number of states. Under assumptons A1 through A4 t s known that the CAPM wll be obtaned f the nvestor s utlty functon s quadratc over the relevant range of outcomes or f all asset returns are drawn from one of the class of separatng dstrbutons defned by Ross (1978). In accordance wth Markowtz (1952) n assumng a one-perod economy. Of course, t s notceable that the usual varatons we observe n a contnuous framework are gnored here. As they are under a multperod settng, the nvestors are wllng to rebalance ther portfolos over tme and sngle-perod nvestment models are not approprate to help nvestors make the optmal allocaton of ther wealth. We calculate the monthly return for each ndex. Ths s the percentage return that would be earned by an nvestor who bought the stock at the end of a partcular month t 1 and sold t at the end of the followng month. For example, for country k, the monthly return R kt s defned as µ Pkt R kt = Ln. P k,t 1 The ndex s converted nto dollars so that dollar returns contan gans or losses on both the stock market and exchange rate changes. Let R f represent the gross rsk-free rate of return. Let W represent ntal wealth, Ỹ represent termnal wealth, B represent the nvestment n a rskless asset, and V j represent the nvestment n a rsky asset j, where j =1,...,N. 13

15 Our modelng assumptons follow prevous lterature on the subject (e.g., Errunza (1977); Madura (1985)). Hence we assume a one-perod economy, whereby the nvestor apples a buy-and-hold strategy throughout the entre perod. The nvestor purchases the portfolo at the begnnng of the perod, and lqudates the entre portfolo at the end of the perod. 10 Investors are rsk-averse, expected utlty maxmzers of ther end-of-perod wealth, wth utlty functon U : R R. Assets are nfntely dvsble wth fxed quanttes. R j s are jontly normally dstrbuted. Ths assumpton mples that nvestors and market makers have quadratc utlty functons. Investors behave as prce takers wth respect to both nternatonal stock prces. In the context of the above assumptons, the nvestor s problem s to select the portfolo that maxmzes the expected utlty of end-of-perod wealth. The nvestor solves the followng optmzaton problem, model (1): Max h E U ³Ỹ, (1) s.t. 1= W B + P N V j j=1 W,and (2) Ỹ = R f B + P N j=1 V j R j. (3) The frst constrant, Equaton (2), s the nvestor s budget constrant, both sdes of whch are dvded by W, the nvestor s ntal wealth. The second constrant, Equaton (3), s the wealth accumulaton constrant. Note here that the ntal modelng (1-3) does not ncorporate the poltcal nstablty rsk n the model. Let X j = V j W represent the nvestment weght for country j and let X f = B W represent the nvestment weght for the rskless asset. It follows that B = WX f,andv j = WX j. Hence, we restate the optmzaton 10 We note a one-perod model facltates analytcal tractablty, allowng understandng of the mean-varance theory n the presence of poltcal nstablty rsk. 14

16 problem as Max h E U ³Ỹ, s.t. 1=X f + P N j=1 X j,and Ỹ = R f WX f + P N j=1 WX j R j. Usng Taylor seres expanson, we expand the nvestor s utlty functon around the expected end-of-perod wealth; thus, the ndvdual s expected utlty may be expressed as h ³ E U ³Ỹ = U E hỹ + 1 ³ 2 U 00 E hỹ ³ σ 2 Ỹ + E [T 3 ], where E[T 3 ]= X n=3 and m ³Ỹ n s the n th central moment of Ỹ. 1 ³ n! U (n) E hỹ ³ m n Ỹ, To maxmze expected utlty of wealth, the nvestor maxmzes a functon of the moments of the portfolo return. We mantan the assumpton of rsk averson, U 00 (.) < 0. We demonstrate n appendx A that Var( R p ) can be specfed as follows: h Var RP = =1 j=1 h X j X Cov Rj, R. (4) As wth Markowtz (1952), portfolo p s a mean-varance effcent portfolo f there s no portfolo q such h h h h that E Rq E Rp and Var Rq <Var Rp. Therefore, the effcent fronter can be descrbed as the 15

