Country, Sector or Style: What matters most when constructing Global Equity Portfolios?

Transcription

1 Country, Sector or Style: What matters most when constructng Global Equty Portfolos? An emprcal nvestgaton from Foort Hamelnk, Hélène Harasty and Perre Hllon Abstract Equty returns are beleved to be strongly nfluenced by country, sector and style effects. A key ssue s to be able to dsentangle those varous effects from one another. In partcular, dfferences between country returns may smply reflect dfferences n the sector composton of country markets, whch makes t clearly dffcult to dsassocate both effects. Smlarly, from the relatve performance of Growth versus Value mght be solely due to the strkng performance of the Technology and Telecommuncaton sectors. For global equty portfolo managers, t s crucal to dentfy whch factors offer the hghest dversfcaton benefts and return potental. We apply a mult-factor approach to estmate pure country, sector and style factor returns. Usng data gong back to 1990, we dentfy the major changes that have occurred n developed markets untl Our varous ndcators clearly pont out the growng nfluence of sector factors. However, country effects reman mportant and there s no clear-cut evdence that sector factors domnate country factors. Style factors such as Growth, Value and Sze also reman sgnfcant, even once sector and country effects are deduced. Fnally, we show that momentum strateges based on sector returns offer substantal gans, whle momentum strateges based on country returns do not. These fndngs suggest that, whle dversfcaton and return benefts from sector strateges have become substantal, managers should contnue to montor carefully country as well as style rewards and rsks. Quanttatve Analyst, Lombard Oder & Ce, Geneva, Swtzerland, and Assocate Professor of Fnance, Vrje Unverstet, Department of Fnance, Amsterdam, The Netherlands. Head of Quanttatve Research, Lombard Oder & Ce, Geneva, Swtzerland. Professor of Fnance, Insead, and Academc Advsor to Lombard Oder & Ce, Geneva, Swtzerland. The current research wll be presented at the Inqure Europe conference on Investment Styles and Multfactor Models to be held n Sntra, Portugal, October 28-30, The authors thank Dana Bösenbacher and Arane Bender for helpful research assstance. They also thank Jeroen Jansen and the partcpants n the Lombard Oder Investment Conference for ther useful comments. They are especally grateful to Anne-Valère Amo for her mportant contrbuton to ths research. 1

2 Executve Summary Evdence of ever-ntegratng fnancal markets has led many fnancal nsttutons to reconsder ther nvestment process. From fundamental analyss to portfolo constructon and management, a clear shft s occurrng from countrybased to sector-based approaches. Smultaneously, style ssues recently rased a large amount of nterest, due to the huge dvergences between style performances from the late 90 s to md Ths topc, whch has been a US-only debate snce long, s now also under scrutny among European portfolo managers. Hence, the debate on the portfolo constructon process s the followng: what matters most, countres, sectors or style? Ths paper answers ths queston. We fnd that sector effects have become domnant, whatever the manner n whch they are dentfed. However, ths s a recent phenomenon, snce countres have been more mportant than sectors for long. The behavor of the technology and the telecommuncaton sectors only partally explans ths trend. Sector effects can therefore be expected to reman at least as mportant as country effects, even when market volatlty returns to lower levels. However, country effects reman very mportant, as do Style factors: Value / Growth and Sze (expressed through the market captalsaton). It s therefore crucal to take these four categores of factors nto account when constructng nternatonally dversfed portfolos. It s mportant to measure the portfolo exposure to Country and Style, even when the portfolo s constructed along actve sector bets. An unwanted under- or over-exposure to one of these factors adds addtonal and unnecessary rsk to the portfolo. In addton, a welldversfed portfolo n terms of sectors may not be dversfed n terms of countres or Style factors. The study s based on fve man ndcators: - The dentfcaton of pure factors s a key ndcator: returns on country (or sector) factors are adjusted to the dfferences n the sector (or country) and Style composton of country markets. For nstance, the pure Swss factor s adjusted to the fact that a hgh concentraton of fnancal and pharmaceutcal companes nfluences the returns on the Swss market heavly. We fnd that hgh returns on pure factors are related to large sectors and small countres. In addton, we dentfy a predomnant Growth factor through sgnfcant returns, even when the effects of typcal Growth sectors (such as TMT) are deduced.

3 - The statstcal sgnfcance of the factors, whch ndcates the homogenety of the asset class, answers the questons: are sectors more homogeneous than countres? are the behavor of pharmaceutcal companes more homogeneous than Swss stocks? Our results show that sectors have ganed n homogenety n tme, whle countres have lost some. Growth and Value stocks are also homogeneous, as well as large captalsaton stocks. - The correlatons between the factors, and therefore the potental dversfcaton benefts are key devces as well. We fnd that correlaton between countres tends to ncrease slghtly, whle the correlaton between sectors s decreasng strongly. Therefore, sector dversfcaton benefts appear more mportant than country. It should be noted that the ncrease n country correlatons s manly due to Euro zone countres. Furthermore, our study s solely based on developed countres, and therefore does not take nto account the potental strong dversfcaton benefts from emergng markets. - The potental achevable returns on country and sector strateges s one of the man ndcators n our study. We show that a manager, who forecasts future returns on the factors perfectly, acheves much hgher returns through sector allocatons than country allocatons. - Fnally, as we all know how dffcult t s to forecast future returns, we evaluate the performance of smple momentum strateges appled to pure country and sector factors. The results of buyng (or over-weghtng) countres or sectors n an upward trend and sellng (or under-weghtng) the others, show that momentum strateges based on sector factors, are very rewardng, whle they are not for country factors. The outperformance of actve sector allocaton based on momentum s 4% on average over the past 10 years, whle no conclusve result s acheved based on actve country allocaton.

