E D H E C I S K A N D A S S E T M A N A G E M E N T E S E A C H C E N T E erformance Measuremen for Tradonal Invesmen Leraure Survey January 007 Véronque Le Sourd Senor esearch Engneer a he EDHEC sk and Asse Managemen esearch Cenre
Table of conens Inroducon... 5. orfolo reurns calculaon... 6.. Basc formula... 6.. Takng capal flows no accoun... 6.3. Evaluaon over several perods...0.4. Choce of frequency o evaluae performance.... Absolue rsk-adjused performance measures...3.. Sharpe rao (966)...3.. Treynor rao (965)...3.3. Measure based on he Va...4 3. elave rsk-adjused performance measures...5 3.. Jensen s alpha (968)...5 3.. Exensons o Jensen s alpha...5 3.3. Informaon rao...0 3.4. M² measure: Modglan and Modglan (997)... 3.5. Marke sk-adjused erformance (MA) measure: Scholz and Wlkens (005)... 3.6. SA measure: Lobosco (999)... 3.7. sk-adjused performance measure n mulmanagemen: M3 Muraldhar (000, 00)... 3.8. SHAAD: Muraldhar (00,00)...4 3.9. A Index: Afalon and once (99)...5 3.0. Graham-Harvey (997) measures...5 3.. Effcency rao: Canalupp and Hug (000)...5 3.. Invesor Specfc erformance Measuremen (ISM): Scholz and Wlkens (004)...6 4. Some new research on he Sharpe rao...7 4.. Crcs and lmaons of Sharpe rao...7 4.. Double Sharpe ao: Vnod and Morey (00)...7 4.3. Generalsed Sharpe rao: Dowd (000)...7 4.4. Negave excess reurns: Israelsen (005)...9 5. Measures based on downsde rsk and hgher momens... 3 5.. Acuaral approach: Melnkoff (998)...3 5.. Sorno rao...3 5.3. Fouse ndex...3 5.4. Upsde poenal rao: Sorno, Van der Meer and lannga (999)...3 5.5. Symmerc downsde-rsk Sharpe rao: Zemba (005)...3 5.6. Hgher momen measure of Hwang and Sachell (998)...3 5.7. Omega measure: Keang and Shadwck (00)...33 6. erformance measuremen mehod usng a condonal bea: Ferson and Schad (996)... 34 6.. The model...34 6.. Applcaon o performance measuremen...35 6.3. Model wh a condonal alpha...36 6.4. The conrbuon of condonal models...37 7. erformance analyss mehods ha are no dependen on he marke model...38 7.. The Cornell measure (979)...38 7.. The Grnbla and Tman measure (989a, b): osve erod Weghng Measure...38 7.3. erformance measure based on he composon of he porfolo: Grnbla and Tman sudy (993)...39 7.4. Measure based on levels of holdngs and measure based on changes n holdngs: Cohen, Coval and asor (005)...39 8. Facor models: more precse mehods for evaluang alphas...4 8.. Explc facor models based on macroeconomc varables...4 8.. Explc facor models based on mcroeconomc facors (also called fundamenal facors)...4 8.3. Implc or endogenous facor models...43 8.4. Applcaon o performance measure...44 8.5. Mul-ndex models...45 9. erformance perssence...48 Concluson...56 Bblography...57 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
Absrac The number of professonally managed funds n he fnancal markes s ncreasng. The muual fund marke s hghly developed wh a wde range of producs proposed. The resulng compeon beween he dfferen esablshmens has served o srenghen he need for clear and accurae porfolo performance analyss, for whch porfolo reurn alone s no suffcen. Ths has led o he search for mehods ha would provde nvesors wh nformaon ha mees her expecaons and explans he ncreasng amoun of academc and professonal research devoed o performance measuremen. The opc of performance analyss s sll n expanson, meeng he needs of boh nvesors and porfolo managers. erformance measuremen brngs ogeher a whole se of echnques, many of whch orgnae n modern porfolo heory. Besde models ssued from porfolo heory, research n he area of performance measuremen has also concerned he consderaon of real marke condons and has developed echnques o f cases where he resrcve hypoheses of porfolo heory are no observed. Ths arcle presens he sae of he ar of performance measuremen n he area of radonal nvesmen, from a smple evaluaon of porfolo reurn o he more sophscaed echnques ncludng rsk n s varous accepaons. I also descrbes models ha ake a sep away from modern porfolo heory and allow a consderaon of cases beyond mean-varance heory. I concludes wh a revew of performance perssence sudes. erformance Measuremen for Tradonal Invesmen Leraure Survey 3
Abou he auhor Véronque Le Sourd has a Maser s Degree n Appled Mahemacs from he erre and Mare Cure Unversy n ars. From 99 o 996, she worked as research asssan whn he Fnance and Economcs deparmen of he French busness school, HEC, and hen joned he research deparmen of Msys Asse Managemen Sysems n Sopha Anpols. She s currenly a senor research engneer a he EDHEC sk and Asse Managemen esearch Cenre. 4 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
Inroducon The number of professonally managed funds n he fnancal markes s ncreasng. The muual fund marke s hghly developed wh a wde range of producs proposed. The resulng compeon beween he dfferen esablshmens has served o srenghen he need for clear and accurae porfolo performance analyss. Invesors wsh o aval of all he nformaon necessary o carry ou manager selecon over comparable bases. They wan o know f managers have succeeded n reachng her objecves,.e. f her reurn was suffcenly hgh o reward he rsks aken, how hey compare o her peers and, fnally, wheher he porfolo managemen resuls were due o luck or because he manager has real skll ha can be denfed and repeaed n he fuure. The porfolo reurn alone does no allow all hese quesons o be answered. Ths has led o he search for mehods ha would provde nvesors wh nformaon ha mees her expecaons and explans he ncreasng amoun of academc and professonal research devoed o performance measuremen. The opc of performance analyss s sll n expanson, meeng he needs of boh nvesors and porfolo managers. erformance measuremen brngs ogeher a whole se of echnques, many of whch orgnae n modern porfolo heory. erformance evaluaon s closely lnked o rsk. Modern porfolo heory has esablshed he quanave lnk ha exss beween porfolo rsk and reurn. The Capal Asse rcng Model (CAM) developed by Sharpe (964) hghlghed he noon of rewardng rsk and produced he frs performance ndcaors, be hey rskadjused raos (Sharpe rao, nformaon rao) or dfferenal reurns compared o benchmarks (alphas). orfolo alpha measuremen s a he core of porfolo managers concerns. Sharpe s model, whch explans porfolo reurns wh he marke ndex as he only rsk facor, has quckly become resrcve. I now appears ha one facor s no enough and ha oher facors have o be consdered. Facor models were developed as an alernave o he CAM, allowng a beer descrpon of porfolo rsks and an accurae evaluaon of managers performance, n parcular a beer evaluaon of porfolo alpha. Besde models ssued from porfolo heory, research n he area of performance measuremen has also concerned he consderaon of real marke condons and has developed echnques o f cases where he resrcve hypoheses of porfolo heory were no observed. The choce of a performance measuremen echnque has o reconcle he ease of mplemenaon and he accuracy and comprehensbly of he resulng nformaon. In order o render hs nformaon accessble o a wde audence, rang agences, by relyng on dfferen performance echnques, propose a rankng of funds whn he varous nvesmen caegores, whereby a ceran number of sars s arbued o each fund. Ths aspec of performance measuremen, whch was he subjec of a separae sudy, wll no be presened here. Afer a descrpon of porfolo reurns esmaon, hs arcle presens he sae of he ar of performance measuremen n he area of radonal nvesmen. As performance measuremen no only serves o evaluae resuls prevously obaned by porfolo managers, bu also as a predcor for her fuure resuls, a revew of sudes concernng performance perssence wll end hs arcle. - To replace he developmen of performance measuremen echnques n he seng of porfolo heory, please refer o Amenc and Le Sourd (003). - Cf. Amenc N., Le Sourd V., ang he angs, EDHEC sk and Asse Managemen esearch Cenre, Aprl 005. erformance Measuremen for Tradonal Invesmen Leraure Survey 5
. orfolo reurns calculaon Calculang reurn, whch s smple for an asse or an ndvdual porfolo, becomes more complex when nvolves muual funds wh varable capal, where nvesors can ener or leave hroughou he nvesmen perod. There are several ways o proceed, dependng on he area ha we are seekng o evaluae. Afer nroducng he basc formula for calculang he reurn on a porfolo, we hen descrbe he dfferen mehods ha allow capal movemens o be aken no accoun, wh her respecve advanages and drawbacks and her mprovemens. In he seng of performance measuremen, he frequency o whch he porfolo s evaluaed s also an mporan choce. Ths wll be developed a he end of hs secon... Basc formula The smples mehod for calculang he reurn on a porfolo for a gven perod s obaned hrough an arhmec calculaon. We calculae he relave varaon of he prce of he porfolo over he perod, ncreased, f applcable, by he dvdend paymen. The reurn of he porfolo s gven by: V V V + where: V denoes he value of he porfolo a he begnnng of he perod; V denoes he value of he porfolo a he end of he perod; D denoes he cash flows generaed by he porfolo durng he evaluaon perod. However, hs formula s only vald for a porfolo ha has a fxed composon hroughou he evaluaon perod. In he area of muual funds, porfolos are subjec o conrbuons and whdrawals of capal on he par of nvesors. Ths leads o he purchase and sale of secures on he one hand, and o an evoluon n he volume of capal managed, whch s ndependen from varaons n sock marke prces, on he oher. The formula mus herefore be adaped o ake hs no accoun. The modfcaons o be made wll be presened below. D.. Takng capal flows no accoun Calculaon mehods have been developed o ake no accoun he volume of capal and he me ha capal s presen n a porfolo. The mehods ha are currenly lsed and used are he nernal rae of reurn, he capalweghed rae of reurn and he me-weghed rae of reurn. Each of hese mehods evaluaes a dfferen aspec of he reurn. These mehods are presened n deal below. We hen look a how hese varous mehods are perceved and used hrough he analyss of varous and somemes conflcng vewpons conaned n he academc leraure.... Capal-weghed rae of reurn mehod Ths rae s equal o he relaonshp beween he varaon n value of he porfolo durng he perod and he average of he capal nvesed durng he perod. Le s frs consder he case where a sngle capal flow s produced durng he perod. The calculaon formula s as follows: VT V0 C CW V0 + C where: V denoes he value of he porfolo a he 0 begnnng of he perod; VT denoes he value of he porfolo a he end of he perod; C denoes he cash flow ha occurred a dae, where C s posve f nvolves a conrbuon and negave f nvolves a whdrawal. Ths calculaon s based on he assumpon ha he conrbuons and whdrawals of funds ake place n he mddle of he perod. A more accurae mehod nvolves akng he real lengh of me ha he capal was presen n he porfolo. The calculaon s hen presened as follows: VT V0 C CW T V0 + C T where T denoes he oal lengh of he perod. 6 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
. orfolo reurns calculaon Le s now assume ha here are n capal flows durng he evaluaon perod. The formula s hen generalsed n he followng manner: CW T + V n V V 0 0 n C T C T where denoes he dae on whch he h cash flow C occurs. Ths calculaon mehod s smple o use, bu acually calculaes an approxmae value of he rue nernal rae of reurn of he porfolo, because does no ake he capalsaon of he conrbuons and whdrawals of capal durng he perod no accoun. If here are a large number of capal flows, he nernal rae of reurn, whch s presened below, wll be more precse. The advanage of hs mehod, however, s ha provdes an explc formulaon of he rae. The capal-weghed rae of reurns measures he oal performance of he fund, so provdes he rue rae of reurn from he fund holder s perspecve. The resul s srongly nfluenced by capal conrbuons and whdrawals.... Inernal rae of reurn mehod Ths mehod s based on an acuaral calculaon. The nernal rae of reurn s he dscoun rae ha renders he fnal value of he porfolo equal o he sum of s nal value and he capal flows ha occurred durng he perod. The cash flow for each sub-perod s calculaed by akng he dfference beween he ncomng cash flow, whch comes from he renvesmen of dvdends and clen conrbuons, and he ougong cash flow, whch resuls from paymens o clens. The nernal rae of reurn I s he soluon o he followng equaon: V 0 + n C ( + ) I VT ( + ) I T where: T denoes he lengh of he perod n years (hs perod s dvded no n sub-perods); denoes he cash flow daes, expressed n years, over he perod; V 0 s he nal value of he porfolo; VT s he fnal value of he porfolo; C s he cash flow on dae, whdrawals of capal are couned negavely and conrbuons posvely. As he formula s no explc, he calculaon s done eravely. The nernal rae of reurn only depends on he nal and fnal values of he porfolo. I s herefore ndependen from he nermedae porfolo values. However, does depend on he sze and daes of he cash flows, so he rae s, agan, a capal-weghed rae of reurn. The nernal rae of reurn mehod allows us o oban a more precse resul han he capalweghed rae of reurn when here are a sgnfcan number of capal flows of dfferen szes, bu akes more me o mplemen. The capal-weghed rae of reurn and he nernal rae of reurn are he only usable mehods f he value of he porfolo s no known a he me he funds are conrbued and whdrawn...3. Tme-weghed rae of reurn mehod The prncple of hs mehod s o break down he perod no elemenary sub-perods, durng whch he composon of he porfolo remans fxed. The reurn for he complee perod s hen obaned by calculang he geomerc mean of he reurns calculaed for he sub-perods. The resul gves a mean reurn weghed by he lengh of he sub-perods. Ths calculaon assumes ha he dsrbued cash flows, such as dvdends, are renvesed n he porfolo. We ake a perod of lengh T durng whch capal movemens occur on daes ( ) n. We denoe he value of he porfolo jus before a capal movemen by V and he value of he cash flow by C. C s posve f nvolves a conrbuon and negave f nvolves a erformance Measuremen for Tradonal Invesmen Leraure Survey 7
. orfolo reurns calculaon whdrawal. The reurn for a sub-perod s hen wren as follows: V ( V + ) C V + C Ths formula ensures ha we compare he value of he porfolo a he end of he perod wh s value a he begnnng of he perod,.e. s value a he end of he prevous perod ncreased by he capal pad or decreased by he capal whdrawn. The reurn for he whole perod s hen gven by he followng formula: / T n TW ( + ) Ths calculaon mehod provdes a rae of reurn per dollar nvesed, ndependenly of he capal flows ha occur durng he perod. The resul depends solely on he evoluon of he value of he porfolo over he perod. Gray and Dewar (97) show ha he me-weghed rae of reurn s he only well-behaved rae of reurn ha s no nfluenced by conrbuons or whdrawals. To mplemen hs calculaon, we need o know he value and he dae of he cash flows, ogeher wh he value of he porfolo a each of he daes. There s one small reservaon, however, when applyng hs mehod. To smplfy maers, we ofen assume ha he cash flows all occur a he end of he monh, nsead of consderng he exac daes. In hs case, he use of a connuous verson of he rae smoohes he errors commed. I s gven by he followng formula: n + V V T rtw ln ln T V0 V + C The me-weghed rae of reurn enables a manager o be evaluaed separaely from he movemens of capal, whch he does no conrol. Ths rae only measures he mpac of he manager s decsons on he performance of he fund. I s hus he bes mehod for judgng he qualy of he manager. I allows he resuls of dfferen managers o be compared objecvely. I s consdered o be he fares mehod, and for ha reason, s recommended by GIS and used by he nernaonal performance measuremen bodes...4. Choce of mehodology The exsence of several mehods for calculang reurns, whch gve dfferen resuls, shows ha a reurn value should always be accompaned by more nformaon. I s approprae o ndcae he calculaon mehod used, ogeher wh he oal lengh of me for he hsorcal daa and he frequency wh whch he reurns were measured. In he seng of performance evaluaon and performance arbuon, he decson o ake no accoun he movemens of capal depends on wha s measured. Several auhors have consdered he varous mehods of evaluang he rae of reurns. Chesopalov and Belaev (004/005) descrbe an analycal approxmaon mehod for calculang he nernal rae of reurn. They show ha approxmaon of he I equaon usng lnear Taylor expanson a a pon wh zero rae of reurn resuls n a Modfed Dez formula, boh for dscree and connuous compoundng. Ths means ha separaon of performance measuremen mehods no money-weghed and me-weghed raes of reurn s somewha arfcal. In fac, he me-weghed rae of reurn presenly adoped as he CFA Insue sandard s derved from he money-weghed rae of reurn as a parcular approxmaon. Spauldng (003) also seems o share he opnon ha he boundary beween me-weghed and money weghed compuaon can somemes be slm. He noces ha when perods are relavely shor and cash flows few, especally when marke volaly s low, me-weghed and moneyweghed end o be relavely close. Bu, as we 8 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
. orfolo reurns calculaon lenghen he me perods and ncrease he cash flows, especally wh ncreased marke volaly, he dfferences dverge and demonsrae he rue dfferences beween he wo mehodologes. Camps (004) explans ha performance arbuon has evolved n parallel wh performance measuremen by accepng he me-weghed reurn as he preferred calculaon mehod. In addon, he nvesmen ndusry has acceped he assumpon ha ncreasng he frequency of calculaon leads o mproved accuracy n boh he calculaon and arbuon of reurn. These assumpons have led o he wholesale abandonmen of he money-weghed reurn calculaon, boh for performance measuremen and performance arbuon. He argues ha whle here s an rrefuable case for accepng he me-weghed reurn as he preferred mehod for measurng he reurn of an nvesmen manager, here s an equally compellng case for accepng he moneyweghed reurn as he approprae mehod for evaluang he source of acve reurn,.e. ha he money-weghed reurn s he correc mehod for performance arbuon. He noces ha me-weghed mehodology canno explan he acve nvesmen process as excludes he very facors ha defne he acve nvesmen process,.e. volaly, he mng of cash flows and he amoun of cash flows. Tme-weghng s approprae for calculang he acve reurn, whle money-weghng s approprae for analysng he manager s conrbuon o reurn and arbuon reurn. Accordng o Camps, an added benef of a money-weghed mehodology s he nuve naure of he calculaon. The porfolo s excess reurn s smply he weghed average of he ssue alphas or secor alphas, and hese can be slced and dced o accommodae a varey of secor and ndusry groupngs, syle groupngs or oher rsk facors ha descrbe he acve process or answer he clen s quesons. Furhermore, perods of less han one year can be calculaed n a sngle sep, elmnang he need o chan lnk arbuon effecs calculaed over shorer perods, a process ha ofen resuls n resduals ha are dffcul o resolve or explan o clens. Meanwhle, Camps underlnes ha he does no recommend he money-weghed mehodology for calculang he manager s reurn; he recommends money-weghng only for evaluang he conrbuon o reurn and arbuon of reurn. Illmer and Mary (003) defend he moneyweghed rae of reurn agans he meweghed rae of reurn (TW). They decompose he money-weghed rae of reurn (MW) no he hree followng effecs: he benchmark effec, he managemen effec and he mng effec. The TW of he porfolo s calculaed by assumng no cash flows bu consderng he acve asse allocaons over he nvesmen perod. Adversely, he MW of he porfolo reflecs no only he acve asse allocaons bu also he mng effecs of he cash flow decsons. Afer calculang he overall reurns of he benchmark and he porfolo, he benchmark effec equals he benchmark reurn, he managemen effec s he dfference beween he TW of he porfolo and he benchmark reurn, and he mng effec s he dfference beween he MW and TW of he porfolo. Illmer and Mary show ha neher he MW calculaon nor he MW decomposon should be negleced bu raher ncorporaed no he performance reporng and evaluaon process. No consderng he MW concep and gnorng he mng effecs of cash flows bears he rsk of msnerpreaon and ncorrec feedback n he nvesmen process. The MW concep sll adds value and s by no means oudaed. All parcpans are encouraged o renroduce he MW concep o he area of performance measuremen as well as o he area of performance arbuon. erformance Measuremen for Tradonal Invesmen Leraure Survey 9
