Aktiv fondsforvaltning af danske Aktier i Danmark er en succes!

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Abstrakt

Vi tester i artiklen Alpha performance[1], på aktivt forvaltede fonde af danske aktier i Danmark, i perioden 2006-2016. Vi tester udelukkende net-fee alpha, hvorved der i artiklen menes, alpha korrigeret for alle indre omkostninger i fondene. På denne måde anvendes direkte, fondenes Net Asset Values (NAV) i afkastberegningerne.[2]

Artiklen læner sig op af litteraturens standardmetode de seneste 5-10 år, for estimation af alpha. Vi udvælger en stikprøve på 26 fonde, som vi tester over 10 år med månedlige observationer. Stikprøven er udvalgt udfra forskellige kriterier, fra en Survivorship Bias database.[3]

Alpha estimeres statistisk signikant, og renset for held, til 2,7% p.a. på tværs af fondene i en foretrukket Fama-French (1993) model. Vi konkluderer derfor, at aktiv forvaltning i danske aktier, er klart at foretrække i risikojusterede termer. Alpha estimatet har stor betydning geometrisk over tid. Se her for graf over den rene performanceudvikling efter omkostninger.

Ligeledes konkluderer vi, at investorer ikke nødvendigvis er afhængig at udvælge de bedste historiske fonde.

Vi fokuserer på resultatet, korrigeret for den relative omkostning mellem den aktive fond, og den alternative passive benchmarkreplika. I forhold til eksisterende litteratur, testes der således direkte for alpha, under antagelse af, at det passive alternativ, ikke er omkostningsfrit replikerbart.

Vi følger litteraturen i udvælgelsen af ligevægtsmodeller til at fange den risikojusterede performance, alpha. Således implementeres, og testes de tidsuafhængige versioner af 1-faktor Jensen (1968), 3-faktor Fama-French (1993) og 4-faktor Carhart (1997), i en top-down og bottom-up modellering, med individuelle og aggregerede fondsregressioner.

Resultatet er stærkt og positivt signifikant. Ikke bare i gennemsnit, men stort set over hele linjen, har fondene leveret stærk alpha. Dog kun med parametrisk t-stat signifikans af alpha i multi-indeks modellerne.

Vi finder en særdeles stærk forklaringsgrad og signifikans i Fama-French (1993) modellen, som udover markedsindekset, også tager højde for en small-cap præmie og en valuepræmie. Alpha i denne model er som sagt 2,7% p.a., og med en-sidet p-værdi under 5%.

Vi finder i modellen, en negativ alpha bias i forhold til Jensen (1968), da small-cap aktier over en bred kam, har gjort det rigtig skidt, de sidste 10 år i Danmark (ca. -8% p.a. mod large-cap). Særligt pga. konkurser i mange mindre banker. Forvalterne får dermed en "kompensation" i alpha for at have taget small-cap risiko på.

Vormodel indikerer således, at forvalterne, inden for small-cap risikoen, har udvalgt de rigtige small-cap aktier.

Analysen viser også, at over 30% af fondene har problemer med den parametriske normalfordelingstest, hvorfor vi må gå ikke-parametrisk til værks. Vi følger, blandt mange, Kosowski et al. (2006), og belyser den faktiske krydssektionelle alphadistribution i forhold til en empirisk bootstrappet (simuleret) distribution. Dog kun for den udvalgte bedste model, Fama-French (1993).

Sammenligning af faktisk og simuleret CDF, viser den overlegne faktiske alpha på tværs af fondene.[4] Yderligere, viser den, at i særligt mellemgruppen af fondsrangeringen, er der relativ stor tilbøjelighed til at skabe værdi.

Individuelt, rangerer foreningen Investin A/S højest, med fonden Prof. Danske Fokus Aktier II. Denne, i Morningstar 5-stjernede fond, er Danmark's bedste aktive fond på danske aktier, når vi evaluerer under vores foretrukne mål, den risikojusterede alpha. Evalueres der udelukkende efter ren alpha, er Danmark's bedste fond, BIL Nordic Invest Danske Small Cap Aktier, som har 4 stjerner hos Morningstar. Se ranking her.

Vi perspektiverer afslutningsvis det solide resultat, i forhold til mulig overestimation af alpha pga. af bla. survivorship bias. Vi viser i artiklen, at den maksimale survivorship bias, der tidligere er beregnet internationalt, er omkring 2,75% p.a. (Malkiel, 1995, Grinblat og Titman, 1989). Sammenholdt med den estimerede alpha på 2,7%, betyder det, at selv i worst-case survivorship bias scenariet, er konklusionen om, at aktiv forvaltning i Danmark kan svare sig på danske aktier, nogenlunde robust.

Sidst, vi uddyber Fama-French (1993) modellens svagheder, og usikkerheder i forhold til det estimerede resultat. Der er mange usikkerheder og potentielle estimationsfejl. Særligt, og klassisk, er valget af benchmarkreplika'en. Denne har været til debat, siden den første kritik af CAPM i 1970'erne (Roll, 1978), og ikke uden grund. Således er vores alphaestimater i de 3 modeller, krydssektionelt, mellem 0,8% - 3,7% p.a 

Fulde artikel:

equityfunds_denmark_fundselection

 

 

 

[1] Alpha er "standard performance" korrigeret for den relative risikoforske,l mellem porteføljen og det replikerede passive benchmark. Alpha kan, som vi viser, beregnes både med udgangspunkt i en gennemsnitlig statisk relativ risikoforskel, og i en dynamisk forskel. Alpha er mere korrekt end simpel performance, da performance risikojusteres i en ligevægtsmodel. En ligevægtsmodel, der estimerer et fair risikostyret forventet afkast. I forhold til et klassisk performancemål som Information Ration'en, eller Sharpe Ration'en, risikokorrigeres performance i tælleren via alpha. NAV er Net Asset Value, dvs. markedsværdien af aktiver fratrukket markedsværdien af passiverne, nettoformuen eller egenkapitalen. De indre omkostninger er bla. en del af passivsiden. NAV er i praksis en indekseret værdi af fondens nettoformue over tid.

[2] Vi gennemgår det senere, men som kontrast til de "indre" omkostninger, står de "ydre" omkostninger, som estimerer investors bruttoomkostninger ved handle ud og ind af fondene. Emissions- og indløsningsomkostninger. ÅOP ("Årlig Omkostnings Procent") målet er et mål, for summen af de "indre" og "ydre" omkostninger. Denne skal dog kun anvendes ved "gross fee" beregninger, som vi ikke er interesserede i.

[3] For at undgå misforståelser. En "survivor-ship bias" database betyder, at alle lukkede fonde ikke er inkluderet. Fonde der er lukkede eller fusionerede ind i andre eksisterende fonde, har i mange internationale analyser vist, at skabe en positv alpha bias, da de er lukkede med dårlige resultater. Altså, alpha er kunstigt for højt.

[4] CDF er den kumulative sandsynlighedsfordeling ("Cumulative Distribution Function")

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