4 1 Introducton Evdence of ever-ntegratng fnancal markets has led many fnancal nsttutons to reconsder ther nvestment process. From fundamental analyss to portfolo constructon and management, a clear shft s occurrng from country-based to sector-based approaches. Smultaneously, style ssues recently rased a large amount of nterest, due to the huge dvergences between style performances from the late 90 s to md Ths topc, whch has been a US-only debate snce long, s now also under scrutny among European portfolo managers. Hence, the debate on the portfolo constructon process s the followng: what matters most, countres, sectors or style? Ths paper answers ths queston. Actually, t has become ncreasngly dffcult to dsentangle country, sector and style effects. Clearly, the strengthenng of sector effects s related to the market euphora engendered by the New Economy. The dramatc and persstent outperformance of the Technology and Telecommuncaton sectors untl March 2000, and the ensung reversal of fortunes have obvously played a major role n the ncrease of sector effects. Some consder that dfferences between country ndex returns are nowadays manly drven by dfferences n ther ndustral composton. If ths s the case, nvestors should defntely consder abandonng cross-country dversfcaton strateges n favor of cross-ndustry. Ths may be partcularly true n areas lke the Euro-zone, where the adopton of a sngle currency has elmnated the proporton of return dfferental that was purely due to exchange rate varatons. Hence, a major source of geographcal dversfcaton benefts has been erased. The recent years have also been characterzed by a resurgence of exceptonally strong style effects compared to hstorcal standards. The Growth style has outperformed the Value style n the late 90 s untl March 2000 and then has strongly underperformed t untl md The shapes of the relatve performances of Growth versus Value and the Technology and Telecommuncaton sectors versus the other sectors are strkngly smlar, wth a reversal occurrng smultaneously n March Of course, the Technology and Telecommuncaton sectors are typcally Growth sectors, showng superor earnngs growth expectatons and expensve valuatons. Hence, the recent perod has been characterzed by ncreasng correspondence between style and sector effects, wth growth stocks beng more and more concentrated n some sectors, or, n other words, each sector becomng gradually more homogenous n terms of style. For the portfolo manager several ssues arse. Frst, what drves stock returns? Is Novarts prmarly a Swss stock, a pharmaceutcal stock, or a growth stock? Have sector effects surpassed country effects? How much style effect s left, once sector effects have been deduced? Second, what s the optmal dversfcaton strategy? Do strateges allocatng across sectors offer hgher dversfcaton benefts than those allocatng across countres? Should nvestors also dversfy across styles, or s style rsk already dversfed, thus elmnated, once sector rsk s? In order to shed lght on these ssues, we apply a mult-factor approach and derve several ndcators of the relatve mportance of the country, sector and style effects. A multfactor model allows us to dentfy country, sector and style factors drvng stock returns. Usng data gong back to 1990, we are able to capture the major changes that have 2

5 occurred n developed markets untl We use returns on ndvdual stocks rather than ndces, and develop alternatve measures of the dfferences and smlartes between country, sector and style factors. In partcular, we assgn a Value and a Growth attrbute to each stock n the unverse on the bass of a set of varables that are more lkely to reflect the actual styles followed by portfolo managers than the tradtonal Prce-to-Book crtera. We analyze pure country, sector and style returns, comparng them over tme on the bass of ther magntude and statstcal sgnfcance. Fnally, we compare the proft on momentum strateges based on country and sector factors. The paper s organzed as follows. In Secton 2, we ntroduce the factor estmaton methodology, and dscuss the data and the selecton of factors. In Secton 3, we present the man results. Secton 4 concludes. 2 The Model and the Factors 2.1 Methodology The Model An mportant methodologcal ssue s to dsentangle country factors from sector factors and from style factors. It s crucal to separate these varous nfluences and elmnate the nteracton between them. Ths goal s clearly not reached when country ndces are used as proxes for country factors, ndustry ndces for ndustry factors and style ndces for style factors. For nstance, f the ndustral composton dffers across countres, then country ndces contan ndustry effects and ndustry ndces, country effects. The same s true between country and style effects, or between sector and style effects. To llustrate ths pont we may take the followng example. Returns on a Swss ndex may dffer from returns on a world ndex for two reasons. Frst, returns may dffer because the ndustral composton of the Swss ndex s dfferent from the ndustral composton of the world ndex. On average, f Healthcare stocks outperform the world ndex and Energy stocks underperform t, the overall effect wll be postve for Swtzerland because ths country ndex has proportonally more Healthcare and less Energy stocks than the broad ndex. Second, returns on the Swss ndex and the world ndex may dffer because returns on Swss companes are dfferent from returns on companes belongng to the same ndustry group but located n a dfferent country. That s why we apply a mult-factor approach to ndvdual stocks. Country, ndustry and style effects can be more easly separated by usng ndvdual stocks rather than ndces, and by estmatng smultaneously pure factor returns through a regresson technque. Wth ths methodology, the Swtzerland effect can be nterpreted as the outperformance of an ndustrally dversfed Swss portfolo relatve to the world ndex. By ndustrally dversfed, we mean that the Swss portfolo has the same ndustry composton as the world ndex. Smlarly, the Healthcare effect s the outperformance of a geographcally dversfed Healthcare portfolo relatve to the world ndex. 3

