Good Harbor Financial: A Multifactor Perspective

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1 Good Harbor Fnancal, Inc. Chcago, IL Good Harbor Fnancal: A ultactor Prspctv Author: Nl. Pplnsk Good Harbor Fnancal, Inc. nl.pplnsk@goodharbornancal.com ABSTACT Th valu o a managr or an nvstmnt stratgy s otn basd upon th ablty to gnrat rturns abov and byond thos provdd by th gnral markt. A common valuaton tchnqu nvolvs a rgrsson o th rturns o ntrst on svral popular actor modls and a look at th rsultng rgrsson alphas. In ths papr I analyz th Good Harbor Asst Allocaton stratgy aganst th CAP, th Fama-Frnch 3-Factor modl and th Carhart 4-Factor modl usng smulatd data rom In ach o ths cass, th alphas ar shown to b statstcally and conomcally sgncant. INTODUCTION Asst prcs vary. As such, rturns on nvstmnts also vary. Consdr th smpl cas o buyng an ndvdual stock. Whl th hop s that th prc wll apprcat so that t can latr b sold at a prot, anyon who has nvstd knows that somtms prcs ar up and somtms thy ar down. Wth w xcptons, t s gnrally not possbl to avod ths luctuaton. Howvr, t s possbl and mportant to gt an da o th sourc and natur o ths volatlty. Knowng how prcs mov can b usul n portolo ormaton as w can otn dampn th volatlty o a portolo by choosng assts that ar uncorrlatd or ngatvly corrlatd to ach othr. It s also usul or assssng th ablty o a managr or nvstmnt stratgy to arn rturns abov and byond thos avalabl rom passv nvstng (.. buy and hold or ndx nvstng). Th most popular tchnqu n us today or valuatng rturns nvolvs rgrssng rturns on mult-actor modls and lookng at th slop and ntrcpt cocnts or statstcal and conomc sgncanc. Atr gvng an ovrvw o ach o th modls usd n ths papr, rsults ar prsntd or th varous rgrssons prormd, ncludng tsts o statstcal sgncanc. CAP OVEVIEW In th 1950 s Harry arkowtz, who latr won a Nobl Prz or hs orts, proposd a ground-brakng thory n nanc. athr than ocus on th undamntals o a company to dtrmn whthr to hold stock n th rm, h thorzd that a propr portolo could b stablshd smply by lookng at th avrag rturn and volatlty o vry stock along wth th corrlatons (covaranc) btwn stocks. Basd on ths noton, h argud that an cnt portolo could b ormd that would maxmz rturn or a gvn amount o rsk (standard dvaton). Thus was born th cnt rontr or man-varanc nvstmnt analyss. Undr th man-varanc ramwork, w plottd vry possbl combnaton o rsky assts n an conomy, w would arrv at a dagram lk th on n Fgur 1 blow (ths s just an xampl plot, gnor th actual valus). Portolo Expctd turn 30.00% 5.00% 0.00% 15.00% 10.00% 5.00% 0.00% Exampl an-varanc Opportunty St and Ecncy Frontr an Varanc Opportunty St Ecncy Frontr n. Varanc Portolo Entr ntror "dcoratd" wth non-cnt portolos. 0.00% 10.00% 0.00% 30.00% 40.00% 50.00% 60.00% 70.00% Portolo Standard Dvaton Fgur 1: Exampl an-varanc Spac From th gur, t s clar whr th trm cnt portolo coms rom. Namly, or a gvn rsk lvl (standard dvaton) th xpctd rturn s maxmzd th portolo s on th bold colord ln, or on th cncy rontr. Fgur 1 s or an conomy that only has rsky assts. I w now allow or a rsk-r nvstmnt, say th U.S. short-trm trasury blls, w now ntroduc a Captal Allocaton Ln (CAL) as sn n Fgur. Good Harbor Fnancal: Gnral Dstrbuton v.1 Pag 1 o 6