17 set of portfolos that satsfy the followng constraned mnmzaton problem: Mn h Var Rp, s.t. (5) μ p = X f R f + P h N j=1 X je Rj,and X f + P N j=1 X j =1. where μ p = E[ R p ], the expected portfolo return. The varance of the j th country s defned as Var( e R j )= 1 m P m t=1 (R j E[ er j ]). We called the model (5) Levy Model, snce work by Levy and Sarnat (1970), s consdered poneer work n nternatonal dversfcaton. They used a smlar model to get the optmal vector X j for varous rates of return, to derve the effcent fronter, that s, the locus of effcent portfolos, and to show the benefts of such nternatonal dversfcaton. 1.2 Approach II: Internatonal Dversfcaton wth Poltcal Instablty Rsk Instablty rsk modelng We have N countres, ndexed by j, where j =1, 2,..., N. Gven the above consderaton, the poltcal nstablty rsk has an nfluence on the nvestment decson. Let e S j measure the nstablty degree for country j. Recall that X j represents the nvestment weght for country j. In the same fashon, portfolo nstablty measure can be defned as E[ e S p ]= j=1 h X j E esj, where E[ e S p ] s the expected portfolo nstablty measure. Because poltcal nstablty rsk s nherently dffcult to quantfy, two types of measures of poltcal 16

18 nstablty rsk have been presented: nstablty governance ndcator and corrupton ndex measures 11. The corrupton ndex s suggested as the frst measure of such nstablty, snce a hgh corrupton level suggests that poltcal nstablty s unavodable. The busness envronment s always nfused by the overall country governance ndcators, and the falure of a government to control corrupton wll ntate dstress for prvate busnesses (Shlefer and Vshny (1993)). The ratng for a country s typcally the average of the correspondents ratngs, whch s subjectve n nature. We used the corrupton measure, whch s based on an average of exstng corrupton ndexes. The best known s the ndex produced by Transparency Internatonal, a German-based non-governmental organzaton devoted to fghtng corrupton Frst Model: Quadratc Programmng Model wth One Addtonal Constrant The orgnal Markowtz model (Markowtz (2002)) can be vewed as an optmzaton problem wth bobjectve optmzaton model: Maxmze the portfolo return and mnmze the rsk. Levy and Markowtz (1979) developed the case of two objectves, mean and varance, and usng the Taylor extenson, derved the result that utlty functon can be approxmated by functons of mean and varance. Problem Statement: An nvestor allocates her wealth among N countres, The portfolo expected nstablty E[ S e p ] and the expected return E[ R e p ] and the varance of portfolo h Var RP are: E[ S e h p ]= X j E esj, E[ R p ]= j=1 j=1 h X j E Rj, 11 Duetospacelmtatonstheresultsofthestabltygovernance ndcator are omtted but avalable upon request from the author. 12 We and Shlefer (2000) ponted out one of the dsadvantages of ths measure that mxng ndexes wth dfferent country averages and methodologes can ntroduce nose nto the measure. But the fact that the purpose of the paper s to obtan the optmal nternatonal portfolo usng an optmzaton approach, we assume dfferent methods n computng these ndexes have no effect on the correlatons. 17