. orfolo reurns calculaon.3. Evaluaon over several perods.3.. Arhmec mean The smples calculaon nvolves compung he arhmec mean of he reurns for he subperods,.e. calculang: T a T where he are obaned arhmecally and T denoes he number of sub-perods. We hus oban he mean reurn realsed for a subperod. Ths mean overesmaes he resul, whch can even be farly far removed from he realy when he sub-perod reurns are very dfferen from each oher. The resul also depends on he choce of sub-perods. The arhmec mean of he reurns from pas perods does, however, have one neresng nerpreaon. I provdes an unbased esmae of he reurn for he followng perod. I s herefore he expeced reurn on he porfolo and can be used as a forecas of s fuure performance..3.. Geomerc mean The geomerc mean (or compound geomerc rae of reurn) allows us o lnk he arhmec raes of reurn for he dfferen perods, n order o oban he real growh rae of he nvesmen over he whole perod. The calculaon assumes ha nermedae ncome s renvesed. The mean rae for he perod s gven by he followng expresson: / T T g ( + ) The geomerc mean gves he real rae of reurn ha s observed over he whole perod, whch s no rue of he arhmec mean. In general, he reurn values for successve perods are no oo dfferen, and he arhmec mean and geomerc mean gve smlar resuls. However, he arhmec mean always gves a value ha s greaer han he geomerc mean, unless he reurns are all equal, n whch case he wo means are dencal. The greaer he varaon n, he greaer he dfference beween he wo means. We ndcaed ha he arhmec mean was nerpreed as he expeced reurn for he followng perod. However, f we are neresed n he expeced reurn over he long-erm, and no jus n he forhcomng perod, s beer o consder he geomerc rae. Accordng o Flbeck and Tompkns (004), geomerc reurns are he approprae measure of hsorcal performance because hey accuraely capure hsorc volaly. Assumng ha pas volaly s a predcor of fuure volaly, geomerc reurns provde a reasonable esmae of fuure reurns..3.3. Arhmec mean versus geomerc mean: wha he leraure says Jacquer, Kane and Marcus (003) nvesgaed wheher one should use arhmec or geomerc mean o forecas fuure fund performance. They explan ha, as s generally noed n fnance exbooks, an unbased forecas of he ermnal value of a porfolo requres compoundng of s nal value a s arhmec mean reurn for he lengh of he nvesmen perod. Despe hs advce, many n he praconer communy seem o prefer geomerc averages. They noce ha compoundng a he arhmec average always produces an upwardly based forecas of fuure porfolo value. Ths bas does no necessarly dsappear even f he sample average reurn s self an unbased esmaor of he rue mean, he average s compued from a long daa seres, and reurns are generaed accordng o a sable dsrbuon. In conras, forecass obaned by compoundng a he geomerc average wll generally be based downward. The bases are emprcally sgnfcan. For nvesmen horzon of 40 years, he dfference n forecass of cumulave performance can easly exceed a facor of. And he percenage dfference n forecass grows wh he nvesmen horzon, as well as wh he mprecson n he esmae of 0 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
. orfolo reurns calculaon he mean reurn. Indeed, he geomerc average s unbased, however, only n he specal case when he sample perod and he nvesmen horzon are of equal lengh. So hey conclude ha, when he arhmec and geomerc averages mus be esmaed subjec o samplng error, neher approach yelds unbased forecass. For ypcal nvesmen horzons, he proper compoundng rae s n beween he arhmec and geomerc values. A weghed average of hese wo compeng mehods may allow an unbased forecas. The proper wegh for he geomerc rae s he rao of he nvesmen horzon o he sample esmaon perod. Therefore, for shor nvesmen horzons, he arhmec average s close o he unbased compoundng rae, and as he horzon approaches he lengh of he esmaon perod, he wegh on he geomerc average approaches. For even longer horzons, boh he geomerc and arhmec average forecass wll be upwardly based. The percenage dfferences n forecas grow as he nvesmen horzon and he mprecson n he esmae of he mean reurn grow..4. Choce of frequency o evaluae performance The mprovemens n echnology have made easer o monor he performance of fund managers on a hgh frequency bass: quarerly, monhly or even daly. Hgh frequency monorng may have he posve effec of reducng perverse manager behavour such as end-of-year wndowdressng and ournamen-nduced changes n rsk levels. However, more frequen nvesmen performance monorng also nfluences he dsrbuon of observed excess reurns. So an overly frequen measure of performance s no always he bes choce, as has been underlned by some auhors. DBarolomeo (003) noces ha n recen years has become more and more commonplace for nvesmen performance arbuon analyss o be carred ou wh a daly observaon perodcy. He explans ha he jusfcaon gven for changng o daly observaon frequency from longer perods (such as monhs) s ha hese analyses are beleved o be beer equpped o accuraely reflec he acual nvesmen reurns on a fund. Bu, DBarolomeo argues, such belefs are based on a seres of operaonal, mahemacal and sascal assumpons ha are demonsrably false. He assers ha applyng ypcal arbuon mehods o daly daa leads o analycal conclusons ha are hghly based and unrelable and deals hs argumen. For example, manager evaluaon s normally performed usng me-weghed reurns (TW) ha are compued o remove he effec of cash flows. As he effec of cash flows n he daa s removed, daly arbuon analyss s no useful o nvesors n undersandng her acual nvesmen resuls. Ths argumen s also developed by Darlng and MacDougall (00), who explan ha here s nformaon los by usng a TW, and he more frequenly he TW s calculaed, he more nformaon may be los. In ha case, daly analyss can be regarded as less useful han monhly analyss. Moreover, lack of synchronzaon over a sngle day would cause an ndex fund o exhb spurous acve reurns where none acually exsed. Mos problems of hs ype dsappear n he case of monhly observaon. Anoher argumen agans measurng performance wh excessvely hgh frequency s relaed o he mperfecons of he assumpons made upon he asse reurns (nvesmen reurns are normally dsrbued; me seres of reurns are dencally dsrbued; here s no seral correlaon beween nvesmen reurns). Academc leraure llusraes ha he mperfecon of he assumpons wh respec o quarerly or monhly reurn daa s small, whle for daly daa hese assumpons are rejeced. For example, Dmson and Jackson (00) examned he mpac ha frequency of performance measuremen has on he probably dsrbuon of observed oucomes. Wh more frequen monorng of rollng reurns, here s a grealy ncreased probably of observng seemngly erformance Measuremen for Tradonal Invesmen Leraure Survey
. orfolo reurns calculaon exreme observaons. They demonsraed ha f performance s apprased by focusng on reurns o dae, s mporan o adjus he defnon of exreme performance for he frequency wh whch reurns are monored. Falure o do so may lead o cosly acons such as sraegy revsons or manager ermnaons, whch ncrease ransacon coss and have dermenal effecs on manager ncenves. Marsh (99) also pons ou ha he danger wh hgh-frequency monorng s he way mgh be used by nvesors who do no undersand how o nerpre such fgures. Judgemens abou manager skll may be dsored by frequen monorng. So s mporan ha nvesors recognze he mpac of hgh frequency monorng on he frequency wh whch hey observe seemngly exreme performance evens. erformng ndusry-sandard arbuon procedures on a daly bass may lead o analycal conclusons ha are lkely o be based and unrelable, leadng o napproprae managemen acons wh respec o nvesmen porfolos. EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
. Absolue rsk-adjused performance measures These measures evaluae funds rsk-adjused reurns, whou any reference o a benchmark... Sharpe rao (966) Ths rao, nally called he reward-o-varably rao, s defned by: S E ( ) F σ ( ) where: E ( ) denoes he expeced reurn of he porfolo; F denoes he reurn on he rsk-free asse; σ ( ) denoes he sandard devaon of he porfolo reurns. Ths rao measures he reurn of a porfolo n excess of he rsk-free rae, also called he rsk premum, compared o he oal rsk of he porfolo, measured by s sandard devaon. I s drawn from he capal marke lne, and no he Capal Asse rcng Model (CAM). I does no refer o a marke ndex and s no herefore subjec o oll s (977) crcsm concernng he fac ha he marke porfolo s no observable. Snce hs measure s based on he oal rsk of he porfolo, made up of he marke rsk and he unsysemac rsk aken by he manager, enables he performance of porfolos ha are no very dversfed o be evaluaed. Ths measure s also suable for evaluang he performance of a porfolo ha represens an ndvdual s oal nvesmen. Ths rao has been subjec o generalsaons snce was nally defned. I hus offers sgnfcan possbles for evaluang porfolo performance, whle remanng smple o calculae. One of he mos common varaons on hs measure nvolves replacng he rsk-free asse wh a benchmark porfolo. The measure s hen called he nformaon rao (cf. Sharpe, 994) and wll be presened n he nex secon descrbng relave rsk-adjused measures... Treynor rao (965) The Treynor rao s defned by: E ( ) F T β where: E ( ) denoes he expeced reurn of he porfolo; F denoes he reurn on he rsk-free asse; β denoes he bea of he porfolo. Ths ndcaor measures he relaonshp beween he reurn on he porfolo, above he rskfree rae, and s sysemac rsk. Ths rao s drawn drecly from he CAM. Calculang hs ndcaor requres a reference ndex o be chosen o esmae he bea of he porfolo. The resuls can hen depend heavly on ha choce, a fac ha has been crcsed by oll. The Treynor rao s parcularly approprae for apprecang he performance of a well-dversfed porfolo, snce only akes he sysemac rsk of he porfolo no accoun,.e. he share of he rsk ha s no elmnaed by dversfcaon. I s also for hs reason ha he Treynor rao s he mos approprae ndcaor for evaluang he performance of a porfolo ha only consues a par of he nvesor s asses. Snce he nvesor has dversfed hs nvesmens, he sysemac rsk of hs porfolo s all ha maers. Srvasava and Essayyad (994) proposed Treynor s ndex, where bea s a compose measure generaed by combnng he expeced asse reurns from he radonal CAM and he mean-lower paral momen CAM. Ther argumen s ha a compose forecas s more accurae han separae forecass: valuable nformaon mssng from one model may be capured by he oher model. They esed hs measure on U.S.-based nernaonal funds and found ha he compose bea s a sascally sgnfcan and meanngful parameer. They also ranked he performance of he funds usng he Treynor ndex wh hree models (he CAM, he mean-lower paral momen CAM and a combnaon of he wo), bu her sample, whch erformance Measuremen for Tradonal Invesmen Leraure Survey 3
. Absolue rsk-adjused performance measures was made up of 5 funds, was oo small o es wheher he dfference n rankng obaned wh he dfferen models was sgnfcan..3. Measure based on he Va The Value-a-sk (Va) s an ndcaor ha enables o sum up he se of rsks assocaed wh a porfolo ha s dversfed over several asse classes n a sngle value. The Va measures he rsk of a porfolo as he maxmum amoun of he loss ha he porfolo can susan for a gven level of confdence. Ths defnon of rsk can be used o calculae a rsk-adjused reurn ndcaor for evaluang he performance of a porfolo. In order o defne a logcal ndcaor, we dvde he Va by he nal value of he porfolo and hus oban a percenage loss compared o he oal value of he porfolo. We hen calculae a Sharpe-lke ype of ndcaor n whch he sandard devaon s replaced wh he rsk ndcaor based on he Va, as was defned or: Va V 0 where: denoes he reurn on he porfolo; F denoes he reurn on he rsk-free asse; Va denoes he Va of he porfolo; V denoes he nal value of he porfolo. 0 Noe ha he calculaon of Va pre-supposes he choce of a confdence hreshold. So he Vabased raos for dfferen porfolos can only be compared for a same confdence level. F 4 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
3. elave rsk-adjused performance measures These measures evaluae funds rsk-adjused reurns n reference o a benchmark. 3.. Jensen s alpha (968) Jensen s alpha s defned as he dfferenal beween he reurn on he porfolo n excess of he rsk-free rae and he reurn explaned by he marke model, or: E ( ) F α + β ( E ( M ) F ) I s calculaed by carryng ou he followng regresson: α + β ( ) + ε F M F The Jensen alpha can be used o rank porfolos whn peer groups. eer groups group ogeher porfolos ha are managed n a smlar manner and herefore have comparable levels of rsk. The Jensen measure s subjec o he same crcsm as he Treynor measure: he resul depends on he choce of reference ndex. In addon, when managers pracce a marke mng sraegy, whch nvolves varyng he bea accordng o ancpaed movemens n he marke, he Jensen alpha ofen becomes negave, and does no hen reflec he real performance of he manager. erformance analyss models akng varaons n bea no accoun have been developed by Treynor and Mazuy and by Henrksson and Meron. The Jensen measure s based on he CAM. The erm β ( E ( M ) F ) measures he reurn on he porfolo forecas by he model. α measures he share of addonal reurn ha s due o he manager s choces. The sascal sgnfcance of alpha can be evaluaed by calculang he -sasc of he regresson, whch s equal o he esmaed value of he alpha dvded by s sandard devaon. Ths value s provded wh he resuls of he regresson. If he alpha values are assumed o be normally dsrbued, a -sasc greaer han wo ndcaes ha he probably of havng obaned he resul hrough luck, and no hrough skll, s srcly less han 5%. In hs case, he average value of alpha s sgnfcanly dfferen from zero. Unlke he Sharpe and Treynor measures, he Jensen measure conans he benchmark. As wh he Treynor measure, only he sysemac rsk s aken no accoun. Ths mehod, unlke he Sharpe and Treynor raos, does no allow porfolos wh dfferen levels of rsk o be compared. The value of alpha s acually proporonal o he level of rsk aken, measured by he bea. To compare porfolos wh dfferen levels of rsk, we can calculae he Black-Treynor rao 3 defned by: α β 3.. Exensons o Jensen s alpha 3... Jensen s alpha based on modfed versons of he CAM 3... Black s zero-bea model (97) Ths verson of he CAM was developed because wo of he model s assumpons were called no queson: he exsence of a rsk-free asse, and herefore he possbly of borrowng or lendng a ha rae, and he assumpon of a sngle rae for borrowng and lendng. Black showed ha he CAM heory was sll vald whou he exsence of a rsk-free asse, and developed a verson of he model by replacng wh an asse or porfolo wh a bea of zero. Insead of lendng or borrowng a he rsk-free rae, s possble o ake shor posons on he rsky asses. Wh he Black model, he alpha s characersed by: E ( ) E ( Z ) α + β ( E ( M ) E ( Z )) 3... Brennan s model (970) akng axes no accoun The basc CAM model assumes ha here are no axes. The nvesor s herefore ndfferen o recevng ncome as a dvdend or a capal 3 - Cf. Treynor and Black (973). erformance Measuremen for Tradonal Invesmen Leraure Survey 5
3. elave rsk-adjused performance measures gan and nvesors all hold he same porfolo of rsky asses. However, axaon of dvdends and capal gans s generally dfferen, and hs s lable o nfluence he composon of he nvesors porfolo of rsky asses. Takng hese axes no accoun can herefore modfy he equlbrum prces of he asses. As a response o hs problem, Brennan developed a verson of he CAM ha allows he mpac of axes on he model o be aken no accoun. Wh he Brennan model, he alpha s characersed by: ( ) F α + β ( E( M ) F T ( D M F )) +T ( D F ) E.. wh: Td T T T where: T d denoes he average axaon rae for dvdends; T denoes he average axaon rae for capal g gans; D M denoes he dvdend yeld of he marke porfolo; D s equal o he weghed sum of he dvdend yelds of he asses n he porfolo, or D n g g x D D denoes he dvdend yeld of asse ; x denoes he wegh of asse n he porfolo. 3... Model where he rsk premum s based on oal rsk Elon and Gruber (995) descrbe a performance measure usng he same prncple as he Jensen measure, namely measurng he dfferenal beween he managed porfolo and a heorecal reference porfolo. However, he rsk consdered s now he oal rsk and he reference porfolo s no longer a porfolo locaed on he Secury Marke Lne, bu a porfolo on he Capal Marke Lne, wh he same oal rsk as he porfolo o be evaluaed. More specfcally, hs nvolves evaluang a manager who has o consruc a porfolo wh a oal rsk of σ. He can oban hs level of rsk by splng he nvesmen beween he marke porfolo and he rsk-free asse. Le A be he porfolo hereby obaned. Ths porfolo s suaed on he Capal Marke Lne. Is reurn and rsk respec he followng relaonshp: E ( A ) F E M ( ) + σ M F σ snce σ A σ. Ths porfolo s he reference porfolo. If he manager hnks ha he possesses parcular sock-pckng sklls, he can aemp o consruc a porfolo wh a hgher reurn for he fxed level of rsk. Le be hs porfolo. The share of performance ha resuls from he manager s choces s hen gven by: E M F E E A E F σ σ ( ) ( ) ( ) ( ) M The reurn dfferenal beween porfolo and porfolo A measures he manager s sock pckng sklls. The resul can be negave f he manager does no oban he expeced resul. Ths measure s called oal rsk alpha (TA) n Scholz and Wlkens (005), who noce ha boh hs measure and he Jensen alpha can be easly manpulaed by means of leverage. In order o faclae our undersandng of he lnk beween he oal rsk alpha and he Sharpe rao, Gresss, hlppaos and Vlahos (986) propose he followng formulaon for he oal rsk alpha: TA σ ( S SM ), where S refers o he Sharpe rao. 3..3. Models sued o evaluang marke mng sraegy The radonal Jensen alpha assumes ha porfolo rsk s saonary. I measures he addonal reurn obaned, compared o he level of rsk aken, by consderng he average value 6 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
3. elave rsk-adjused performance measures of he rsk over he evaluaon perod. The wo frs models presened below enable o ake no accoun varaons n he porfolo s bea over he nvesmen perod n porfolo performance evaluaon. They acually nvolve sascal ess, whch allow for qualave evaluaon of a marke mng sraegy, when ha sraegy s followed for he porfolo. These models allow us o measure he porfolo s Jensen alpha, and o assess wheher he resul was obaned hrough he rgh nvesmen decsons beng aken a he rgh me or hrough luck. The hrd model presens a decomposon of he Jensen measure, due o Grnbla and Tman (989b), and whch enables mng o be evaluaed. 3..3.. The Treynor and Mazuy model (966) Ths model used a quadrac verson of he CAM, whch provdes us wh a beer framework for akng he adjusmens made o he porfolo s bea no accoun, and hus for evaluang a manager s marke mng capacy. Managers who ancpaes marke evoluons correcly wll lower her porfolo s bea when he marke falls. Ther porfolo wll hus deprecae less han f hey had no made he adjusmen. Smlarly, when hey ancpae a rse n he marke, hey ncrease her porfolo s bea, whch enables hem o make hgher profs. The relaonshp beween he porfolo reurn and he marke reurn, n excess of he rsk-free rae, should herefore be beer approxmaed by a curve han by a sragh lne. The model s formulaed as follows: F α + β ( ) + δ ( ) + ε M F where: denoes he porfolo reurn vecor for he perod suded; M denoes he vecor of he marke reurns for he same perod, measured wh he same frequency as he porfolo reurns; F denoes he rae of he rsk-free asse over he same perod. The α, β and δ coeffcens n he equaon are esmaed hrough regresson. If δ s posve and sgnfcanly dfferen from M F zero, we can conclude ha he manager has successfully pracsed a marke mng sraegy. Ths model was formulaed emprcally by Treynor and Mazuy (966). I was hen heorecally valdaed by Jensen (97) and Bhaacharya and flederer (983). 3..3.. The Henrksson and Meron model (98,984) 4 There are n fac wo models: a non-paramerc model and a paramerc model. They are based on he same prncple, bu he paramerc model seems o be more naural o mplemen. The nonparamerc model s less frequenly menoned n he leraure. The non-paramerc verson of he model s older, and does no use he CAM. I was developed by Meron (98) and uses opons heory. The prncple s ha of an nvesor who can spl hs porfolo beween a rsky asse and a rskfree asse, and who modfes he spl over me, accordng o hs ancpaons on he relave performance of he wo asses. If he sraegy s perfec, he nvesor only holds socks when her performance s beer han ha of he rsk-free asse and only holds cash n he oppose case. The porfolo can be modelled by an nvesmen n cash and a call on he beer of he wo asses. If he forecass are no perfec, he manager wll only hold a fracon of opons f, suaed beween and. The value of f allows us o evaluae he manager. To do so, we defne wo condonal probables: denoes he probably of makng an accurae forecas, gven ha he socks bea he rsk-free asse; denoes he probably of makng an accurae forecas, gven ha he rsk-free asse beas he socks. We hen have f + and he manager has a marke mng capacy f f > 0,.e. f he sum of he wo condonal probables s greaer han one. 4 - Cf. Meron (98), Henrksson and Meron (98) and Henrksson (984). erformance Measuremen for Tradonal Invesmen Leraure Survey 7