6 In very general terms, mult-factor models specfy the return on asset at tme t as the sum of the product of K factor returns and factor loadngs (equvalently called beta coeffcents). The factor loadngs are known n advance (the stock market captalsaton, the country or sector belongng of a stock, etc.). The methodology seeks to estmate the returns on these factors. In ths study, we examne country and sector factors, as well as the Value, Growth and Sze factors. The model, whch s fully descrbed n the Appendx, s specfed as follows: N C R,t = F t + k=1 D C k F C k t + N S k=1 D S k F S k t + p G,tFt G + p V,tFt V + SZ,t F SZ t + ε,t, (1) where R,t s the return on stock at tme t. N C and N S are the number of country and sector factors respectvely. D C k (D S k ) s a dummy varable, set to one f stock belongs to Country (Sector) k, wth k = 1,..., N C (N S ). p G,t and p V,t are Salomon Smth Barney s (SSB) Growth and Value probablty weghts of stock at tme t (see secton for a detaled descrpton of ther constructon). SZ,t s the Sze exposure of stock at tme t. In the above equaton, the unknowns are F t (the return on the Common factor, whch s equvalent to the weghted average of all stock returns), F C k t (the returns on the country factors), F S k t (the returns on the sector factors), Ft G and Ft G (the returns on the Growth and the Value factors), and Ft SZ (the return on the Sze factor). Fnally, ε,t s the stock-specfc return, whch means the return on stock at tme t regardless of ts country, sector or style attrbuton. In order to estmate the above model and ensure that a world portfolo has zero exposure to each factor, we need to mpose some addtonal restrctons on the parameters. They are fully descrbed n the Appendx and may be summarzed n the followng way: the weghted average of the returns of each factor category (countres, sectors, Value/Growth and Sze) should equal zero. Wth these constrants, a portfolo replcatng a world ndex has zero exposure to each factor. Hence, by constructon, the Common factor equals the world ndex return. The substtuton of the constrants n equaton (1) allows us to work on an unconstraned regresson. It may occur that only very few stocks are found n a gven country or sector. In order to obtan country and sector factors that are representatve of a substantal group of stocks, we decde to remove country or sector dummes when the set comprses less than fve stocks. In ths case, the correspondng stock returns only contrbute to the estmaton of the Common factor Correlaton ssues In the selecton of the a pror factors to be consdered n the model, t s mportant to choose carefully the correlaton structure on the rsk factors. Two man approaches can be found n the lterature, and ths s also how commercal rsk models dfferentate. The frst approach s to estmate the factor returns n stages. At each stage, the returns on one factor category are estmated usng regresson resduals of the prevous stage. For example, we may begn calculatng the Common factor. The error terms of ths frst regresson could then be used to estmate the country factor returns. The error terms of 4

7 ths second regresson could then be used to estmate the sector factor returns, etc. N C (1) R,t = F t + ε 1,t, (2) ε 1,t = k=1 D C k F C k t + ε 2,t, (3) ε 2,t = N S k=1 D S k F S k t + ε 3,t,... The advantage of ths approach s that we set zero-correlatons between factor categores. However, the man drawback, whch s the reason why we have not adopted ths methodology, s the lack of economc foundaton to justfy n whch order the varous factors should be estmated. For nstance, why should country factors be estmated before sector factors? In the case of strongly correlated factors, such as Technology and Growth, the factor returns obtaned from the regressons may sgnfcantly dffer. For example, f sector factors are estmated frst, and the Growth factor second, the latter should be weaker than f t were estmated frst. Unless there s a good reason for estmatng a partcular factor pror to another, t s less arbtrary to consder all factors at the same level of mportance. Ths brngs us to ntroduce the second approach, whch s used n ths paper. The dea s to estmate all factor returns at once, leadng to a large varance-covarance matrx of factors for whch there s no reason to fnd off-dagonal elements equal to zero. In partcular, we expect strong correlatons between the Growth factor and factors such as Technology or Telecommuncatons Weghtng schemes of the cross-sectonal regressons The cross-sectonal regressons may be run to get the factor returns by usng ether a value-weghted OLS regresson method or an equal-weghted OLS. The two approaches are found n the lterature and we beleve that a preference for one or another depends on the practcal use. On one hand, analyss based on value-weghted regressons s probably more accurate for a portfolo manager amng at a low trackng error aganst a captalsatonweghted benchmark. Ths portfolo manager wll ndeed have factor bets through large captalsaton stocks, n order to keep hs trackng error under control. On the other hand, a portfolo manager whose strategy s to nvest n a lmted number of stocks wthout beng concerned by ther captalsaton, should focus on the equal-weghted model. Such a manager wll actually bet on factors through hs stocks of strong convcton whatever ther benchmark weghts. Consequently, hs trackng error s lkely to be substantal. In ths study, we prmarly focus on the value-weghted (VW) regresson technque for the unhedged sample, but we present some results for the equal-weghted (EW) regressons and the hedged sample for comparatve purposes. 2.2 The Factors Data In ths study, we focus on the consttuents of the SSB World Prmary Market Index (PMI). We choose ths ndex rather than the MSCI World Index, for several reasons. To 5