19 and h Var RP = =1 j=1 h X j X Cov Rj, R respectvely. The nvestor s goal s to select an optmal portfolo X =(X 1,...,X N ) to maxmze her expected value of U ³Ỹ. Thus, the problem can be mathematcally stated as a three-objectve programmng problem. The optmal selecton should mnmze both the expected nstablty measure and the varance as well as to maxmze the expected return. Subject to h Mn Var Rp h MnE esp h Max E R p (6) P N j=1 X j =1 X j > 0,j =1,...,N An nternatonal portfolo s sad to be attanable f t satsfes all the constrants of model (6). The h feasble portfolo p s sad to be effcent f there exsts no other feasble portfolo q such that E Rq h h h h h E Rp, E esq <E esp and Var Rq <Var Rp. Also, model (6) ndcates the mpossblty of short sellng. Short sellng may be mpossble for feasblty reasons (exchanges or brokers may not allow t for certan nstruments) or, more frequently, for regulatory reasons applyng to specfc types of nvestors. In response to the perceved rskness assocated wth short postons, many ndvdual and nsttutonal nvestors do not engage n short sales, ether by choce or due to regulaton. In addton, there are costs specfc to short sales that are dffcult to model. In response to these consderatons, n ths secton, the analytcal dervaton of the effcent fronter wth nstablty rsk s provded, under the assumpton that there are no short sales. Quadratc programmng derves effcent portfolos n whch some stocks are held long (postve proportons), whle all the other stocks are omtted (held n zero proportons). Moreover, the effcent fronter 18

20 derved wthout short sales always ncludes an effcent portfolo consstng of a sngle stock, wth the maxmum expected return. Under the theory of sngle-objectve optmzaton, an effcent portfolo can be acheved by solvng the parametrc programmng model: Subject to P Mn N P h N X =1 j=1 X jx Cov Rj, R j P h N j=1 X je esj φ p P h N j=1 X je Rj μ p (7) P N j=1 X j =1 X j > 0,j =1,...,N In model (7), we search the vector of weghts that mnmzes the varance of the portfolo return under the constrant that the expected return on the portfolo must be greater than μ p and the expected nstablty rsk must be greater or equal to φ p. 13 The frst constrant defnes the expected nstablty rsk, whch results from lmtng the nvestment unverse to countres that have a low expected nstablty rsk; the second constrant defnes the expected return to be reached, where μ p s a parameter; the thrd constrant s smply the asserton that the vector Xj 0 s defnes a portfolo. The nvestor solves the followng utlty maxmzaton problem: Mn X j =1 j=1 s.t. φ p = P h N j=1 X je esj, μ p = P N j=1 X je P N j=1 X j =1. h X j X Cov Rj, R, (8) h Rj,and 13 The model suggests that a country wth low poltcal nstablty measure s desrable to be ncluded n the optmal nternatonal portfolo. φ P represents a parameter or threshold value or score (mnmum) that the nvestor s lookng to exceed. 19

21 Usng Lagrange multplers, we rewrte the objectve functon as: F (X, λ 1,λ 2,λ 3 )= +λ 2 μ p j=1 Mn X j,λ 1,λ 2 =1 j=1 h X j E Rj + λ 3 1 h X j X Cov Rj, R + λ 1 φ p j=1 h X j E esj j=1 X j. (9) The Karush-Kuhn-Tucker condtons of equaton (9) are 0 =1 0 = φ p 0 = μ p 0 = 1 h X σ j λ 1 E esj λ 2 E[ R e j ] λ 3,j =1,..,N (10) j=1 j=1 h X j E esj, (11) h X j E Rj, (12) X j, (13) j=1 0 = L X j X j,j=1,..,n, (14) X j 0, (15) where: h σ j = Cov Rj, R. (16) If every varable s postve then nequaltes (10) are equaltes because of the complementary condtons n (14). The X j s that satsfy the frst-order condtons mnmze the varance for every gven level of expected return, and are unque. Inequaltes (10) mply Equaton (17). 0= =1 h X σ j λ 1 E esj λ 2 E[ R e j ] λ 3, j =1,..,N, (17) 20

