Consrucing Absolue Reurn Funds wih ETFs: A Dynamic Risk-Budgeing Approach July 2008 Noël Amenc Direcor, EDHEC Risk & Asse Managemen Research Cenre Professor of Finance, EDHEC Business School noel.amenc@edhec-risk.com Felix Golz Senior Research Engineer, EDHEC Risk & Asse Managemen Research Cenre felix.golz@edhec-risk.com Adina Grigoriu Head of Asse Allocaion EDHEC Invesmen Research adina.grigoriu@edhec-risk.com Auhors address: EDHEC Risk & Asse Managemen Research Cenre, 400 promenade des Anglais - BP 3116 F-06202 Nice cedex 3 - France Tel.: +33 (0)4.93.18.99.66 1
Absrac This aricle develops an applicaion of ETFs o he managemen of an absolue reurn fund. The use of dynamic core-saellie porfolio managemen makes i possible o consruc absolue reurn funds using ETFs on sock and bond indices. As a resul of he ease wih which hey are raded, ETFs make an ideal vehicle for puing dynamic risk budgeing ino pracice. The advanage of he dynamic core-saellie porfolio is ha, unlike convenional sraegic or acical asse allocaion, i relies solely on he observable price pah of differen ETFs, and a range of predefined parameers. So he problems of esimaion and predicion uncerainy of he wo convenional allocaion mehods are avoided. The combinaion of advanced dynamic risk-budgeing echniques and highly liquid and ransparen insrumens may provide a more invesor-friendly way o deliver a given absolue reurn wih a arge level of volailiy, independen of prevailing marke condiions. 2
Inroducion Absolue reurn funds have seen widespread growh in he asse managemen indusry in recen years. These funds claim o provide relaively smooh reurns wih a limied level of risk. No unlike hedge fund managers, absolue reurn managers do no sae a benchmark in erms of a marke index or a peer group; insead, hey ry o obain a given absolue reurn for given volailiy, independen of prevailing marke condiions. As migh be expeced, hese funds appeal o invesors, bu how he manager realises he objecives is he crucial poin. Tradiionally, here are wo broad echniques ha make i possible o achieve reurns above he risk-free ineres rae while keeping volailiy in check. The firs borrows from modern porfolio heory. Managers aemp o obain a broadly diversified porfolio across asse classes, diversificaion ha allows significan risk reducion. Wih such sraegic asse allocaion, he correlaions beween he asse classes under consideraion are needed as an inpu o he opimisaion problem. While low correlaion beween asse classes or sub-classes allows enhanced risk reducion, hese correlaions are no known ex ane. Raher, fuure correlaions mus be esimaed from hisorical daa, a necessiy ha poses wo problems. Firs, he correlaions ha are used as inpu mus be esimaed from hisorical daa. This leads o esimaion risk: he correlaions used as inpu may be differen from he rue correlaions and lead o erroneous porfolio weighs. While he problem of esimaion risk can be alleviaed by imposing srucure on he correlaion marix or by using saisical shrinkage echniques, hese mehods are no widely used, as shown by a recen survey (EDHEC 2008). Second, correlaion coefficiens are subjec o change over ime or across saes of he economy. Indeed, in pracice, hey change grealy over ime. Asses ha were uncorrelaed in he pas may become highly correlaed. Mulivariae GARCH models (see Engle 2002 for a popular example) can be used o model his ime dependence. In addiion, correlaions are no only ime-dependen bu also sae-dependen. For example, Longin and Solnik (1995) have shown ha he correlaion of sock marke reurns in differen counries is no consan and ha i ends o increase in volaile marke environmens. A second echnique involves acical asse allocaion, which is based on he predicion of he reurns of differen asse classes or sub-classes over shor ime horizons. The reurn predicions mus hus be ransformed ino porfolio holdings ha benefi where predicions are accurae. For profiabiliy, hen, hese sraegies rely on he capaciy of he manager o predic fuure price movemens, hrough eiher economeric models or qualiaive assessmens. More