3. elave rsk-adjused performance measures f can be esmaed by usng he followng formula: I α + α + ε 0 y where: I, f he manager forecass ha he socks wll perform beer han he rsk-free asse durng monh, oherwse 0; y, f he socks acually dd perform beer han he rsk-free asse, oherwse 0. The coeffcens n he equaon are esmaed hrough regresson. α 0 gves he esmaon of and α gves he esmaon of +. We hen es he hypohess α 0. > Henrksson and Meron (98) hen developed a paramerc model. The dea s sll he same, bu he formulaon s dfferen. I consss of a modfed verson of he CAM whch akes he manager s wo rsk objecves no accoun, dependng on wheher he forecass ha he marke reurn wll or wll no be beer han he rsk-free asse reurn. The model s presened n he followng form: α + β D ( ) + ε F ( M F ) + β wh: D 0, f M F > 0 D, f M < 0 The α, β and β coeffcens n he equaon are esmaed hrough regresson. The β coeffcen allows us o evaluae he manager s capacy o ancpae marke evoluon. If β s posve and sgnfcanly dfferen from zero, he manager has a good mng capacy. These models have been presened whle assumng ha he porfolo was nvesed n socks and cash. More generally, hey are vald for a porfolo ha s spl beween wo caegores of asses, wh one rsker han he oher, for example socks and bonds, and for whch we adjus he composon accordng o ancpaons on her relave performance. F M F Goezmann, Ingersoll and Ivkovc (000) have suded he bas assocaed wh hs model used wh monhly reurns when marke mers can make daly decsons. Ther smulaons sugges ha hs measure of mng skll s weak and based downward when appled o he monhly reurns of a daly mer. They propose an adjusmen ha mgaes hs problem whou he need o collec daly mer reurns. Ther approach consss n usng daly reurns o an ndex correlaed o he mer s rsky asse. Values of a daly pu on he ndex are hen cumulaed over each monh o form a regressor ha capures mng skll. 3..3.3. Decomposon of Jensen measure: Grnbla and Tman (989b) The Jensen measure has been subjec o numerous crcsms, he man one beng ha a negave performance can be arbued o a manager who pracces marke mng. As we menoned above, hs comes from he fac ha he model uses an average value for bea, whch ends o overesmae he porfolo rsk, whle he manager vares hs bea beween a hgh bea and a low bea accordng o hs expecaons for he marke. Grnbla and Tman (989b) presen a decomposon of he Jensen measure n hree erms: a erm measurng he bas n he bea evaluaon, a mng erm and a selecvy erm. In order o esablsh hs decomposon, we assume ha here are n rsky asses raded on a frconless marke,.e. no ransacon coss, no axes and no resrcons on shor sellng. We assume ha here s a rsk-free asse. The assumpons are herefore hose of he CAM. We seek o evaluae he nvesor s performance over T me perods, by lookng a he rsk-adjused reurns of hs porfolo. We denoe as: r, he reurn on asse n excess of he rsk-free rae for perod ; x, he wegh of asse n he nvesor s porfolo for perod. The reurn on he nvesor s porfolo for perod, n excess of he rsk-free rae, s hen gven by: 8 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
3. elave rsk-adjused performance measures r n We denoe as r B he reurn n excess of he rsk-free rae of a porfolo ha s meanvarance effcen from an unnformed nvesor s vewpon. We can hen wre: r β r + ε where: β x B r cov( r, rb ) var( r ) B and: E ( ε ) 0 I should be noed ha b can be dfferen from βˆ. Ths s he case when a manager pracces marke mng. βˆ s hen a weghed mean of he wo beas used for he porfolo, whle b s he regresson coeffcen obaned, whou concernng oneself wh he fac ha he manager pracces marke mng. We can wre: rˆ T plm T r or, by replacng r wh s expresson: T rˆ plm ( β rb + ε ) T The porfolo reurn s hen wren as: wh: and: r β β r + ε n B x β n x ε ε In order o esablsh he decomposon, we consder he lm, n he probablsc sense, of he Jensen measure, whch s wren as follows: J rˆ b rˆ where: b p s he probably lm of he coeffcen from he me-seres regresson of he porfolo reurns agans he reference porfolo seres of reurns; rˆ s he probably lm of he sample mean of he r seres; rˆ B s he probably lm of he sample mean of he r B seres. Formally, he probably lm of a varable s defned as: T rˆ plm r T B By arrangng he erms n he expresson, we oban: T r βˆ ˆ rˆ B + plm β ( rb rˆ B ) + εˆ T By usng hs formula n he Jensen measure expresson, we oban: J T ( βˆ b ) rˆ B + plm T β ( r Ths expresson reveals hree dsnc erms: B rˆ B ) + εˆ - a erm ha resuls from he bas n esmaed bea: ( βˆ b ) rˆ - a erm ha measures mng: T plm β ( rb rˆ B ) T - a erm ha measures selecvy: εˆ If he weghngs of he porfolo o be evaluaed are known, he hree erms can be evaluaed separaely. When he manager has no parcular nformaon n erms of mng, βˆ b. B erformance Measuremen for Tradonal Invesmen Leraure Survey 9
3. elave rsk-adjused performance measures 3..4. Exensons o Jensen s alpha for nernaonal porfolos 3..4.. McDonald s model (973) McDonald proposed a performance measure whch s an exenson o he Jensen measure. Hs model apples o a porfolo of socks nvesed n he French and Amercan markes. I s wren as follows: Φ + β ) + e F * * ( M, F ) + β ( M, F 3..4.. ogue, Solnk and ousseln s model (974) ogue, Solnk and ousseln (974) also proposed an exenson o he Jensen measure for nernaonal porfolos. Ther model measures he performance of funds nvesed n French and nernaonal socks, whou any lm on he number of counres, and n French bonds. The model s wren as follows:.. α + x OF, β OF, (I OF, F )+ x AF, β AF, (I AF, F )+ x W β.. α + x OF, β OF, (I OF, F )+ x AF, β AF, (I AF, F )+ x W β W (I W W )+e where: M, denoes he rae of reurn of he French where: marke n perod ; F denoes he neres rae of he rsk-free M, denoes he rae of reurn of he Amercan asse n he French marke; marke n perod ; W denoes he eurodollar rae; F denoes he rae of reurn of he rsk-free I OF,, I AF,, I W, denoe he reurns on he asse n he French marke n perod ; hree represenave ndces: he French bond * * β x β and β x β, wh x marke ndex, he French sock marke ndex and and x beng he proporons of he fund he worldwde sock marke ndex for perod ; nvesed n each of he wo markes and β x OF,, x AF, and x denoe he proporon W and β he fund s coeffcens of sysemac of he porfolo nvesed n each marke; rsk compared o each of he wo markes. β OF,, β AF, and βw, denoe he sysemac rsk of each subse of he porfolo; The overall excess performance of he fund Φ α denoes he porfolo s overall excess s broken down no: performance. Φ x d + x d The resul measures he manager s capacy o where d and d denoe he excess choose he mos promsng markes and hs skll performance of each of he wo markes. n selecng he bes socks n each marke. Wh hs mehod we can arbue he conrbuon of each marke o he oal performance of he porfolo. Ths n urn allows us o evaluae he manager s capacy o selec he bes-performng nernaonal secures and o nves n he mos profable markes. McDonald s model only consders nvesmens n socks and represens nernaonal nvesmen as he Amercan marke alone. However, he model can be generalsed for he case of nvesmen n several nernaonal markes, and for porfolos conanng several asse classes. Ths s wha ogue, Solnk and ousseln propose. I s possble o go furher n he analyss and breakdown of performance, by usng mulfacor models for nernaonal nvesmen. 3.3. Informaon rao The nformaon rao, whch s somemes called he apprasal rao, s defned by he resdual reurn of he porfolo compared o s resdual rsk. The resdual reurn of a porfolo corresponds o he share of he reurn ha s no explaned by he benchmark. I resuls from he choces made by he manager o overwegh secures ha he hopes wll have a reurn greaer han ha of he benchmark. The resdual, or dversfable, rsk measures he resdual reurn 0 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
3. elave rsk-adjused performance measures varaons. I s he rackng error of he porfolo and s defned by he sandard devaon of he dfference n reurn beween he porfolo and s benchmark. The lower s value, he closer he rsk of he porfolo o he rsk of s benchmark. Sharpe (994) presens he nformaon rao as a generalsaon of hs rao, n whch he rskfree asse s replaced by a benchmark porfolo. The nformaon rao s defned hrough he followng relaonshp: where porfolo. B E ( ) E ( B ) I σ ( ) B denoes he reurn on he benchmark Managers seek o maxmse s value,.e. o reconcle a hgh resdual reurn and a low rackng error. Ths rao allows us o check ha he rsk aken by he manager, n devang from he benchmark, s suffcenly rewarded. The nformaon rao s an ndcaor ha allows us o evaluae he manager s level of nformaon compared o he publc nformaon avalable, ogeher wh hs skll n achevng a performance ha s beer han ha of he average manager. As hs rao does no ake he sysemac porfolo rsk no accoun, s no approprae for comparng he performance of a well-dversfed porfolo wh ha of a porfolo wh a low degree of dversfcaon. 3.4. M² measure: Modglan and Modglan (997) Modglan and Modglan (997) showed ha he porfolo and s benchmark mus have he same rsk o be compared n erms of bass pons of rsk-adjused performance. So hey propose ha he porfolo be leveraged or deleveraged usng he rsk-free asse. They defned he followng measure: σ M A ( F ) + F σ where: σ M s he leverage facor; σ σ M denoes he annualsed sandard devaon of he marke reurns; σ denoes he annualsed sandard devaon of he reurns of fund ; denoes he annualsed reurn of fund ; denoes he rsk-free rae. F Ths measure evaluaes he annualsed rskadjused performance (A) of a porfolo n relaon o he marke benchmark, expressed n percenage erms. Accordng o Modglan and Modglan, hs measure s easer o undersand by he average nvesor han he Sharpe rao. Modglan and Modglan propose he use of he sandard devaon of a broad-based marke ndex, such as he S& 500, as he benchmark for rsk comparson, bu oher benchmarks could also be used. For a fund wh any gven rsk and reurn, he Modglan measure s equvalen o he reurn he fund would have acheved f had he same rsk as he marke ndex. The relaonshp herefore allows us o suae he performance of he fund n relaon o ha of he marke. The mos neresng funds are hose wh he hghes A value. The Modglan measure s drawn drecly from he capal marke lne. I can be expressed as he Sharpe rao mes he sandard devaon of he benchmark ndex: he wo measures are drecly proporonal. So Sharpe rao and Modglan measure lead o he same rankng of funds. 3.5. Marke sk-adjused erformance (MA) measure: Scholz and Wlkens (005) Scholz and Wlkens (005) noe ha, as he A measure developed by Modglan and Modglan (997) uses he sandard devaon as rsk measure, s relevan only o nvesors who nves her enre savngs n a sngle fund. So hey propose a measure called marke rsk-adjused performance (MA), followng he same prncple as Modglan and Modglan s measure, bu measurng reurns relave o marke rsk nsead of oal rsk. As a resul, he MA s suable for nvesors who nves n many dfferen asses. erformance Measuremen for Tradonal Invesmen Leraure Survey
3. elave rsk-adjused performance measures The dea s o compare funds on he bass of measure of marke rsk ha s dencal for all funds. The naural choce s he bea facor of he marke ndex, β M. The marke rskadjused performance for fund s obaned by (de-)leverng n order o acheve a bea equal o one. If he fund s sysemac rsk exceeds ha of he marke ( β > ), hs procedure can be nerpreed as a fcous sale of some fracon d of fund holdngs and hen an nvesmen of he proceeds a he rsk-free rae ( d < 0 ). Smlarly, f he fund s sysemac rsk falls below ha of he marke ndex ( β < ), he procedure corresponds o a fcous loan a he rsk-free rae, amounng o some fracon d, n order o ncrease nvesmens no he fund ( d > 0 ). The fracon d s calculaed as follows: d β The marke-rsk-adjused performance of fund (MA) s obaned by averagng he reurn of he marke rsk-adjused fund (MAF): MA μmaf ( + d ) μ d r f ( μ r f ) + r f β On hs bass, a fund, adjused for marke rsk, ouperformed he marke ndex whenever s marke rsk-adjused performance exceeds he reurn of he marke ndex. ankng funds accordng o her MAs corresponds o rankng hem based on her Treynor aos, as: MA T + r f where T refers o he Treynor ao. The Treynor ao can also be expressed usng Jensen Alpha (JA): JA JA T + μm r f + T M β β Then: JA JA MA + μm + T M + β β r f Ths mples ha rankng based on MA s also equvalen o rankng based on alpha-bea rao. Lke he M² measure, he MA measure s easy o nerpre as s expressed n bass pons. 3.6. SA measure: Lobosco (999) Ths measure, descrbed by Lobosco (999), s a rsk-adjused performance measure ha ncludes he managemen syle as defned by Sharpe (99). The SA (Syle/sk-Adjused erformance s nspred by he work of Modglan and Modglan (997). I s obaned as he dfference beween he A measure (or M²) for he porfolo and he A measure for he syle benchmark represenng he syle of he porfolo. The frs sep o calculae he SA s o denfy he combnaon of ndces ha bes represens he manager s syle. The use of a syle benchmark nsead of a broad marke ndex enables a beer and more accurae evaluaon of managers performance 3.7. sk-adjused performance measure n mulmanagemen: M3 Muraldhar (000, 00) Muraldhar has developed a new rsk-adjused performance measure ha allows us o compare he performance of dfferen managers whn a group of funds wh he same objecves (a peer group). Ths measure does conrbue new elemens compared o he Modglan and Modglan measure. I ncludes no only he sandard devaons of each porfolo, bu also he correlaon of each porfolo wh he benchmark and he correlaons beween he porfolos hemselves. The mehod proposed by Muraldhar allows us o consruc porfolos ha are spl opmally beween a rsk-free asse, a benchmark and several managers, whle akng he nvesors objecves no accoun, boh n erms of rsk and, above all, he relave rsk compared o he benchmark. The prncple nvolves reducng he porfolos o hose wh he same rsk n order o be able EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
3. elave rsk-adjused performance measures o compare her performance. Ths s he same dea as n Modglan and Modglan (997) who compared he performance of a porfolo and s benchmark by defnng ransformaons n such a way ha he ransformed porfolo and benchmark had he same sandard devaon. To creae a correlaon-adjused performance measure, Muraldhar consders an nvesor who spls hs porfolo beween a rsk-free asse, a benchmark and an nvesmen fund. We assume ha hs nvesor acceps a ceran level of annualsed rackng error compared o hs benchmark, whch we call objecve rackng error. The nvesor wshes o oban he hghes rsk-adjused value of alpha for a gven porfolo rackng error and varance. We defne as a, b and ( a b) he proporons nvesed respecvely n he nvesmen fund, he benchmark B and he rsk-free asse F. The porfolo hereby obaned s sad o be correlaon-adjused. I s denoed by he nals CA (for correlaon-adjused porfolo). The reurn on hs porfolo s gven by: ( CA ) a( manager) + b( B) + ( a b) ( F ) The proporons o be held mus be chosen n an approprae manner, so ha he porfolo obaned has a rackng error equal o he objecve rackng error and s sandard devaon s equal o he sandard devaon of he benchmark. The consran on rackng error creaes a unque arge correlaon beween he CA and he benchmark. Ths arge correlaon wh ha of he benchmark s gven by: TE (Targe) ρtb σ The coeffcens a and b are gven by: and: σ B ( ρtb ) a σ ( ρb ) σ b ρtb a ρ B σ B B The search for he bes reurn, n vew of he consrans, leads o he calculaon of opmal proporons ha depend on he sandard devaons and correlaons of he dfferen elemens n he porfolo. The problem s consdered here wh a sngle fund, bu can be generalsed o he case of several funds, o handle he case of porfolos spl beween several managers, and o fnd he opmal allocaon beween he dfferen managers. The formulas ha gve he opmal weghngs n he case of several managers have he same srucure as hose obaned n he case of a sngle manager, bu hey use he weghngs arbued o each manager ogeher wh he correlaons beween he managers. Once he opmal proporons have been calculaed, he reurn on he correlaon-adjused porfolo has been fully deermned. By carryng ou he calculaon for each fund beng suded, we can rank he dfferen funds. The Muraldhar measure s ceranly useful compared o he rsk-adjused performance measure ha had been developed prevously. We observe ha he Sharpe rao, he nformaon rao and he Modglan and Modglan measure urn ou o be nsuffcen o allow nvesors o rank dfferen funds and o consruc her opmal porfolo. These rsk-adjused measures only nclude he sandard devaons of he porfolos and he benchmark, even hough s also necessary o nclude he correlaons beween he porfolos and beween he porfolos and he benchmark. The Muraldhar model herefore provdes a more approprae rskadjused performance measure, because akes no accoun boh he dfferences n sandard devaon and he dfferences n correlaons beween he porfolos. I produces a rankng of funds ha s dfferen from ha obaned wh he oher measures. In addon, neher he nformaon rao nor he Sharpe rao ndcaes how o consruc porfolos n order o produce he objecve rackng error, whle he Muraldhar measure provdes he composon of he porfolos ha sasfy he nvesors objecves. erformance Measuremen for Tradonal Invesmen Leraure Survey 3
3. elave rsk-adjused performance measures The composon of he porfolo obaned hrough he Muraldhar mehod enables us o solve he problem of an nsuonal nvesor s opmal allocaon beween acve and passve managemen, wh he possble use of a leverage effec o mprove he rsk-adjused performance. 3.8. SHAAD: Muraldhar (00,00) Muraldhar underlnes ha he M² and M 3 measures do no ake no accoun dfferences n daa hsory among porfolos, whch requres he use of he same daa perod o compare her resuls, namely he lowes common daa perod. Muraldhar explans ha he longer he hsory, he hgher he degree of confdence n he manager s skll. So he proposes a new measure wh all he properes of he M3 measure, bu whch also allows dfferences n daa hsory o be aken no accoun. He names hs measure SHAAD for Skll, Hsory and sk-adjused. Ambarsh and Segel (996) demonsrae ha he mnmum number of daa pons, or me Hsory H, requred for skll o emerge from he nose s gven by he followng relaon: S H > ( σ ρσ σ B + σ B ) σ σ B B formula, he expresson can be rewren n erms of S, where S s a funcon of I. S < σ H I ( ) σ B TE ( ) The confdence n skll s derved from converng S o percenage erms for a normal dsrbuon, whch s equvalen o compung he cumulave probably of a un normal dsrbuon wh a sandard devaon S. If one defnes C(S) as he cumulave probably of a un normal wh sandard devaon of S for fund, C(S) wll be he measure of confdence n skll. When he erm σ σ B s generally small TE ( ) or nsgnfcan, he I and lengh of daa hsory wll largely deermne he confdence n skll. Ths s he case when rackng error s subsanal and drven largely by low correlaon beween he porfolo and he benchmark (.e. σ σ B ). As a resul, wo porfolos wh dencal varances, nformaon raos and rackng errors, bu dfferng only n lengh of hsory, wll have dfferen confdence n skll. The SHAAD measure for porfolo s a probably-adjused measure, defned as: SHAAD C ( S ) * ( CA ) where: s he reurn of he manager s porfolo; B s he reurn of he benchmark; σ s he sandard devaon of he manager s porfolo; σ B s he sandard devaon of he benchmark; ρ s he correlaon of reurns beween he manager s porfolo and he benchmark; S s he number of sandard devaons for a gven confdence level. As H s gven by performance hsory, Muraldhar solves for he degree of confdence S. Usng he nformaon rao (I) and rackng error (TE) Ths measure has all he properes of M 3 and, n addon, accouns for daa perod n a manner ha s conssen wh he skll evaluaon. 3.9. A Index: Afalon and once (99) Ths performance ndcaor s defned as he dfference beween he annual average expeced reurn of he porfolo and ha of s benchmark, from whch s deduced he produc of he dfference beween he porfolo rsk ( σ ) and he benchmark rsk ( σ B ), mulpled by he prce of rsk X: 4 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