22 So, Equatons (17) mples that: X k = λ 1 N X h X N h X N M k E esj + λ 2 M k E R + λ 3 M k,k=1,..,n (18) =1 =1 =1 In appendx B we demonstrate that the soluton to the above problem n the no short-sales case yelds Equaton (19). Unlke the model where short sales are permtted, the mnmum-varance fronter n meanvarance space s an arc of a parabola, not the orgnal entre parabola (Szego (1980)). σ 2 ³ R p = μ 2 p α + φ 2 pδ 2μ p φ p β 2φ p ϕ + μ p γ + ψ. (19) Second Model: A Mult-objectve Model In other words, the goal programmng and mult-objectve lterature (e.g., Tamz (1996)) suggests that realstcally several conflctng goals may compete n the allocaton decson. Along that lne the multobjectve technque s sutable for problems where nvestors seek to satsfy two objectves. In the context of the present paper, we suggest the use of mult-objectve programmng for nternatonal portfolo selecton. We propose that the nvestor allocates her wealth among N countres, usng another formulaton that takes nto account the varablty of the percentage change of corrupton ndex as a proxy for the nstablty rsk. That suggests that a hgh varablty of the percentage change of corrupton measure (or poltcal stablty measure) over a specfed perod (e.g., fve years) ndcates that the evaluators of the representatve ndex beleve that the country s not stable and the rsk s very hgh. Vce versa, a low varablty of the measure (corrupton ndex or nstablty measure) mples that the poltcal nstablty rsk s low. Thus, the nstablty rsk of a country j s defned as Var( S g j ),wherej =1,...,N. The varance s computed based on the gven measure of corrupton (or poltcal stablty measure gven by World Bank Kaufmann, Kraay, and Mastruzz (2005)). Thus, the portfolo nstablty rsk s measured as: h Var esp = =1 j=1 h X j X Cov g Sj, S g 21

23 The nvestor goal s to select an optmal portfolo X =(X 1,...,X N ) to maxmze her expected value of U ³Ỹ. Thus, the problem can be mathematcally stated as a three-objectve programmng problem. The optmal selecton should mnmze both the expected nstablty rsk and the varance as well as maxmze the expected return. Note that by mnmzng the varance of portfolo return and portfolo poltcal nstablty rsk, the nvestor stll needs to constran the nvestment problem by specfyng the mnmum acceptable level of nstablty (threshold value) she s wllng to accept. Otherwse an undesrable country could be ncluded f ts varance measured by the percentage change of ether corrupton measure or poltcal stablty measure s very small. Thus, an addtonal constrant should be ncluded to reflect the mnmum requrement j=1 h X j E esj = φ p Under the theory of mult-objectve optmzaton, an effcent portfolo can be acheved va solvng the parametrc programmng model: Subject to P Mn N P h N X =1 j=1 X jx Cov Rj, R j P Mn N P h N X =1 j=1 X jx Cov g Sj, g S j P h N j=1 X je esj = φ p P h N j=1 X je Rj = μ p (20) P N j=1 X j =1 X j > 0,j =1,...,N In model (20), we search the vector of weghts that mnmzes the varance of the portfolo return and the varance of the portfolo nstablty rsk under the constrant that the expected return on the portfolo must be equal to μ p and the expected nstablty rsk must be equal to φ p. The optmal selecton should mnmze the varance and nstablty rsk. A country portfolo X = 22