2 Good Harbor Fnancal, Inc. Chcago, IL Portolo Expctd turn 30.00% 5.00% 0.00% 15.00% 10.00% 5.00% Exampl an-varanc Opportunty St and Ecncy Frontr an Varanc Opportunty St Ecncy Frontr n. Varanc Portolo Captal Allocaton Ln Tangncy Portolo Entr ntror "dcoratd" wth non-cnt portolos. Followng th sam ramwork (and usng th sam assumptons) Sharp wnt on to show that th rsk prmum o th markt portolo s proportonat to th volatlty o th markt and th rsk-avrson o a rprsntatv nvstor. All o whch s ancy talk or th ollowng: Sharp drvd a smpl ormula dscrbng th xpctd xcss rturn (rturn abov th rsk-r rat) o th markt and showd that t s rlatd to how much nvstors dslk rsk. athmatcally: sk Fr at 0.00% 0.00% 10.00% 0.00% 30.00% 40.00% 50.00% 60.00% 70.00% Portolo Standard Dvaton Fgur : Ecncy Frontr wth a sk-fr asst. Th CAL touchs th rsky-asst cncy curv at only on locaton namd th tangncy portolo. Tak a scond to absorb ths pctur. What you ll ralz s qut proound. I th tangncy portolo rprsnts a tradabl scurty or a combnaton o tradabl scurts, w can maxmz our rturn or a gvn lvl o rsk (rght down to 0% standard dvaton) by holdng only th tangncy portolo and th rsk-r asst n propr proportons. That s t. No nd or xpnsv nvstmnt managrs amd at ntror dcoratng o portolos. All w nd to do s dnty th tangncy portolo, dn our rsk lvl, st up a passv nvstmnt account and w r don. arkowtz s thory was arthshattrng. Unortunatly dntyng th tangncy portolo was not so smpl. In act, arkowtz wrot hs papr n 195 and t wasn t untl 1 yars latr that Wllam Sharp proposd hs Captal Asst Prcng odl (CAP) whch ctvly drvd th tangncy portolo. Sharp s thory, whch was ormulatd undr many dalstc assumptons, ctvly stablshd that th tangncy portolo was n act th markt portolo. Undr hs assumptons, not th last o whch s that all nvstors bls about asst man and varancs ar th sam and that ths man and varancs ar constant ovr tm, Sharp showd that n an qulbrum condton all nvstors wll choos to hold a portolo o rsky assts n proportons that duplcat th rprsntaton o th assts n th ntr markt. For xampl, Company XYZ stock rprsnts 1% o th ntr markt, thn ach nvstor wll hold 1% o hs rsky-asst portolo n Company XYZ. Th sam holds tru or all othr assts. Thortcally th tangncy portolo s a wghtd avrag o ALL rsky assts n th conomy (.. stocks, bonds, ral-stat, collctbls, tc.). In practc w otn us a stock ndx, such as th S&P 500, as a proxy. ) ) A A Equaton 1: arkt rsk prmum. In words Equaton 1 s sayng that bcaus th markt s volatl ( ) and nvstors don t lk rsk (A), th markt can only ntc partcpaton by orng a hghr xpctd rturn than th rsk-r rat. In th sam mannr, Sharp showd that th rsk prmum or an ndvdual asst (.. how much rturn an asst must gv n ordr or an nvstor to buy t) s just a scald vrson o th markt prmum, wth th scalng actor bng dpndnt on how th asst movs wth markt. Agan, mathmatcally: E ( ) ) cov(, ) ) ) Equaton : Indvdual asst prmum. Or n trms o xcss rturns: ) Equaton 3: CAP n trms o xcss rturns. Aaaah, nally! Atr all that w rach th roots o th namous CAP bta. But what do w rally hav now? Th CAP ctvly provds an asst prcng modl that allows us to dtrmn th xpctd rturn on any asst smply by valuatng how ths asst movs wth rspct to th markt. And dspt th act that s was dvlopd undr som vry dalstc assumptons, th CAP actually works rmarkably wll n practc. al assts that hav rturns hghr than th S&P 500 ndx, or xampl, gnrally hav btas gratr than on. Lkws scurts that rturn lss than th markt ndx gnrally hav btas lss than on. And as you may hav gussd, scurts that hav th sam rturn as th ) Good Harbor Fnancal: Gnral Dstrbuton v.1 Pag o 6