8 begn wth, the SSB data s avalable back to 1990, whle no compled data s avalable n agreement wth MSCI s new ndustry classfcaton before Furthermore, an ex post reclassfcaton accordng to a new classfcaton system may nduce an addtonal bas. The other reason the SSB data s preferred, s the avalablty of the unque SSB Value/Growth classfcaton on a hstorcal bass (for detals see secton 2.2.4). However, we beleve our global results should be lttle affected by the choce of one world ndex rather than another. 1 The SSB World PMI s a sub-ndex of the SSB World Broad Market Index (BMI), whch conssts of 23 developed market country ndces. Each BMI country ndex comprses companes wth an nvestable market captalsaton (defned as a float-adjusted market captalsaton) greater than USD 100 mllon. For each country, the largest companes are assgned to the PMI untl 80% of the BMI nvestable market value s reached. It s thus composed of medum to large captalsatons. As of August 30, 2001, the World PMI ncluded 1036 stocks. It s mportant to avod a survval bas and estmate hstorcal returns on factors usng the hstorcal composton of the unverse rather than the current one. We collect prce data as of month t for all the stocks that were n the unverse at month t 1. The data conssts of the prce level at the end of month t and at end of month t 1. The prces are n local currency and n US dollars. Two seres of returns are derved, one characterzng an nvestor who hedges hs foregn nvestment, not the other who therefore rsks an unexpected currency movement. We refer to these two seres of returns as the Hedged and Unhedged samples. Unhedged returns are defned as ln[p,t $ /P,t 1 $ ], where P,t $ s the adjusted prce of stock n US dollars at tme t. Hedged returns are obtaned from local prces together wth the nterest rate dfferental. Denotng r the short-term (3-month) nterest rate of the foregn country, and r the domestc or reference (here, the US) short term rate, the hedged returns may be expressed as: ln[p,t Loc /P,t 1] Loc + ln[(1 + r)/(1+r )], where P,t Loc s the adjusted prce of stock n local currency at tme t. It should be noted that the methodology descrbed above does not consttute a perfect hedge, as between t 1 and t the stock prce may have moved n such a way that the forward sale of foregn currency s ether nsuffcent (f the prce has ncreased) or too mportant (the prce has gone down and the proceeds from the sale of the stock are nsuffcent to buy a predetermned amount of reference currency). However, we choose ths hedgng approach because t corresponds to what s feasble to a typcal portfolo manager. It s clear that n the case of unhedged returns, currency movements wll affect the country factors. However, lookng at unhedged returns may be more relevant, owng to the many portfolo managers who do not hedge for whatever reasons (the cost of hedgng, the beleved mean-revertng pattern of currences, the natural hedge provded by multnatonals and other large frms, etc.). It should be emphaszed that ths s ncorrect from a theoretcal pont of vew (see Solnk, 1974, for nstance), because addtonal rsk s added to the portfolo wthout any correspondng rsk premum. 2 1 Estmatons performed on the FTSE Multnatonals ndex produce very smlar results, whch are avalable from the authors upon request. 2 Ths s true uncondtonally but not condtonally. Condtonally, there s evdence that foregn exchange rate rsk s tme-varyng and prced, suggestng that nvestors are rewarded for ths rsk (see for nstance De Sants et al., 1999). 6

9 2.2.2 Country and Sector Factors For each stock, we also collect data related to the domcle country, as well as to ts sector. Ths agan s done each month based on the stock belongng to the unverse as of the prevous month. Although we do not expect many frms to change country or sector over tme very often, ths careful data checkng procedure should elmnate any potental survval bas Sze Factor Gven the large lterature documentng the varous effects of the Sze factor, we also construct a sze ndcator. Dfferent approaches have been taken prevously (Fama and MacBeth, 1973, took the logarthm of the market captalsaton, other research calculated the exposure to the returns on the x% largest stocks mnus the returns on the x% smallest stocks, etc.). We are takng here a slghtly dfferent approach. As shown n detal n the Appendx, the Sze exposure of each stock s obtaned from the transformaton of ts ndex weghtng n such a way that, at each perod: a) the ndex has a zero exposure to the Sze factor, and b) the largest consttuent has an exposure of 1. The latter restrcton ensures an economc nterpretaton of the magntude of the Sze factor Value/Growth Factor An mportant ssue s the assgnment of a gven stock to ether the Value or the Growth category. Snce the semnal study of Fama and French (1992), a Value stock s often defned as a stock the ssung frm of whch has a large Book-to-Prce (B/P). Fama and French found that, for the US market, the stocks belongng to the decles characterzed by the lowest and the hghest Book Value to Market Value (BV/MV) had respectvely an average annualzed return of 5.8% and 22.4%. They concluded that the market tends to reward the BV/MV rato, such that the equlbrum expected returns ncrease when the rato ncreases. Ths fndng has had a huge mpact on equty style nvestng. Although ths outcome ntally only defned the Value style, t has led to the wde acceptance that hgh Book-to-Prce stocks are Value stocks and that low Book-to-Prce stocks are Growth stocks. Several ndex provders have developed a Value/Growth classfcaton based on ths sngle measure (S&P/Barra for the US, MSCI for nternatonal or country style ndces). The lowest Book-to-Prce stocks are consdered as Growth stocks, and the hghest, as Value stocks. MSCI, for nstance, ranks the consttuents of each country standard ndex by the latest reported B/P, and then splts the unverse n two groupngs. The stocks wth the smallest B/P are assgned to the Growth ndex untl one half of the total ndex market value s reached. The remanng stocks, characterzed by a larger B/P, are then assgned to the Value ndex. These style ndces are rebalanced twce a year to reflect any change n 3 The Sze effect s lkely to be downward based as our sample, the SSB PMI World Index, only ncludes medum to large captalsaton stocks. 7