3. elave rsk-adjused performance measures.. Ạ [E( ) E( B )] X[σ σ B ] The excess average reurn of he porfolo compared o s benchmark conrbues posvely n hs ndex, whle he excess rsk conrbues negavely. The prce of rsk, whch has he same dmenson as an average expeced reurn dvded by a sandard devaon, allows he wo erms n he A ndex o have he same dmenson. I represens he addonal reurn (n percen) ha nvesors requre on average for each addonal pon of rsk. I can be esmaed wh economerc mehods usng hsorcal daa for fve o en years. A ndex has he same dmenson as Jensen alpha. I allows porfolos wh he same benchmark o be ranked by decreasng A ndex. Ths ndex s an alernave o he Sharpe rao when rsk premums are negave, makng negave Sharpe raos dffcul o nerpre. The A ndex has a form relavely smlar o he Sharpe s alpha descrbed by lannga and de Groo (00, 00) and whch s gven by he followng formula:.. α E( ) Aσ where: E ( ) s he expeced rae of reurn of he porfolo; σ s he sandard devaon; A s he parameer drvng he level of rsk averson. 3.0. Graham-Harvey (997) measures Graham and Harvey have developed wo measures o make up for wo problems encounered wh he Sharpe rao. Frs, he esmaes are no precse enough when fund volales are oo dfferen. Second, he calculaon of he Sharpe rao s made assumng ha he rsk-free rae s consan and no correlaed o rsky asse reurns. The wo measures provde dfferen perspecves. The frs measure (GH) s obaned by drawng an effcen froner usng a reference ndex and cash. Ths resuls n a hyperbola as he varaons of shor-erm neres raes are correlaed wh marke reurn. Searchng for he pon wh he same volaly as he fund under analyss and calculang he dfference beween he reurn of hs porfolo and ha of he porfolo beng analysed provdes us wh he GH measure. The second measure (GH) s obaned by searchng for he se of porfolos ha combnes a gven fund wh cash. The dfference beween he reurn of he porfolo wh he same volaly as he marke ndex and he marke ndex reurn provdes us wh he GH measure. The GH measure s smlar o he M² measure proposed by Modglan and Modglan (997). However, Modglan and Modglan do no allow for curvaure n he effcen froner. Tha s, hey assume ha he cash reurn has zero varance and zero covarance wh oher asses. 3.. Effcency rao: Canalupp and Hug (000) Whle he relave mehods of performance measuremen end o answer he queson Wha s he performance of a porfolo relave o oher porfolos?, he effcency rao mehodology proposed by Canalupp and Hug ends o answer he queson Whch performance could have been acheved by he porfolo?. To explan how hs measure works, Canalupp and Hug consder wo porfolos, named A and B, wh porfolo A havng a hgher Sharpe rao han porfolo B. However, porfolo B s on he effcen froner, whle porfolo A s no. The effcency rao s compued as he dsance o he ex pos effcen froner. The effcency rao of porfolo A s obaned by dvdng s reurn by ha of a porfolo wh smlar volaly, bu locaed on he effcen froner. The effcency rao of porfolo B s equal o 00%, as s locaed on he effcen froner, whle ha of porfolo A s srcly lower han 00% and erformance Measuremen for Tradonal Invesmen Leraure Survey 5
3. elave rsk-adjused performance measures ISM herefore lower han he porfolo B effcency rao. A porfolo rankng based on he effcency rao s hus dfferen from one obaned usng he Sharpe rao. 3.. Invesor-Specfc erformance Measuremen (ISM): Scholz and Wlkens (004) Scholz and Wlkens consder he suaon of an nvesor holdng a porfolo and wanng o nves addonal money whou changng hs nal porfolo. The addonal amoun wll be pu n a porfolo D. The overall porfolo of he nvesor wll hen be made up of porfolo n proporon ( wd ), and porfolo D. n proporon w D. orfolo D s made up of a fund n proporon w, and he rsk-free rae n proporon w ). ( The ISM performance measure s based on classc domnance consderaons. The sarng pon s ha a a predeermned expeced reurn of he overall porfolo, he porfolo wh he lowes varance domnaes all he oher porfolos wh hgher varance. Gven he expeced reurn of he overall porfolo μ +, an nvesor can buld G an approprae overall porfolo for each fund and hen denfy he fund whch domnaes he oher ones. The ISM measure s defned as: μ r μ r D f D f σ + + μ r f wd ( wd ) μ r f σ / σ σ Hence s referred o as he nvesor-specfc performance measure. A fund j wh a hgher ISM s superor o a fund k wh a lower ISM a a gven porfolo srucure and a predeermned expeced reurn of he overall porfolo. The lower he ISM of a fund, he hgher he varance of he reurns of he overall porfolo for a gven expeced reurn μ +. G If he porfolo s he marke ndex he formula can be rewren n he followng form: ISM wh: r D f M μ + σ μ + r D f wd ( wd ) S T μ μ + G M μ + + D wd where: S s he Sharpe rao of fund ; T s he Treynor rao of fund. I appears ha he value of ISM for dfferen expeced reurns of he overall porfolo s deermned by he Sharpe rao and he Treynor rao of fund. No furher fund specfc nformaon s needed o assess he performance of he parcular fund. Accordng o he formula above, he hgher he Sharpe rao and he Treynor rao of a fund, he hgher he fund s ISM. μ M wh: μ μ + G μ + + D wd μ μ as he expeced reurn of he porfolo ; r as he rsk free rae; f Invesors can compare funds based on he ISM measure. Ths measure depends on he nvesorspecfc porfolo srucure and he nvesorspecfc expeced reurn of he overall porfolo. 6 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
4. Some new research on he Sharpe rao 4.. Crcs and lmaons of he Sharpe rao The CAM assumes eher ha all asse reurns are normally dsrbued and hus symmercal or ha nvesors have mean-varance preferences and hus gnore skewness. Assumng only ha he rae of reurn on he marke porfolo s ndependenly and dencally dsrbued and ha markes are perfec, Leland (999) shows ha he CAM and s rsk measures are nvald: he marke porfolo s mean-varance neffcen, and he CAM alpha msmeasures he value added by nvesmen managers. Cvanc, Lazrak and Wang (004) show ha he ypcal mean-varance effcency jusfcaon for usng he Sharpe rao, vald n a sac seng, ypcally fals n a mul-perod seng. The radng sraegy ha leads o he mos desrable porfolo for each quarer and for four consecuve quarers s no he same as he sraegy ha gves he hghes Sharpe rao for a year. As a consequence, unless he nvesor s nvesmen horzon exacly maches he performance measuremen perod of he porfolo manager, he porfolo wh he hghes Sharpe rao s no necessarly he mos desrable from he nvesor s pon of vew. 4.. Double Sharpe ao: Vnod and Morey (00) One problem wh he Sharpe rao s ha s denomnaor s random, as s compued usng a daa sample of reurns on a gven hsory and no he whole populaon of reurns. So s dffcul o evaluae s rsk esmaon. Vnod and Morey (00) proposed a modfed verson of he Sharpe rao, called he Double Sharpe rao, o ake no accoun esmaon rsk. Ths rao s defned as follows: S DS σ ( S ) where σ ( S ) s he sandard devaon of he Sharpe rao esmae, or he esmaon rsk. To calculae hs sandard devaon hey use boosrap mehodology o generae a grea number of resamples from he orgnal reurns sample and derve a seres of Sharpe raos. Usng he 30 larges-growh muual funds, Vnod and Morey found ha he rankng of muual funds by he Sharpe and Double Sharpe raos can be que dfferen. 4.3. Generalsed Sharpe rao: Dowd (000) Dowd proposes an approach based on he Va o evaluae an nvesmen decson. Dowd consders he case of an nvesor who holds a porfolo ha he s hnkng of modfyng, by nroducng, for example, a new asse. He wll sudy he rsk and reurn possbles lnked o a modfcaon of he porfolo and choose he suaon for whch he rsk-reurn balance seems o be suffcenly favourable. To do ha, he could decde o defne he rsk n erms of he ncrease n he porfolo s Va. He wll change he porfolo f he resulng ncremenal Va (IVa) s suffcenly low compared o he reurn ha he can expec. Ths can be formalsed as a decson rule based on Sharpe s decson rule. Sharpe s rule saes ha he mos neresng asse n a se of asses s he one ha has he hghes Sharpe rao. By calculang he exsng Sharpe rao and he Sharpe rao for he modfed porfolo and comparng he resuls, we can hen judge wheher he planned modfcaon of he porfolo s desrable. By usng he defnon of he Sharpe rao, we fnd ha s useful o modfy he porfolo f he reurns and sandard devaons of he porfolo before and afer he modfcaon are lnked by he followng relaonshp: new old σ new σ old where: old new and denoe, respecvely, he reurn on he porfolo before and afer he modfcaon; σ old and σ new denoe, respecvely, he sandard devaon of he porfolo before and afer he modfcaon. erformance Measuremen for Tradonal Invesmen Leraure Survey 7
4. Some new research on he Sharpe rao We assume ha par of he new porfolo s made up of he exsng porfolo, n proporon ( a), and he oher par s made up of asse A n proporon a. The reurn on hs porfolo s wren as follows: a + ( a) new A old where A denoes he reurn on asse A. new By replacng wh s expresson n he nequaly beween he Sharpe raos, we oban: old old a A + ( a) σ σ new old whch fnally gves: old new old σ A + a σ old Ths relaonshp ndcaes he nequaly ha he reurn on asse A mus respec for o be advanageous o nroduce no he porfolo. The relaonshp depends on proporon a. I shows ha he reurn on asse A mus be a leas equal o he reurn on he porfolo before he modfcaon, o whch s added a facor ha depends on he rsk assocaed wh he acquson of asse A. The hgher he rsk, he hgher he adjusmen facor and he hgher he reurn on asse A wll have o be. Under ceran assumpons, hs relaonshp can be expressed hrough he Va nsead of he sandard devaon. If he porfolo reurns are normally dsrbued, he Va of he porfolo s proporonal o s sandard devaon, or: Va ασ W where: α denoes he confdence parameer for whch he Va s esmaed; W s a parameer ha represens he sze of he porfolo; σ s he sandard devaon of he porfolo reurns. By usng hs expresson of he Va, we can calculae: new new Va W σ new old old Va W σ old whch enables us o oban he followng relaonshp: σ new old new Va W old new σ old Va W We assume ha he sze of he porfolo s old new conserved. We herefore have W W. We herefore oban smply, afer subsung no he reurn on A relaonshp: old new old Va A + old a Va The ncremenal Va beween he new porfolo and he old porfolo, denoed by IVa, s equal o he dfference beween he old and new value, old or IVa Va new Va. By replacng he erm.. Va new Va old n he nequaly accordng o he IVa, we oban: old old IVa old IVa + + A old old a Va a Va By defnng funcon we can wre: η A as: IVa ηa ( Va ) old a Va ( + η ( Va )) A A old where η A (Va ) denoes he percenage ncrease n he Va occasoned by he acquson of asse A, dvded by he proporon nvesed n asse A. 8 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
4. Some new research on he Sharpe rao Dowd also consders he case where he reference s no more he rsk-free asse, bu a benchmark porfolo. In ha case, he sandard devaon of he dfference beween he porfolo and s benchmark s no longer equal o σ p, bu s gven by: σ σ + σ ρ d p b pb The decson rule s now o acqure he new poson f: ().. Ṛ A b ( old p b )+(σ new d /σ old d )( old p b )/a Snce d s he dfference beween he relevan (.e., old or new) porfolo reurn and he benchmark reurn, we can regard he sandard devaon of d as he sandard devaon of he reurn o a combned poson ha s long he relevan porfolo and shor he benchmark. Ths combned poson has s own Va, whch Dembo (997) calls he benchmark-va, or BVa. Assumng normaly, he rao of sandard devaons n () s hen equal o he rao of he new o old BVas, as gven by he followng equaon (): ().. σ new d /σ old d BVa new /BVa old Subsung () n () and rewrng n s BVa form, we oban: σ p σ b.. A b (+η A (BVa ))( old p b ) Ths rule s an exac analogue of he prevous old rule, bu wh A b and p b nsead old of A and, and he BVa elascy nsead p of he earler Va elascy. The generalzed Sharpe rao s superor o he sandard Sharpe rao because s vald regardless of he correlaons of he nvesmens beng consdered wh he res of he porfolo. Snce s derved n a mean-varance world, should be used cauously where deparures from normaly are consderable. 4.4. Negave excess reurns: Israelsen (005) Israelsen (005) noces ha he Sharpe rao and nformaon rao, wo performance ndcaors ofen used o rank muual funds, may lead o spurous rankng when fund excess reurns are negave. In ha case, he fund wh he hgher rao s no always he bes one. Ths can be easly seen n he followng example. The argumen below concerns he nformaon rao, bu s smlar n he case of he Sharpe rao. Excess reurn over he S& 500 Trackng error Informaon rao Fund A -6.96 3.86-0.50 Fund B -3.6 5.03-0.7 The able shows ha he nformaon rao of fund A s hgher han ha of fund B, hough fund B s preferable o fund A as s excess reurn s hgher and s rackng error lower. Israelsen proposes o correc hs anomaly by modfyng he sandard nformaon rao and Sharpe rao. He nroduces an exponen o he denomnaor of hese raos, equal o he fund excess reurn dvded by s absolue value. Usng he prevous noaons, he modfed Sharpe rao s defned as: E( S modfed ) F.. σ( ) (E ( p ) F )/abs (E ( p ) F ) and he modfed nformaon rao s defned as: E( I modfed ) E( B ).. σ ( B ) (E ( p ) F )/abs (E ( p ) F ) We noe ha hese modfed raos concde wh he sandard ones, when excess reurns are posve. Applyng he modfed nformaon rao o he example leads o a value of -96.47 for fund A and a value of -8. for fund B, whch reverse he rankng comparavely o he sandard erformance Measuremen for Tradonal Invesmen Leraure Survey 9
4. Some new research on he Sharpe rao rao. The raos proposed by Israelsen allow us o conssenly rank funds, wheher he fund excess reurns are posve or negave. As he modfcaon n he raos causes enormous range n s sze, Israelsen pons ou ha her values gve no useful nformaon and should only be used as a rankng creron. 30 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
5. Measures based on downsde rsk and hgher momens 5.. Acuaral approach: Melnkoff (998) In hs approach, he nvesor s averson o rsk s characersed by a consan (W ) whch measures hs gan-shorfall equlbrum,.e. he relaonshp beween he expeced gan desred by he nvesor o make up for a fxed shorfall rsk. The average annual rsk-adjused reurn s hen gven by: A ( W ) S where: S denoes he average annual shorfall rae; W denoes he wegh of he gan-shorfall averson; denoes he average annual rae of reurn obaned by akng all he observed reurns. For an average ndvdual, W s equal o wo, whch means ha he ndvdual wll agree o nves f he expeced amoun of hs gan s double he shorfall. In hs case, we have smply: A S 5.. Sorno rao 5 An ndcaor such as he Sharpe rao, based on he sandard devaon, does no allow us o know wheher he dfferenals compared o he mean were produced above or below he mean. The noon of sem-varance brngs a soluon o hs problem by akng no accoun he asymmery of rsk. The calculaon prncple s he same as ha of he varance, apar from he fac ha only he reurns ha are lower han he mean are aken no accoun. I herefore provdes a skewed measure of he rsk, whch corresponds o he needs of nvesors, who are only neresed n he rsk of her porfolo losng value. I s wren as follows: ( Ṗ ) T.. 0 T < Ṗ where denoes he reurn on porfolo for sub-perod ; denoes he mean reurn on asse over he whole perod; T denoes he number of sub-perods. The lower paral momen generalses he noon of sem-varance. I measures he rsk of fallng below a arge reurn se by he nvesor. The mean reurn s replaced n hs formula by he value of he arge reurn below whch he nvesor does no wsh o drop. Ths noon can hen be used o calculae he rsk-adjused reurn ndcaors ha are more specfcally approprae for asymmercal reurn dsrbuons. The bes known ndcaor s he Sorno rao. I s defned on he same prncple as he Sharpe rao. However, he rsk-free rae s replaced wh he mnmum accepable reurn (MA),.e. he reurn below whch he nvesor does no wsh o drop, and he sandard devaon of he reurns s replaced wh he sandard devaon of he reurns ha are below he MA, or: E ( ) MA Sorno ao T ( MA) T < 0 MA Ths measure allows a dsncon beween good and bad volaly: does no penalse porfolos wh reurns ha are far from her mean reurn, bu hgher han hs mean, conrary o he Sharpe rao. 5.3. Fouse ndex Sorno and rce (994) descrbed a measure usng uly heory n a mean-downsde rsk envronmen he Fouse ndex: Fouse E ( ) Bδ where: B s a parameer represenng he degree of rsk averson of he nvesor; δ s he downsde rsk wh respec o he mnmal accepable rae of reurn. Ths ndex s equvalen o Sharpe s alpha 6 n a mean-downsde rsk envronmen. 5 - Cf. Sorno and Van der Meer (99). 6 - Cf. lannga and de Groo (00). erformance Measuremen for Tradonal Invesmen Leraure Survey 3
5. Measures based on downsde rsk and hgher momens 5.4. Upsde poenal rao: Sorno, Van der Meer and lannga (999) Ths rao, developed by Sorno, Van der Meer and lannga, s he probably-weghed average of reurns above he reference rae. I s defned as: U T T + ι ( MA) T ι ( MA) T / where T s he number of perods n he sample, s he reurn of an nvesmen n perod, + + ι f > MA, ι 0 f MA, ι f.. MA and ι 0 f > MA. The numeraor of he Upsde oenal rao s he expeced reurn above he MA and can be hough of as he poenal for success. The denomnaor s downsde rsk as calculaed n Sorno and van der Meer (99) and can be hough of as he rsk of falure. An mporan advanage of usng he upsde poenal rao raher han he Sorno rao s he conssency n he use of he reference rae for evaluang boh profs and losses. Accordng o Sorno, Mller and Messna (997), more sable esmaes of rsk are possble by employng syle analyss. Sharpe (99) developed a procedure for denfyng a manager s syle n erms of a se of passve ndexes whch enables o consruc a syle benchmark for he manager. Usng he dsrbuon of reurns of he syle benchmark, nsead of he manager s reurn dsrbuon, s possble o calculae downsde rsk usng a longer daa hsory han ha of he manager. 5.5. Symmerc downsde-rsk Sharpe rao: Zemba (005) The Sharpe rao reles on mean-varance heory, so s only sued for quadrac preferences or normal dsrbuons. Lo (00) pons ou ha care mus be used n Sharpe rao esmaons when he nvesmen reurns are no ndependen and dencally dsrbued (d). In order o 3 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE penalze a fund manager for losng, bu no for wnnng, Zemba calculaes a Sharpe rao usng downsde varance nsead of varance. He defnes he downsde varance as: n ( x ) σ x n where he x aken are hose below zero. The reference s zero nsead of he mean of he reurns, so measures he downsde rsk. The oal varance s compued as wce he downsde varance. And he correspondng Sharpe rao s gven by: S F σ x Ths measure s closely relaed o he Sorno rao, whch consders downsde rsk only. 5.6. Hgher momen measure of Hwang and Sachell (998) When porfolos reurns are no normally dsrbued, hgher momens such as skewness and kuross need o be consdered o adjus for he non-normaly and o accoun for he falure of varance o measure rsk accuraely. In hese cases, a hgher-momen CAM should prove more suable han he radonal CAM and so a performance measure based on hgher momens may also be more accurae. Assumng he valdy of he hree-momen CAM and a quadrac reurn generang process of he form:.. r r f a 0p +a p (r m r f )+a p (r m E(r m )) +ε p we can defne a performance measure of a porfolo under he hree-momen CAM as :.. a p μ p λ μ m λ (β pm γ pm ) where: λ γ mγ pm (θ m )β pm.. γ m (θ m ) γ λ m σ m.. γ m (θ m )
5. Measures based on downsde rsk and hgher momens wh: and: γ m.. μ p E(r p r f ).. μ m E(r m r f ).. σ m E[(r m re(r m )) ] / γ m E[(r m E(r m )) 3 ] 3.. σ m θ m E[(r m E(r m )) 4 ] 4.. σ m β pm E[(r p E(r p ))(r m E(r m ))].. E[(r m E(r m )) ] γ pm E[(r p E(r p ))(r m E(r m )) ].. E[(r m E(r m )) 3 ] and θ m are he skewness and kuross of he marke reurns, and β pm and γ pm are bea and coskewness respecvely. If he marke reurns are normal, hen λ β pm and λ 0 and he alpha measure s herefore equvalen o Jensen s alpha. Ths measure suffers from he same lmaons as Jensen s alpha bu does accoun for non-gaussanny. 5.7. Omega measure: Keang and Shadwck (00) As nofed by her auhors, he analyss underlyng he omega measure developmen s o be relaed wh downsde rsk, lower paral momens and gan-loss leraure. Keang and Shadwck observe ha an assumpon ha he wo frs momens,.e. mean and varance, fully descrbe a dsrbuon of reurns causes naccuraces n performance measuremen. Accordng o hem, performance measuremen also requres hgher momens. They also advocae he usefulness of a reurn level reference, asde from he mean reurn n he descrpon of he rsk-reward characerscs of a porfolo. In response o hese observaons, hey nroduce a performance evaluaon measure called omega whch ncorporaes all of he hgher momens of a reurns dsrbuon. Omega also akes no accoun he level of reurn agans whch a gven oucome wll be vewed as a gan or a loss, whch s addonal nformaon, even n he case where reurns are normally dsrbued. The prncple of he measure consss n paronng reurns no loss and gan relave o a reurn hreshold correspondng o he mnmum accepable reurn (MA) for an nvesor, and hen consderng he probably weghed rao of reurns above and below he paronng. The Omega measure s defned as a funcon of he MA hreshold n he followng way: b ( F (x ))dx MA Ω(MA) MA F (x)dx.. a where: (a, b) s he nerval of possble reurns; F s he cumulave dsrbuon funcon for he reurns. Omega may be used o rank manager performance. The rankngs wll depend on he nerval of reurns under consderaon and wll ncorporae all hgher momen effecs. Because of he addonal nformaon employs, omega s expeced o produce sgnfcan dfferen rankngs of porfolos compared o hose derved wh Sharpe raos, alphas or value-a-rsk. Ths measure s specfcally recommended for evaluang porfolos ha do no exhb normally dsrbued reurn dsrbuons. For hs reason, usually appears n a seng of hedge fund porfolos. Meanwhle, he ssue of no normal dsrbuon also exss n he conex of radonal nvesmen, hough o a lesser exen. Noe ha n he cases where hgher momens are of lle sgnfcance, he omega measure s n accordance wh radonal measure and avods he need o esmae means and varances. erformance Measuremen for Tradonal Invesmen Leraure Survey 33