3 Good Harbor Fnancal, Inc. Chcago, IL markt hav a bta qual to on. So ths s ntrstng, and arkowtz and Sharp wr obvously brllant acadmcs, but how s ths actually usul? In practc, th CAP can b usd or a multtud o purposs. Wthn th scop o ths papr, th CAP s partcularly usul or prormanc attrbuton. I w dscovr an asst or an nvstmnt stratgy that has a hghr xpctd rturn than that suggstd by ts bta (whch w can gt rom a tmsrs rgrsson), w hav a supror approach to nvstng. In othr words, w v batn th cncy rontr. W ll s how ths works whn w analyz rturns rom th Good Harbor Fnancal asst allocaton modl. FAA-FENCH 3-FACTO ODEL As mntond brly n th prvous scton, th CAP prorms rmarkably wll consdrng th assumptons undr whch t was drvd. But just how wll s rmarkably wll? In a rgrsson sns, th CAP otn lads to valus n th 80%-90%+ rang. Emprcally ths s prtty mprssv, but alas thr ar just a w too many nstancs whr th CAP alls short. A thory that dosn t rally xplan vrythng maks nanc prossors nrvous and as such th CAP alurs hav spawnd numrous avnus o rsarch amd at mprovng upon th CAP rsults. On o th outputs o ths rsarch was a thr actor modl dvlopd by Eugn Fama and Knnth Frnch. CAP posturs that th only stat varabl o concrn to nvstors s th volatlty o th ovrall markt ( stat varabl o concrn s just a ancy way o sayng what rsks nvstors car about). In thr analyss, Fama and Frnch dscovrd that thr was as sprad n th avrag rturns o compans sortd by book/markt rato and by sz that was not bng accuratly capturd by th CAP bta. In ssnc, Fama and Frnch proposd that n addton to ovrall markt volatlty, nvstors also car about whthr an asst s a valu stock (hgh book/markt rato) as wll as whthr t s a small rm compard to othrs. Ths ld to th Fama- Frnch 3-Factor odl (FF3F): ) ) h E HL s ESB Equaton 4: Fama-Frnch 3-Factor modl. Hr HL s a portolo ormd by buyng valu stocks and shortng growth stocks. SB s a portolo ormd by buyng small-szd rms and sllng larg cap rms. Th dntons o ths portolos hav bn clarly dntd by Fama-Frnch, and n act data on ths actors ar actvly mantand by Fama-Frnch or th purpos o supportng FF3F modl analyss. How wll dos th FF3F modl work? Compard to CAP, th FF3F modl tnds to do a bttr job n dscrbng rturn varatons ovrall, and by dsgn, ctvly capturs th sz and book/markt cts that wr mssd by th CAP. Howvr, snc th CAP s so wdly quotd, almost all nvstmnt analyss wll nclud a CAP basln chck. CAHAT 4-FACTO ODEL Unortunatly, whl bttr than th CAP, th FF3F modl also has ts struggls, partcularly n xplanng rturns rom portolos ormd by buyng past wnnrs and sllng past losrs. Ths so-calld momntum portolos produc rturns that ar not ully capturd by th, HL or SB actors. As such Carhart (1997) stablshs yt anothr actor, ladng to th Carhart 4- Factor (C4F) modl. )... s E ) h EHL... SB u EUD Equaton 5: Carhart's 4-actor modl. As you may hav gussd, UD rprsnts a portolo ormd by buyng prvous wnnrs and sllng prvous losrs. Unlk th othr actors whch hav bn argud to b proxs or rsks that nvstors car about (rcall th stat varabls o concrn?), UD has not rally bn wll stablshd as a orm o rsk. As such, Carhart s modl sn t gnrally accptd as an asst prcng modl. Howvr, or prormanc attrbuton t dos just n. call that what w r rally atr s whthr th rturns rom an nvstmnt can b xpland usng radly avalabl normaton. I ys, thn th und managr sn t rally provdng valu, snc th rturns could b duplcatd usng a passv or mchancal nvstmnt stratgy. In othr words, no nd to pay an nvstmnt managr or somthng you can do yoursl. In ths sns, Carhart s modl works n and n act s otn ctd n ltratur or just ths purpos. EGESSIONS AND ALPHA As suggstd arlr, th abov modls srv a vry usul purpos n dtrmnng a stratgy or managr s skll. By runnng tm srs rgrssons on actual rturns, w can xtract stmats or th varous modl paramtrs. Consdr th CAP. In ths cas w run th ollowng tm-srs rgrsson: Good Harbor Fnancal: Gnral Dstrbuton v.1 Pag 3 o 6