10 the B/P structure. Internatonal Value/Growth ndces are calculated usng each country Value and Growth consttuents. Classfcatons based exclusvely on the Book-to-Prce attrbute are lttle satsfactory, both from a theoretcal and a practcal pont of vew. Frst of all, Growth style s thought of as just the opposte of Value style, Value nvestng beng defned as buyng cheap stocks, and cheapness beng measured by the Book-to-Prce rato. Ths mples that Growth managers are buyers of expensve stocks, regardless of the true growth prospects of the ssung frm. The unvarate Book-to-Prce methodology fals to dentfy what Growth style really s, namely buyng stocks of companes the earnngs of whch are growng faster than the average. Second, every stock s assumed to be ether a pure Growth stock or a pure Value stock. Realstcally, some stocks may be nether Growth nor Value (expensve wthout superor earnngs growth). Other stocks may be a mxture of both styles (cheap stocks wth superor earnngs growth). Thrd, n the ranked unverse, the last Value stocks have almost the same Book-to-Prce as the frst Growth stocks, but the former are consdered pure Value stocks and the latter, pure Growth stocks. Fnally, snce frms belongng to the same ndustry tend to have smlar book values, both Value and Growth ndces nclne to be composed of a few ndustres only. A more satsfyng way of defnng style s to focus on the dfferent crtera shared by nvestors followng the same nvestment style. For nstance, f nvestors consder that hgh Book-to-Prce s the fundamental characterstc of a Value stock, then ths rato should be used to measure ts amount of Value style. Smlarly, f nvestors consder that hgh earnngs per share (EPS) growth s the fundamental characterstc of a Growth stock, then ths rate should be used to measure ts amount of Growth style. Wth such an approach, Value and Growth styles are defned separately, thus allowng a stock to be pure Growth or Value, none of them, or a mxture. For the US market, the Frank Russell Style Indces, the Wlshre Assocates Style Indces and the Prudental Securtes Equty Style Indces are constructed on the bass of such a multvarate methodology. Global Style ndces based on such an approach are only provded by SSB. In ths paper, we use the Growth and Value characterzaton developed by Salomon Smth Barney. The SSB methodology can be summarzed as follows. Frst, varables defnng and characterzng the two styles are dentfed. A set of 10 Growth varables that measure the company growth (for nstance, the fve-year hstorcal Earnngs per Share Growth) s chosen. Smlarly, a set of 5 Value varables that measure the relatonshp between ntrnsc and market value (for nstance, the Earnngs per share to Prce per Share) s selected. These varables are standardzed by regon. Cluster analyss s then appled to determne whch varables contrbute effectvely and sgnfcantly to the dfferentaton between Growth and non-growth, or between Value and non-value stocks. A total of 3 Growth and 4 Value varables have been retaned. For each stock of a gven SSB Country PMI Index, Growth and Value scores are derved from the level of these varables. Fnally, Value and Growth probablty weghts are deduced from these scores and assgned to each stock. These probabltes are constructed n order to ensure that ) each SSB Country Style Index represents exactly 50% of the total float-adjusted market captalsaton of the correspondng SSB Country PMI Index, and, ), for each stock, the sum of the Growth and Value probablty weghts equals one. These probablty weghts are revsed once a year based on the nformaton avalable, at the end of March, for company reported data, 8

11 and at the end of May, for prce data. They become effectve on the 1 st July, and are then held constant durng the subsequent year. In our study, the SSB Growth and Value probablty weghts are the factor loadngs labeled p G,t and p V,t n equaton (1). As shown n the Appendx, t results from SSB methodology that, n our value-weghted model, pure Value returns are the exact opposte of pure Growth returns as estmated by our value-weghted regresson technque. Hence, n the subsequent parts of the paper, we shall drop the Value label and focus exclusvely on the Growth factor, keepng n mnd the smple relaton between both factors under the value-weghted scheme. However, the relaton between the Growth and the Value factors s more complex n the case of an equal-weghted regresson technque (see secton for a descrpton of the dfferent regresson technques). 3 Results 3.1 The pure factors Returns on pure factors are shown as cumulated log-returns n Fgures 1 to 7. Fgure 1 shows the cumulated log-returns on the Common Factor for the four dfferent samples (hedged/unhedged, EW/VW). All return seres are calculated from a US nvestor s vewpont. The dfference between the cumulated EW and VW returns s due to the outperformance of large stocks relatve to small stocks snce The dfference between the cumulated hedged and unhedged returns s very small, whch s not surprsng as the US represent the largest captalsaton n the sample. Fgure 2 reports the cumulated returns on the Sze (Panel A) and the Growth (Panel B) factors, both for the EW and the VW samples. It should be emphaszed here that the returns are pure factor returns, net of all other factor returns. The fgure shows how small the return on the pure Growth factor was pror to 1999, whle the pure Sze factor has revealed a steady postve trend from 1995 to Snce many large frms are Growth frms, the results may be msleadng f Sze s not dsassocated from Growth. For nstance, t s often clamed that Growth performed well n the second half of the 90 s. We beleve t was rather a Sze effect untl Another mportant outcome s that the strong Growth effect that emerged n 1999 s not only due to extraordnarly strong Sector effects concentrated n a few Growth-orented sectors lke Technology and Telecommuncatons. 4 We also appled ths methodology to a sub-sample composed of the European stocks makng up the SSB World PMI ndex. One of the most strkng dfferences s the behavour of the pure Sze factor n Europe, whch followed a strong negatve trend over the same perod. Ths result does not only contrast sharply wth the Sze pattern of the full SSB World PMI ndex (Fgure 7), but t also beles the Sze effect measured conventonally. Indeed, the most common way to measure the Sze effect s to smply plot the performance of large versus small captalsaton stocks, whch tends to show the outperformance of Sze. Our mult-factor decomposton reveals the pure performance contrbuton of each factor separately (Country, Sector, Sze and Value/Growth), whereas the outperformance of a set of large captalsaton stocks mght be only due to a specfc Country, Sector or Value/Growth concentraton. Hence, n the case of Europe, the outperformance of large over small European stocks s not due to ther sze but rather to ther country, sector or Value/Growth composton. 9