24 (X 1,...,X N ) s sad to be feasble to model (20) f t satsfes all the constrants. A feasble portfolo h X s sad to be effcent f there exsts no other feasble portfolo q such that Var esq <Varh esx, h h h h Var Rq <Varh RX and E Rq E RX, E Rq <Eh RX. The frst constrant defnes the expected nstablty rsk, whch results from lmtng nvestment to countres that have a low expected nstablty rsk; the second constrant defnes the expected return to be reached, but μ p s a parameter; the thrd s smply the asserton that the vector Xj 0 s defnes a portfolo. One of the greatest dffcultes obstructng the successful applcaton of non-lnear programmng technques to real problems s the presence of multple crtera (e.g., Steuer and Sun (1995); Dyer, Fshburn, Steuer, Wallenus, and Zonts (1992); Daellenbach and Kluyver (1980); Geoffron, Dyer, and Fenberg (1972)). 14 The soluton of model (20) could be acheved n one of three methods: A Sequental Quadratc Programmng (SQM) Approach. Wlamowsky, Epsten, and Dckman (1990) suggest a sequental optmzaton of multple objectves (SQM) model. The SQM frst optmzes wth respect to the hghest-prorty objectve functon (portfolo rsk or nstablty rsk) usng standard Quadratc Programmng (QP) to acheve the optmal soluton Z1. Next, the frst objectve functon s set equal to the level acheved n the frst step and added as a new constrant, and then the problem s solved agan for the second objectve and the process s repeated untl all the objectves have been optmzed. We note the frst step by SQModelA by mnmzng the portfolo rsk ( P N P h N =1 j=1 X jx Cov Rj, R ) then set the frst objectve ( P N =1 P N j=1 X jx Cov h Rj, R ) equal to the level acheved n frst step and added as a new constrant, then we solve the QM model by mnmzng the second objectve functon ( P N P h N =1 j=1 X jx Cov g Sj, S g ) ncludng the new constrant from frst step. We note the other sequence as SQModelB by reversng order of the sequence by startng wth the second objectve and solve the QP, then we proceed to the second quadratc optmzaton takng nto account the level acheved n the frst step, whch equals the nstablty portfolo rsk, then mnmze the frst objectve functon wth the new constrant. By dong ths we are n lne wth Wlamowsky, Epsten, 14 A bblography on applcatons of multple-objectve methods has been gven by Whte (1990). 23

25 and Dckman (1990) who suggested that ther method can be appled to non-lnear and nteger multpleobjectve problems. 15 An Interactve Procedure for Solvng Multple Objectve Approach Korhonen and Yu (1998) proposed an nteractve process for solvng multple problems. They dealt wth multple lnear objectves and one quadratc objectve (MOQLP). However, n our problem there are two quadratc objectve functons and lnear constrants. The suggested method by Korhonen and Yu (1997) s not applcable n ts format. Model (20) s equvalent to the model (21): Subject to h MnV (X) =Var erp = X 0 DX X j Mn X j h S(X) =Var esp = X 0 CX (21) AX = b X j > 0,j =1,...,N where D s a symmetrc postve semdefnte matrx of order N N, C s a symmetrc postve semdefnte φ p matrx of order N N. A s the k N matrx of coeffcents of the lnear constrants. b = μ p s a 1 3-vector of the rght hand sde and X s an N-vector of the decson varables. We note that the objectve functon vector by F (X) and refer to ts components as follows: F (X) = V (X). S(X) Problem (21) can be wrtten as follows: Subject to Mn F(X) x X = {x/ax = b, x j > 0, j=1,...,n} (22) 15 The author s aware of the comments presented by Parton (1991); Hartley (1991) and responses of Wlamowsky, Epsten, and Dckman (1991). See also Scholtes (2004). 24

26 Defnton 1 (Korhonen and Yu (1997)) x X s effcent f and only x X such that F (x) F (x ) and F (x) 6= F (x ) To generate nondomnated solutons s acheved by usng the weghted sums of objectve functons. n o Mn λ 0 F (X)/x X (23) f λ>0 then the soluton vector X of Equaton (23) s effcent such that λ s a scalar varable. Based on the use of scalarzng functon to solve the two-objectve problem (21), we wll use a weghted sum as a scalarzng functon, and formulate the problem as follows: Subject to MnλX 0 DX +(1 λ)x 0 CX X j AX = b X j > 0,j =1,...,N (24) λ (0, 1) Here the parameter λ can be nterpreted as the rsk averson factor of the nvestor. The greater the factor λ, the more rsk averson the nvestor has toward portfolo rsk and less toward poltcal nstablty rsk. When λ =1, the nvestor s poltcally rsk neutral, consders only the portfolo rsk, and pay no attenton to the poltcal nstablty rsk. Conversely, λ =0, means that the nvestor s completely poltcally rsk averse. Theorem 2 x X s an optmal soluton to model (24) for some λ (0, 1) f and only f x s the properly effcent soluton of the problem (21). Proof. (Geoffron (1968) (Theorem 2) p. 620) Snce λ>0, dvdng the objectve functon of problem (24) by λ and re-arrangng μ =( 1 λ ) 1,we can 25