imporanly, in order o generae no jus high reurns, bu also he smooh pahs associaed wih absolue reurn funds, he manager mus make correc predicions very consisenly. In pracice, hese wo echniques are frequenly combined, wih managers performing sraegic asse allocaion based on hisorical correlaions and making acical bes. However, an alernaive o such heavy reliance on hisorical esimaes of correlaion coefficiens and chancy predicions abou fuure reurns is o use dynamic risk managemen echniques, such as Amenc, Malaise, and Marellini s (2004) dynamic core-saellie approach. In a nushell, his approach aemps o capure he upside of a saellie porfolio, while limiing he downside in he even ha he saellie porfolio underperforms he core porfolio. Since i relies on dynamic exposure o broadly diversified porfolios, exchange-raded funds (ETFs) are ideally suied o serve as he building blocks in such an approach. The combinaion of a low-risk ETF in he core wih a performance-seeking ETF in he saellie may well resul in an absolue reurns vehicle in which downside proecion is achieved hrough dynamic rading in he ETFs. The advanage of he dynamic core-saellie is ha, unlike sraegic or acical asse allocaion, i relies solely on he observable price pah of differen ETFs, and a range of predefined parameers. So he problems of esimaion and predicion uncerainy of he wo convenional mehods are avoided. The objecive of his paper is o develop an applicaion of ETFs o he managemen of an absolue reurn fund. The remainder of he paper proceeds as follows. Firs, we will describe he risk budgeing echnique we use. Second, we use fixed-income and equiy ETFs o consruc an absolue reurns fund. A hird secion compares his approach and radiional acive managemen, in which he manager has views on he ouperformance of an asse class and adjuss he weighs accordingly. The aim of his secion is o deermine he rae of successful predicions necessary o aain he risk conrol obained wih dynamic risk budgeing. A final secion concludes. 3
1. The Dynamic Core-Saellie Porfolio Process In his secion, we describe he mehodological backbone of dynamic risk budgeing: he dynamic core-saellie approach, a novel echnique for risk managemen proposed by Amenc, Malaise, and Marellini (2004). I is of ineres ha hrough his nonlinear risk managemen echnology payoffs ha involve a ype of relaive reurn guaranee can be achieved hrough dynamic rading in ETFs. In essence, he core-saellie concep makes i possible o manage he racking error of he overall allocaion. If he invesor has a given racking error budge, he arge racking error can be achieved wih saic definiions of he proporion invesed in he core and ha invesed in he saellie. However, managemen of he racking error budge can also be made dynamic; he proporion invesed in he acive porfolio can vary as a funcion of he curren cumulaive ouperformance of he overall porfolio wih respec o he benchmark. This objecive is achieved by ransporing he mehod of radiional consan proporion porfolio insurance (CPPI) o coresaellie porfolio managemen, so as o allow more efficien relaive risk conrol. Sandard CPPI, which was inroduced by Black and Jones (1987) and Black and Perold (1992), allows he producion of opion-like posiions hrough sysemaic rading rules. This procedure dynamically allocaes oal asses o a risky asse in proporion o a muliple of he cushion, i.e., he difference beween curren wealh and a desired proecive floor. The effec is similar o ha of owning a pu opion. Under such a sraegy, he exposure of he porfolio ends o zero as he cushion approaches zero; when he cushion is zero, he porfolio is compleely invesed in cash. Thus, in heory, he guaranee is perfec: he sraegy of exposure ensures ha he porfolio never falls below he floor; in he even ha i ouches he floor, he fund is dead, i.e., i can deliver no performance beyond he guaranee. These consan proporion porfolio insurance echniques, originally designed o ensure absolue performance, can be exended o a relaive reurn conex. The new mehod devised by Amenc, Malaise, and Marellini (2004) makes