Mov­ing from fund per­for­mance to man­ager skill

Finweek English Edition - - COLLECTIVE INSIGHT -

Past per­for­mance is not in­dica­tive of fu­ture re­sults. This is surely one of the great bumper stick­ers of fund man­age­ment. De­spite this ex­plicit warn­ing though, al­pha (de­fined sim­ply as ex­cessto-bench­mark ret urn) is rou­tinely re­garded, by pro­fes­sional and oc­ca­sional

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WIN­TER 2014 in­vestors alike, as a re­li­able mea­sure of fu­ture man­ager per­for­mance. Sadly, in its orig­i­nal form, it is not. What is be­ing in­cor­rectly con­flated is the idea of per­for­mance and skill.

The is­sue is elo­quently sum­marised by Roberto Stein in his paper, Not

Fooled by Ran­dom­ness. To para­phrase, al­though skill is no guar­an­tee of fu­ture out­per­for­mance, strong past per­for­mance which is based on skill is much more likely to be re­peated than that based on luck.

Un­for­tu­nately, per­for­mance is ob­serv­able while skill is not. Per­for­mance alone is not suf­fi­cient to in­fer man­ager skill.

Thank­fully, the el­e­ment of skill can be teased out of al­pha by adding one key in­gre­di­ent.

WHEN DOES PER­FOR­MANCE NOT EQUATE TO SKILL?

Be­fore we show you how to move from per­for­mance to skill, it is worth il­lus­trat­ing just how far re­moved per­for­mance and skill gen­er­ally are. C Baker and R Pen­fold, in Do Not Hire Man­agers

for Past Per­for­mance, out­line an el­e­gant thought ex­per­i­ment.

Con­sider a mar­ket in which there are three cat­e­gories of man­ager: skilled, aver­age and poor. We ex­pect that each cat­e­gory of man­ager will re­alise an aver­age al­pha of +3%, 0% and -2% re­spec- tively and that the level of vari­a­tion in al­phas will be around 5% for all man­agers. As­sum­ing rea­son­able fees, the prob­a­bil­ity that a man­ager will re­alise a net al­pha of 2% or more is roughly 46%, 28% and 11% re­spec­tively per man­ager cat­e­gory. One might then con­clude that the ma­jor­ity (54%) of out­per­form­ing man­agers are likely to be skilled. What is lack­ing here is con­text.

Clearly, there are not – and never will be – as many skilled man­agers as there are aver­age and poor man­agers. If we es­ti­mate that 10% of man­agers are skilled, 30% are aver­age and 60% are poor (in­ter­na­tional re­search ac­tu­ally sug­gests more ex­treme fig­ures) we find a very dif­fer­ent and more real­is­tic pic­ture than that given above. Af­ter ac­count­ing for the dif­fer­ences in size of each man­ager cat­e­gory, we re­alise that less than one in four out­per­form­ing funds (23%) are likely to be in­dica­tive of skill. Thus, to an­swer the ques­tion: when does per­for­mance not equate to skill? More of­ten than you think!

COR­RECT­ING AL­PHA FOR THE UN­DER­LY­ING OP­POR­TU­NITY SET

In all things, con­text mat­ters. As we saw above, our in­ter­pre­ta­tion of the same per­for­mance prob­a­bil­i­ties changed dra­mat­i­cally af­ter ac­count­ing for the size of each man­ager cat­e­gory. A sim­i­lar cor­rec­tion is nec­es­sary for al­pha to be­come a more re­li­able mea­sure of skill.

In truth, the idea is in­cred­i­bly sim­ple. Con­sider the per­for­mance of an ac­tive man­ager over two years. In Year 1, she man­ages to in­vest in five of 20 avail­able op­por­tu­ni­ties and re­alises an al­pha of 5%. In Year 2, she man­ages to in­vest in f ive of six avail­able op­por­tu­ni­ties and re­alises an al­pha of 5%.

Clearly, out­per­for­mance is equiv­a­lent but the in­fer­ence from each al­pha on man­ager skill is def­i­nitely not. Armed with the knowl­edge of the to­tal op­por­tu­ni­ties per year, the 5% al­pha in Year two from five of only six op­por­tu­ni­ties is a much more re­li­able in­di­ca­tor of skill than the 5% al­pha in Year 1 from f ive of 20 op­por­tu­ni­ties. Clearly one needs to con­tex­tu­alise al­pha with the avail­able op­por­tu­nity set over the given pe­riod.