12 Indeed, a strong Growth effect remans once sector effects are solated. In Fgure 3, we represent the country factor returns of the G5. The shape of the cumulated returns on Japan s strkng. Whle Fgure 3 pertans to the unhedged VW sample, Fgure 4 shows the Japan factor for the 4 dfferent samples. The pattern of the two unhedged samples clearly shows the strong yen apprecaton of It s a nce llustraton of how dfferent the results are, accordng to the weghtng scheme (EW or VW) and the hedgng assumpton. In Fgure 5, we show the results for several other major European countres and we fnd that dfferences between country factors are strkng even wthn Europe. Fgure 6 represents the cumulated returns on sector factors. The returns on the Technology and Telecommuncaton sectors are clearly recognzable. It should be remembered that sector and Growth factors are estmated smultaneously. Hence, the correlaton between sectors and Growth s not zero. In order to better understand the relaton between hghly correlated factors, we also show n Fgure 7 three factors for whch the a pror correlaton s hgh: Telecommuncatons, Technology and Growth. These three factors show ther peak n March The graph also ndcates that pror to 1996 the correlaton between them was far less mportant. Fgure 1: Cumulated log-returns on the Common factor for the varous samples. 10

13 Fgure 2: Cumulated log-returns on the Growth and the Sze factors for the unhedged sample. Panel A: Growth factor Panel B: Sze factor 11

14 Fgure 3: Cumulated log-returns on country factors for the G5 (Unhedged - VW sample).! Fgure 4: Cumulated log-returns on the Japan factor for the varous samples. 12

15 Fgure 5: Cumulated log-returns on varous European country factors (Unhedged - VW sample).!" Fgure 6: Cumulated log-returns on sector factors (Unhedged - VW sample).!" 13

16 Fgure 6 (contnued):!"#!" $%&" $'' $! ( Fgure 7: Cumulated log-returns on three hghly correlated factors (Unhedged - VW sample). 14

17 3.2 Homogenety of country, sector and style factors It s also mportant to nvestgate the sgnfcance of each factor n the cross-sectonal regressons. Two factors may have smlar behavors over tme, whle one s hghly sgnfcant n each cross-sectonal regresson, and not the other. We mantan that the cross-sectonal t-statstc s an ndcator of the homogenety of each factor. A hgh cross-sectonal sgnfcance ndcates a farly good homogenety of a gven factor. For nstance, f the Healthcare factor s constantly sgnfcant over tme, whle the Swtzerland factor s not, we can nfer that the behavor of Healthcare stocks s more homogenous than the Swss stocks. We therefore calculate the factor t-statstcs for each monthly cross-sectonal regresson, whch are ndependent of the sgn or the magntude of factor returns. We report n Table 1 the average t-statstc of each factor, and show f ts average value over tme s sgnfcantly larger than the crtcal value of Several nterestng results emerge from the table. The results are overall very smlar for the hedged and the unhedged samples, even for the country factors. Large countres are generally sgnfcant, whle small countres are not. Most sectors are hghly sgnfcant for the VW samples (9 out of 14), but are less sgnfcant for the EW samples (5 out of 14). Sze and Growth are hghly sgnfcant for the VW samples and nsgnfcant for the EW. In order to vsualze how factor sgnfcance evolves over tme, we represent the 12-month movng average of the t-statstcs n Fgure 8. The top graph shows the results of the EW sample and the bottom, the VW, both based on unhedged returns. Here we dscover several mportant dfferences between factor categores. The sgnfcance of country factors has been fallng snce 1991, whle the opposte has occurred (although to a lesser extent) for sector factors. Ths s true for both the equalweghted and the value-weghted regressons. The average t-statstc of the Country factor was very hgh at the begnnng of the 90 s, well above the Sector factor. At the end of the decade, the Country factor was hardly sgnfcant (slghtly below 2), whle the sgnfcance of the Sector factor rose above 2.5. Hence, we can conclude that sectors clearly became more homogeneous than countres. The Growth factor was dstnctly sgnfcant n the late 90 s, but ths s far from true for the whole decade. It seems that the behavor of Growth stocks lost homogenety especally n the md-90 s. The Sze factor has been sgnfcant snce 1991 for the VW sample. For the EW sample, ths factor was only margnally sgnfcant durng 1997 (although Fgure 2/Panel B shows that ths factor s large n magntude). In 2001, Sze was only sgnfcant for the VW sample. 15