i possible for invesors o gain full access o good racking error, while keeping bad racking error largely a bay; he mehod involves opimal dynamic adjusmen of he fracion invesed in he core and ha invesed in he saellie. I is, in a sense, a srucured form of acive managemen, as well as a naural exension of CPPI echniques. An approach similar o sandard CPPI can be aken o offer he invesor a relaive performance guaranee; in oher words, a guaranee ha any underperformance of he benchmark will be limied o a specified amoun. The echniques of radiional CPPI sill apply, provided ha he risky asse is re-inerpreed as he saellie porfolio, which conains relaive risk wih respec o he benchmark, and ha he risk-free asse is re-inerpreed as he core porfolio, which conains no relaive risk wih respec o he benchmark. Exhibi 1: Tradiional CPPI versus Relaive Approach CPPI Tradiional CPPI Relaive Approach CPPI Risky Asse Saellie Porfolio Risk-free Asse Core Porfolio This able compares he radiional CPPI o he relaive approach CPPI Assume, for example, ha he benchmark is a passive invesmen, e.g., a bond index. The guaranee is se a 90% of he benchmark value and we assume ha he muliplier is equal o 4. A he iniial dae T 0, porfolio value and benchmark value are normalised a 100, wih a floor se a 90% of he benchmark value. The floor is hus 0.9 100 = 90. The cushion is herefore 100 90 = 10. The invesmen in he saellie is hen 10 4 = 40, which resuls in 100 40 = 60 in he core. A dae T 1, le us assume ha he difference beween he saellie and he benchmark is +10%, as a resul of he following scenario: S = 0%, C = - 10%. In his case, he posiion invesed in he core has decreased by 10%, from 60 o 54. Besides, he acive porfolio value has remained sable a 40, while he benchmark has also decreased by 10%, from 100 o 90. The difference beween he fund value (94 = 54 + 40) and he benchmark value (90) is now equal o 4. The floor has dropped from 0.9 100 o 0.9 90 = 81. Thus, he cushion is now 94-81=13. The new opimal fracion o inves in he saellie is 13 4 = 52, which leaves 94 52 = 42 in he core porfolio. On dae T 1 he resuling allocaion is herefore 52/94 = 55% in he saellie and 42/94 = 45% in he core porfolio. Le us assume, on he oher hand, ha he difference beween he saellie and he benchmark is -10%, as a resul of he following scenario: S = 0%, C = +10%. In his case, he posiion invesed in he core has increased by 10%, from 60 o 66. Besides, he acive porfolio value has remained sable a 40, while he benchmark has also 4
increased by 10%, from 100 o 110. The floor is now a 0.9 110 = 99. The difference beween he fund value (106 = 66 + 40) and he floor (99) is now equal o 7, meaning ha he cushion has decreased from is iniial value of 10. The new opimal fracion o inves in he saellie porfolio is 7 4 = 28, which leaves 106 28 = 78 in he core porfolio. On dae T 1 he resuling allocaion is herefore 28/106 = 26% in he saellie and 78/106 = 74% in he core porfolio. As can be seen from his example, he mehod leads o an increase in he fracion allocaed o he saellie (from 40% o 55%) when he saellie has ouperformed he benchmark. Indeed, he accumulaion of pas ouperformance has resuled in an increase in he cushion, and hus greaer poenial for a more aggressive (and hence higher racking error) sraegy in he fuure. If, on he oher hand, he saellie has underperformed he benchmark, he mehod leads o a igher racking error sraegy (hrough a decrease of he fracion invesed in he saellie porfolio) in an aemp o ensure ha he relaive performance objecive is me. This approach allows dissymmeric managemen of racking error, ensuring ha he underperformance of he porfolio wih respec o he benchmark will be limied o a given level, while leing he invesor gain fuller access o excess reurns poenially generaed by he acive porfolio. The benefi of his approach is ha a dynamic version of a core-saellie approach allows an invesor o runcae he relaive reurn disribuion so as o allocae he probabiliy weighs away from severe relaive underperformance o he profi of more poenial for