# Moving from fund performance to manager skill

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