18 Table 1: Cross-sectonal t-statstcs of factor returns. Unhedged Hedged EW VW EW VW Common Factor Japan Unted States Greece Italy Unted Kngdom Hong Kong Canada Sngapore France Sweden Germany Australa Norway Austra Belgum Denmark Span Swtzerland New Zealand Portugal Netherlands Ireland Technology Non-Property Fnancals Energy Utltes Basc Materals Consumer Non-Cyclcals Healthcare Telecommuncatons Consumer Cyclcals Industral Goods & Servces Property Transportaton Conglomerates Cyclcal Conglomerates Growth Sze Note: ( ) ndcates f the sample mean t s above the dstrbuton mean 1.96 at 5% (10%) level. 16

19 Fgure 8: Average absolute t-statstcs of countres, sectors, Growth and Sze over tme (12- month movng average) for the EW and the VW samples. Panel A: Unhedged - EW Panel B: Unhedged - VW 17

20 3.3 Benefts from country, sector and style dversfcaton Dversfcaton benefts arse from low correlaton among asset classes. In partcular, the benefts of nternatonal dversfcaton arsng from low correlatons among Equty markets are well documented. Nevertheless, the man sources drvng correlatons reman controversal among both academcs and practtoners. Low correlatons may be due to dfferences n economc condtons across natonal borders, lke varatons n regulatory envronment, economc polces and growth rates. If ths s the case, cross-country dversfcaton strateges should produce sgnfcant benefts. On the contrary, low correlatons among Equty markets may be explaned by the specfc ndustral composton of each country. For nstance, an nvestment n the Swss market actually mples a hgh exposure to the bankng sector, whle an nvestment n the Dutch market, to the energy sector. Equty markets are maybe mperfectly correlated only because ndustres are. If ths s the case, allocaton strateges across sectors could offer hgher dversfcaton benefts than across countres. In ths subsecton, we report varous dsperson and correlaton measures among country and sector factors, as well as ndcators of ther magntude n nternatonal strateges. To begn wth, we calculate the monthly cumulatve cross-sectonal dsperson among pure country and pure sector returns n order to dentfy turbulent perods (for a revew of cross-sectonal dsperson, see Solnk and Roulet, 1999). Hence, for each month, we get the cumulatve cross-sectonal dsperson of country and sector returns and then we sort them by decreasng order. Fgure 9 ndcates the 20 hghest cumulatve varances. The frst bar shows that n September 2000, sector returns were twce as volatle as country returns. In February 2001, sectors were even 3 tmes more volatle than countres. Most of the tme, however, the dsperson of country returns s much hgher than sector returns (16 months out of 20). Ths suggests hgher dversfcaton benefts from cross-country allocaton n tmes of hgh volatlty. Ths also holds for the overall perod: the dsperson of country returns s on average 0.25% per month, whle t s as low as 0.10% for sector returns. Table 2 reports the full correlaton matrx among pure sector returns (Panel A) and among pure country returns (Panel B). It should be realzed that there are non-zero correlatons between country and sector factors, although we do not report them. 5 Correlatons are generally low or even negatve, both among country and sector returns. Pure factors appear to be very lttle correlated, as opposed to factors ncludng the Common factor (whch s not a surprse). The correlatons among country (or sector) factors ncreased by the Common factor are strongly nfluenced by the Common factor tself. Therefore, we beleve here that the correlaton among pure factors s the only measure that really matters when performance s measured aganst a benchmark, and for an actve nvestor who wants to make bets on ether country or sector factors. Nevertheless, for comparson purposes, we also report factor results ncludng the Common factor. As correlatons among pure country and sector factors are very low, the dversfcaton mpact (both along countres and sectors) should be hgh. 5 Full results are avalable from the authors upon request. 18

21 Fgure 9: The 20 hghest cumulatve cross-sectonal dspersons of country and sector factors from 1990 to Table 2: Correlatons among pure factors (Unhedged - VW sample). Panel A: Sector factors Basc Materals Conglomerates Consumer Cyclcals Consumer Non-Cyclcals Cyclcal Conglomerates Basc Materals 1 Conglomerates Consumer Cyclcals Consumer Non-Cyclcals Cyclcal Conglomerates Energy Healthcare Industral Goods & Servces Non-Property Fnancals Property Technology Telecommuncatons Transportaton Utltes Energy Healthcare Industral Goods & Servces Non-Property Fnancals Property Technology Telecommuncatons Transportaton Utltes 19

22 Panel B: Country factors Australa Austra Belgum Canada Denmark France Germany Greece Hong Kong Ireland Italy Japan Netherlands New Zealand Norway Portugal Sngapore Span Sweden Swtzerland Unted Kngdom Unted States Australa 1 Austra Belgum Canada Denmark France Germany Greece Hong Kong Ireland Italy Japan Netherlands New Zealand Norway Portugal Sngapore Span Sweden Swtzerland UK US