ouperformance. I is sandard pracice o consruc core-saellie porfolios by placing asses ha are supposed o ouperform he core in he saellies. However, during periods of emporarily unfavourable condiions hese asses may underperform he core. The dynamic core-saellie approach described above makes i possible o reduce he impac of he saellie on performance during a period of relaive underperformance, while maximising he benefis of he periods of ouperformance. Indeed, observaion of invesor behaviour shows ha invesor expecaions are rarely symmeric. In oher words, when sock marke indices perform well, invesors are happy o be earning relaive reurns, bu when hey perform poorly, hey much prefer absolue reurns. Techniques such as Value-a-Risk minimisaion or volailiy minimisaion allow only symmeric risk managemen. For example, he minimum variance process leads o a renunciaion of upside poenial in he performance of commercial indices in exchange for lower exposure o downside risk, hrough racking error consrains. While his sraegy allows long-erm ouperformance, i can lead o significan shor-erm underperformance. I is also very hard o recover from severe marke drawdowns. In wha follows, we describe non-linear dynamic allocaion, a se of echniques ha make i possible o focus on asymmeric risk managemen. From an absolue reurn perspecive, i is possible o propose a rade-off beween he performance of he core and saellie. This rade-off is no symmeric, as i involves maximising he invesmen in he saellie when i is ouperforming he core and, conversely, minimising he weigh of he saellie when i underperforms he core. The aim of his kind of dynamic allocaion is o allow ouperformance, in erms of risk-adjused reurns wih regard o a saic core-saellie allocaion. This dynamic allocaion firs requires a lower limi on underperformance wih respec o he benchmark on he erminal dae, i.e., V ( T ) > kb( T ), where k is lower han one, e.g., k = 90%, and B() is he benchmark value a dae. I is hen necessary o provide access o poenial ouperformance of he benchmark based on invesmen in a saellie whose value on dae is denoed by S(). As menioned above, Amenc, Malaise, and Marellini (2004) devise a mehod, known as he dynamic coresaellie managemen process, which allows invesors o achieve asymmeric racking error managemen. This mehod leads o an increase in he fracion allocaed o he saellie when he saellie has ouperformed he benchmark. Indeed, he accumulaion of pas ouperformance has resuled in an increase in he cushion, and herefore in he poenial for a more aggressive (and hence higher racking error) sraegy in he fuure. If he saellie has fallen shor of he benchmark, he mehod leads o a igher racking error sraegy (hrough a decrease of he fracion invesed in he saellie porfolio). This dual objecive is achieved by a suiable exension of he CPPI o a conex of relaive risk managemen. The concep of his process was inroduced above. Le V() be he porfolio on dae. I can be divided ino a floor and a cushion, according o he relaion V() = F() + C(). The floor is given by F() = kb(). Take he invesmen in he saellie, i.e., he risky asse in a relaive conex, o be E() = mc(), wih m as a consan muliplier, while he remainder of he porfolio V() - E() is invesed in he benchmark. 5
The process for cushion growh ells us abou he upside poenial and allows us o calibrae an opimal value for m. ds db dc = dv df = E + ( V E ) df S B ds db db dc = mc + ( C + F mc ) F S B B ds db dc = C m + ( 1 m) S B I is useful o wrie explicily he final value of he porfolio and he cushion. We consider a floor given as F() = e-r(t-)k, where K is he guaraneed capial. The overall porfolio value is A(). Moreover, we consider a risky porfolio ha is invesed in equiy. The fracion of he porfolio invesed in equiy E() is given by he fixed rule E()=mC()=m(A()-F()), while he remainder of he porfolio A()-E() is invesed in he risk-free asse. We have he following dynamics for asse and porfolio value: ds = μd + σdw S db = rd B ds db da = E + ( A E ) B S The value of he porfolio a erminal dae is hen A(T) = F(T) + C(T) = K + C(T). To esimae C(T), noe ha ds db dc = da df = E { + A { E { df { S mc B = = C+ F = mc db or dc ds db db ds db = m + (1 m) = + m C S B B S B = F B One can solve he previous sochasic differenial equaion o obain: m 2 S T 1 2 2σ 0 exp σ S0 2 2 CT = C r m r m T m 2 S T 1 2 2σ 0 exp σ S0 2 2 AT = FT + C r m r m T To conclude and before applying he approach o a pracical case of managing a porfolio of ETFs le us reierae he raionale behind he dynamic core-saellie approach. The core porfolio makes i possible o respec he invesor s long-erm risk reurn objecives, while he saellie porfolio provides access o upside poenial of he saellie porfolio. The dynamic allocaion process will sysemaic increases in exposure o he saellie 6
porfolio when i does well, while conrolling risks by shifing o he core when he saellie does poorly. Thus, his approach allows an invesor o runcae he relaive reurn disribuion so as o allocae he probabiliy weighs away from severe relaive underperformance in favour of more poenial for ouperformance. In shor, asymmeric racking error managemen is made possible; he underperformance of he porfolio wih respec o he benchmark will be limied o a given level, while he invesor gains fuller access o excess reurns poenially generaed by he acive porfolio. 2. Consrucing Absolue Reurn Funds wih ETFs To illusrae how dynamic risk budgeing may be used o design absolue reurn funds wih ETFs, we combine a core porfolio ha invess in medium-erm bonds and a saellie porfolio ha invess in an equiy ETF. The objecive of he proposed sraegy is o achieve smooh reurns because of he low volailiy of he core porfolio. In addiion, he aim is o benefi from he reurns on he sock marke ETF if socks ouperform bonds, while achieving a proecion from he downside risk of he equiy invesmen. The deails of he sraegy are as follows: he core is made up of he EuroMTS for bonds wih hree o five years o mauriy and he saellie invess in he EuroSoxx 50. The daa used are monhly reurns including coupon or dividend paymens for he period from January 1999 o December 2007. The saring period is deermined by he bond daa, available only as of he inroducion of he Euro, as is ypical for daa on Euro-denominaed bonds. The value of he muliplier is se o six, while he floor is defined a 90% of he value of he bond core porfolio. The weigh in he saellie is consrained o a maximum of 60% of he overall porfolio. Furhermore, we use an exension o he basic dynamic core-saellie approach o achieve he absolue reurns objecive. In paricular, we inroduce a maximum drawdown limi equal o 10% in order o ake ino accoun he invesor s aversion o drawdowns in he absolue value of he overall porfolio. In fac, here are suiable exensions of he sandard dynamic asse allocaion sraegies ha can accommodae he presence of maximum drawdown consrains. These sraegies are developed by Esed and Krizman (1988), who label hem ime invarian porfolio proecion sraegies (TIPP), and formalised by Grossman and Zhou (1993) and Cvianic and Karazas (1995). By imposing a maximum drawdown consrain of 10% and using our muliplier of six, we noe ha he maximum allocaion o he saellie porfolio is 60%. Hence, he defensive bond porfolio used as he core will always consiue a leas 40% of he overall porfolio. Exhibi 2 shows he cumulaive reurns of he sraegy we use, as well as hose of he core and saellie porfolios. In addiion, o highligh he buil-in proecion of his invesmen sraegy, he level of he floor is displayed. 7