EN­TER CROSS-SEC­TIONAL VO­LATIL­ITY

Cross-sec­tional vo­latil­ity, or CSV, is a mea­sure of the dis­per­sion within a bas­ket of un­der­ly­ing as­sets re­turns over a par­tic­u­lar pe­riod. It is es­ti­mated by cal­cu­lat­ing the re­turn of each as­set in the bas­ket and de­ter­min­ing the stan­dard de­vi­a­tion of these re­turns. It is a re­mark­ably f lex­i­ble mea­sure of the in­vestable op­por­tu­nity set and gives an in­di­ca­tion of how dif­fer­ent the per­for­mances of in­di­vid­ual as­sets are from each other. Fig­ure 1 il­lus­trates how in­dex CSV has changed over time and gives an in­di­ca­tion of the cur­rent op­por­tu­nity in dif-

fer­ent sec­tors. The higher the CSV, the greater the op­por­tu­nity set.

If the monthly CSV of the All-Share In­dex equals 0%, there would be no dis­per­sion in the un­der­ly­ing stocks and ev­ery re­turn would be equal. In such a ‘one-stock’ uni­verse, skill is ir­rel­e­vant and all man­agers would be tied for first place, bar­ring fees.

How­ever, if monthly CSV is 15% (as in July 2008), there would be a high de­gree of dis­per­sion in the un­der­ly­ing stock re­turns and the rel­e­vance of skill be­comes in­creas­ingly im­por­tant. In this case, we are edg­ing to­wards the ‘20 op­por­tu­ni­ties’ sce­nario given above.

As shown by De Silva et al in their ar­ti­cle, Re­turn Dis­per­sion and Ac­tive Man­age­ment, when there is large dis­per­sion in the bench­mark’s un­der­ly­ing as­set re­turns, there is also large dis­per­sion in the re­turns of the fund man­agers’.

What this means then, is that the aver­age num­ber of funds that show pos­i­tive al­phas will al­ways be higher dur­ing high CSV pe­ri­ods, re­gard­less of skill. This is a di­rect re­sult of the ef­fect of luck in large op­por­tu­nity sets as well as the pro­por­tion of skilled and aver­age man­agers ver­sus poor man­agers.

We can eas­ily cor­rect for this bias. In this method, the his­tor­i­cal re­turn of the fund rel­a­tive to the bench­mark for a num­ber of pe­ri­ods is cal­cu­lated. How­ever, in­stead of set­ting the al­pha es­ti­mate equal to the sim­ple aver­age of these re­turns (as is typ­i­cally done), each re­turn is weighted ac­cord­ing to the in­verse of the pre­vail­ing CSV of t he bench­mark. This method will es­sen­tially un­der­weight the his­tor­i­cal rel­a­tive re­turns dur­ing high CSV pe­ri­ods (the ‘ f ive of 20’ sce­nar­ios) and over­weight those rel­a­tive re­turns dur­ing the low CSV pe­ri­ods (the ‘ f ive of six’ sce­nar­ios). There­fore, the CSV-ad­justed al­phas should be a much bet­ter in­di­ca­tor of man­ager skill and thus a bet­ter pre­dic­tor of fu­ture fund per­for­mance.

As a prac­ti­cal ex­am­ple, con­sider the 60 do­mes­tic gen­eral eq­uity funds that have a track record of at least eight years. We cal­cu­late re­turns rel­a­tive to the re­spec­tive fund bench­mark (All-Share or Swix All-Share) over the last f ive years and rank the funds on their aver­age five-year raw al­phas (i.e. cal­cu­lated as an equally weighted aver­age). We then fol­low the process out­lined above to cal­cu­late CSVad­justed five-year al­phas and again rank the funds ac­cord­ingly.

Fig­ure 2 il­lus­trates the dif­fer­ence in ranks when us­ing the raw al­pha (left side) ver­sus CSV-ad­justed al­pha (right). Grey lines in­di­cate those funds whose ranks re­main un­changed, red lines in­di­cate funds whose rank has fallen and green lines in­di­cate funds whose rank has im­proved. The dif­fer­ences in the raw and ad­justed fund ranks, which are gen­er­ally pro­fuse and oc­ca­sion­ally ex­treme, em­pha­sise the im­por­tance of cor­rectly mov­ing from pure past per­for­mance to con­tex­tu­alised man­ager skill. As the bumper sticker de­clares, past per­for­mance (sans op­por­tu­nity set) is not in­dica­tive of fu­ture re­sults. Caveat in­vestor!

Em­lyn Flint Florence Chiku­runhe Anthony Sey­mour

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