6. erformance measuremen mehod usng a condonal bea: Ferson and Schad (996) 6.. The model The mehod s based on a condonal verson of he CAM, whch s conssen wh he semsrong form of marke effcency as nerpreed by Fama (970). The condonal formulaon of he CAM allows he reurn of each asse o be wren as follows: r β I r u (a) wh:, + m ( ) m, + +, + E ( u, + / I ) 0 (b) Usng asse reurn relaonshps, we can esablsh a porfolo reurn relaonshp. By hypohessng ha he nvesor uses no nformaon oher han he publc nformaon, we deduce ha he nvesor s porfolo bea β m only depends on I. By usng a developmen from Taylor, we can approxmae hs bea hrough a lnear funcon, or: ' β ( I ) b + B m b 0 0 In hs relaonshp, can be nerpreed as an average bea. I corresponds o he uncondonal mean of he condonal bea, or: b E ( β ( I )) 0 m and: E u r / I ) 0 (c) (, + m, + The elemens of vecor B p are he response coeffcens of he condonal bea wh respec o he nformaon varables I. r denoes he reurn on asse n excess of he rsk-free rae, or: r F denoes he vecor of he dfferenals of I compared o s mean, or: I E (I ) where perod. F denoes he rsk-free neres rae for In he same way, rm denoes he reurn on he marke n excess of he rsk-free rae, or: r m m These relaonshps are vald for 0,..., n, where n denoes he number of asses, and for 0,..., T, where T denoes he number of perods. I denoes he vecor ha represens he publc nformaon a me. The bea of he regresson, β m ( I ), s a condonal bea,.e. depends on he nformaon vecor I. Bea wll herefore vary over me dependng on a ceran number of facors. When I s he only nformaon used, no alpha erm appears n he regresson equaon, because he laer s null. The error erm n he regresson s ndependen from he nformaon, whch s ranslaed by relaonshp (b). Ths corresponds o he effcen marke hypohess. F From hs we deduce a condonal formulaon of he porfolo reurn: ' r b r + B r u wh: and:, + 0 m, + m, + +, + E ( u, + / I ) 0 E ( u, + rm, + / I ) 0 The model s sochasc facor s a lnear funcon of he marke reurn, n excess of he rsk-free rae, he coeffcens of whch depend lnearly on I. The model hereby developed enables he radonal performance measures, whch came from he CAM, o be adaped by negrang a me componen. These applcaons are dscussed n he followng secon. 34 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
6. erformance measuremen mehod usng a condonal bea: Ferson and Schad (996) 6.. Applcaon o performance measuremen 7 The condonal bea s hen wren as follows: β + b dy b b b0 + 6... The Jensen measure The radonal Jensen measure does no provde sasfacory resuls when he rsk and reurn are no consan over me. The model proposed enables hs problem o be solved... To evaluae he performance of porfolos, we employ an emprcal formulaon of he model whch uses he erm α, or: C ' r α + b r + B r e, + C 0 m, + p m, + +, + α C represens he average dfference beween he excess reurn of he managed porfolo and he excess reurn of a dynamc reference sraegy. Ths model provdes a beer forecas of alpha. A manager wh a posve condonal alpha s a manager who has a hgher reurn han he average reurn of he dynamc reference sraegy. The frs sep nvolves deermnng he conen of he nformaon o be used. Ths s he same as usng explanaory facors. Ferson and Schad (996) propose lnkng he porfolo rsk o marke ndcaors, such as he marke ndex dvdend yeld ( DY ) and he reurn on shor-erm T-blls ( TB ), lagged by one r perod compared o he αc + b0 rm, + + esmaon perod. The dy and b varables denoe he dfferenals compared o he average of he varables DY and TB, or: dy DY E ( DY ) b TB E ( TB ) We herefore have: r α C dy + b 0 b or: b B p b from whch we have he condonal formulaon of he Jensen model:.. r, + α cp +b 0p r m, + +b p dy r m, + +b p b r m, + +e p, + r, + α cp +b 0p r m, + +b p dy r m, + +b p b r m, + +e p, + where αcp represens he condonal performance measure, b 0 denoes he p condonal bea and b p and b p measure he varaons n condonal bea compared o he dvdend yeld and he reurn on he T-blls. The coeffcens are evaluaed hrough regresson from he me-seres of he varables. 6... The Treynor and Mazuy model The non-condonal approach does no draw a dsncon beween he skll n usng macroeconomc nformaon ha s avalable o everybody and a manager s specfc sock-pckng skll. The condonal approach allows hese o be separaed. The condonal formulaon, appled o he Treynor and Mazuy model, nvolves addng a condonal erm o he frs order, or: ' r αc + b0 rm, + + B rm, + + γ r ' r + γ r e 7 - Cf. Ferson and Schad, + m, + + e, (996), + Chrsopherson, Ferson and Turner (999)., + B m, + m, + +, + where γ denoes he marke mng coeffcen. The condonal formulaon s only used n he par ha s shared wh he Jensen measure and no n he model s addonal erm. By usng an nformaon vecor wh wo componens, we oban: r αc + b0 rm, + + b dy rm, + + b b r + b b r + γ r e, + m, + + γ rm, + + e, +, + rm, + + b dy rm, + m, + m, + +, + The coeffcens of he relaonshp are esmaed hrough ordnary regressons. erformance Measuremen for Tradonal Invesmen Leraure Survey 35
6. erformance measuremen mehod usng a condonal bea: Ferson and Schad (996) 6..3. The Henrksson and Meron model The manager seeks o forecas he dfferenal beween he marke reurn and he expecaon of he reurn ha s condonal on he avalable nformaon, or: u m, + rm, + E ( rm, + / I Dependng on wheher he resul of hs forecas s posve or negave, he manager chooses a dfferen value for he condonal bea of hs porfolo. If he forecas s posve, hen: β ( I ) b + B up 0 up ' up If he forecas s negave, hen: ' β ( I ) b + B and:.. * r m, +.. Δ B up B d r m, + I{ r m, + E(r m, + /I ) > 0} where I {}. denoes he ndcaor funcon. More explcly, f r E r / I ) 0, m, + ( m, + > ` hen:.. r, + α C +b 0up r m, + +B up r m, + +u, + and f r E r / I ) 0, m, + ( m, + ) By agan akng our example of an nformaon vecor wh wo componens, he model s wren: r, + α C +b 0d r m, + +b d dy r m, + +b d b r m, +.. wh: * +γ c r m, + * +δ dy r m, + B up b up b.. up B d b d.. b d Δ δ δ.. b up b d b up b d * +δ b r m, + +u, + d 0d d The marke mng sraegy s evaluaed by deermnng he coeffcens of he equaon Henrksson and Meron s condonal model s hrough regresson. In he absence of marke wren as follows: mng, γ c and he componens of Δ are null. If he manager successfully pracces marke ' * * mng, we mus have γ c + Δ > 0, whch.. r, + α C +b 0d r m, + +B d` r m, + +γ c r m, + + Δ` r m, + +u, + means ha he condonal bea s hgher when * * +b 0d r m, + +B d` r m, + +γ c r m, + + Δ` r m, + +u, + he marke s above s condonal mean, gven wh: he publc nformaon, han when s below s.. γ c b 0up b 0d condonal mean. 8 - Cf. Chrsopherson, Ferson and Turner (999). 6.3. Model wh a condonal alpha 8 The evaluaon of condonal performance enables he porfolo rsk and reurn o be forecas wh more accuracy. A beer esmaon of he bea leads o a beer esmaon of he alpha. Bu o be more specfc n evaluang porfolo performance, we can assume ha he alpha also follows a condonal process. Ths allows us o evaluae excess performance ha vares over me, nsead of assumng ha s consan. The relaonshp gven by he condonal alpha s wren as follows: hen:.. r, + α C +b 0d r m, + +B d` r m, + +u, +.. α C a ( ) a 0 + A ` 36 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
6. erformance measuremen mehod usng a condonal bea: Ferson and Schad (996) The regresson equaon ha enables he Jensen alpha o be evaluaed s hen wren:.. r a + A `, + 0 +b 0 r m, + +B ` r m, + +u, + By agan akng he nformaon model ha s made up of wo varables, he alpha componen s wren: α C.. a 0 +a dy +a b wh: A a.. a The model s hen wren.. ṛ, + a 0 +a dy +a b +b 0 r m, + +b r m, + dy +b r m, + b +u, +..... b 0 r m, + +b r m, + dy +b r m, + b +u, + The coeffcens of he equaon are esmaed hrough regresson. 6.4. The conrbuon of condonal models The sudy of muual funds shows ha her exposure o rsk changes n lne wh avalable nformaon on he economy. The use of a condonal measure elmnaes he negave Jensen alphas. Ther value s brough back o around zero. The vewpon developed n Chrsopherson, Ferson and Turner (999) s ha a sraegy ha only uses publc nformaon should no generae superor performance. The mehods for measurng he performance of marke mng sraeges, such as Treynor and Mazuy s and Henrksson and Meron s, are also mproved by nroducng a condonal componen no he model. erformance Measuremen for Tradonal Invesmen Leraure Survey 37
7. erformance analyss mehods ha are no dependen on he marke model 9 - Cf. also Grnbla and Tman (989 b). The oll crcsm, by underlnng he mpossbly of measurng he rue marke porfolo, cas doub over he performance measuremen models ha refer o he marke porfolo. Measures ha were ndependen from he marke model were herefore developed o respond o he crcsms of he model and propose an alernave. These measures are manly used for evaluang a manager s marke mng sraegy. 7.. The Cornell measure (979) 9 The Cornell measure nvolves evaluang a manager s superory as hs capacy o pck socks ha have a hgher reurn han her normal reurn. Ths measure does no use he marke porfolo. The asse reurns are he drec references used. The dffculy s o defne he reurn ha s consdered o be normal for each asse. In pracce, he Cornell measure s calculaed as he average dfference beween he reurn on he nvesor s porfolo, durng he perod n whch he porfolo s held, and he reurn on a reference porfolo wh he same weghngs, bu consdered for a dfferen perod han he nvesor s holdng perod. The calculaon can herefore only be carred ou when he secures are no longer held n he nvesor s porfolo,.e. a he end of he nvesmen managemen perod. The lmaons of hs measure relae o he number of calculaons requred o mplemen and he possbly ha ceran secures wll dsappear durng he perod. Formally, by usng he noaon from secon 3..3.3., presenng he decomposon of he Jensen measure, he asympoc value of he Cornell measure can be wren as follows: C rˆ βˆ rˆ By replacng rˆ wh s expresson esablshed n secon 3..3.3, or: T r βˆ ˆ rˆ B + plm β ( rb rˆ B ) + εˆ T B we oban: T C plm β T ( r B rˆ B ) + εˆ.e. he sum of he selecvy and mng componens from he decomposon of he Jensen measure. The Jensen and Cornell measures boh arbue a null performance o an nvesor who has no parcular skll n erms of mng or n erms of selecvy. 7.. The Grnbla and Tman measure (989a, b): osve erod Weghng Measure The Cornell measure does correc he problem of he Jensen measure, whch wrongly arbues a negave performance o managers who pracce marke mng. Bu hs measure requres he weghngs of he asses ha make up he managed porfolo o be known. Grnbla and Tman proposed a measure ha s an mprovemen on he Jensen measure, enablng he performance of marke mers o be evaluaed correcly, bu whch does no requre nformaon on porfolo weghngs. Ths model s based on he followng prncple. When a manager ruly possesses marke-mng sklls, hs performance should end o repea over several perods. The mehod herefore nvolves akng porfolo reurns over several perods, and arbung a posve weghng o each of hem. The weghed average of he reference porfolo reurns n excess of he rsk-free rae mus be null. Ths condon ranslaes he fac ha he measure arbues a null performance o unnformed nvesors. The Grnbla and Tman measure s hus defned by: GB T w ( F ) 38 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
7. erformance analyss mehods ha are no dependen on he marke model wh: and: T T w w ( B F ) 0 where: denoes he reurn on he porfolo for perod ; denoes he reurn on he reference porfolo B for perod ; F denoes he rsk-free rae for perod ; w denoes he weghng arbued o he reurn for perod. A posve Grnbla and Tman measure ndcaes ha he manager accuraely forecased he evoluon of he marke. Ths mehod presens he dsadvanage of no beng very nuve. In addon, n order o mplemen we need o deermne he weghngs o be assgned o he porfolo reurns for each perod. 7.3. erformance measure based on he composon of he porfolo: Grnbla and Tman sudy (993) Grnbla and Tman also proposed a mehod for evaluang marke mng based on sudyng he evoluon of he porfolo s composon. The mehod s herefore farly dfferen from mos oher performance measuremen mehods. The mehodology s smlar o Cornell s (979). The measure s based on he sudy of changes n he composon of he porfolo. I reles on he prncple ha an nformed nvesor changes he weghngs n hs porfolo accordng o hs forecas on he evoluon of he reurns. He overweghs he socks for whch he expecs a hgh reurn and lowers he weghngs of he oher socks. A non-null covarance beween he weghngs of he asses n he porfolo and he reurns on he same asses mus ensue. The measure s pu ogeher by aggregang he covarances. I s defned by: n T ( r ( x x, k )) / where: r denoes he reurn on secury, n excess of he rsk-free rae, for perod ; x and x, denoe he weghng of secury k a he begnnng of each of he perods and k. The expecaon of hs measure wll be null f an unnformed manager modfes he porfolo. I wll be posve f he manager s nformed. Ths measure does no use reference porfolos. I requres he reurns on he asses and her weghngs whn he porfolo o be known. Lke he Cornell measure, hs mehod s lmed by he sgnfcan number of calculaons and daa requred o mplemen. 7.4. Measure based on levels of holdngs and measure based on changes n holdngs: Cohen, Coval and asor (005) Cohen, Coval and asor (005) observe ha he radonal measures ha rely solely on hsorcal reurns are mprecse, because reurn hsores are ofen shor. They develop a performance evaluaon approach n whch a fund manager s skll s judged by he exen o whch he manager s nvesmen decsons resemble he decsons of managers wh dsngushed performance records. They proposed wo performance measures ha use hsorcal reurns and holdngs of many funds o evaluae he performance of a sngle fund. The frs measure s based on level of holdngs, whle he second one s based on changes n holdngs. They compare her new measures wh hose proposed by Grnbla and Tman (993), whch also rely on fund and noe ha hese measures do no explo he nformaon conaned n he holdngs and reurns of oher funds. Ths specfc pon s he nnovaon of her new measures. T erformance Measuremen for Tradonal Invesmen Leraure Survey 39
7. erformance analyss mehods ha are no dependen on he marke model 7.4.. Measure based on levels of holdngs For each sock n, Cohen, Coval and asor defne a qualy measure as he average skll of all managers who hold sock n n her porfolos, weghed by how much of he sock hey hold,.e. wh: v δ mn M n v mn m M w m mn w where: α m denoes he reference measure of skll for manager m. I s supposed o be measured agans a benchmark akng no accoun any syle effecs for whch he manager should no be rewarded (he auhors noce ha several choces of skll measures are possble); wmn denoes he curren wegh on sock n n manager m s porfolo; M s he oal number of managers; N s he oal number of socks. Socks wh hgh qualy are hose ha are held mosly by hghly sklled managers. Managers who hold socks of hgh qualy are lkely o be sklled because her nvesmen decsons are smlar o hose of oher sklled managers. The measure of a manager s performance s hen gven by: δ * m mn α m M w mn δ m m Ths s he average qualy of all socks n he manager s porfolo, where each sock conrbues accordng o s porfolo wegh. Ths s a weghed average of he usual skll measure across all managers. The correspondng esmaed value s obaned by replacng α by s esmaor αˆ m. m δˆ M N * j n m M m w w mn mn w jn αˆ The wegh assgned o he performance of manager j s a loose measure of covarance beween he weghs of managers m and j. 7.4.. Measure based on changes n holdngs Cohen, Coval and asor also propose o compare managers rades. Ther rade-based performance measure judges a manager s skll by he exen o whch recen changes n hs holdngs mach hose of managers wh ousandng pas performance. Ths measure s also a weghed average of he radonal skll measures, bu now he weghs are essenally he covarances beween he concurren changes n he manager s porfolo weghs and hose of he oher managers. Accordng o he rade-based measure, he manager s sklled f he ends o buy socks ha are concurrenly purchased by oher managers who have performed well, and f he ends o sell socks ha are concurrenly purchased by managers who have performed poorly. Ths performance measure explos smlares beween changes n he managers holdngs, raher han her levels. The auhors underlne ha her approach adds value only f here s some commonaly n he managers nvesmen decsons. They argue ha her measures are parcularly useful for funds wh relavely shor reurn hsores. A vas majory of real-world muual funds have reurn hsores shorer han 0 years. They also found ha her measures are well-sued for emprcal applcaons ha nvolve rankng managers. They have conduced an emprcal sudy, successvely usng he CAM alpha, he Fama- French (993) alpha, and he four-facor alpha followng Carhar (997). Usng her measures o rank managers, he auhors found srong predcably n he reurns of U.S. equy funds. They observe ha he perssence n performance weakens when he momenum j 40 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
7. erformance analyss mehods ha are no dependen on he marke model facor s ncluded. They compared he predcve power of alpha and her wo new measures and found ha hese hree measures seem capable of predcng fund reurns, wh an advanage for he measure based on levels of holdngs. They also nvesgaed wheher her measures conan useful nformaon for forecasng fund reurns no conaned n alpha and found ha her measure provdes nformaon abou fuure fund reurns ha s no conaned n he sandard measures. Ther resuls sugges ha he measure based on levels of holdngs conans sgnfcan nformaon abou fuure fund reurns above and beyond alpha and ha mos of he nformaon conaned n alpha s already n he measure based on levels of holdngs. The measure based on changes n holdngs also adds ncremenal nformaon abou fuure fund reurns over and above alpha. However, alpha seems o conan some ncremenal nformaon beyond hs measure. As a resul, muual fund porfolo sraeges would benef from combnng he nformaon n hese measures. They noce ha her measures of manager s skll rely on he manager s mos recen holdngs or rades, whou consderng hs hsorcal holdngs. The dea s ha a manager s curren decsons should be more nformave han hs pas decsons abou fuure performance. The auhors sugges ha hsorcal holdngs could conan useful nformaon abou manageral skll and ha would be neresng o desgn performance measures ha explo smlares n hsorcal holdngs or rade across managers, and perhaps also he correlaon beween hsorcal holdngs and subsequen holdng reurns as n Grnbla and Tman (993). Snce such measures use ye more nformaon, hey mgh be able o predc fund reurns even more effecvely han he smple measures proposed here. erformance Measuremen for Tradonal Invesmen Leraure Survey 4