Exhibi 2: Absolue Reurn Fund: Evoluion of he Core, he Saellie, and he DCS porfolios 190 170 150 130 110 90 70 50 12-1998 06-1999 12-1999 06-2000 12-2000 06-2001 12-2001 06-2002 12-2002 06-2003 12-2003 06-2004 12-2004 06-2005 12-2005 06-2006 12-2006 06-2007 12-2007 Core Saellie DCS Floor From his exhibi, a number of conclusions can be drawn. The dynamics of he core porfolio confirm he conservaive characer of he core invesmen. However, we also see ha performance of he bond core was quie fla over he las wo years of he period. For he saellie porfolio, we observe ha reurns are higher if we look a he enire period. More imporanly, flucuaions of he value of he saellie porfolio are remendous, wih a sharp increase in value up o he year 2000 and a radical decline from hen unil 2003, followed again by a seady increase unil he end of 2007. The dynamic core saellie (DCS) combines he advanages of each of is ingrediens ha is, he smooh performance of he bond core and he upside poenial of he equiy saellie. As a resul, performance is smooh over he enire period, and cumulaive reurns a he end of he period are acually higher han hose of he saellie. I is also ineresing o look a he dynamics of he floor. As he value of he dynamic core-saellie fund increases, he floor is pulled up o increase he level of proecion. I is also insrucive o look a he performance in he sock marke downurn beginning in he year 2000. In fac, he dynamic core-saellie porfolio is lile affeced. As he porfolio value approaches he floor, he allocaion is shifed o he core porfolio. This behaviour is illusraed in exhibi 3, which shows he weighs held in he core and he saellie over ime. 8
Exhibi 3: Absolue Reurn Fund: Evoluion of he Allocaion o he Core and he Saellie Porfolios 100% Allocaion o he core 80% 60% 40% 20% Allocaion o he saellie 0% 12-1998 06-1999 12-1999 06-2000 12-2000 06-2001 12-2001 06-2002 12-2002 06-2003 12-2003 06-2004 12-2004 06-2005 12-2005 06-2006 12-2006 06-2007 12-2007 I is imporan o recall he objecive of he sraegy analysed here. The conservaive naure of he core and he dynamic risk managemen process boh aim o achieve smooh reurns over ime. Exhibi 4 shows he reurn obained over rolling periods of one year. From his exhibi, we see ha he dynamic core-saellie porfolio achieves posiive reurns over mos rolling windows of one year. Even in he period afer he year 2000, reurns are close o zero, hough slighly negaive. In fac, he maximum loss over a one-year rolling period is -6.68%. This is in sark conras o he saellie, which displays reurns below -20% over a range of annual periods. In fac, he behaviour of he dynamic core-saellie porfolio is close o ha of he defensive bond porfolio ha makes up he core. Exhibi 4: Absolue Reurn Fund: Performance of he Core, he Saellie, and he DCS over a One-Year Rolling Period 50% 25% 0% -25% -50% 12-1999 06-2000 12-2000 06-2001 12-2001 06-2002 12-2002 06-2003 12-2003 06-2004 12-2004 06-2005 12-2005 06-2006 12-2006 06-2007 12-2007 Core Saellie DCS 9
Risk and reurn saisics for he dynamic core-saellie sraegy confirm he conclusions from he figures analysed above. In paricular, exhibi 5 shows ha he average reurn exceeds hose of he core by roughly 337 basis poins, while mainaining low levels of risk. Exhibi 5: Absolue Reurn Fund: Risk and Reurn Saisics for he Core, he Saellie, and he DCS. Average reurn* Max DD Volailiy* VaR** CVaR** Sharpe*** Core 4.00% -3.08% 2.40% 0.83% 1.15% 0.83 Saellie 5.16% -59.90% 18.41% 8.56% 12.90% 0.17 DCS - base case 7.37% -9.01% 6.42% 1.97% 2.57% 0.84 * annualised saisics are given ** non-annualised 5%-quaniles are esimaed *** risk-free rae and MAR are fixed a 2% 3. A comparison wih acive managemen based on reurn forecass. We have seen ha he dynamic risk-budgeing approach is able o provide sound absolue reurn managemen. The remarkable rai of he approach is he absence of any predicion. The sysemaic allocaion based on pas values of he core and saellie porfolios means ha he invesor bears no forecasing risk. An alernaive is o forecas he relaive reurns of he saellie. If he saellie is expeced o have higher reurns han he core, he weigh of he saellie should be increased; oherwise, i should be decreased. Predicions may be founded eiher on an economeric process or on qualiaive assessmen by he manager or an ouside exper. Of course, performance will depend on he accuracy of predicions. If he predicions are accurae mos of he ime, we expec he porfolio o display aracive performance. In his secion, we firs assess he performance displayed by a manager wih posiive predicion skill and hen analyse how he resuls change if we increase his skill. The deailed seup of he