4 Good Harbor Fnancal, Inc. Chcago, IL, t Equaton 6: CAP tm-srs rgrsson. From ths rgrsson w gt stmats or alpha and bta. Pr Equaton 3, th CAP modl s corrct, thn all assts should l on th Scurty arkt Ln (SL) and all rgrsson alphas should b zro. I th alpha s postv, thn w hav a scurty that s arnng a hghr rturn than that prdctd by CAP (s Fgur 3 blow). ) 16.00% 14.00% 1.00% 10.00% 8.00% 6.00% 4.00%.00% 0.00% Scurty arkt Ln (Accordng to CAP, all assts ln on a straght ln.) Asst wth postv alpha Bta Fgur 3: Scurty arkt Ln (SL). Is arnng a postv alpha a good thng or a bad thng? Ths smngly smpl quston s actually not so straght orward. I th alpha s ral, thn t s obvously a good thng, snc w v ound an nvstmnt that s gvng a hghr rturn than what t should b accordng to ts rsk. Howvr, t s possbl that a postv alpha s just a sgn that our modl s wrong. In ths cas, th alpha could just b compnsaton or rsk that was not proprly capturd by our modl and as such dos not rlct th skll o th portolo managr or th valu o an nvstmnt stratgy. Th nvstmnt s arnng a hghr rturn smply bcaus t s rskr, whch may b undsrabl. Ths s on o th man motvatons or runnng rgrssons usng multpl modls. W want to try and tst our stratgy aganst th wll known rsk actors (HL, SB, UD, tc.) and not rly solly on CAP. In practc th alphas ar rarly xactly zro. Thror th standard t-tst s run and a corrspondng t-statstc s gvn. From ths w can asss whthr th valu w dd obsrv s statstcally drnt rom zro. A gnral rul o thumb s any t-statstc gratr than two s sgncant. t statstcally sgncant (t-statstc o two or gratr) and conomcally sgncant (a judgmnt call, how much alpha do you want?) atr runnng all th modls, thn w crtanly hav somthng o potntal valu. EGESSION ESULTS Th Good Harbor Fnancal, Inc. asst allocaton stratgy ams at algnng nvstmnt allocatons wth th busnss cycl. In ssnc whn th conomy s n a rcsson, th modl attmpts to wght a portolo mor towards dnsv scurts (such as bonds) and whn th conomy s xpandng (.. stock markt rally) th modl looks to b n a stock sctor that s posd to contnu hghr. Usng a proprtary algorthm and computr smulaton, a stram o rturns basd on ths prms was gnratd rom 1981 to 008. Svral rgrsson analyss wr thn conductd usng th modls outlnd abov to s a postv alpha was gnratd. Th rsults o ths rgrssons ar lstd n th ollowng tabls. For comparson purposs, rsults rom rgrssons usng S&P 500 rturns ar also lstd CAP grsson: t = + (,t) + t Tm Prod: Fb Dcmbr 008 Good Harbor Paramtr odl S&P 500 onthly an Excss turn E[ ] (%) Annual an Excss turn E[ ] (%) Sharp ato onthly (%) Annualzd (%) t( Tabl 1: CAP rgrsson rsults. FF3F grsson: t = + (,t) + h (HL t ) + s (SB t ) + t Tm Prod: Fb Dcmbr 008 Good Harbor Paramtr odl S&P 500 onthly an Excss turn E[ ] (%) Annual an Excss turn E[ ] (%) Sharp ato onthly (%) Annualzd (%) t( h s Tabl : Fama-Frnch 3-actor rgrsson rsults. Lk th CAP, smlar alpha chcks can b don wth th othr actor modls (FF3F, C4F). I our alphas ar Good Harbor Fnancal: Gnral Dstrbuton v.1 Pag 4 o 6