8. Facor models: more precse mehods for evaluang alphas 0 - Cf. Fama and French (99, 993, 995, 996). Facor models have been developed as an alernave o he CAM, followng oll s (977) crcsm. As hey rely on fewer hypoheses han he CAM, hey may be valdaed emprcally. These models enable us o explan porfolo reurns wh a se of facors (varous marke ndexes, macroeconomc facors, fundamenal facors), nsead of jus he heorecal and non observable marke porfolo, and hus provde more specfc nformaon on rsk analyss and evaluaon of manageral performance. These models generalsed Jensen s alpha. Ther general formulaon s as follows: α + K k b k F k + ε where: denoes he rae of reurn for asse ; α denoes he expeced reurn for asse ; bk denoes he sensvy (or exposure) of asse o facor k; F k denoes he reurn of facor k wh E ( F k ) 0 ; ε denoes he resdual (or specfc) reurn of asse,.e. he share of he reurn ha s no explaned by he facors, wh E ( ε ) 0. The resdual reurns of he dfferen asses are ndependen from each oher and ndependen from he facors. We herefore have: cov( ε, ε j ) 0, for j and cov( ε, ) 0, for all and k. F k There are several ypes of facor models. These models are derved drecly from Arbrage rcng Theory (AT) developed by oss (976). The rsk facors ha affec asse reurns are approxmaed by observable macroeconomc varables ha can be forecased by economss. The choce of he number of facors, namely fve macroeconomc facors and he marke facor, comes from he frs emprcal ess carred ou by oll and oss wh he help of a facor analyss mehod. The classc facors n he AT models are ndusral producon, neres raes, ol prces, dfferences n bond rangs and he marke facor. These facors are descrbed n Chen, oll and oss (986). 8.. Explc facor models based on mcroeconomc facors (also called fundamenal facors) Ths approach s much more pragmac. The am now s o explan he reurns on he asses wh he help of varables ha depend on he characerscs of he frms hemselves, and no longer from dencal economc facors for all asses. The modellng no longer uses any heorecal assumpons bu consders a facor breakdown of he average asse reurns drecly. The model assumes ha he facor loadngs of he asses are funcons of he frms arbues, called fundamenal facors. The realsaons of he facors are hen esmaed by regresson. Here agan, he choce of explanaory varables s no unque. The facors used are, among ohers, he sze, he counry, he ndusral secor, ec. Below are some examples of hs knd of models, among he mos popular. 8... Fama and French s hree-facor model 0 Fama and French have hghlghed wo mporan facors ha characerse a company s rsk, as a complemen o he marke bea: he book-omarke rao and he company s sze measured by s marke capalsaon. They herefore propose a hree-facor model, whch s formulaed as follows: 8.. Explc facor models based E ( ) F b ( E ( M ) F ) + b E ( SMB ) + b 3 on macroeconomc E ( varables ) F b ( E ( M ) F ) + b E ( SMB ) + b 3 E ( HML ) E where: E ( ) denoes he expeced reurn of asse ; F denoes he rae of reurn of he rsk-free asse; E ( M ) denoes he expeced reurn of he marke porfolo; SMB (small mnus bg) denoes he dfference beween reurns on wo porfolos: a smallcapalsaon porfolo and a large-capalsaon porfolo; 4 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
8. Facor models: more precse mehods for evaluang alphas HML (hgh mnus low) denoes he dfference 8.3. Implc or endogenous facor beween reurns on wo porfolos: a porfolo models wh a hgh book-o-marke rao and a porfolo The dea behnd hs approach s o use he asse wh a low book-o-marke rao; reurns o characerse he unobservable facors. bk denoes he facor loadngs. I s naural o assume ha he facors whch nfluence he reurns leave an denfable race. 8... Carhar s four-facor model (997) These facors are herefore exraced from he Ths model s an exenson of Fama and French s asse reurn daabase hrough a facor analyss hree-facor model. The addonal facor s mehod and he facor loadngs are jonly momenum, whch enables he perssence of he calculaed. To do hs, we perform a prncpal reurns o be measured. Ths facor was added componen analyss whch enables us o explan o ake he anomaly revealed by Jegadeesh and he behavour of he observed varables usng a Tman (993) no accoun. Wh he same smaller se of non observed mplc varables. noaon as above, hs model s wren: From a mahemacal pon of vew, hs consss E ( ) F b ( E ( M ) F ) + b E ( SMB ) + n burnng 3 E ( HML ou ) a + se b of 4 ( n correlaed Y) varables n a F ) + 4 + b E ( SMB ) + b 3 E ( HML ) b ( Y) where Y denoes he dfference beween he average of he hghes reurns and he average of he lowes reurns from he prevous year. 8..3. The Barra model The Barra mulfacor model s he bes known example of commercal applcaon of a fundamenal facor model. The model uses hreen rsk ndces. The reurns are characersed by he followng facor srucure: K k b k α k + u where: denoes he reurn on secury n excess of he rsk-free rae; bk denoes he facor loadng or exposure of asse o facor k; αk denoes he reurn on facor k; u denoes he specfc reurn on asse. Ths model assumes ha asse reurns are deermned by he fundamenal characerscs of he frm. These characerscs consue he exposures or beas of he asses. The approach herefore assumes ha he exposures are known and hen calculaes he facors. se of orhogonal varables (he mplc facors), whch reproduce he orgnal nformaon ha was n he correlaon srucure. Each mplc facor s defned as a lnear combnaon of he nal varables. As he mplc varables are chosen for her explanng power, seems naural ha a gven number of explc facors may explan a larger par of he varance-covarance marx of asse reurns han he same number of explc facors. Ths approach was orgnally used for he frs ess on he AT model. Ths ype of model s used by he frms Quanal and Advanced orfolo Technology (AT). However, he search of mplc facors has he drawback of no allowng us o denfy he naure of he facors, excep he frs one whch exhbs a srong correlaon wh he marke ndex. The explc facor models appear, a leas n heory, o be smpler o use, bu hey assume ha he facors ha generae he asse reurns are known and ha hey can be observed and measured whou errors. As mulfacor model heory does no specfy he number or naure of he facors, her choce resuls from emprcal sudes and here s no uncy. Implc facor models solve he problem of he choce of facors, snce he model does no make any pror assumpons abou he number and naure of he facors. As hey are drecly exraced from asse reurns, herefore enables he rue facors o be used: here s no rsk of ncludng bad facors, or omng good ones. However, facors are hus - A dealed ls of he facors used can be found n Amenc and Le Sourd (003). erformance Measuremen for Tradonal Invesmen Leraure Survey 43
8. Facor models: more precse mehods for evaluang alphas mue varables and may be dffcul o gve hem an economc sgnfcance. f K α ˆ + βˆ λˆ + ζ k k k 8.4. Applcaon o performance measure The mulfacor models have a drec applcaon n nvesmen fund performance measuremen. In analysng porfolo rsk accordng o varous dmensons, s possble o denfy he sources of rsk o whch he porfolo s submed and o evaluae he assocaed reward. The resul s a beer conrol of porfolo managemen and an orenaon of hs one oward he good sources of rsk, whch lead o an mprovemen of s performance. These models conrbue more nformaon o performance analyss han he Sharpe, Treynor and Jensen ndces. The asse reurns could be decomposed lnearly accordng o several rsk facors common o all he asses, bu wh specfc sensvy o each. Once he model has been deermned, we can arbue he conrbuon of each facor o he overall porfolo performance. Ths s easly done when he facors are known, whch s he case for models ha use macroeconomc facors or fundamenal facors, bu becomes more dffcul when he naure of he facors has no been denfed. erformance analyss hen consss of evaluang wheher he manager was able o oren he porfolo owards he mos rewardng rsk facors. raccally speakng, he mplemenaon of facor models s carred ou n wo sages. Frs, beas are esmaed hrough regresson of asse reurns on facors reurns: K 0 + k β β F + ε Lambdas are hen esmaed hrough crossseconal regresson for each dae. The dependen varables are he reurns n excess of he rskfree rae f, for,..., n, assumng here are n asses (or funds, or porfolos). The dependen varables are he esmaed βˆ. The k followng regresson s performed for each : k k The frs sep s no necessary for facor models based on explc mcroeconomc facors, where he sensvy s an observed varable. In he case of mplc facor models, he sensvy s one of he resuls calculaed by he AC. In he equaon above, αˆ s an esmaon of he excess reurn comng from he manager s skll and λˆ s an esmaon of he rsk premum k assocaed o he k h rsk facor a me. The λˆ k allows a calculaon he average rsk premum: λ k T. λ k.. T If he value of λ s sgnfcanly posve, he k facor s kep as a rewardng facor. If he value of λ k s no sgnfcanly dfferen from zero, he facor s dscarded. The wo sep analyss s carred ou agan wh he remanng facors. When he ls of facors s esablshed and he rsk premum calculaed, he fund performance s gven by: α f K k βˆ λ The AT-based performance measure was formulaed by Connor and Korajczyk (986). I should be noed ha he esmaon procedure of facor models conans some dffcules. There are several mehods for esmang he facor sensves of ndvdual secures and several porfolo-formaon procedures ha use he esmaed facor loadngs and dosyncrac varances. In addon, here are mporan daa-analyc choces ncludng he number of secures o nclude n he frs-sage esmaon as well as he perodcy of daa approprae for esmang he facor loadngs. Lehmann and Modes (986) examned wheher dfferen mehods for consrucng reference porfolos lead o dfferen conclusons abou he relave performance of muual funds and showed ha alernave AT mplemenaons ofen suggesed subsanally dfferen absolue and relave k k 44 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
8. Facor models: more precse mehods for evaluang alphas F muual fund rankngs. The fund rankng based on alpha s very sensve o he mehod used o consruc he AT benchmark. 8.5. Mul-ndex models 8.5.. Elon, Gruber, Das and Hlavka s model (993) The Elon, Gruber, Das and Hlavka model s a hree-ndex model ha was developed n response o a sudy by Ippolo (989) whch shows ha performance evaluaed n comparson wh an ndex ha badly represens he dversy of he asses n he fund can gve a based resul. Ther model s presened n he followng form: S F S ) + β ( ) + β ( ) + ε F L B where: L denoes he reurn on he ndex ha represens large-cap secures; S denoes he reurn on he ndex ha represens small-cap secures; B denoes he reurn on a bond ndex; ε denoes he resdual porfolo reurn ha s no explaned by he model. Ths model s a generalsaon of he sngle ndex model. I uses ndces quoed on he markes, specalsed by asse ype. The use of several ndces herefore gves a beer descrpon of he dfferen ypes of asses conaned n a fund, such as socks or bonds, bu also, a a more dealed level, he large or small marke capalsaon secures and he asses from dfferen counres. The mul-ndex model s smple o use because he facors are known and easly avalable. 8.5.. Sharpe s (99) syle analyss model The heory developed by Sharpe spulaes ha a manager s nvesmen syle can be deermned by comparng he reurns on hs porfolo wh hose of a ceran number of seleced ndces. Inuvely, he smples echnque for denfyng he syle of a porfolo nvolves successvely comparng hs reurns o hose of he dfferen L B F F S S syle ndces. The goodness of f beween he porfolo reurns and he reurns on he ndex s measured wh he help of a quany called whch measures he proporon of varance explaned by he model. If he value of s hgh, he proporon of unexplaned varance s mnmal. The ndex for whch he s hghes s herefore he one ha bes characerses he syle of he porfolo. Bu managers rarely have a pure syle, hence Sharpe s dea o propose a mehod ha would enable us o fnd he combnaon of syle ndces whch gves he hghes wh he reurns on he porfolo beng suded. The Sharpe model s a generalsaon of he mulfacor models, where he facors are asse α + β ( ) + β ( classes. Sharpe presens hs model wh welve ) + β ( ) + ε asse F classes. B These B asse F classes nclude several caegores of domesc socks,.e. Amercan n he case of he model: value socks, growh socks, large-cap socks, md-cap socks and small-cap socks. They also nclude one caegory for European socks and one caegory for Japanese socks, along wh several major bond caegores. Each of hese classes, n a broad sense, corresponds o a managemen syle and s represened by a specalsed ndex. The model s wren as follows: K b k k F k + ε where: F denoes he reurn on ndex k; k b denoes he sensvy of he porfolo o k ndex k and s nerpreed as he weghng of class k n he porfolo; ε represens he porfolo s resdual reurn erm for perod. Unlke ordnary mulfacor models, where he values of he coeffcens can be arbrary, hey represen here he dsrbuon of he dfferen asse groups n he porfolo, whou he possbly of shor sellng, and mus herefore respec he followng consrans: erformance Measuremen for Tradonal Invesmen Leraure Survey 45
8. Facor models: more precse mehods for evaluang alphas and: 0 b k K b k k These consrans enable us o nerpre he coeffcens as weghngs. These weghngs are deermned by a quadrac program, whch consss of mnmsng he varance of he porfolo s resdual reurn. A cusomsed benchmark, fed o he porfolo syle, s hen consruced by akng he weghed lnear combnaon of he varous asse classes. Once he benchmark has been consruced for a represenave perod, he manager s performance s calculaed as beng he dfference beween he reurn on hs porfolo and he reurn on he benchmark. We hereby solae he share of performance ha comes from asse allocaon and s explaned by he benchmark. The resdual share of performance no explaned by he benchmark consues he managemen s value-added and comes from he sock pckng, whn each caegory, ha s dfferen from ha of he benchmark. I s he manager s acve reurn. The proporon of he varance no explaned by he model,.e. he quany var( ε ), measures he var( ) mporance of sock pckng quanavely. The Sharpe model uses an analyss ha s called reurn-based,.e. based solely on he reurns. The advanage of hs mehod s ha s smple o mplemen. I does no requre any parcular knowledge abou he composon of he porfolo. The nformaon on he syle s obaned smply by analysng he monhly or quarerly reurns of he porfolo hrough mulple regresson. Bu he major dsadvanage of hs mehod les n he fac ha s based on he pas composon of he porfolo and does no herefore allow us o correcly evaluae he modfcaons n syle o whch may have been subjeced durng he evaluaon perod. Anoher possbly for analysng porfolo syle consss n usng a porfolo-based analyss, based on porfolo characerscs and whch consss n analysng each of he secures ha make up he porfolo. The secures are suded and ranked accordng o he dfferen characerscs ha allow her syle o be descrbed. The resuls are hen aggregaed a he porfolo level o oban he syle of he porfolo as a whole. Ths mehod herefore requres he presen and hsorcal composon of he porfolo, ogeher wh he weghngs of he dfferen secures ha conans, o be known wh precson (cf. Danel, Grnbla, Tman and Wermers, 997). As an up-o-dae composon of funds s no ofen avalable, hs second mehod s more dffcul o use and Sharpe s mehod remans he mos used. I s empng o nerpre he skll or oal excess reurn ε n syle analyss as an abnormal reurn measure. There are however wo mporan drawbacks o hs. Frs, nroducng he consrans on he facor weghngs (hey mus be posve and sum up o one) no syle analyss dsors he resuls of he sandard regresson. As a resul, he sandard properes desrable n lnear regresson models are no respeced. In parcular, he correlaon beween he error erm and he benchmark can be non-null (Deroon, Njman, er Hors, 000). Moreover, an analyss of ha sor does no provde an explanaon for he abnormal reurn on a rsk-adjused bass. In order o brng a soluon o hs problem, s possble o use a mul-ndex model, where he marke ndces are used as facors. Ths model s wren n he followng way (cf. Amenc, Curs and Marelln, 003): f α + K k β k ( F ) + ζ Ths facor model generalses he CAM Secury Marke Lne. I s n he same ven as he one used by Elon e al. (993) o evaluae managers fund performance. Ths equaon can be seen as a weak form of syle analyss conssng of relaxng coeffcen consrans and ncludng a consan erm n he regresson. Excess reurns are used. From a praccal pon of vew, hs k f 46 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
8. Facor models: more precse mehods for evaluang alphas approach enables one o consder benchmark consrucon and performance measuremen n a unfed seng: once he sued ndces have been seleced, hey can be used boh for reurns-based syle analyss (srong form of syle analyss wh consrans on coeffcens) and for measurng porfolo abnormal reurn (weak form of syle analyss appled o reurns n excess of rsk-free rae). The performance s hen gven by he followng formula: α f K k β k λ k erformance Measuremen for Tradonal Invesmen Leraure Survey 47
9. erformance perssence - Ths callng no queson of effcen markes s responsble for he srong growh n TAA (Taccal Asse Allocaon) echnques. The queson of performance perssence n funds s ofen addressed n wo ways. The frs s lnked o he noon of marke effcency. If we adm ha markes are effcen, he sably of fund performance canno be guaraneed over me. Neverheless, accordng o MacKnlay and Lo (998), he valdy of he random marke heory s now beng called no queson, wh sudes showng ha weekly reurns are, o a ceran exen, predcable for socks quoed n he Uned Saes. Ths ype of affrmaon s, however, conesed by oher unversy research, whch connues o promoe he heory of marke effcency, accordng o whch prces ake all avalable nformaon no accoun, and as a resul of whch acve porfolo managemen canno creae added value. The second par of he problem posed by he exsence or non-exsence of performance perssence s nended o be less heorecal or axomac and more pragmac: Are he wnners always he same? Are ceran managers more sklful han ohers? Of course, f ceran managers bea he marke regularly, over a sascally sgnfcan perod, hey wll prove de faco ha acve nvesmen makes sense and cas doub over he marke effcency paradgm. Bu ha s no he purpose of he queson. A manager who beas he marke regularly by akng advanage of arbrage opporunes from very emporary neffcences wll no prove ha he marke s neffcen over a long perod. rofessonals speak more wllngly of checkng wheher an nvesmen performance s he fru of he real skll of he manager, and no jus luck, raher han showng ha he markes n whch hey nves are neffcen. In pracce, one s ofen emped o beleve ha a manager who has performed well one year s more lkely o perform well he followng year han a manager who has performed poorly. The publcaon of fund rankngs by he fnancal press s based on ha dea. Bu he resuls of sudes ha end o verfy hs assumpon are conradcory and do no allow us o affrm ha pas performance s a good ndcaor of fuure performance. The resuls depend on he perod suded, bu generally would seem ha he poores performances have more of a endency o perss han he bes performances. The resuls are also dfferen dependng on wheher equy funds or bond funds are nvolved. The leraure descrbes wo phenomena ha depend on he lengh of he perod suded. In he long erm (hree o fve years) and he shor erm (one monh or less) we observe a reversal of rends: pas losers become wnners and vce versa. Over he medum erm (sx o welve monhs), he oppose effec s observed: wnners and losers conserve her characerscs over he followng perods and n hs case here s performance sably. Emprcal sudes carred ou o sudy he phenomenon of performance perssence have enabled performance measuremen models o be developed and mproved. A large amoun of boh academc and professonal research s devoed o performance perssence n Amercan muual funds. The resuls seem o sugges ha here s a ceran amoun of performance perssence, especally for he wors funds. Bu pars of hese sudes also sugges ha managers who perform conssenly beer han he marke do exs. In wha follows we summarse he resuls of a ceran number of sudes. Kahn and udd (995) presen a farly horough sudy of he subjec, n whch hey also refer o earler basc research. The earles observaons generally lead o he concluson ha here s no performance perssence, whle he mos recen arcles conclude ha a ceran amoun of performance perssence exss. The auhors, for her par, observed slgh performance perssence for bond funds, bu no for equy funds. Ther sudy akes no accoun syle effecs, managemen fees and daabase errors. They conclude ha s more profable o nves n ndex funds han n funds ha have performed well n he pas. Among he sudes ha concluded ha here was an absence of manager skll n sock pckng, we can ce Jensen (968) and Gruber 48 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