analysis is as follows. The assumpions below are used in a simulaion of an acive manager s approach: - if he manager hinks ha he saellie will ouperform he core on he following monh, he will allocae 60% of his porfolio o he saellie, he maximum allowed in he dynamic risk-budgeing process above. The remaining 40% is allocaed o he saellie - if he manager hinks ha he core will ouperform he saellie on he following monh, he will allocae 100% of he porfolio o he core - he manager rebalances his holdings on a monhly basis and, on average, is righ seven of every welve monhs Using he same ime period as above (January 1999 o December 2007) and he same core and saellie, we simulae 1,000 scenarios. Each scenario corresponds o a ime series of reurns for he acive manager, given his bes. As he basis for he simulaion, we use a hi raio of 58.3%, i.e., he average acive manager is righ, on average, seven of every welve monhs. The 1,000 scenarios hus represen he reurns obained by 1,000 hypoheical acive managers who have a hi raio of 58.3%. Exhibi 6 displays risk and reurn saisics for he average over hese 1,000 scenarios and compares hem o he base case sraegy from above, i.e., he dynamic core-saellie sraegy. The average over all scenarios corresponds o an equal-weighed porfolio of he 1,000 acive managers. The firs wo lines of able 4 reproduce he saisics for he core and he saellie porfolio. I is insrucive o compare he ime series of he acive manager porfolio o he series of he dynamic coresaellie sraegy. The average annualised reurn of he dynamic core saellie (7.37%) is slighly higher han ha for his porfolio (7.25%). Moreover, he maximum drawdown, volailiy, VaR, and CVaR are significanly lower for he dynamic core saellie. The higher risk saisics for he porfolio of acive managers show he impac of bad predicions. In fac, even hough hese managers are righ mos of he ime, hey err five monhs per year, hus exposing he invesor o a significan downside risk. This resul holds for he equal-weighed porfolio ha is diversified across 1,000 managers. Using a single manager wih he same abiliy leads o greaer uncerainy, as resuls may be much beer or much worse. Firs, he resuls obained by a single manager depend on he acual hi raio displayed over he sample period as 10
opposed o his rue long-erm hi raio. Second, given a realised hi raio, porfolio performance depends on he consequences of his correc or wrong predicions. Predicing ouperformance over a monh during which he saellie underperforms by 1% is hardly he same as predicing ouperformance over a monh during which he saellie underperforms by 10%, even hough boh are insances of forecas error. Likewise, predicing ouperformance over a monh during which he saellie ouperforms by 10% is more valuable han predicing ouperformance over a monh during which he saellie ouperforms by 1%, hough boh are insances of an accurae forecas. The dispersion beween managers wih he same forecasing abiliy is shown in he lower par of able 4. The wors performing manager (or scenario) achieves average annualised reurns of 0.64% while he bes manager achieves 13.35%. Likewise, maximum drawdown and oher risk measures vary widely from one manager or scenario o anoher. Exhibi 6: Risk and Reurn Saisics for he Core, he Saellie and he Acive Managemen Scenarios. Average reurn Max DD Volailiy* VaR** CVaR** Sharpe*** Core 4.00% -3.08% 2.40% 0.83% 1.15% 0.83 Saellie 5.16% -59.90% 18.41% 8.56% 12.90% 0.17 DCS - base case 7.37% -9.01% 6.42% 1.97% 2.57% 0.84 Average of 1000 scenarios 7.25% -14.72% 7.60% 2.84% 5.36% 0.70 Wors performing scenario 0.64% -29.61% 8.12% 4.16% 6.44% -0.17 Bes performing scenario 13.35% -2.81% 6.25% 0.76% 1.53% 1.81 * annualized figures ** 5% quarile *** RFR = 2% Overall, he resuls show ha an acively managed porfolio buil on largely accurae forecass lead o resuls worse han hose of he dynamic core-saellie process. Moreover, if a single manager is chosen, here is an addiional risk. In fac, a given manager may produce poor resuls despie his forecasing abiliy. I is ineresing o examine he parameer