27 present the problem n the followng form: Subject to MnX 0 DX + μx 0 CX X j AX = b X j > 0,j =1,...,N (25) μ>0 To search the nondomnated fronter of problem (25), we parametrze μ and formulate the parametrzaton problem as follows, accordng to (Korhonen and Yu (1997)): Subject to MnX 0 DX +(μ + t μ)x 0 CX X j AX = b X j > 0,j =1,...,N μ>0 By varyng μ we may search a nondomnated fronter. We may use the Karush-Kuhn-Tucker condtons of quadratc programmng and reduce the problem to a lnear complementarty problem (Korhonen and Yu (1998)). The weghted sums for combnng the quadratc functon (portfolo rsk) wth the quadratc functon (nstablty rsk) are used as parameters to mplement the free search of nondomnated solutons. Wth a parametrc lnear complementarty problem formulaton, the soluton could be acheved. Utlty Approach Accordng to Deng, L, and Wang (2005), the ratonal nvestor expects not only to mnmze the varance of portfolo return (portfolo rsk) but also to mnmze the varance of nstablty rsk. Thus,shemustmakeatrade-off between the two objectves. Let λ and 1 λ be the weghts assocated 26

28 wth crtera V(X) and S(X) respectvely. Then the nvestor attempts to mnmze F (X j ) λ =1 j=1 h X j X Cov Rj, R +[1 λ] =1 j=1 h X j X Cov g Sj, S g The effcent fronter can also be generated by solvng the followng problem: P λ : Subject to MnλX 0 DX +(1 λ)x 0 CX X j AX = b X j > 0,j =1,...,N (26) λ (0, 1) wth parameter λ varyng n [0,1]. The (1-λ) andλ are weghts assocated wth crtera V and S respectvely. For a ratonal nvestor, she must make a trade-off between the two objectves. Let 1 λ and λ be the h h weghts assocated wth crtera Var RP and Var esp respectvely. P λ s a quadratc problem that can be solved by a number of methods for solvng quadratc programmng problems. Some of the methods can be found n the book by Kunz and Krelle (1966). The Lagrangan functon of P λ s Υ(X, π 1,π 2,π 3 )=λ +π 1 φ p j=1 =1 j=1 h X j E esj + π 2 μ p h X j X Cov Rj, R +[1 λ] j=1 =1 j=1 h X j E Rj + π 3 1 h X j X Cov esj, S e j=1 X j. (27) where π 1,π 2,π 3 0 are the Lagrangan multplers. The Karush-Kuhn-Tucker condtons necessary and suffcent condtons for an optmal soluton to the concave quadratc programmng problem (26) based on 27

29 Equaton (27) are: Υ X j = λ =1 h X Cov Rj, R +[1 λ] =1 h X Cov esj, S e h π 1 E esj π 2 E[ R e j ] π 3 =0, j =1,..,N Υ π 1 = φ p j=1 h X j E esj =0 Υ π 2 = μ p j=1 h X j E Rj =0 Υ π 3 =1 X j =0 j=1 Theoretcally the effcent fronter can be generated by solvng the problem wth the parameter λ varyng n [0, 1] as suggested prevously. However, t s not effcent enough to be used for practcal purposes because such repeated computaton s expensve. For a ratonal nvestor, her goal s to seek the most effcent portfolo from the effcent fronter accordng to her own preference n both rsks. Hence to select the value of the parameter λ such that the correspondng effcent portfolo s the best to the nvestor s also mportant. Followng a smlar procedure suggested by Lu, Wang, and Qu (2003), we suggest a method to select λ as follows: Let denote Φ = {X =(X 1,X 2,...,X N ):AX = B; X j 0; j =1,...,N}, V 0 =mn V (X) =V X Φ (X(1) ); V = V (X (2) ), and S 0 =mn S(X) X Φ =S(X(2) ); S = S(X (1) ). Defne the followng utlty functon: U(X) = α 1 V (X) α 2 S(X) (28) 28