9. erformance perssence (996). Carhar (997) shows ha performance perssence n muual funds s no a reflecon of he manager s superor sock pckng sklls. Insead, he common asse reurn facors and he dfferences n fees and ransacon coss explan he predcable characer of fund reurns. In addon, he observes ha he rankng of funds from one year o anoher s random. The funds a he op of he rankngs one year may perhaps have a slghly greaer chance of remanng here han he ohers. In he same way, he wors ranked funds are very lkely o be badly placed agan or even dsappear. However, he rankng can vary grealy from one year o he nex and he wnnng funds of one year could be he losng funds of he followng year and vce versa. Oher sudes brough o lgh perssence n he performance of muual funds. Ths s he case of Hendrcks, ael and Zeckhauser (993), who hghlghed a phenomenon of performance perssence for boh good managers and bad managers. Malkel (995) observed sgnfcan performance perssence for good managers n he 970s, bu no conssency n fund reurns n he 980s. Hs resuls also sugges ha one should nves n funds ha have performed bes n he pas. These funds perform beer han he average funds over ceran perods, and her performance s no worse han ha of he average funds for oher perods. However, he qualfes hs resuls slghly wh several remarks: he resuls obaned are no robus, he reurns calculaed mus be reduced by he amoun of he fees and he survvorshp bas mus be aken no accoun. In addon, he performance of he funds for he perod suded s worse han ha of he reference porfolos over he same perod, boh before and afer deducng managemen fees. He also analyses fund fees o deermne wheher hgh fees resul n beer performance. The sudy fnds no relaonshp beween he amoun of fees and he value of reurns before hose fees are deduced. He also concludes, lke Kahn and udd (995), ha can be much more profable for nvesors o buy ndex funds wh reduced fees, raher han ryng o selec an acve fund manager who seems o be parcularly sklful. Carhar (997) observed performance perssence for managers whose performance was negave. Brown, Goezmann, Ibboson and oss (99) showed ha shor-erm performance perssed, bu ha he survvorshp bas aached o he daabase (.e. he fac ha funds ha perform badly end o dsappear) could sgnfcanly affec he resuls of performance sudes and could n parcular gve an appearance of sgnfcan perssence. Malkel (995) and Carhar (997) also show ha he perssence hey denfed could be arbued eher o survvorshp bas or o a poor choce of benchmark. Malkel (995) observes ha around 3% of muual funds dsappear every year. As a resul, performance sascs n he long run do no conan he resuls of he bad funds ha have dsappeared. So he survvorshp bas s much more mporan han prevous sudes suggesed. More recen sudes have hus used daabases ha are correced for survvorshp bas. Malkel herefore concludes ha he nvesmen sraegy mus no be based on a belef n reurn perssence over he long-erm. A sudy by Lenormand- Touchas (998), carred ou on French equy muual funds for he perod from January 990 o December 3 995, shows ha here s no long-erm performance perssence, unless a slgh perssence n negave performance s couned. In he shor erm, on he oher hand, a ceran amoun of performance perssence can be observed, whch s more sgnfcan when he performance measuremen echnque used negraes a rsk creron. Jegadeesh and Tman (993) show, wh NYSE and AMEX secures over he perod 965-989, ha a momenum sraegy ha consss of buyng he wnners from he prevous sx monhs,.e. he asses a he op of he rankngs, and sellng he losers from he prevous sx monhs,.e. he asses a he boom of he rankngs, earns around % per monh over he followng sx monhs. Ths shows ha asse reurns exhb momenum, whch means ha he wnners of he pas connue o perform well and he losers of he pas connue o perform badly. ouwenhors erformance Measuremen for Tradonal Invesmen Leraure Survey 49
9. erformance perssence (998) obans smlar resuls wh a sample of European counres for he perod 980-995. Alhough he earles sudes were only based on performance measures drawn from he CAM, such as Jensen s alpha, he more recen sudes used models ha ook facors oher han marke facors no accoun. These facors are sze, book-o-marke rao and momenum. Fama and French are responsble for he model ha uses hree facors (marke facor, sze and book-o-marke rao). In an arcle from 996, Fama and French sress ha her model does no explan he shor-erm perssence of reurns hghlghed by Jegadeesh and Tman (993) and sugges ha research could be dreced owards a model negrang an addonal rsk facor. I was Carhar (997) who nroduced momenum, whch allows shor-erm performance perssence o be measured, as an addonal facor. He suggess ha he ho hands phenomenon (.e. a manager s ably o pck he bes performng socks) s prncpally due o he momenum effec over one year descrbed by Jegadeesh and Tman (993). Usng a four-facor model, Danel, Grnbla, Tman and Wermers (997) suded fund performance o see wheher he manager s sock pckng skll compensaed for he managemen fees. The auhors conclude ha performance perssence n funds s due o he use of momenum sraeges by he fund managers, raher han he managers beng parcularly sklful a pckng wnnng socks. Brown and Goezmann (995) suded performance perssence for equy funds. Ther resuls ndcae ha relave (.e. measured n relaon o a benchmark) rsk-adjused performance persss. oor performance also ends o ncrease he probably ha he fund wll dsappear. Blake and Tmmermann (998) analysed he performance of muual funds n he Uned Kngdom, underlnng he fac ha mos performance sudes concern Amercan funds and ha here are very few on European funds. As happens, he equy muual fund managemen ndusry n he Uned Kngdom s very advanced and s he one n Europe for whch we have he mos hsorcal daa. The sudy shows ha equy funds perform slghly worse han he marke on a rsk-adjused bass. erformance seems o perss o he exen ha, on average, a porfolo made up of funds ha have performed bes n hsorcal erms wll perform beer n he followng perod han a porfolo made up of funds ha have performed wors n hsorcal erms. Elon, Gruber and Blake (996) confrmed he ho hands resul prevously descrbed by Hendrcks, ael and Zeckhauser ha hgh reurn can predc hgh reurn n he shor run. However, usng rsk-adjused reurns o rank funds, hey found ha pas performance s predcve of fuure rsk-adjused performance n boh he shor erm and long erm. Moreover, hey found ha here s sll predcably even afer he major mpacs of expenses have been removed. Jan and Hung (004) found ha shor-run muual fund performance s lkely o perss n he long run. Subsequen-year performance s predced no only by pas shor-run performance, bu also by pas long-run performance. Ther sudy reveals ha n he subsequen year he bes funds sgnfcanly ouperformed he wors funds. Moreover, funds wh srong boh shor- and long-run performance sgnfcanly ouperform funds wh weak boh shor- and long-run performance. Accordng o hem, muual fund nvesors can lkely benef from selecng funds on he bass of no only pas shor-run performance bu also pas long-run performance. Bollen and Busse (005) consdered perssence n muual fund performance on a shor-erm horzon. Observng ha superor performance s shor-lved, hey sugges ha a shor measuremen horzon provdes a more precse mehod of denfyng op performers. So hey propose o use hree-monh measuremen perods wh daly reurns. They no only nvesgae performance perssence n sock selecon bu also n marke mng sraegy, whch s new compared o prevous sudes. They found ha 50 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
9. erformance perssence he op decle of funds generaes a sascally sgnfcan abnormal reurn n he pos-rankng quarer. Increasng he lengh of me over whch hey measure rsk-adjused reurns, hey found ha he abnormal reurn of he op decle dsappears. They also observed ha he superory of he op decle over he boom decle s more pronounced when hey used rsk-adjused reurns raher han raw reurns. They hus concluded ha superor performance appears o be a shorlved phenomenon ha s no deecable usng annual measuremen wndows. They also noce ha, alhough her fndngs are sascally sgnfcan and robus o a baery of dagnosc ess, he economc sgnfcance of perssence n muual fund abnormal reurns s quesonable. Afer akng no accoun ransacon coss and axes, nvesors may generae superor reurns by followng a naïve buy-and-hold approach raher han a performance-chasng sraegy, even f shor-erm performance s predcable. Moreover, we can observe ha sock markes are subjec o cycles. Therefore, ceran nvesmen syles produce beer performances durng ceran perods, and worse performances durng ohers. The exsence of hese cycles can hus explan he performance of a specalsed manager perssng over a ceran perod, f he cycle s favourable, and hen sufferng from a reversal n he rend when he cycle becomes unfavourable. The dfferen resuls observed for performance perssence accordng o he perods suded can be lnked o he fac ha more marke rends, such as seasonal effecs and day of he week effecs, have been observed n recen years. However, f performance perssence exss n he shor erm, s seldom seen over he long erm and, as mos sudes sress, only performance perssence ha s observed over a number of years would really allow us o conclude ha s sascally sgnfcan. In he absence of a perod ha s suffcenly long, s no possble o dsngush luck from skll. Fnally, he sudes ha seek o check wheher s possble for he manager o add value whn he framework of an effcen marke were carred ou on funds ha were nvesed n a sngle asse class, generally eques or bonds. Whle he conrbuon of sock pckng o performance n an effcen marke s quesonable, he same canno be sad for he conrbuon of asse allocaon o performance. All he sudes conclude ha asse allocaon s mporan n buldng performance and ofen he queson of perssence canno be separaed from he asse allocaon choces. erformance Measuremen for Tradonal Invesmen Leraure Survey 5
9. erformance perssence The able below summarses he resuls from he man sudes presened n hs secon. Auhors Type of daa/erod/models esuls Jensen (968) Brown, Goezmann, Ibboson, oss (99) Hendrcks, ael, Zeckhauser (993) Jegadeesh, Tman (993) Brown, Goezmann (995) Kahn, udd (995) Malkel (995) Fama, French (996) Gruber (996) 945 o 964 5 muual funds 976 o 987 Invesgaon of he survvorshp bas problem. 974 o 988 65 of Wesenberger s equy muual funds. 965 o989 Funds made up of NYSE and AMEX secures. Three-facor model (he momenum facor s no ncluded n he model). 976 o 988 Wesenberger s equy muual funds. Sample free of survvorshp bas. 983 o 993 for he equy funds. 988 o 993 for he bond funds. 97 o 99 Analyss of fund fees. Sudy of he survvorshp bas. 963 o 993 NYSE, AMEX and NASDAQ socks. Three-facor model (marke facor, sze and book-o-marke rao). 985 o 994 70 of Wesenberger s equy muual funds. Sample free from survvorshp bas. Sngle ndex and four ndex model. No evdence of performance perssence. Shor-erm performance perssence. The survvorshp bas aached o he daabase could sgnfcanly affec he resul of performance sudes and could n parcular gve an appearance of sgnfcan perssence. erformance perssence for boh good and bad managers. erformance perssence for boh good and bad managers. Asses reurns exhb momenum: he wnners of he pas connue o perform well and he losers of he pas connue o perform badly. erformance perssence s due o he use of momenum sraeges. erformance perssence for equy funds on a rsk-adjused bass. oor performance ends o ncrease he probably ha he fund wll dsappear. Slgh performance perssence for bond funds, bu no for equy funds. The analyss akes no accoun syle effecs, managemen fees and daabase errors. Sgnfcan performance perssence for good managers n he 970s, bu no conssency n fund reurns n he 980s. No long-erm perssence. The perssence denfed could be due o survvorshp bas. Ther model does no explan he shorerm perssence of reurns hghlghed by Jegadeesh and Tman (993). Sugges ha research could be dreced owards a model negrang an addonal rsk facor. Evdence of perssence n performance. 5 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
9. erformance perssence Elon, Gruber and Blake (996) Carhar (997) Danel, Grnbla, Tman, Wermers (997) Blake, Tmmermann (998) Lenormand-Touchas (998) ouwenhors (998) Jan and Hung (004) Bollen and Busse (005) 977-993 88 of Wesenberger s common sock funds Model ncludng he hree facors of Fama and French plus an ndex o accoun for growh versus value. 96 o 993 Equy funds made up of NYSE, AMEX and NASDAQ socks. Free from survvorshp bas. Four-facor model (Fama and French s hree-facor model wh momenum as addonal facor). 975 o 994 500 equy funds made up of socks from NYSE, AMEX and NASDAQ. Four-facor model. Sudy of managemen fees. 97 o 995 Muual funds n he Uned Kngdom. Three-facor model. 990 o 995 French equy muual funds. 980 o 995 A sample of funds from European counres. January 96 o June 000 336 Equy funds from he CS Survvor-Bas Free US Muual Fund Daabase. Carhar s four-facor model. 985 o 995 30 of Wesenberger s common sock muual funds wh a maxmum capal gan, growh or growh and ncome nvesmen objecve. Carhar s four-facor model. Hgh reurn can predc hgh reurn n he shor run. as performance s predcve of fuure rsk-adjused performance, n boh he shor run and long run. erformance perssence for bad managers. Shor-erm performance perssence s due o he use of momenum sraeges. ankng of fund from one year o anoher s random. erformance perssence s due o he use of momenum sraeges, raher han he managers beng parcularly sklful a pckng wnnng socks. erformance perssence for equy funds: on average, a porfolo made up of funds ha have performed bes n hsorcal erms wll perform beer n he followng perod han a porfolo made up of funds ha have performed wors n hsorcal erms. Shor-erm performance perssence, more sgnfcan when he performance measuremen echnque used negraes a rsk creron. No long-erm performance perssence, unless a slgh perssence n negave performance s couned. erformance perssence for boh good and bad managers. Asse reurns exhb momenum. Shor-erm muual fund performance s lkely o perss n he long run. Superor performance s a shor-lved phenomenon ha s observable only when funds are evaluaed several mes a year. erformance Measuremen for Tradonal Invesmen Leraure Survey 53
9. erformance perssence These performance perssence sudes do no gve very conclusve resuls as o wheher perssence really exss. Over a long perod, here s a greaer endency o observe underperformance perssence on he par of poor managers han over-performance perssence from good managers. However, he sudes do no ake he nvesmen syle followed by he managers no accoun. We do, neverheless, observe ha dfferen nvesmen syles are no all smulaneously favoured by he marke. Markes are subjec o economc cycles and a syle ha s favourable for one perod,.e. whch offers a performance ha s beer han ha of he marke, can be less favourable over anoher perod and lead o under-performance compared o he marke. Ths can be measured by comparng he reurns of he dfferen syle ndces wh he reurns of a broad marke ndex. The fac ha an nvesmen syle performs well or badly should no be confused wh he manager s skll n pckng he rgh socks whn he syle ha he has chosen. As we menoned a lle earler, a manager s skll n pracsng a well-defned syle should be evaluaed n comparson wh a benchmark ha s adaped o ha syle. Few sudes have addressed he subjec of performance perssence for managers who specalse n a specfc syle. The resuls of he sudes ha have been performed are conradcory and do no allow us o conclude ha perssence exss. For example, Coggn, Fabozz and ahman (993) carred ou a sudy on Amercan penson funds over a perod from 983 o 990. Ther sudy relaes o denfcaon of boh he marke mng effec and he selecvy effec. They used wo broad ndces: he S& 500 ndex and he ussell 3000 ndex, and four specalsed ndces: he ussell 000 ndex for large-cap socks, he ussell 000 ndex for small-cap socks, a ussell ndex specalsed n value socks and a ussell ndex specalsed n growh socks. They showed ha he mng effec and he selecvy effec were boh sensve o he choce of benchmark and he perod of he sudy. They found a posve selecvy effec compared o he specfc ndces, whle ha effec was negave compared o he broad ndces. However, hey found a negave marke mng effec n boh cases. The sudy shows, herefore, ha specalsaon s a source of value-added. Managers succeed n performng beer han her reference syle ndex, even f hey do no manage o bea he marke as a whole. Over he perod suded, he dfferen syle ndces dd no all perform n lne wh he marke. The performance of he value sock ndex was approxmaely equal o ha of he marke, whch mples ha he sudy perod was favourable for value socks. The performance of he growh sock ndex was slghly worse. As far as he small-cap sock ndex was concerned, s performance was half as good as ha of he marke ndex. However, Kahn and udd (995, 997) concluded ha fund performance was no perssen for a sample of 300 US funds over a perod from Ocober 988 o Ocober 995. Anoher neresng sudy s ha of Chan, Chen and Lakonshok (999). Ths sudy concerns Mornngsar funds. The sudy shows ha on he whole here s a ceran conssency n he syle of he funds. Neverheless, funds ha have performed badly n he pas are more lable o modfy her syle han ohers. Ths sudy shows ha s preferable o avod managers who change syle regularly. They make more dffcul o opmse a porfolo ha s shared beween several managers and produce worse performances han managers whose syle s conssen. Fnally, Ibboson and ael (00) nvesgaed U.S. domesc equy funds performance perssence afer adjusng for he nvesmen syle of he funds. They measured he skll of managers agans a benchmark ha adjuss for he syle of he fund. The syle adjusmen was made by usng reurns-based syle analyss o consruc cusomzed benchmarks. Ther resuls ndcae ha wnnng funds do repea good performance. 54 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
9. erformance perssence When fund syle s n queson, he problem of fund msclassfcaon has o be consdered. DBarolomeo and Wkowsk (997) noe ha a large proporon of muual funds are msclassfed, renderng performance comparsons nadequae. Muual fund managers somemes msclassfy her nvesmen sraegy n order o show more compeve resuls. DBarolomeo and Wkowsk fnd ha 40% of muual funds are msclassfed, and 9% serously so. They ce ambguy of classfcaon sysems and compeve pressures as he major reasons for msclassfcaon. Km, Shukla and Tomas (000) agree ha a majory of muual funds are msclassfed (one-hrd serously msclassfed), bu hey do no fnd evdence ha fund managers are gamng her objecves (.e., dvergng from saed objecves n order o acheve a hgher rankng). erformance Measuremen for Tradonal Invesmen Leraure Survey 55
Concluson Throughou hs paper, we have presened he man research avalable n he area of performance evaluaon and developed snce he end of he 950s. We have seen he evoluon of performance evaluaon from elemenary measures of reurns o more sophscaed mehods ha nclude he varous aspecs of rsk hrough mulfacor models and also ake no accoun he non saonary of rsk hrough dynamc evaluaon. Selecng an nvesmen manager s a maer of choosng he manager who can produce he bes numbers n he fuure. Arno and Darnell (003) underlne ha he same se of numbers drawn from he pas can ofen presen wo very dfferen pcures. Changng he benchmark, changng he fscal year, rsk-adjusng he performance can all make a bad produc look good or a good produc look bad. He concludes ha he ques for a sngle, smple measure of performance ofen leads o an overly smplsc vew of he pas, whch can lead o poor choces for he fuure. For hs purpose, Kuenz (003) proposes he use of sraegy benchmarks. He chooses hs erm sraegy benchmarks nsead of he more common erm cusom benchmarks o emphasse he fac ha hese benchmarks are relaed o a manager s specfc sraegy and unverse of secures. Kuenz explans ha he choce of an napproprae benchmark may dsor he porfolo rsk and performance analyss and does no ensure he negry of performance measures. Kuenz underlnes ha whle nvesors are prepared o bear he benchmark rsk, managers are supposed o bear he acve rsk. Consequenly, he concep of rsk conrols becomes dsored f he manager employs a benchmark ha s no represenave of hs porfolo s rue neural weghs. Usng an napproprae benchmark makes manager evaluaon more dffcul. More aenon could also be gven o performance perssence evaluaon, specfcally he perssence of a porfolo manager s skll. 3 - For more deals on hs subjec see N. Amenc, F. Golz and V. Le Sourd, Assessng he Qualy of Sock Marke Indces: equremens for Asse Allocaon and erformance Measuremen, EDHEC sk and Asse Managemen esearch Cenre publcaon, 006. Besde he performance measuremen self, we mus no forge ha he choce of a benchmark for he porfolo o be evaluaed and he desgn of hs benchmark are mporan elemens n performance evaluaon. orfolo performance s mosly presened as beng relave o a benchmark, even f he porfolo managemen s sad o be benchmark-free. In hs specfc area, some mprovemens are sll possble, n order o choose he mos accurae benchmark o evaluae performance. In parcular, we observe ha mos managers do no gve all he aenon requred o hs choce, and ofen use a marke ndex as benchmark. I s no approprae o compare porfolo performance o broad marke ndexes, whch usually consue neffcen nvesmens 3. I s necessary o derve benchmarks ha mmc he porfolo o be evaluaed n he bes possble way, and specfcally benchmarks ha ake he manager s skll no accoun. Ths choce of benchmark defnes he level and he knd of rsk suppored by he porfolo durng he nvesmen perod and hus s fuure performance. 56 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