5 Good Harbor Fnancal, Inc. Chcago, IL C4F grsson: t = + (,t) + h (HL t ) + s (SB t ) + u (UD t ) + t Tm Prod: Fb Dcmbr 008 Good Harbor Paramtr odl S&P 500 onthly an Excss turn E[ ] (%) Annual an Excss turn E[ ] (%) Sharp ato onthly (%) Annualzd (%) t( h s u Tabl 3: Carhart 4-actor rgrsson rsults. Th Good Harbor modl arns almost twc as much xcss rturn compard to th S&P 500 and t dos so wth lowr rsk as suggstd by th Sharp ato. Th alpha s postv and sgncant n all cass. Intrstngly th S&P 500 has a ngatv alpha. Ths s du to th act that th rgrssons us th valuwghtd rturn on all NYSE, AEX, and NASDAQ stocks as th markt proxy. Usng th S&P 500 as th markt proxy rsults n a Good Harbor alpha that s slghtly largr than thos lstd CAP Fama-Frnch 3-Factor Carhart 4-Factor 0 Excss turn Alpha -10 1/88 1/93 1/98 1/03 1/08 Fgur 4: turns and alphas ovr multpl prods. Fgur 4 compars alphas and rturns rom varous 5- yar sub-sampls (nd dat s lstd on th x-axs) or ach o th modls. As llustratd, th alphas and rturns vary ovr tm prods. In prods whr rturns and alphas ar smlar (.. 1/003) w can conclud that th Good Harbor modl s producng rturns vrtually ndpndnt o th modls (.. rturn = alpha and th actors ar zro). Cass whr th alpha s nar zro suggst that th modls ar ully capturng th Good Harbor rturns n thos prods. Ths mght b th cas, or xampl, whn th Good Harbor asst allocaton s havly nvstd n stocks and thror w mght xpct th Good Harbor rturns to b wll dscrbd by th ) actor n th cas o th CAP modl. ) -% t-stat ) -% t-stat CAP FF3F * * C4F * * Tabl 4: turn and alpha man statstcs. Tabl 4 contans th mans or ach o th curvs n Fgur 4. As bor, th avrag alpha s both statstcally and conomcally sgncant. SUAY & CONCLUSIONS Whn compard aganst th CAP, th Fama-Frnch 3- Factor modl and th Carhart 4-Factor modl usng smulatd data rom , th Good Harbor asst allocaton stratgy ylds conomcally and statstcally sgncant alphas. In th ull sampl CAP cas th alpha xcds 5% annually. For Fama-Frnch 3-Factor and Carhart 4-Factor th alpha s vn hghr. Usng alpha sgncanc as a mans o prormanc attrbuton, ths rsults suggst that th Good Harbor Fnancal modl ors valu to a dynamcally allocatd nvstmnt portolo. APPENDIX A: VAIABLE DEFINITIONS.) Expctaton (. avrag or man). ) Expctd rturn on th markt. sk-r rat (.. rturn on T-blls). A Invstor s rsk-avrson actor. Varanc o markt rturns. arkt xcss-rturn (.. markt rturn lss th rsk-r rat. 1-prod rturn on nvstmnt. E Expctd xcss-rturn rom nvstmnt. Loadng or th markt actor. HL Hypothtcal portolo mad by buyng hgh book/markt (valu) stocks and sllng low book/markt (growth) stocks. SB Hypothtcal portolo mad by buyng small company stocks and sllng larg company stocks. UD Hypothtcal portolo mad by buyng stocks wth th hghst rturns th prvous 1 months and sllng stocks wth th lowst rturns n th prvous 1 months. prsnts th uncondtonal man o nvstmnt. sults rom a tm-srs rgrsson. As a masur o prormanc, largr alphas ar dsrabl. t grsson rror trm at tm t., Excss rturn o th markt at tm t. t Good Harbor Fnancal: Gnral Dstrbuton v.1 Pag 5 o 6

6 Good Harbor Fnancal, Inc. Chcago, IL APPENDIX B: EFEENCES [1] Fama, E.F., and K.. Frnch (199). ultactor Explanatons o Asst Prcng Anomals, Journal o Fnanc Volum 51, Issu 1: [] Carhart,.. (1997). On prsstnc n mutual und prormanc, Journal o Fnanc Volum 5, Issu 1:57-8. [3] Bod, Z., A. Kan, and A.J. arcus (005). Invstmnts (cgraw-hll, Nw York). [4] Brnstn, P.L. (1993). Captal Idas Th Improbabl Orgns o odrn Wall Strt (Fr Prss, Nw York). [5] Cochran, J.H. (005). Asst Prcng (Prncton Unvrsty Prss, Nw Jrsy). [6] mba.tuck.dartmouth.du/pags/aculty/ kn.rnch/data_lbrary.html. [7] Lhabtant, F.S. (004). Hdg Funds Quanttatv Insghts (John Wly & Sons, England). Good Harbor Fnancal: Gnral Dstrbuton v.1 Pag 6 o 6