23 We report n Fgure 10 the average correlaton among country and sector factors over tme. At each pont n tme, the correlatons are measured over the prevous 36 months and then averaged among factors of each category. Panel A shows correlatons among factors ncreased by the Common factor, whle Panel B reports correlatons among pure factors. Our results are very comparable to prevous research on the topc (see for nstance Cavagla, 2000). Panel A reveals that country correlatons were below 50% untl the 1998 crss. They ncreased over roughly 55% n summer 1998 and have remaned at ths level untl md Sector correlatons have shown a clear decreasng trend over the whole perod, but have remaned above country correlatons untl the end of In md-2001, sector correlatons were around 40%, whle country correlatons, close to 55%. The usual nterpretaton s that, although dversfyng along sectors s becomng more and more benefcal (because of decreasng correlatons), country factors stll offer hgh dversfcaton benefts (because the average correlaton s stll relatvely low). Another mportant fndng s that, whle correlatons among country returns tend to ncrease sharply durng market correctons, as n summer 1998, correlatons among sectors appear to be more reslent to such shocks, snce they ncrease only margnally. Thus, dversfcaton along sectors seems to be more robust than along countres when the global nvestor needs t most, e.g. durng correcton perods. 6 Panel B of Fgure 10 offers an alternatve way of analyzng potental dversfcaton benefts through the average correlaton among pure country and sector returns. The average correlaton between pure sector returns s very stable between 5% and +2%, whle t s between 7% and 17% among pure country returns. Gven these results, sector factors seem to offer slghtly hgher dversfcaton benefts. In order to better assess the mportance of the Growth factor for dversfcaton purposes, we show n Fgure 11 ts correlatons wth all the other factors. Unsurprsngly, the strongest correlatons are wth Technology (45%), followed by the Common factor (almost 40%) and the Telecommuncatons (almost 30%). Strong negatve correlatons are wth Transportaton ( 50%) and Consumer non-cyclcals ( 47%). 6 Ths fndng seems to be n contradcton to Fgure 9, whch shows that cross-sectonal dsperson among country returns ncreased dramatcally n August Actually, covarances between country returns ncreased even more, producng hgher country correlatons despte hgher varances. 21

24 Fgure 10: Average correlaton among country and sector factors (36-month rollng), (Unhedged - VW sample). Panel A: Factors ncludng the Common factor Panel B: Pure factors 22

25 Fgure 11: Correlatons between the Growth factor and all the other factors (Unhedged - VW sample). Netherlands Australa Sze Property Italy Ireland France Denmark Swtzerland Belgum Non-Property Fnancals Consumer Cyclcals Norway Energy Cyclcal Conglomerates Austra Unted Kngdom New Zealand Greece Utltes Healthcare Basc Materals Consumer Non-Cyclcals Transportaton Technology Common Factor Telecommuncatons Canada Industral Goods & Servces Sweden Unted States Sngapore Hong Kong Conglomerates Germany Span Portugal Japan Growth 3.4 The magntude of country, sector and style effects Another measure of potental benefts from cross-country and cross-ndustry strateges has been proposed by Rouwenhorst (1999). He suggested to use the Mean Absolute Devaton (MAD) ndcator, defned as the weghted average of the absolute devatons from the mean return at a gven date t. Ths ndcator provdes a measure of the opportuntes of outperformng an ndex through actve country or ndustry exposures. The country (respectvely the ndustry) MAD can thus be consdered as the gans from a perfect foresght strategy based exclusvely on country (respectvely ndustry) bets. The strategy would be to hold a long poston n rsng factors and a short poston n declnng factors, n proporton to ther weght. Ther contrbuton can be ether equal-weghted or captalsaton-weghted. For example, we consder a unverse comprsng only 2 countres (the US and Swtzerland) and 2 sectors (Technology and Healthcare), where each factor s equal-weghted wthn each category. If pure country returns happen to be +1% and 1% (for the US and Swtzerland respectvely) over a gven month, then the perfect foresght strategy return s 1% (reflectng a long poston n the US and a short poston n Swtzerland). The country MAD equals 1%. Now, f pure sector returns are +10% and 10% (for the Technology and Healthcare sectors respectvely), then the perfect foresght strategy return s 10%. 23

26 The sector MAD equals 10%. In ths case, the mpact of sector factors s much stronger than country factors. Snce the MAD s generally a qute volatle ndcator, some prevous research appled a smoothng by takng a 52-week movng average (Cavagla et al., 2000), or a 48-month movng average (Baca et al., 2000, used the varance nstead of the absolute mean). Fgure 12 shows the MAD 12-month movng average over the whole perod. Panel A shows the equal-weghted MAD and panel B, the value-weghted MAD. Our results are akn to prevous fndngs: from 1991 to the late 90 s, the country MAD has been above the sector MAD. However, the sector MAD has ncreased dramatcally between 1997 and the end of The equal-weghted MAD caught up wth the level of the country MAD at the end of 2000, whle the value-weghted MAD has largely exceeded the country MAD over ths perod. Between md-2000 and md-2001, all MADs have been followng a comparable slghtly decreasng trend. Ths sheds doubt on all defntve conclusons on a persstent downward trend for country effects as opposed to a persstent upward trend for sector effects. However, a general concluson s that, whle country factors have not lost much n magntude, sector factors have undoubtedly ganed mportance between 1998 and In Fgure 13, we represent the mportance of weghted average absolute returns on the Common Factor, the pure Country, Sector and Growth + Value factors, as well as the average absolute stock-specfc returns, as a percentage of the whole. 7 Agan, Panel A shows equal-weghted returns and Panel B, value-weghted returns. The Growth factor has clearly ganed mportance over tme. For both weghtng schemes, t was at least as mportant as the average absolute country or sector returns by md The decrease of the Country contrbuton s obvous n both panels but s much more mportant when returns are value-weghted. The average absolute stock-specfc returns accounted for more than 30% of the total over the whole perod, suggestng the large potental added-value of stock pckng. 7 Here the Growth factor s actually multpled by 2 n order to rentegrate the Value factor nto the return decomposton. Ths decomposton s drectly derved from equaton (1), whch explctly takes the Value factor nto account. The Appendx shows that the Value factor s the exact opposte of the Growth factor n the case of the VW sample. 24