Bblography Arno. D. and Darnell M., Wha s Behnd he Numbers?, Journal of Invesng, vol., n, summer 003. Ambarsh., Segel L., Tme s he essence, sk, vol. 9, n 8, Augus 996. Amenc N., Curs S. and Marelln L., The Alpha and Omega of Hedge Fund erformance Measuremen, Workng aper, EDHEC sk and Asse Managemen esearch Cenre, January 003. Amenc N. and Le Sourd V., orfolo Theory and erformance Analyss, Wley, 003. Bhaacharya S., flederer., A Noe on erformance Evaluaon, Techncal epor 74, Graduae School of Busness, Sanford Unversy, 983. Black F., Capal Marke Equlbrum wh esrced Borrowng, Journal of Busness, n 45, July 97, pp. 444-455. Blake D. and Tmmermann A., Muual Fund erformance: Evdence from he UK, European Fnance evew, 998, pp. 57-77. Bollen N.. B. and Busse J. A., Shor-Term erssence n Muual Fund erformance, evew of Fnancal Sudes, vol. 8, n, summer 005. Brennan M., Taxes, Marke Valuaon and Corporae Fnancal olcy, Naonal Tax Journal 5, 970, pp. 47-47. Brown S. J. and Goezmann W. N., erformance erssence, Journal of Fnance, vol. 50, n, June 995, pp. 679-698. Brown S. J., Goezmann W., Ibboson. G. and oss S. A., Survvorshp Bas n erformance Sudes, evew of Fnancal Sudes, vol. 5, 99, pp. 553-580. Camps S., The Case for Money-Weghed erformance Arbuon, Journal of erformance Measuremen, vol. 8, n 3, sprng 004. Canalupp L. and Hug., Effcency ao: A New Mehodology for erformance Measuremen, Journal of Invesng, vol. 9, n, summer 000. Carhar M. M., On erssence n Muual Fund erformance, Journal of Fnance, vol. 5, n, March 997, pp. 57-8. Chan L. K. C., Chen H.-L. and Lakonshok J., On Muual Fund Invesmen Syles, Workng aper n 75, Naonal Bureau of Economc esearch, 999. Chesopalov I. and Belaev S., A Smplfed Mehod for Calculang he Money-Weghed ae of eurn, Journal of erformance Measuremen, vol. 9, n, wner 004/005. Chrsopherson J. A., Ferson W. E. and Turner A. L., erformance Evaluaon Usng Condonal Alphas and Beas, Journal of orfolo Managemen, vol. 6, n, fall 999, pp.59-7. erformance Measuremen for Tradonal Invesmen Leraure Survey 57
Bblography Coggn T. D., Fabozz F. J. and ahman S., The Invesmen erformance of U.S. Equy enson Fund Managers: An Emprcal Invesgaon, Journal of Fnance, vol. 48, n 3, July 993, pp. 039-055. Cohen. B., Coval J. D. and asor L., Judgng Fund Managers by he Company hey Keep, Journal of Fnance, vol. 60, n 3, June 005. Connor G. and Korajczyk., erformance Measuremen wh he Arbrage rcng Theory: A New Framework for Analyss, Journal of Fnancal Economcs, vol. 5, 986, pp. 374-394. Cornell B., Asymmerc Informaon and orfolo erformance Measuremen, Journal of Fnancal Economcs, vol. 7(4), December 979, pp. 38-390. Cvanc J., Lazrak A. and Wang T., Sharpe ao as a erformance Measure n a Mul-erod Seng, Workng aper, July 004. Danel K., Grnbla M., Tman S. and Wermers., Measurng Muual Fund erformance wh Characersc-Based Benchmarks, Journal of Fnance, vol. 5, n 3, July 997, pp. 035-058. Darlng. and MacDougall A., Usng erformance Sascs: Have he Measurers Los he lo?, WM Company, Workng aper, Sepember 00. Dembo. S., Value-a-sk and eurn, Ne exposure: The Elecronc Journal of Fnancal sk, vol., Ocober 997, pp. -. Deoon F., Njman T. and er Hors J., Evaluang Syle Analyss, Workng aper, Quanave Invesmen esearch Europe, 000. DBarolomeo D., Jus Because We Can Doesn Mean We Should Why Daly Observaon Frequency n erformance Arbuon s No Beer, Journal of erformance Measuremen, vol. 7, n 3, sprng 003. DBarolomeo D. and Wkowsk E., Muual Fund Msclassfcaon: Evdence Based on Syle Analyss, Fnancal Analyss Journal, vol. 53, Sepember/Ocober 997, pp. 3-43. Dmson E. and Jackson A., Hgh-Frequency erformance Monorng, Journal of orfolo Managemen, vol. 8, n, fall 00. Dowd K., Adjusng for sk: An Improved Sharpe ao, Inernaonal evew of Economcs and Fnance, vol. 9, n 3, 000, pp. 09-. Elon E. J. and Gruber M. J., Modern orfolo Theory and Invesmen Analyss, 5h ed., Wley, 995. Elon E. J., Gruber M. J. and Blake C.., The erssence of sk-adjused Muual Fund erformance, Journal of Busness, vol. 69, n, 996. Elon E. J., Gruber M. J., Das S. and Hlavka M., Effcency wh Cosly Informaon: A enerpreaon of Evdence from Managed orfolos, evew of Fnancal Sudes, vol. 6, n, 993, pp. -. 58 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
Bblography Fama E. F., Effcen Capal Markes: A evew of Theory and Emprcal Work, Journal of Fnance, vol. 5, n, March 970, pp. 383-47. Fama E. F. and French K.., Mulfacor Explanaons of Asse rcng Anomales, Journal of Fnance, vol. 5, n, March 996, pp. 55-8. Ferson W. E. and Schad. W., Measurng Fund Sraegy and erformance n Changng Economc Condons, Journal of Fnance, vol. 5, n, June 996, pp. 45-46. Flbeck G. and Tompkns D. L., Managemen Tenure and sk-adjused erformance of Muual Funds, Journal of Invesng, vol. 3, n, summer 004. Goezmann W., N., Ingersoll Jr. J. and Ivkovc Z., Monhly Measuremen of Daly Tmers, Journal of Fnancal and Quanave Analyss, vol. 35, n 3, Sepember 000. Graham J.. and Harvey C.., Gradng he erformance Marke-Tmng Newsleers, Fnancal Analyss Journal, November/December 997. Gray Jr. K. B. and Dewar. B. K., Axomac Characerzaon of he Tme-Weghed ae of eurn, Managemen Scence, vol. 8, n, Ocober 97. Gresss N., hlppaos G. C. and Vlahos G., Ne Selecvy as a Componen Measure of Invesmen erformance, Fnancal evew, vol., n, 986. Grnbla M. and Tman S., Muual Fund erformance: an Analyss of Quarerly orfolo Holdngs, Journal of Busness, vol. 6 n 3, 989 a, pp. 393-46. Grnbla M. and Tman S., orfolo erformance Evaluaon: Old Issues and New Insghs, evew of Fnancal Sudes, vol., 989 b, pp. 393-4. Grnbla M. and Tman S., erformance Measuremen whou Benchmarks: an Examnaon of Muual Fund eurns, Journal of Busness, vol. 66, n, 993, pp. 47-68. Gruber M. J., Anoher uzzle: The Growh n Acvely Managed Muual Funds, Journal of Fnance, vol. 5, 996, pp. 783-80. Hendrcks D., ael J. and Zeckhauser., Ho Hands n Muual Funds: Shor-un erssence of elave erformance, 974-988, Journal of Fnance, vol. 48, March 993, pp. 93-30. Henrksson. D., Marke Tmng and Muual Fund erformance: an Emprcal Invesgaon, Journal of Busness, vol. 57, n, 984, pp. 73-96. Henrksson. D. and Meron. C., On Marke Tmng and Invesmen erformance II: Sascal rocedures for Evaluang Forecasng Sklls, Journal of Busness, vol. 54, n 4, 98, pp. 53-533. Hwang S. and Sachell S., Evaluaon of Muual Fund erformance n Emergng Markes, Emergng Markes Quarerly, vol., n 3, 998, pp. 39-50. erformance Measuremen for Tradonal Invesmen Leraure Survey 59
Bblography Ibboson. G. and ael A. K., Do Wnners epea wh Syle?, Workng aper, February 00. Illmer S. and Mary W., Decomposng he Money-Weghed ae of eurn, Journal of erformance Measuremen, vol. 7, n 4, summer 003. Ippolo., Effcency wh Cosly Informaon: a Sudy of Muual Fund erformance, 965-84, Quarerly Journal of Economcs, vol. 04, 989, pp. -3. Israelsen C. L., A efnemen o he Sharpe ao and Informaon ao, Journal of Asse Managemen, vol. 5, n 6, Aprl 005. Jacquer E., Kane A. and Marcus A. J., Geomerc or Arhmec Mean: A econsderaon, Fnancal Analyss Journal, vol. 59, n 6, November/December 003. Jan Y.-C. and Hung M.-W., Shor-un and Long-un erssence n Muual Funds, Journal of Invesng, vol. 3, n, sprng 004. Jegadeesh N. and Tman S., eurns o Buyng Wnners and Sellng Losers: Implcaons for Sock Marke Effcency, Journal of Fnance, vol. 48, 993, pp. 65-9. Jensen M. C., The erformance of Muual Funds n he erod 945-964, Journal of Fnance, vol. 3, May 968, pp. 389-49. Jensen M., Opmal Ulzaon of Marke Forecass and he Evaluaon of Invesmen erformance, n Mahemacal Mehods n Invesmen and Fnance, G.. Szego and K. Shell eds., Elsever, 97. Kahn. N. and udd A., Does Hsorcal erformance redc Fuure erformance? Barra Newsleer, sprng 995. Kahn. N. and udd A., The erssence of Equy Syle erformance: Evdence from Muual Fund Daa, n The Handbook of Equy Syle Managemen, T. Danel Coggn, Frank J. Fabozz, ober D. Arno, eds., nd ed., Frank J. Fabozz Assocaes, 997. Keang C. and Shadwck W.F., A Unversal erformance Measure, Journal of erformance Measuremen, vol. 6, n 3, 00. Km M., Shukla. and Tomas M., Muual Fund Objecve Msclassfcaon, Journal of Economcs and Busness, vol. 5, July/Augus 000, pp. 309-33. Kuenz D.E., Sraegy Benchmarks, Journal of orfolo Managemen, vol. 9, n, wner 003, pp. 46-56. Lehmann B. and Modes D., Muual Fund erformance Evaluaon: A Comparson of Benchmarks and Benchmark Comparsons, Journal of Fnance, vol., 987, pp. 33-65. Leland H. E., Beyond Mean-Varance: erformance Measuremen n a Nonsymmercal World, Fnancal Analyss Journal, January/February 999. 60 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
Bblography Lenormand-Touchas G., Eude de la sablé des performances: le cas des Scav acons françases, Banque e Marchés n 36, Sepember-Ocober 998. Lo A. W., The Sascs of Sharpe raos, Fnancal Analyss Journal, vol. 56, 00, pp. 36-5. Lobosco A., Syle/sk-Adjused erformance, Journal of orfolo Managemen, vol. 5, n 3, sprng 999, pp.65-68. McDonald J., French Muual Fund erformance: Evaluaon of Inernaonally Dversfed orfolos, Journal of Fnance, vol. 8, n 5, 973, pp. 6-80. Malkel B. G., eurns from Invesng n Equy Muual Funds 97 o 99, Journal of Fnance, vol. 50, n, June 995, pp. 549-57. Marsh., Fund Managers and Quarerly erformance Measuremen, n Shor Termsm on Tral, London: IFMA, 99. Melnkoff M., Invesmen erformance Analyss for Invesors, Journal of orfolo Managemen, vol. 5, n, fall 998, pp. 95-07. Meron. C., On Marke Tmng and Invesmen erformance I: an Equlbrum Theory of Value for Marke Forecass, Journal of Busness, vol. 54, n 3, 98. Modglan F. and Modglan L., sk-adjused erformance, Journal of orfolo Managemen, wner 997, pp.45-54. Muraldhar A. S., sk-adjused erformance: The Correlaon Correcon, Fnancal Analyss Journal, vol. 56, n 5, Sepember-Ocober 000, pp.63-7 Muraldhar A. S., Opmal sk-adjused orfolos wh Mulple Managers, Journal of orfolo Managemen, vol. 7, n 3, sprng 00, pp. 97-04. Muraldhar A. S., Skll, Hsory and sk-adjused erformance, Journal of erformance Measuremen, wner 00-00. lannga A. and de Groo S., sk-adjused erformance Measures and Impled sk-audes, Journal of erformance Measuremen, vol. 6, n, wner 00/00, pp. 9-9. ogue G., Solnk B. and ousseln A., Inernaonal Dversfcaon: A Sudy of he French Muual Funds, MIT, Workng aper, 974. oll., A Crque of he Asse rcng Theory s Tess, Journal of Fnancal Economcs, March 977, pp. 9-76. ouwenhors K. G., Inernaonal Momenum Sraeges, Journal of Fnance, vol. 53, n, February 998, pp. 67-84. erformance Measuremen for Tradonal Invesmen Leraure Survey 6
Bblography Scholz H. and Wlkens M., Invesor Specfc erformance Measuremen A Jusfcaon of Sharpe ao and Treynor ao, Workng aper, 004. Scholz H. and Wlkens M., A Jgsaw uzzle of Basc sk-adjused erformance Measures, Journal of erformance Measuremen, sprng 005. Sharpe W. F., Capal Asse rces: A Theory of Marke Equlbrum under Condons of sk, Journal of Fnance, vol. 9, Sepember 964, pp.45-44. Sharpe W. F., Muual Fund erformance, Journal of Busness, January 966, pp. 9-38. Sharpe W. F., Asse Allocaon: Managemen Syle and erformance Measuremen, Journal of orfolo Managemen, vol. 8, wner 99, pp. 7-9. Sharpe W. F., The Sharpe ao, Journal of orfolo Managemen, fall 994. Sorno F.A., Mller G. and Messna J., Shor Term sk-adjused erformance : A Syle Based Analyss, Journal of Invesng, summer 997. Sorno F. A. and rce L. N., erformance Measuremen n a Downsde sk Framework, Journal of Invesng, vol. 3, n 3, 994. Sorno F. A. and van der Meer., Downsde sk, Journal of orfolo Managemen, 99, pp. 7-3. Sorno F. A., van der Meer. and lannga A., The Duch Trangle, Journal of orfolo Managemen, vol. 8, summer 999, pp. 50-59. Spauldng D., Is he Modfed Dez Formula Money-Weghed or Tme-Weghed?, Journal of erformance Measuremen, vol. 7, n 3, sprng 003. Srvasava S. C. and Essayyad M., Invesgang a New mehodology for ankng Inernaonal Muual Funds, Journal of Economcs and Fnance, vol. 8, n 3, fall 994. Treynor J. L., How o ae Managemen of Invesmen Funds, Harvard Busness evew 43, January- February 965, pp. 63-75. Treynor J. L. and Black F., How o Use Secury Analyss o Improve orfolo Selecon, Journal of Busness, vol. 46 n, 973, pp. 6-86. Treynor J. and Mazuy K., Can Muual Funds Ouguess he Marke?, Harvard Busness evew 44, July-Augus 966, pp. 3-36. Vnod H. D. and Morey M.., A Double Sharpe ao, Workng aper, 00. Zemba W. T., The Symmerc Downsde-sk Sharpe ao, Workng aper, Aprl 005. 6 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
Abou he EDHEC sk and Asse Managemen esearch Cenre EDHEC s one of he op fve busness schools n France and was ranked 7 h n he Fnancal Tmes Masers n Managemen ankngs 006 owng o he hgh qualy of s academc saff (over 00 permanen lecurers from France and abroad) and s prvleged relaonshp wh professonals ha he school has been developng snce was esablshed n 906. EDHEC Busness School has decded o draw on s exensve knowledge of he professonal envronmen and has herefore concenraed s research on hemes ha sasfy he needs of professonals. EDHEC s one of he few busness schools n Europe o have receved he rple nernaonal accredaon: AACSB (US-Global), Equs (Europe-Global) and AMBA (UK-Global). EDHEC pursues an acve research polcy n he feld of fnance. Is sk and Asse Managemen esearch Cenre carres ou numerous research programmes n he areas of asse allocaon and rsk managemen n boh he radonal and alernave nvesmen unverses. The choce of asse allocaon The EDHEC sk and Asse Managemen esearch Cenre srucures all of s research work around asse allocaon. Ths ssue corresponds o a genune expecaon from he marke. On he one hand, he prevalng sock marke suaon n recen years has shown he lmaons of acve managemen based solely on sock pckng as a source of performance. ercenage of varaon beween funds 3.5% Commssons % Sock ckng 45.5% Allocaon acque 40% Allocaon Sraégque On he oher, he appearance of new asse classes (hedge funds, prvae equy), wh rsk profles ha are very dfferen from hose of he radonal nvesmen unverse, consues a new opporuny n boh concepual and operaonal erms. Ths sraegc choce s appled o all of he cenre's research programmes, wheher hey nvolve proposng new mehods of sraegc allocaon, whch negrae he alernave class; measurng he performance of funds whle akng he accal allocaon dmenson of he alphas no accoun; akng exreme rsks no accoun n he allocaon; or sudyng he usefulness of dervaves n consrucng he porfolo. An appled research approach In a desre o ensure ha he research carres ou s ruly applcable n pracce, EDHEC has mplemened a dual valdaon sysem for he work of he EDHEC sk and Asse Managemen esearch Cenre. All research work mus be par of a research programme, he relevance and goals of whch have been valdaed from boh an academc and a busness vewpon by he cenre's advsory board. Ths board s made up of boh nernaonally recognsed researchers and he cenre's busness parners. The managemen of he research programmes respecs a rgorous valdaon process, whch guaranees boh he scenfc qualy and he operaonal usefulness of he programmes. To dae, he cenre has mplemened sx research programmes: Mul-syle/mul-class allocaon Ths research programme has receved he suppor of Msys Asse Managemen Sysems, SG Asse Managemen and FIMAT. The research carred ou focuses on he benefs, rsks and negraon mehods of he alernave class n asse allocaon. From ha perspecve, EDHEC s makng a sgnfcan conrbuon o he research conduced n he area of mul-syle/mul-class porfolo consrucon. Source: EDHEC (00) and Ibboson, Kaplan (000) erformance Measuremen for Tradonal Invesmen Leraure Survey 63
Abou he EDHEC sk and Asse Managemen esearch Cenre erformance and syle analyss The scenfc goal of he research s o adap he porfolo performance and syle analyss models and mehods o accal allocaon. The resuls of he research carred ou by EDHEC hereby allow porfolo alphas o be measured no only for sock pckng bu also for syle mng. Ths programme s par of a busness parnershp wh he frm Euroerformance (par of he Fnnfo group). Indces and benchmarkng EDHEC carres ou analyses of he qualy of ndces and he crera for choosng ndces for nsuonal nvesors. EDHEC also proposes an orgnal propreary syle ndex consrucon mehodology for boh he radonal and alernave unverses. These ndces are nended o be a response o he crques relang o he lack of represenavy of he syle ndces ha are avalable on he marke. EDHEC was he frs o launch compose hedge fund sraegy ndces as early as 003. The ndces and benchmarkng research programme s suppored by AFI, Euronex, BGI, BN arbas Asse Managemen and UBS Global Asse Managemen. Asse allocaon and exreme rsks Ths research programme relaes o a sgnfcan concern for nsuonal nvesors and her managers ha of mnmsng exreme rsks. I noably nvolves adapng he curren ools for measurng exreme rsks (Va) and consrucng porfolos (sochasc check) o he ssue of he longerm allocaon of penson funds. Ths programme has been desgned n co-operaon wh Inra's Omega laboraory. Ths research programme also nends o cover oher poenal sources of exreme rsks such as lqudy and operaons. The objecve s o allow for beer measuremen and modellng of such rsks n order o ake hem no consderaon as par of he porfolo allocaon process. Asse allocaon and dervave nsrumens Ths research programme focuses on he usefulness of employng dervave nsrumens n he area of porfolo consrucon, wheher nvolves mplemenng acve porfolo allocaon or replcang ndces. assve replcaon of acve hedge fund ndces hrough porfolos of dervave nsrumens s a key area n he research carred ou by EDHEC. Ths programme s suppored by Eurex and Lyxor. ALM and asse managemen Ths programme concenraes on he applcaon of recen research n he area of asse-lably managemen for penson plans and nsurance companes. The research cenre s workng on he dea ha mprovng asse managemen echnques and parcularly sraegc allocaon echnques has a posve mpac on he performance of Asse- Lably Managemen programmes. The programme ncludes research on he benefs of alernave nvesmens, such as hedge funds, n long-erm porfolo managemen. arcular aenon s gven o he nsuonal conex of ALM and noably he negraon of he mpac of he IFS sandards and he Solvency II drecve projec. Ths programme s sponsored by AXA IM. esearch for busness To opmse exchanges beween he academc and busness worlds, he EDHEC sk and Asse Managemen esearch Cenre manans a webse devoed o asse managemen research for he ndusry: www.edhec-rsk.com, crculaes a monhly newsleer o over 75,000 praconers, conducs regular ndusry surveys and consulaons, and organses annual conferences for he benef of nsuonal nvesors and asse managers. The cenre s acves have also gven rse o he busness offshoos EDHEC Invesmen esearch and EDHEC Asse Managemen Educaon. EDHEC Invesmen esearch suppors nsuonal nvesors and asse managers n he mplemenaon of he cenre s research resuls and proposes asse allocaon servces n he conex of a core-saelle approach encompassng alernave nvesmens. EDHEC Asse Managemen Educaon helps nvesmen professonals o upgrade her sklls wh advanced rsk and asse managemen ranng across radonal and alernave classes. 64 EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE
Noes............................................................ erformance Measuremen for Tradonal Invesmen Leraure Survey 65
EDHEC ISK AND ASSET MANAGEMENT ESEACH CENTE 393-400 promenade des Anglas 060 Nce Cedex 3 Tel.: +33 (0)4 93 8 78 4 Fax: +33 (0)4 93 8 78 40 e-mal: research@edhec-rsk.com Web: www.edhec-rsk.com