for forecas abiliy in greaer deail. However, i is no our objecive o make a saemen abou which degree of forecas accuracy is realisic or how correc forecass can be obained. Raher, i is ineresing o assess he resuls assuming even higher hi raios. Above, we have assumed a hi raio of 58.3%. Below, we repea he simulaion using average hi raios of 7/12, 8/12, 9/12, 10/12, and 11/12. In paricular, we simulae he same acive managemen approach wih increasing hi raios and observe he hi raio necessary o achieve he same maximum level of risk (maximum drawdown and wors performance over a rolling one-year period) and he same probabiliy of no losing more han 10% of he capial over a one-year period. Exhibi 7 shows he resuls. Exhibi 7: Evoluion of he Risk and Reurn Saisics as a Funcion of he Hi raio of he Acive Manager Hi raio DCS 7/12 8/12 9/12 10/12 11/12 Average reurn 7.37% 7.25% 10.02% 12.85% 15.75% 18.68% Max DD -9.01% -14.72% -11.70% -9.18% -7.08% -4.71% Worse performance over a rolling one year period -6.68% -30.5% -30.5% -24.7% -19.0% -11.4% Probabiliy of losing more han 10% on a rolling one year period 0.00% 3.02% 1.29% 0.38% 0.11% 0.00% The resuls show ha a hi raio of seven ou of welve is necessary o generae reurns ha are equivalen o hose of he dynamic core-saellie approach. To obain a maximum drawdown equal o ha of he dynamic coresaellie approach, a hi raio of nine ou of welve is necessary. If we look a he probabiliy of losing more han 10% of capial over a one-year period, he necessary hi raio is eleven ou of welve. I should be noed ha he resuls in able are for he equal-weighed porfolio of 1,000 hypoheical managers. The addiional risk of manager selecion borne by an invesor who akes such an approach is hus ignored. Conclusion We have argued ha he core-saellie approach can be exended o dynamic invesmen of a porfolio of ETFs, allowing invesors o proec heir porfolio from excessive loss. Our applicaion of dynamic core-saellie porfolio managemen shows ha i makes i possible o use ETFs on sock and bond indices o consruc 11
absolue reurn funds based on his dynamic allocaion approach. In paricular, he approach makes i possible o shake off he dependence on forecas accuracy ha radiional echniques for absolue reurn fund consrucion are saddled wih. In shor, for generaing absolue reurns, dynamic risk-budgeing echniques are a more reliable alernaive, even if one has managers wih excellen forecasing abiliy a one s disposal. As a resul of he ease wih which hey are raded, ETFs make an ideal vehicle for puing such dynamic risk budgeing ino pracice. The combinaion of advanced dynamic risk-budgeing echniques and highly liquid and ransparen insrumens may provide a more invesor-friendly way o deliver a given absolue reurn wih a arge level of volailiy, independen of prevailing marke condiions. References Amenc, N., P. Malaise, and L. Marellini, 2004, Revisiing Core-Saellie Invesing A Dynamic Model of Relaive Risk Managemen, Journal of Porfolio Managemen, vol. 31, no. 1, 64-75. Black, F., and R. Jones, 1987, Simplifying Porfolio Insurance, Journal of Porfolio Managemen, vol. 14, fall, 48-51. Black, F., and A. Perold, 1992, Theory of Consan Proporion Porfolio Insurance, Journal of Economic Dynamics and Conrol, vol. 16, 403-426. Cvianic, J., and I. Karazas, 1995, On Porfolio Opimizaion under Drawdown Consrains, IMA Volumes in Mahemaics and is Applicaions, 65, 35-46. EDHEC, 2008, European Invesmen Pracices Survey. Engle, Rober, 2002, Dynamic Condiional Correlaion A Simple Class of Mulivariae GARCH Models, Journal of Business and Economic Saisics, vol. 20, no. 3. Esed T., and M. Krizman, 1988, TIPP: Insurance wihou Complexiy, Journal of Porfolio Managemen, Grossman, S. J., and Z. Zhou, 1993, Opimal Invesmen Sraegies for Conrolling Drawdowns, Mahemaical Finance, vol. 3, no. 3, 241-276. Longin F., and B. Solnik, 1995, Is he Correlaion in Inernaional Equiy Reurns Consan? Journal of Inernaional Money and Finance, vol. 14, 3-26. Meron, R. C., 1973, An Ineremporal Capial Asse Pricing Model, Economerica, 41, 867-888. 12